Safe Haskell	None
Language	Haskell2010

Control.Lens.Utils

Synopsis

class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where
- traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
class Contravariant (f :: Type -> Type) where
- contramap :: (a -> b) -> f b -> f a
- (>$) :: b -> f b -> f a
class Bifunctor (p :: Type -> Type -> Type) where
- bimap :: (a -> b) -> (c -> d) -> p a c -> p b d
newtype Identity a = Identity {
- runIdentity :: a
}
newtype Const a (b :: k) :: forall k. Type -> k -> Type = Const {
- getConst :: a
}
(&) :: a -> (a -> b) -> b
(<&>) :: Functor f => f a -> (a -> b) -> f b
class Profunctor (p :: Type -> Type -> Type) where
- dimap :: (a -> b) -> (c -> d) -> p b c -> p a d
- lmap :: (a -> b) -> p b c -> p a c
- rmap :: (b -> c) -> p a b -> p a c
defaultFieldRules :: LensRules
makeFieldsNoPrefix :: Name -> DecsQ
makeFields :: Name -> DecsQ
abbreviatedNamer :: FieldNamer
abbreviatedFields :: LensRules
classUnderscoreNoPrefixNamer :: FieldNamer
classUnderscoreNoPrefixFields :: LensRules
camelCaseNamer :: FieldNamer
camelCaseFields :: LensRules
underscoreNamer :: FieldNamer
underscoreFields :: LensRules
makeWrapped :: Name -> DecsQ
declareLensesWith :: LensRules -> DecsQ -> DecsQ
declareFields :: DecsQ -> DecsQ
declareWrapped :: DecsQ -> DecsQ
declarePrisms :: DecsQ -> DecsQ
declareClassyFor :: [(String, (String, String))] -> [(String, String)] -> DecsQ -> DecsQ
declareClassy :: DecsQ -> DecsQ
declareLensesFor :: [(String, String)] -> DecsQ -> DecsQ
declareLenses :: DecsQ -> DecsQ
makeLensesWith :: LensRules -> Name -> DecsQ
makeClassyFor :: String -> String -> [(String, String)] -> Name -> DecsQ
makeLensesFor :: [(String, String)] -> Name -> DecsQ
makeClassy_ :: Name -> DecsQ
classyRules_ :: LensRules
classyRules :: LensRules
mappingNamer :: (String -> [String]) -> FieldNamer
lookingupNamer :: [(String, String)] -> FieldNamer
lensRulesFor :: [(String, String)] -> LensRules
underscoreNoPrefixNamer :: FieldNamer
lensRules :: LensRules
lensClass :: Lens' LensRules ClassyNamer
lensField :: Lens' LensRules FieldNamer
createClass :: Lens' LensRules Bool
generateLazyPatterns :: Lens' LensRules Bool
generateUpdateableOptics :: Lens' LensRules Bool
generateSignatures :: Lens' LensRules Bool
simpleLenses :: Lens' LensRules Bool
data LensRules
type FieldNamer = Name -> [Name] -> Name -> [DefName]
data DefName
- = TopName Name
- | MethodName Name Name
type ClassyNamer = Name -> Maybe (Name, Name)
makeClassyPrisms :: Name -> DecsQ
makePrisms :: Name -> DecsQ
iat :: At m => Index m -> IndexedLens' (Index m) m (Maybe (IxValue m))
sans :: At m => Index m -> m -> m
ixAt :: At m => Index m -> Traversal' m (IxValue m)
iix :: Ixed m => Index m -> IndexedTraversal' (Index m) m (IxValue m)
icontains :: Contains m => Index m -> IndexedLens' (Index m) m Bool
type family Index s :: Type
class Contains m where
- contains :: Index m -> Lens' m Bool
type family IxValue m :: Type
class Ixed m where
- ix :: Index m -> Traversal' m (IxValue m)
class Ixed m => At m where
- at :: Index m -> Lens' m (Maybe (IxValue m))
class Each s t a b | s -> a, t -> b, s b -> t, t a -> s where
- each :: Traversal s t a b
gplate :: (Generic a, GPlated a (Rep a)) => Traversal' a a
parts :: Plated a => Lens' a [a]
composOpFold :: Plated a => b -> (b -> b -> b) -> (a -> b) -> a -> b
para :: Plated a => (a -> [r] -> r) -> a -> r
paraOf :: Getting (Endo [a]) a a -> (a -> [r] -> r) -> a -> r
holesOnOf :: Conjoined p => LensLike (Bazaar p r r) s t a b -> Over p (Bazaar p r r) a b r r -> s -> [Pretext p r r t]
holesOn :: Conjoined p => Over p (Bazaar p a a) s t a a -> s -> [Pretext p a a t]
holes :: Plated a => a -> [Pretext ((->) :: Type -> Type -> Type) a a a]
contextsOnOf :: ATraversal s t a a -> ATraversal' a a -> s -> [Context a a t]
contextsOn :: Plated a => ATraversal s t a a -> s -> [Context a a t]
contextsOf :: ATraversal' a a -> a -> [Context a a a]
contexts :: Plated a => a -> [Context a a a]
transformMOnOf :: Monad m => LensLike (WrappedMonad m) s t a b -> LensLike (WrappedMonad m) a b a b -> (b -> m b) -> s -> m t
transformMOf :: Monad m => LensLike (WrappedMonad m) a b a b -> (b -> m b) -> a -> m b
transformMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m a) -> s -> m t
transformM :: (Monad m, Plated a) => (a -> m a) -> a -> m a
transformOnOf :: ASetter s t a b -> ASetter a b a b -> (b -> b) -> s -> t
transformOf :: ASetter a b a b -> (b -> b) -> a -> b
transformOn :: Plated a => ASetter s t a a -> (a -> a) -> s -> t
transform :: Plated a => (a -> a) -> a -> a
cosmosOnOf :: (Applicative f, Contravariant f) => LensLike' f s a -> LensLike' f a a -> LensLike' f s a
cosmosOn :: (Applicative f, Contravariant f, Plated a) => LensLike' f s a -> LensLike' f s a
cosmosOf :: (Applicative f, Contravariant f) => LensLike' f a a -> LensLike' f a a
cosmos :: Plated a => Fold a a
universeOnOf :: Getting [a] s a -> Getting [a] a a -> s -> [a]
universeOn :: Plated a => Getting [a] s a -> s -> [a]
universeOf :: Getting [a] a a -> a -> [a]
universe :: Plated a => a -> [a]
rewriteMOnOf :: Monad m => LensLike (WrappedMonad m) s t a b -> LensLike (WrappedMonad m) a b a b -> (b -> m (Maybe a)) -> s -> m t
rewriteMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m (Maybe a)) -> s -> m t
rewriteMOf :: Monad m => LensLike (WrappedMonad m) a b a b -> (b -> m (Maybe a)) -> a -> m b
rewriteM :: (Monad m, Plated a) => (a -> m (Maybe a)) -> a -> m a
rewriteOnOf :: ASetter s t a b -> ASetter a b a b -> (b -> Maybe a) -> s -> t
rewriteOn :: Plated a => ASetter s t a a -> (a -> Maybe a) -> s -> t
rewriteOf :: ASetter a b a b -> (b -> Maybe a) -> a -> b
rewrite :: Plated a => (a -> Maybe a) -> a -> a
children :: Plated a => a -> [a]
deep :: (Conjoined p, Applicative f, Plated s) => Traversing p f s s a b -> Over p f s s a b
(...) :: (Applicative f, Plated c) => LensLike f s t c c -> Over p f c c a b -> Over p f s t a b
class Plated a where
- plate :: Traversal' a a
class GPlated a (g :: Type -> Type)
type family Zoomed (m :: Type -> Type) :: Type -> Type -> Type
type family Magnified (m :: Type -> Type) :: Type -> Type -> Type
class (MonadState s m, MonadState t n) => Zoom (m :: Type -> Type) (n :: Type -> Type) s t | m -> s, n -> t, m t -> n, n s -> m where
- zoom :: LensLike' (Zoomed m c) t s -> m c -> n c
class (Magnified m ~ Magnified n, MonadReader b m, MonadReader a n) => Magnify (m :: Type -> Type) (n :: Type -> Type) b a | m -> b, n -> a, m a -> n, n b -> m where
- magnify :: LensLike' (Magnified m c) a b -> m c -> n c
alaf :: (Functor f, Functor g, Rewrapping s t) => (Unwrapped s -> s) -> (f t -> g s) -> f (Unwrapped t) -> g (Unwrapped s)
ala :: (Functor f, Rewrapping s t) => (Unwrapped s -> s) -> ((Unwrapped t -> t) -> f s) -> f (Unwrapped s)
_Unwrapping :: Rewrapping s t => (Unwrapped s -> s) -> Iso (Unwrapped t) (Unwrapped s) t s
_Wrapping :: Rewrapping s t => (Unwrapped s -> s) -> Iso s t (Unwrapped s) (Unwrapped t)
_Unwrapping' :: Wrapped s => (Unwrapped s -> s) -> Iso' (Unwrapped s) s
_Wrapping' :: Wrapped s => (Unwrapped s -> s) -> Iso' s (Unwrapped s)
op :: Wrapped s => (Unwrapped s -> s) -> s -> Unwrapped s
_Unwrapped :: Rewrapping s t => Iso (Unwrapped t) (Unwrapped s) t s
_Wrapped :: Rewrapping s t => Iso s t (Unwrapped s) (Unwrapped t)
_Unwrapped' :: Wrapped s => Iso' (Unwrapped s) s
_GWrapped' :: (Generic s, D1 d (C1 c (S1 s' (Rec0 a))) ~ Rep s, Unwrapped s ~ GUnwrapped (Rep s)) => Iso' s (Unwrapped s)
pattern Wrapped :: forall s. Rewrapped s s => Unwrapped s -> s
pattern Unwrapped :: forall t. Rewrapped t t => t -> Unwrapped t
class Wrapped s where
- type Unwrapped s :: Type
- _Wrapped' :: Iso' s (Unwrapped s)
class Wrapped s => Rewrapped s t
class (Rewrapped s t, Rewrapped t s) => Rewrapping s t
unsnoc :: Snoc s s a a => s -> Maybe (s, a)
snoc :: Snoc s s a a => s -> a -> s
(|>) :: Snoc s s a a => s -> a -> s
_last :: Snoc s s a a => Traversal' s a
_init :: Snoc s s a a => Traversal' s s
_tail :: Cons s s a a => Traversal' s s
_head :: Cons s s a a => Traversal' s a
uncons :: Cons s s a a => s -> Maybe (a, s)
cons :: Cons s s a a => a -> s -> s
(<|) :: Cons s s a a => a -> s -> s
pattern (:<) :: forall b a. Cons b b a a => a -> b -> b
pattern (:>) :: forall a b. Snoc a a b b => a -> b -> a
class Cons s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _Cons :: Prism s t (a, s) (b, t)
class Snoc s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _Snoc :: Prism s t (s, a) (t, b)
pattern Empty :: forall s. AsEmpty s => s
class AsEmpty a where
- _Empty :: Prism' a ()
coerced :: (Coercible s a, Coercible t b) => Iso s t a b
seconding :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> Iso (f x s) (g y t) (f x a) (g y b)
firsting :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> Iso (f s x) (g t y) (f a x) (g b y)
bimapping :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> AnIso s' t' a' b' -> Iso (f s s') (g t t') (f a a') (g b b')
rmapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> Iso (p x s) (q y t) (p x a) (q y b)
lmapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> Iso (p a x) (q b y) (p s x) (q t y)
dimapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> AnIso s' t' a' b' -> Iso (p a s') (q b t') (p s a') (q t b')
contramapping :: Contravariant f => AnIso s t a b -> Iso (f a) (f b) (f s) (f t)
imagma :: Over (Indexed i) (Molten i a b) s t a b -> Iso s t' (Magma i t b a) (Magma j t' c c)
magma :: LensLike (Mafic a b) s t a b -> Iso s u (Magma Int t b a) (Magma j u c c)
involuted :: (a -> a) -> Iso' a a
reversed :: Reversing a => Iso' a a
lazy :: Strict lazy strict => Iso' strict lazy
flipped :: Iso (a -> b -> c) (a' -> b' -> c') (b -> a -> c) (b' -> a' -> c')
uncurried :: Iso (a -> b -> c) (d -> e -> f) ((a, b) -> c) ((d, e) -> f)
curried :: Iso ((a, b) -> c) ((d, e) -> f) (a -> b -> c) (d -> e -> f)
anon :: a -> (a -> Bool) -> Iso' (Maybe a) a
non' :: APrism' a () -> Iso' (Maybe a) a
non :: Eq a => a -> Iso' (Maybe a) a
mapping :: (Functor f, Functor g) => AnIso s t a b -> Iso (f s) (g t) (f a) (g b)
enum :: Enum a => Iso' Int a
under :: AnIso s t a b -> (t -> s) -> b -> a
auf :: Optic (Costar f) g s t a b -> (f a -> g b) -> f s -> g t
au :: Functor f => AnIso s t a b -> ((b -> t) -> f s) -> f a
cloneIso :: AnIso s t a b -> Iso s t a b
withIso :: AnIso s t a b -> ((s -> a) -> (b -> t) -> r) -> r
from :: AnIso s t a b -> Iso b a t s
iso :: (s -> a) -> (b -> t) -> Iso s t a b
pattern Strict :: forall s t. Strict s t => t -> s
pattern Lazy :: forall t s. Strict t s => t -> s
pattern Swapped :: forall (p :: Type -> Type -> Type) c d. Swapped p => p d c -> p c d
pattern Reversed :: forall t. Reversing t => t -> t
pattern List :: forall l. IsList l => [Item l] -> l
type AnIso s t a b = Exchange a b a (Identity b) -> Exchange a b s (Identity t)
type AnIso' s a = AnIso s s a a
class Bifunctor p => Swapped (p :: Type -> Type -> Type) where
- swapped :: Iso (p a b) (p c d) (p b a) (p d c)
class Strict lazy strict | lazy -> strict, strict -> lazy where
- strict :: Iso' lazy strict
simple :: Equality' a a
simply :: (Optic' p f s a -> r) -> Optic' p f s a -> r
fromEq :: AnEquality s t a b -> Equality b a t s
mapEq :: AnEquality s t a b -> f s -> f a
substEq :: AnEquality s t a b -> ((s ~ a) -> (t ~ b) -> r) -> r
runEq :: AnEquality s t a b -> Identical s t a b
data Identical (a :: k) (b :: k1) (s :: k) (t :: k1) :: forall k k1. k -> k1 -> k -> k1 -> Type where
- Identical :: forall k k1 (a :: k) (b :: k1) (s :: k) (t :: k1). Identical a b a b
type AnEquality (s :: k1) (t :: k2) (a :: k1) (b :: k2) = Identical a (Proxy b) a (Proxy b) -> Identical a (Proxy b) s (Proxy t)
type AnEquality' (s :: k2) (a :: k2) = AnEquality s s a a
itraverseByOf :: IndexedTraversal i s t a b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> s -> f t
itraverseBy :: TraversableWithIndex i t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> t a -> f (t b)
ifoldMapByOf :: IndexedFold i t a -> (r -> r -> r) -> r -> (i -> a -> r) -> t -> r
ifoldMapBy :: FoldableWithIndex i t => (r -> r -> r) -> r -> (i -> a -> r) -> t a -> r
imapAccumL :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b)
imapAccumR :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b)
iforM :: (TraversableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m (t b)
imapM :: (TraversableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m (t b)
ifor :: (TraversableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f (t b)
itoList :: FoldableWithIndex i f => f a -> [(i, a)]
ifoldlM :: (FoldableWithIndex i f, Monad m) => (i -> b -> a -> m b) -> b -> f a -> m b
ifoldrM :: (FoldableWithIndex i f, Monad m) => (i -> a -> b -> m b) -> b -> f a -> m b
ifind :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Maybe (i, a)
iconcatMap :: FoldableWithIndex i f => (i -> a -> [b]) -> f a -> [b]
iforM_ :: (FoldableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m ()
imapM_ :: (FoldableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m ()
ifor_ :: (FoldableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f ()
itraverse_ :: (FoldableWithIndex i t, Applicative f) => (i -> a -> f b) -> t a -> f ()
none :: Foldable f => (a -> Bool) -> f a -> Bool
inone :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
iall :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
iany :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
index :: (Indexable i p, Eq i, Applicative f) => i -> Optical' p (Indexed i) f a a
indices :: (Indexable i p, Applicative f) => (i -> Bool) -> Optical' p (Indexed i) f a a
icompose :: Indexable p c => (i -> j -> p) -> (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> c a b -> r
(<.>) :: Indexable (i, j) p => (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> p a b -> r
reindexed :: Indexable j p => (i -> j) -> (Indexed i a b -> r) -> p a b -> r
selfIndex :: Indexable a p => p a fb -> a -> fb
(.>) :: (st -> r) -> (kab -> st) -> kab -> r
(<.) :: Indexable i p => (Indexed i s t -> r) -> ((a -> b) -> s -> t) -> p a b -> r
class Functor f => FunctorWithIndex i (f :: Type -> Type) | f -> i where
- imap :: (i -> a -> b) -> f a -> f b
- imapped :: IndexedSetter i (f a) (f b) a b
class Foldable f => FoldableWithIndex i (f :: Type -> Type) | f -> i where
- ifoldMap :: Monoid m => (i -> a -> m) -> f a -> m
- ifolded :: IndexedFold i (f a) a
- ifoldr :: (i -> a -> b -> b) -> b -> f a -> b
- ifoldl :: (i -> b -> a -> b) -> b -> f a -> b
- ifoldr' :: (i -> a -> b -> b) -> b -> f a -> b
- ifoldl' :: (i -> b -> a -> b) -> b -> f a -> b
class (FunctorWithIndex i t, FoldableWithIndex i t, Traversable t) => TraversableWithIndex i (t :: Type -> Type) | t -> i where
- itraverse :: Applicative f => (i -> a -> f b) -> t a -> f (t b)
- itraversed :: IndexedTraversal i (t a) (t b) a b
newtype ReifiedLens s t a b = Lens {
- runLens :: Lens s t a b
}
type ReifiedLens' s a = ReifiedLens s s a a
newtype ReifiedIndexedLens i s t a b = IndexedLens {
- runIndexedLens :: IndexedLens i s t a b
}
type ReifiedIndexedLens' i s a = ReifiedIndexedLens i s s a a
newtype ReifiedIndexedTraversal i s t a b = IndexedTraversal {
- runIndexedTraversal :: IndexedTraversal i s t a b
}
type ReifiedIndexedTraversal' i s a = ReifiedIndexedTraversal i s s a a
newtype ReifiedTraversal s t a b = Traversal {
- runTraversal :: Traversal s t a b
}
type ReifiedTraversal' s a = ReifiedTraversal s s a a
newtype ReifiedGetter s a = Getter {
- runGetter :: Getter s a
}
newtype ReifiedIndexedGetter i s a = IndexedGetter {
- runIndexedGetter :: IndexedGetter i s a
}
newtype ReifiedFold s a = Fold {
- runFold :: Fold s a
}
newtype ReifiedIndexedFold i s a = IndexedFold {
- runIndexedFold :: IndexedFold i s a
}
newtype ReifiedSetter s t a b = Setter {
- runSetter :: Setter s t a b
}
type ReifiedSetter' s a = ReifiedSetter s s a a
newtype ReifiedIndexedSetter i s t a b = IndexedSetter {
- runIndexedSetter :: IndexedSetter i s t a b
}
type ReifiedIndexedSetter' i s a = ReifiedIndexedSetter i s s a a
newtype ReifiedIso s t a b = Iso {
- runIso :: Iso s t a b
}
type ReifiedIso' s a = ReifiedIso s s a a
newtype ReifiedPrism s t a b = Prism {
- runPrism :: Prism s t a b
}
type ReifiedPrism' s a = ReifiedPrism s s a a
ilevels :: Applicative f => Traversing (Indexed i) f s t a b -> IndexedLensLike Int f s t (Level i a) (Level j b)
levels :: Applicative f => Traversing ((->) :: Type -> Type -> Type) f s t a b -> IndexedLensLike Int f s t (Level () a) (Level () b)
sequenceByOf :: Traversal s t (f b) b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> s -> f t
traverseByOf :: Traversal s t a b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (a -> f b) -> s -> f t
confusing :: Applicative f => LensLike (Curried (Yoneda f) (Yoneda f)) s t a b -> LensLike f s t a b
deepOf :: (Conjoined p, Applicative f) => LensLike f s t s t -> Traversing p f s t a b -> Over p f s t a b
failing :: (Conjoined p, Applicative f) => Traversing p f s t a b -> Over p f s t a b -> Over p f s t a b
ifailover :: Alternative m => Over (Indexed i) ((,) Any) s t a b -> (i -> a -> b) -> s -> m t
failover :: Alternative m => LensLike ((,) Any) s t a b -> (a -> b) -> s -> m t
elements :: Traversable t => (Int -> Bool) -> IndexedTraversal' Int (t a) a
elementsOf :: Applicative f => LensLike (Indexing f) s t a a -> (Int -> Bool) -> IndexedLensLike Int f s t a a
element :: Traversable t => Int -> IndexedTraversal' Int (t a) a
elementOf :: Applicative f => LensLike (Indexing f) s t a a -> Int -> IndexedLensLike Int f s t a a
ignored :: Applicative f => pafb -> s -> f s
traversed64 :: Traversable f => IndexedTraversal Int64 (f a) (f b) a b
traversed1 :: Traversable1 f => IndexedTraversal1 Int (f a) (f b) a b
traversed :: Traversable f => IndexedTraversal Int (f a) (f b) a b
imapAccumLOf :: Over (Indexed i) (State acc) s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
imapAccumROf :: Over (Indexed i) (Backwards (State acc)) s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
iforMOf :: (Indexed i a (WrappedMonad m b) -> s -> WrappedMonad m t) -> s -> (i -> a -> m b) -> m t
imapMOf :: Over (Indexed i) (WrappedMonad m) s t a b -> (i -> a -> m b) -> s -> m t
iforOf :: (Indexed i a (f b) -> s -> f t) -> s -> (i -> a -> f b) -> f t
itraverseOf :: (Indexed i a (f b) -> s -> f t) -> (i -> a -> f b) -> s -> f t
cloneIndexedTraversal1 :: AnIndexedTraversal1 i s t a b -> IndexedTraversal1 i s t a b
cloneIndexPreservingTraversal1 :: ATraversal1 s t a b -> IndexPreservingTraversal1 s t a b
cloneTraversal1 :: ATraversal1 s t a b -> Traversal1 s t a b
cloneIndexedTraversal :: AnIndexedTraversal i s t a b -> IndexedTraversal i s t a b
cloneIndexPreservingTraversal :: ATraversal s t a b -> IndexPreservingTraversal s t a b
cloneTraversal :: ATraversal s t a b -> Traversal s t a b
dropping :: (Conjoined p, Applicative f) => Int -> Over p (Indexing f) s t a a -> Over p f s t a a
taking :: (Conjoined p, Applicative f) => Int -> Traversing p f s t a a -> Over p f s t a a
beside :: (Representable q, Applicative (Rep q), Applicative f, Bitraversable r) => Optical p q f s t a b -> Optical p q f s' t' a b -> Optical p q f (r s s') (r t t') a b
both1 :: Bitraversable1 r => Traversal1 (r a a) (r b b) a b
both :: Bitraversable r => Traversal (r a a) (r b b) a b
holesOf :: Conjoined p => Over p (Bazaar p a a) s t a a -> s -> [Pretext p a a t]
unsafeSingular :: (HasCallStack, Conjoined p, Functor f) => Traversing p f s t a b -> Over p f s t a b
singular :: (HasCallStack, Conjoined p, Functor f) => Traversing p f s t a a -> Over p f s t a a
iunsafePartsOf' :: Over (Indexed i) (Bazaar (Indexed i) a b) s t a b -> IndexedLens [i] s t [a] [b]
unsafePartsOf' :: ATraversal s t a b -> Lens s t [a] [b]
iunsafePartsOf :: (Indexable [i] p, Functor f) => Traversing (Indexed i) f s t a b -> Over p f s t [a] [b]
unsafePartsOf :: Functor f => Traversing ((->) :: Type -> Type -> Type) f s t a b -> LensLike f s t [a] [b]
ipartsOf' :: (Indexable [i] p, Functor f) => Over (Indexed i) (Bazaar' (Indexed i) a) s t a a -> Over p f s t [a] [a]
partsOf' :: ATraversal s t a a -> Lens s t [a] [a]
ipartsOf :: (Indexable [i] p, Functor f) => Traversing (Indexed i) f s t a a -> Over p f s t [a] [a]
partsOf :: Functor f => Traversing ((->) :: Type -> Type -> Type) f s t a a -> LensLike f s t [a] [a]
iloci :: IndexedTraversal i (Bazaar (Indexed i) a c s) (Bazaar (Indexed i) b c s) a b
loci :: Traversal (Bazaar ((->) :: Type -> Type -> Type) a c s) (Bazaar ((->) :: Type -> Type -> Type) b c s) a b
scanl1Of :: LensLike (State (Maybe a)) s t a a -> (a -> a -> a) -> s -> t
scanr1Of :: LensLike (Backwards (State (Maybe a))) s t a a -> (a -> a -> a) -> s -> t
mapAccumLOf :: LensLike (State acc) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumROf :: LensLike (Backwards (State acc)) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
transposeOf :: LensLike ZipList s t [a] a -> s -> [t]
sequenceOf :: LensLike (WrappedMonad m) s t (m b) b -> s -> m t
forMOf :: LensLike (WrappedMonad m) s t a b -> s -> (a -> m b) -> m t
mapMOf :: LensLike (WrappedMonad m) s t a b -> (a -> m b) -> s -> m t
sequenceAOf :: LensLike f s t (f b) b -> s -> f t
forOf :: LensLike f s t a b -> s -> (a -> f b) -> f t
traverseOf :: LensLike f s t a b -> (a -> f b) -> s -> f t
type ATraversal s t a b = LensLike (Bazaar ((->) :: Type -> Type -> Type) a b) s t a b
type ATraversal' s a = ATraversal s s a a
type ATraversal1 s t a b = LensLike (Bazaar1 ((->) :: Type -> Type -> Type) a b) s t a b
type ATraversal1' s a = ATraversal1 s s a a
type AnIndexedTraversal i s t a b = Over (Indexed i) (Bazaar (Indexed i) a b) s t a b
type AnIndexedTraversal1 i s t a b = Over (Indexed i) (Bazaar1 (Indexed i) a b) s t a b
type AnIndexedTraversal' i s a = AnIndexedTraversal i s s a a
type AnIndexedTraversal1' i s a = AnIndexedTraversal1 i s s a a
type Traversing (p :: Type -> Type -> Type) (f :: Type -> Type) s t a b = Over p (BazaarT p f a b) s t a b
type Traversing1 (p :: Type -> Type -> Type) (f :: Type -> Type) s t a b = Over p (BazaarT1 p f a b) s t a b
type Traversing' (p :: Type -> Type -> Type) (f :: Type -> Type) s a = Traversing p f s s a a
type Traversing1' (p :: Type -> Type -> Type) (f :: Type -> Type) s a = Traversing1 p f s s a a
class Ord k => TraverseMin k (m :: Type -> Type) | m -> k where
- traverseMin :: IndexedTraversal' k (m v) v
class Ord k => TraverseMax k (m :: Type -> Type) | m -> k where
- traverseMax :: IndexedTraversal' k (m v) v
foldMapByOf :: Fold s a -> (r -> r -> r) -> r -> (a -> r) -> s -> r
foldByOf :: Fold s a -> (a -> a -> a) -> a -> s -> a
idroppingWhile :: (Indexable i p, Profunctor q, Applicative f) => (i -> a -> Bool) -> Optical (Indexed i) q (Compose (State Bool) f) s t a a -> Optical p q f s t a a
itakingWhile :: (Indexable i p, Profunctor q, Contravariant f, Applicative f) => (i -> a -> Bool) -> Optical' (Indexed i) q (Const (Endo (f s)) :: Type -> Type) s a -> Optical' p q f s a
ifiltered :: (Indexable i p, Applicative f) => (i -> a -> Bool) -> Optical' p (Indexed i) f a a
findIndicesOf :: IndexedGetting i (Endo [i]) s a -> (a -> Bool) -> s -> [i]
findIndexOf :: IndexedGetting i (First i) s a -> (a -> Bool) -> s -> Maybe i
elemIndicesOf :: Eq a => IndexedGetting i (Endo [i]) s a -> a -> s -> [i]
elemIndexOf :: Eq a => IndexedGetting i (First i) s a -> a -> s -> Maybe i
(^@?!) :: HasCallStack => s -> IndexedGetting i (Endo (i, a)) s a -> (i, a)
(^@?) :: s -> IndexedGetting i (Endo (Maybe (i, a))) s a -> Maybe (i, a)
(^@..) :: s -> IndexedGetting i (Endo [(i, a)]) s a -> [(i, a)]
itoListOf :: IndexedGetting i (Endo [(i, a)]) s a -> s -> [(i, a)]
ifoldlMOf :: Monad m => IndexedGetting i (Endo (r -> m r)) s a -> (i -> r -> a -> m r) -> r -> s -> m r
ifoldrMOf :: Monad m => IndexedGetting i (Dual (Endo (r -> m r))) s a -> (i -> a -> r -> m r) -> r -> s -> m r
ifoldlOf' :: IndexedGetting i (Endo (r -> r)) s a -> (i -> r -> a -> r) -> r -> s -> r
ifoldrOf' :: IndexedGetting i (Dual (Endo (r -> r))) s a -> (i -> a -> r -> r) -> r -> s -> r
ifindMOf :: Monad m => IndexedGetting i (Endo (m (Maybe a))) s a -> (i -> a -> m Bool) -> s -> m (Maybe a)
ifindOf :: IndexedGetting i (Endo (Maybe a)) s a -> (i -> a -> Bool) -> s -> Maybe a
iconcatMapOf :: IndexedGetting i [r] s a -> (i -> a -> [r]) -> s -> [r]
iforMOf_ :: Monad m => IndexedGetting i (Sequenced r m) s a -> s -> (i -> a -> m r) -> m ()
imapMOf_ :: Monad m => IndexedGetting i (Sequenced r m) s a -> (i -> a -> m r) -> s -> m ()
iforOf_ :: Functor f => IndexedGetting i (Traversed r f) s a -> s -> (i -> a -> f r) -> f ()
itraverseOf_ :: Functor f => IndexedGetting i (Traversed r f) s a -> (i -> a -> f r) -> s -> f ()
inoneOf :: IndexedGetting i Any s a -> (i -> a -> Bool) -> s -> Bool
iallOf :: IndexedGetting i All s a -> (i -> a -> Bool) -> s -> Bool
ianyOf :: IndexedGetting i Any s a -> (i -> a -> Bool) -> s -> Bool
ifoldlOf :: IndexedGetting i (Dual (Endo r)) s a -> (i -> r -> a -> r) -> r -> s -> r
ifoldrOf :: IndexedGetting i (Endo r) s a -> (i -> a -> r -> r) -> r -> s -> r
ifoldMapOf :: IndexedGetting i m s a -> (i -> a -> m) -> s -> m
backwards :: (Profunctor p, Profunctor q) => Optical p q (Backwards f) s t a b -> Optical p q f s t a b
ipreuses :: MonadState s m => IndexedGetting i (First r) s a -> (i -> a -> r) -> m (Maybe r)
preuses :: MonadState s m => Getting (First r) s a -> (a -> r) -> m (Maybe r)
ipreuse :: MonadState s m => IndexedGetting i (First (i, a)) s a -> m (Maybe (i, a))
preuse :: MonadState s m => Getting (First a) s a -> m (Maybe a)
ipreviews :: MonadReader s m => IndexedGetting i (First r) s a -> (i -> a -> r) -> m (Maybe r)
previews :: MonadReader s m => Getting (First r) s a -> (a -> r) -> m (Maybe r)
ipreview :: MonadReader s m => IndexedGetting i (First (i, a)) s a -> m (Maybe (i, a))
preview :: MonadReader s m => Getting (First a) s a -> m (Maybe a)
ipre :: IndexedGetting i (First (i, a)) s a -> IndexPreservingGetter s (Maybe (i, a))
pre :: Getting (First a) s a -> IndexPreservingGetter s (Maybe a)
hasn't :: Getting All s a -> s -> Bool
has :: Getting Any s a -> s -> Bool
foldlMOf :: Monad m => Getting (Endo (r -> m r)) s a -> (r -> a -> m r) -> r -> s -> m r
foldrMOf :: Monad m => Getting (Dual (Endo (r -> m r))) s a -> (a -> r -> m r) -> r -> s -> m r
foldl1Of' :: HasCallStack => Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> a) -> s -> a
foldr1Of' :: HasCallStack => Getting (Dual (Endo (Endo (Maybe a)))) s a -> (a -> a -> a) -> s -> a
foldlOf' :: Getting (Endo (Endo r)) s a -> (r -> a -> r) -> r -> s -> r
foldrOf' :: Getting (Dual (Endo (Endo r))) s a -> (a -> r -> r) -> r -> s -> r
foldl1Of :: HasCallStack => Getting (Dual (Endo (Maybe a))) s a -> (a -> a -> a) -> s -> a
foldr1Of :: HasCallStack => Getting (Endo (Maybe a)) s a -> (a -> a -> a) -> s -> a
lookupOf :: Eq k => Getting (Endo (Maybe v)) s (k, v) -> k -> s -> Maybe v
findMOf :: Monad m => Getting (Endo (m (Maybe a))) s a -> (a -> m Bool) -> s -> m (Maybe a)
findOf :: Getting (Endo (Maybe a)) s a -> (a -> Bool) -> s -> Maybe a
minimumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a
maximumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a
minimum1Of :: Ord a => Getting (Min a) s a -> s -> a
minimumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a
maximum1Of :: Ord a => Getting (Max a) s a -> s -> a
maximumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a
notNullOf :: Getting Any s a -> s -> Bool
nullOf :: Getting All s a -> s -> Bool
last1Of :: Getting (Last a) s a -> s -> a
lastOf :: Getting (Rightmost a) s a -> s -> Maybe a
first1Of :: Getting (First a) s a -> s -> a
firstOf :: Getting (Leftmost a) s a -> s -> Maybe a
(^?!) :: HasCallStack => s -> Getting (Endo a) s a -> a
(^?) :: s -> Getting (First a) s a -> Maybe a
lengthOf :: Getting (Endo (Endo Int)) s a -> s -> Int
concatOf :: Getting [r] s [r] -> s -> [r]
concatMapOf :: Getting [r] s a -> (a -> [r]) -> s -> [r]
notElemOf :: Eq a => Getting All s a -> a -> s -> Bool
elemOf :: Eq a => Getting Any s a -> a -> s -> Bool
msumOf :: MonadPlus m => Getting (Endo (m a)) s (m a) -> s -> m a
asumOf :: Alternative f => Getting (Endo (f a)) s (f a) -> s -> f a
sequenceOf_ :: Monad m => Getting (Sequenced a m) s (m a) -> s -> m ()
forMOf_ :: Monad m => Getting (Sequenced r m) s a -> s -> (a -> m r) -> m ()
mapMOf_ :: Monad m => Getting (Sequenced r m) s a -> (a -> m r) -> s -> m ()
sequence1Of_ :: Functor f => Getting (TraversedF a f) s (f a) -> s -> f ()
for1Of_ :: Functor f => Getting (TraversedF r f) s a -> s -> (a -> f r) -> f ()
traverse1Of_ :: Functor f => Getting (TraversedF r f) s a -> (a -> f r) -> s -> f ()
sequenceAOf_ :: Functor f => Getting (Traversed a f) s (f a) -> s -> f ()
forOf_ :: Functor f => Getting (Traversed r f) s a -> s -> (a -> f r) -> f ()
traverseOf_ :: Functor f => Getting (Traversed r f) s a -> (a -> f r) -> s -> f ()
sumOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a
productOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a
noneOf :: Getting Any s a -> (a -> Bool) -> s -> Bool
allOf :: Getting All s a -> (a -> Bool) -> s -> Bool
anyOf :: Getting Any s a -> (a -> Bool) -> s -> Bool
orOf :: Getting Any s Bool -> s -> Bool
andOf :: Getting All s Bool -> s -> Bool
(^..) :: s -> Getting (Endo [a]) s a -> [a]
toNonEmptyOf :: Getting (NonEmptyDList a) s a -> s -> NonEmpty a
toListOf :: Getting (Endo [a]) s a -> s -> [a]
foldlOf :: Getting (Dual (Endo r)) s a -> (r -> a -> r) -> r -> s -> r
foldrOf :: Getting (Endo r) s a -> (a -> r -> r) -> r -> s -> r
foldOf :: Getting a s a -> s -> a
foldMapOf :: Getting r s a -> (a -> r) -> s -> r
lined :: Applicative f => IndexedLensLike' Int f String String
worded :: Applicative f => IndexedLensLike' Int f String String
droppingWhile :: (Conjoined p, Profunctor q, Applicative f) => (a -> Bool) -> Optical p q (Compose (State Bool) f) s t a a -> Optical p q f s t a a
takingWhile :: (Conjoined p, Applicative f) => (a -> Bool) -> Over p (TakingWhile p f a a) s t a a -> Over p f s t a a
filtered :: (Choice p, Applicative f) => (a -> Bool) -> Optic' p f a a
iterated :: Apply f => (a -> a) -> LensLike' f a a
unfolded :: (b -> Maybe (a, b)) -> Fold b a
cycled :: Apply f => LensLike f s t a b -> LensLike f s t a b
replicated :: Int -> Fold a a
repeated :: Apply f => LensLike' f a a
folded64 :: Foldable f => IndexedFold Int64 (f a) a
folded :: Foldable f => IndexedFold Int (f a) a
ifoldring :: (Indexable i p, Contravariant f, Applicative f) => ((i -> a -> f a -> f a) -> f a -> s -> f a) -> Over p f s t a b
foldring :: (Contravariant f, Applicative f) => ((a -> f a -> f a) -> f a -> s -> f a) -> LensLike f s t a b
ifolding :: (Foldable f, Indexable i p, Contravariant g, Applicative g) => (s -> f (i, a)) -> Over p g s t a b
folding :: Foldable f => (s -> f a) -> Fold s a
_Show :: (Read a, Show a) => Prism' String a
nearly :: a -> (a -> Bool) -> Prism' a ()
only :: Eq a => a -> Prism' a ()
_Void :: Prism s s a Void
_Nothing :: Prism' (Maybe a) ()
_Just :: Prism (Maybe a) (Maybe b) a b
_Right :: Prism (Either c a) (Either c b) a b
_Left :: Prism (Either a c) (Either b c) a b
matching :: APrism s t a b -> s -> Either t a
isn't :: APrism s t a b -> s -> Bool
below :: Traversable f => APrism' s a -> Prism' (f s) (f a)
aside :: APrism s t a b -> Prism (e, s) (e, t) (e, a) (e, b)
without :: APrism s t a b -> APrism u v c d -> Prism (Either s u) (Either t v) (Either a c) (Either b d)
outside :: Representable p => APrism s t a b -> Lens (p t r) (p s r) (p b r) (p a r)
prism' :: (b -> s) -> (s -> Maybe a) -> Prism s s a b
prism :: (b -> t) -> (s -> Either t a) -> Prism s t a b
clonePrism :: APrism s t a b -> Prism s t a b
withPrism :: APrism s t a b -> ((b -> t) -> (s -> Either t a) -> r) -> r
type APrism s t a b = Market a b a (Identity b) -> Market a b s (Identity t)
type APrism' s a = APrism s s a a
reuses :: MonadState b m => AReview t b -> (t -> r) -> m r
reuse :: MonadState b m => AReview t b -> m t
reviews :: MonadReader b m => AReview t b -> (t -> r) -> m r
(#) :: AReview t b -> b -> t
review :: MonadReader b m => AReview t b -> m t
re :: AReview t b -> Getter b t
un :: (Profunctor p, Bifunctor p, Functor f) => Getting a s a -> Optic' p f a s
unto :: (Profunctor p, Bifunctor p, Functor f) => (b -> t) -> Optic p f s t a b
getting :: (Profunctor p, Profunctor q, Functor f, Contravariant f) => Optical p q f s t a b -> Optical' p q f s a
(^@.) :: s -> IndexedGetting i (i, a) s a -> (i, a)
iuses :: MonadState s m => IndexedGetting i r s a -> (i -> a -> r) -> m r
iuse :: MonadState s m => IndexedGetting i (i, a) s a -> m (i, a)
iviews :: MonadReader s m => IndexedGetting i r s a -> (i -> a -> r) -> m r
iview :: MonadReader s m => IndexedGetting i (i, a) s a -> m (i, a)
ilistenings :: MonadWriter w m => IndexedGetting i v w u -> (i -> u -> v) -> m a -> m (a, v)
listenings :: MonadWriter w m => Getting v w u -> (u -> v) -> m a -> m (a, v)
ilistening :: MonadWriter w m => IndexedGetting i (i, u) w u -> m a -> m (a, (i, u))
listening :: MonadWriter w m => Getting u w u -> m a -> m (a, u)
uses :: MonadState s m => LensLike' (Const r :: Type -> Type) s a -> (a -> r) -> m r
use :: MonadState s m => Getting a s a -> m a
(^.) :: s -> Getting a s a -> a
views :: MonadReader s m => LensLike' (Const r :: Type -> Type) s a -> (a -> r) -> m r
view :: MonadReader s m => Getting a s a -> m a
ilike :: (Indexable i p, Contravariant f, Functor f) => i -> a -> Over' p f s a
like :: (Profunctor p, Contravariant f, Functor f) => a -> Optic' p f s a
ito :: (Indexable i p, Contravariant f) => (s -> (i, a)) -> Over' p f s a
to :: (Profunctor p, Contravariant f) => (s -> a) -> Optic' p f s a
type Getting r s a = (a -> Const r a) -> s -> Const r s
type IndexedGetting i m s a = Indexed i a (Const m a) -> s -> Const m s
type Accessing (p :: Type -> Type -> Type) m s a = p a (Const m a) -> s -> Const m s
_19' :: Field19 s t a b => Lens s t a b
_18' :: Field18 s t a b => Lens s t a b
_17' :: Field17 s t a b => Lens s t a b
_16' :: Field16 s t a b => Lens s t a b
_15' :: Field15 s t a b => Lens s t a b
_14' :: Field14 s t a b => Lens s t a b
_13' :: Field13 s t a b => Lens s t a b
_12' :: Field12 s t a b => Lens s t a b
_11' :: Field11 s t a b => Lens s t a b
_10' :: Field10 s t a b => Lens s t a b
_9' :: Field9 s t a b => Lens s t a b
_8' :: Field8 s t a b => Lens s t a b
_7' :: Field7 s t a b => Lens s t a b
_6' :: Field6 s t a b => Lens s t a b
_5' :: Field5 s t a b => Lens s t a b
_4' :: Field4 s t a b => Lens s t a b
_3' :: Field3 s t a b => Lens s t a b
_2' :: Field2 s t a b => Lens s t a b
_1' :: Field1 s t a b => Lens s t a b
class Field1 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _1 :: Lens s t a b
class Field2 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _2 :: Lens s t a b
class Field3 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _3 :: Lens s t a b
class Field4 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _4 :: Lens s t a b
class Field5 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _5 :: Lens s t a b
class Field6 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _6 :: Lens s t a b
class Field7 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _7 :: Lens s t a b
class Field8 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _8 :: Lens s t a b
class Field9 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _9 :: Lens s t a b
class Field10 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _10 :: Lens s t a b
class Field11 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _11 :: Lens s t a b
class Field12 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _12 :: Lens s t a b
class Field13 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _13 :: Lens s t a b
class Field14 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _14 :: Lens s t a b
class Field15 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _15 :: Lens s t a b
class Field16 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _16 :: Lens s t a b
class Field17 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _17 :: Lens s t a b
class Field18 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _18 :: Lens s t a b
class Field19 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _19 :: Lens s t a b
fusing :: Functor f => LensLike (Yoneda f) s t a b -> LensLike f s t a b
united :: Lens' a ()
devoid :: Over p f Void Void a b
(<#=) :: MonadState s m => ALens s s a b -> b -> m b
(<#~) :: ALens s t a b -> b -> s -> (b, t)
(#%%=) :: MonadState s m => ALens s s a b -> (a -> (r, b)) -> m r
(<#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m b
(<#%~) :: ALens s t a b -> (a -> b) -> s -> (b, t)
(#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m ()
(#=) :: MonadState s m => ALens s s a b -> b -> m ()
(#%%~) :: Functor f => ALens s t a b -> (a -> f b) -> s -> f t
(#%~) :: ALens s t a b -> (a -> b) -> s -> t
(#~) :: ALens s t a b -> b -> s -> t
storing :: ALens s t a b -> b -> s -> t
(^#) :: s -> ALens s t a b -> a
(<<%@=) :: MonadState s m => Over (Indexed i) ((,) a) s s a b -> (i -> a -> b) -> m a
(<%@=) :: MonadState s m => Over (Indexed i) ((,) b) s s a b -> (i -> a -> b) -> m b
(%%@=) :: MonadState s m => Over (Indexed i) ((,) r) s s a b -> (i -> a -> (r, b)) -> m r
(%%@~) :: Over (Indexed i) f s t a b -> (i -> a -> f b) -> s -> f t
(<<%@~) :: Over (Indexed i) ((,) a) s t a b -> (i -> a -> b) -> s -> (a, t)
(<%@~) :: Over (Indexed i) ((,) b) s t a b -> (i -> a -> b) -> s -> (b, t)
overA :: Arrow ar => LensLike (Context a b) s t a b -> ar a b -> ar s t
(<<>=) :: (MonadState s m, Monoid r) => LensLike' ((,) r) s r -> r -> m r
(<<>~) :: Monoid m => LensLike ((,) m) s t m m -> m -> s -> (m, t)
(<<~) :: MonadState s m => ALens s s a b -> m b -> m b
(<<<>=) :: (MonadState s m, Monoid r) => LensLike' ((,) r) s r -> r -> m r
(<<&&=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool
(<<||=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool
(<<**=) :: (MonadState s m, Floating a) => LensLike' ((,) a) s a -> a -> m a
(<<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> m a
(<<^=) :: (MonadState s m, Num a, Integral e) => LensLike' ((,) a) s a -> e -> m a
(<<//=) :: (MonadState s m, Fractional a) => LensLike' ((,) a) s a -> a -> m a
(<<*=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
(<<-=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
(<<+=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
(<<?=) :: MonadState s m => LensLike ((,) a) s s a (Maybe b) -> b -> m a
(<<.=) :: MonadState s m => LensLike ((,) a) s s a b -> b -> m a
(<<%=) :: (Strong p, MonadState s m) => Over p ((,) a) s s a b -> p a b -> m a
(<&&=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool
(<||=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool
(<**=) :: (MonadState s m, Floating a) => LensLike' ((,) a) s a -> a -> m a
(<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> m a
(<^=) :: (MonadState s m, Num a, Integral e) => LensLike' ((,) a) s a -> e -> m a
(<//=) :: (MonadState s m, Fractional a) => LensLike' ((,) a) s a -> a -> m a
(<*=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
(<-=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
(<+=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
(<%=) :: MonadState s m => LensLike ((,) b) s s a b -> (a -> b) -> m b
(<<<>~) :: Monoid r => LensLike' ((,) r) s r -> r -> s -> (r, s)
(<<&&~) :: LensLike' ((,) Bool) s Bool -> Bool -> s -> (Bool, s)
(<<||~) :: LensLike' ((,) Bool) s Bool -> Bool -> s -> (Bool, s)
(<<**~) :: Floating a => LensLike' ((,) a) s a -> a -> s -> (a, s)
(<<^^~) :: (Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> s -> (a, s)
(<<^~) :: (Num a, Integral e) => LensLike' ((,) a) s a -> e -> s -> (a, s)
(<<//~) :: Fractional a => LensLike' ((,) a) s a -> a -> s -> (a, s)
(<<*~) :: Num a => LensLike' ((,) a) s a -> a -> s -> (a, s)
(<<-~) :: Num a => LensLike' ((,) a) s a -> a -> s -> (a, s)
(<<+~) :: Num a => LensLike' ((,) a) s a -> a -> s -> (a, s)
(<<?~) :: LensLike ((,) a) s t a (Maybe b) -> b -> s -> (a, t)
(<<.~) :: LensLike ((,) a) s t a b -> b -> s -> (a, t)
(<<%~) :: LensLike ((,) a) s t a b -> (a -> b) -> s -> (a, t)
(<&&~) :: LensLike ((,) Bool) s t Bool Bool -> Bool -> s -> (Bool, t)
(<||~) :: LensLike ((,) Bool) s t Bool Bool -> Bool -> s -> (Bool, t)
(<**~) :: Floating a => LensLike ((,) a) s t a a -> a -> s -> (a, t)
(<^^~) :: (Fractional a, Integral e) => LensLike ((,) a) s t a a -> e -> s -> (a, t)
(<^~) :: (Num a, Integral e) => LensLike ((,) a) s t a a -> e -> s -> (a, t)
(<//~) :: Fractional a => LensLike ((,) a) s t a a -> a -> s -> (a, t)
(<*~) :: Num a => LensLike ((,) a) s t a a -> a -> s -> (a, t)
(<-~) :: Num a => LensLike ((,) a) s t a a -> a -> s -> (a, t)
(<+~) :: Num a => LensLike ((,) a) s t a a -> a -> s -> (a, t)
(<%~) :: LensLike ((,) b) s t a b -> (a -> b) -> s -> (b, t)
cloneIndexedLens :: AnIndexedLens i s t a b -> IndexedLens i s t a b
cloneIndexPreservingLens :: ALens s t a b -> IndexPreservingLens s t a b
cloneLens :: ALens s t a b -> Lens s t a b
locus :: IndexedComonadStore p => Lens (p a c s) (p b c s) a b
alongside :: LensLike (AlongsideLeft f b') s t a b -> LensLike (AlongsideRight f t) s' t' a' b' -> LensLike f (s, s') (t, t') (a, a') (b, b')
chosen :: IndexPreservingLens (Either a a) (Either b b) a b
choosing :: Functor f => LensLike f s t a b -> LensLike f s' t' a b -> LensLike f (Either s s') (Either t t') a b
inside :: Corepresentable p => ALens s t a b -> Lens (p e s) (p e t) (p e a) (p e b)
(??) :: Functor f => f (a -> b) -> a -> f b
(%%=) :: MonadState s m => Over p ((,) r) s s a b -> p a (r, b) -> m r
(%%~) :: LensLike f s t a b -> (a -> f b) -> s -> f t
(&~) :: s -> State s a -> s
ilens :: (s -> (i, a)) -> (s -> b -> t) -> IndexedLens i s t a b
iplens :: (s -> a) -> (s -> b -> t) -> IndexPreservingLens s t a b
lens :: (s -> a) -> (s -> b -> t) -> Lens s t a b
type ALens s t a b = LensLike (Pretext ((->) :: Type -> Type -> Type) a b) s t a b
type ALens' s a = ALens s s a a
type AnIndexedLens i s t a b = Optical (Indexed i) ((->) :: Type -> Type -> Type) (Pretext (Indexed i) a b) s t a b
type AnIndexedLens' i s a = AnIndexedLens i s s a a
imapOf :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t
mapOf :: ASetter s t a b -> (a -> b) -> s -> t
assignA :: Arrow p => ASetter s t a b -> p s b -> p s t
(.@=) :: MonadState s m => AnIndexedSetter i s s a b -> (i -> b) -> m ()
imodifying :: MonadState s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m ()
(%@=) :: MonadState s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m ()
(.@~) :: AnIndexedSetter i s t a b -> (i -> b) -> s -> t
(%@~) :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t
isets :: ((i -> a -> b) -> s -> t) -> IndexedSetter i s t a b
iset :: AnIndexedSetter i s t a b -> (i -> b) -> s -> t
iover :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t
icensoring :: MonadWriter w m => IndexedSetter i w w u v -> (i -> u -> v) -> m a -> m a
censoring :: MonadWriter w m => Setter w w u v -> (u -> v) -> m a -> m a
ipassing :: MonadWriter w m => IndexedSetter i w w u v -> m (a, i -> u -> v) -> m a
passing :: MonadWriter w m => Setter w w u v -> m (a, u -> v) -> m a
scribe :: (MonadWriter t m, Monoid s) => ASetter s t a b -> b -> m ()
(<>=) :: (MonadState s m, Monoid a) => ASetter' s a -> a -> m ()
(<>~) :: Monoid a => ASetter s t a a -> a -> s -> t
(<?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m b
(<.=) :: MonadState s m => ASetter s s a b -> b -> m b
(<~) :: MonadState s m => ASetter s s a b -> m b -> m ()
(||=) :: MonadState s m => ASetter' s Bool -> Bool -> m ()
(&&=) :: MonadState s m => ASetter' s Bool -> Bool -> m ()
(**=) :: (MonadState s m, Floating a) => ASetter' s a -> a -> m ()
(^^=) :: (MonadState s m, Fractional a, Integral e) => ASetter' s a -> e -> m ()
(^=) :: (MonadState s m, Num a, Integral e) => ASetter' s a -> e -> m ()
(//=) :: (MonadState s m, Fractional a) => ASetter' s a -> a -> m ()
(*=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m ()
(-=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m ()
(+=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m ()
(?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m ()
modifying :: MonadState s m => ASetter s s a b -> (a -> b) -> m ()
(%=) :: MonadState s m => ASetter s s a b -> (a -> b) -> m ()
(.=) :: MonadState s m => ASetter s s a b -> b -> m ()
assign :: MonadState s m => ASetter s s a b -> b -> m ()
(&&~) :: ASetter s t Bool Bool -> Bool -> s -> t
(||~) :: ASetter s t Bool Bool -> Bool -> s -> t
(**~) :: Floating a => ASetter s t a a -> a -> s -> t
(^^~) :: (Fractional a, Integral e) => ASetter s t a a -> e -> s -> t
(^~) :: (Num a, Integral e) => ASetter s t a a -> e -> s -> t
(//~) :: Fractional a => ASetter s t a a -> a -> s -> t
(-~) :: Num a => ASetter s t a a -> a -> s -> t
(*~) :: Num a => ASetter s t a a -> a -> s -> t
(+~) :: Num a => ASetter s t a a -> a -> s -> t
(<?~) :: ASetter s t a (Maybe b) -> b -> s -> (b, t)
(<.~) :: ASetter s t a b -> b -> s -> (b, t)
(?~) :: ASetter s t a (Maybe b) -> b -> s -> t
(.~) :: ASetter s t a b -> b -> s -> t
(%~) :: ASetter s t a b -> (a -> b) -> s -> t
set' :: ASetter' s a -> a -> s -> s
set :: ASetter s t a b -> b -> s -> t
over :: ASetter s t a b -> (a -> b) -> s -> t
cloneIndexedSetter :: AnIndexedSetter i s t a b -> IndexedSetter i s t a b
cloneIndexPreservingSetter :: ASetter s t a b -> IndexPreservingSetter s t a b
cloneSetter :: ASetter s t a b -> Setter s t a b
sets :: (Profunctor p, Profunctor q, Settable f) => (p a b -> q s t) -> Optical p q f s t a b
setting :: ((a -> b) -> s -> t) -> IndexPreservingSetter s t a b
argument :: Profunctor p => Setter (p b r) (p a r) a b
contramapped :: Contravariant f => Setter (f b) (f a) a b
lifted :: Monad m => Setter (m a) (m b) a b
mapped :: Functor f => Setter (f a) (f b) a b
type ASetter s t a b = (a -> Identity b) -> s -> Identity t
type ASetter' s a = ASetter s s a a
type AnIndexedSetter i s t a b = Indexed i a (Identity b) -> s -> Identity t
type AnIndexedSetter' i s a = AnIndexedSetter i s s a a
type Setting (p :: Type -> Type -> Type) s t a b = p a (Identity b) -> s -> Identity t
type Setting' (p :: Type -> Type -> Type) s a = Setting p s s a a
type Lens s t a b = forall (f :: Type -> Type). Functor f => (a -> f b) -> s -> f t
type Lens' s a = Lens s s a a
type IndexedLens i s t a b = forall (f :: Type -> Type) (p :: Type -> Type -> Type). (Indexable i p, Functor f) => p a (f b) -> s -> f t
type IndexedLens' i s a = IndexedLens i s s a a
type IndexPreservingLens s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Functor f) => p a (f b) -> p s (f t)
type IndexPreservingLens' s a = IndexPreservingLens s s a a
type Traversal s t a b = forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t
type Traversal' s a = Traversal s s a a
type Traversal1 s t a b = forall (f :: Type -> Type). Apply f => (a -> f b) -> s -> f t
type Traversal1' s a = Traversal1 s s a a
type IndexedTraversal i s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Applicative f) => p a (f b) -> s -> f t
type IndexedTraversal' i s a = IndexedTraversal i s s a a
type IndexedTraversal1 i s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Apply f) => p a (f b) -> s -> f t
type IndexedTraversal1' i s a = IndexedTraversal1 i s s a a
type IndexPreservingTraversal s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Applicative f) => p a (f b) -> p s (f t)
type IndexPreservingTraversal' s a = IndexPreservingTraversal s s a a
type IndexPreservingTraversal1 s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Apply f) => p a (f b) -> p s (f t)
type IndexPreservingTraversal1' s a = IndexPreservingTraversal1 s s a a
type Setter s t a b = forall (f :: Type -> Type). Settable f => (a -> f b) -> s -> f t
type Setter' s a = Setter s s a a
type IndexedSetter i s t a b = forall (f :: Type -> Type) (p :: Type -> Type -> Type). (Indexable i p, Settable f) => p a (f b) -> s -> f t
type IndexedSetter' i s a = IndexedSetter i s s a a
type IndexPreservingSetter s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Settable f) => p a (f b) -> p s (f t)
type IndexPreservingSetter' s a = IndexPreservingSetter s s a a
type Iso s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Profunctor p, Functor f) => p a (f b) -> p s (f t)
type Iso' s a = Iso s s a a
type Review t b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Choice p, Bifunctor p, Settable f) => Optic' p f t b
type AReview t b = Optic' (Tagged :: Type -> Type -> Type) Identity t b
type Prism s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Choice p, Applicative f) => p a (f b) -> p s (f t)
type Prism' s a = Prism s s a a
type Equality (s :: k1) (t :: k2) (a :: k1) (b :: k2) = forall k3 (p :: k1 -> k3 -> Type) (f :: k2 -> k3). p a (f b) -> p s (f t)
type Equality' (s :: k2) (a :: k2) = Equality s s a a
type As (a :: k2) = Equality' a a
type Getter s a = forall (f :: Type -> Type). (Contravariant f, Functor f) => (a -> f a) -> s -> f s
type IndexedGetter i s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Contravariant f, Functor f) => p a (f a) -> s -> f s
type IndexPreservingGetter s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Contravariant f, Functor f) => p a (f a) -> p s (f s)
type Fold s a = forall (f :: Type -> Type). (Contravariant f, Applicative f) => (a -> f a) -> s -> f s
type IndexedFold i s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Contravariant f, Applicative f) => p a (f a) -> s -> f s
type IndexPreservingFold s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Contravariant f, Applicative f) => p a (f a) -> p s (f s)
type Fold1 s a = forall (f :: Type -> Type). (Contravariant f, Apply f) => (a -> f a) -> s -> f s
type IndexedFold1 i s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Contravariant f, Apply f) => p a (f a) -> s -> f s
type IndexPreservingFold1 s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Contravariant f, Apply f) => p a (f a) -> p s (f s)
type Simple (f :: k -> k -> k1 -> k1 -> k2) (s :: k) (a :: k1) = f s s a a
type Optic (p :: k1 -> k -> Type) (f :: k2 -> k) (s :: k1) (t :: k2) (a :: k1) (b :: k2) = p a (f b) -> p s (f t)
type Optic' (p :: k1 -> k -> Type) (f :: k1 -> k) (s :: k1) (a :: k1) = Optic p f s s a a
type Optical (p :: k2 -> k -> Type) (q :: k1 -> k -> Type) (f :: k3 -> k) (s :: k1) (t :: k3) (a :: k2) (b :: k3) = p a (f b) -> q s (f t)
type Optical' (p :: k1 -> k -> Type) (q :: k1 -> k -> Type) (f :: k1 -> k) (s :: k1) (a :: k1) = Optical p q f s s a a
type LensLike (f :: k -> Type) s (t :: k) a (b :: k) = (a -> f b) -> s -> f t
type LensLike' (f :: Type -> Type) s a = LensLike f s s a a
type IndexedLensLike i (f :: k -> Type) s (t :: k) a (b :: k) = forall (p :: Type -> Type -> Type). Indexable i p => p a (f b) -> s -> f t
type IndexedLensLike' i (f :: Type -> Type) s a = IndexedLensLike i f s s a a
type Over (p :: k -> Type -> Type) (f :: k1 -> Type) s (t :: k1) (a :: k) (b :: k1) = p a (f b) -> s -> f t
type Over' (p :: Type -> Type -> Type) (f :: Type -> Type) s a = Over p f s s a a
class (Applicative f, Distributive f, Traversable f) => Settable (f :: Type -> Type)
retagged :: (Profunctor p, Bifunctor p) => p a b -> p s b
class (Profunctor p, Bifunctor p) => Reviewable (p :: Type -> Type -> Type)
data Magma i t b a
data Level i a
class Reversing t where
- reversing :: t -> t
newtype Bazaar (p :: Type -> Type -> Type) a b t = Bazaar {
- runBazaar :: forall (f :: Type -> Type). Applicative f => p a (f b) -> f t
}
type Bazaar' (p :: Type -> Type -> Type) a = Bazaar p a a
newtype Bazaar1 (p :: Type -> Type -> Type) a b t = Bazaar1 {
- runBazaar1 :: forall (f :: Type -> Type). Apply f => p a (f b) -> f t
}
type Bazaar1' (p :: Type -> Type -> Type) a = Bazaar1 p a a
data Context a b t = Context (b -> t) a
type Context' a = Context a a
asIndex :: (Indexable i p, Contravariant f, Functor f) => p i (f i) -> Indexed i s (f s)
withIndex :: (Indexable i p, Functor f) => p (i, s) (f (j, t)) -> Indexed i s (f t)
indexing64 :: Indexable Int64 p => ((a -> Indexing64 f b) -> s -> Indexing64 f t) -> p a (f b) -> s -> f t
indexing :: Indexable Int p => ((a -> Indexing f b) -> s -> Indexing f t) -> p a (f b) -> s -> f t
class (Choice p, Corepresentable p, Comonad (Corep p), Traversable (Corep p), Strong p, Representable p, Monad (Rep p), MonadFix (Rep p), Distributive (Rep p), Costrong p, ArrowLoop p, ArrowApply p, ArrowChoice p, Closed p) => Conjoined (p :: Type -> Type -> Type) where
- distrib :: Functor f => p a b -> p (f a) (f b)
- conjoined :: ((p ~ ((->) :: Type -> Type -> Type)) -> q (a -> b) r) -> q (p a b) r -> q (p a b) r
class Conjoined p => Indexable i (p :: Type -> Type -> Type) where
- indexed :: p a b -> i -> a -> b
newtype Indexed i a b = Indexed {
- runIndexed :: i -> a -> b
}
data Traversed a (f :: Type -> Type)
data Sequenced a (m :: Type -> Type)
data Leftmost a
data Rightmost a
class (Foldable1 t, Traversable t) => Traversable1 (t :: Type -> Type) where
- traverse1 :: Apply f => (a -> f b) -> t a -> f (t b)
foldBy :: Foldable t => (a -> a -> a) -> a -> t a -> a
foldMapBy :: Foldable t => (r -> r -> r) -> r -> (a -> r) -> t a -> r
traverseBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (a -> f b) -> t a -> f (t b)
sequenceBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> t (f a) -> f (t a)
class Profunctor p => Choice (p :: Type -> Type -> Type) where
- left' :: p a b -> p (Either a c) (Either b c)
- right' :: p a b -> p (Either c a) (Either c b)
type NestedIxedCtx a = (NestedCtx a, Ixed a, Ixed (IxValue a))
type NestedAtCtx a = (NestedCtx a, At a, At (IxValue a))
type NestedCtx a = (Index a ~ Index (IxValue a), IxValue a ~ IxValue (IxValue a))
nestedAt :: (NestedAtCtx a, Mempty (IxValue a)) => NonEmpty (Index a) -> Lens' a (Maybe (IxValue a))
nestedDefAt :: NestedAtCtx a => IxValue a -> NonEmpty (Index a) -> Lens' a (Maybe (IxValue a))
nestedAt' :: (NestedAtCtx a, Mempty (IxValue a)) => NonEmpty (Index a) -> Lens' a (IxValue a)
nestedIx :: NestedIxedCtx a => NonEmpty (Index a) -> Traversal' a (IxValue a)
emptyMap :: Prism' (Map k a) ()
subMapAt :: (Functor f, Ord p) => p -> (Maybe a -> f (Maybe a)) -> Maybe (Map p a) -> f (Maybe (Map p a))
at' :: (Functor f, Ord p) => p -> (Maybe a -> f (Maybe a)) -> Maybe (Map p a) -> f (Maybe (Map p a))
unsafeLensedMapAt :: (Ord k, Default v) => k -> Lens' v a -> Lens' (Map k v) (Maybe a)
makeLenses' :: Name -> DecsQ
makeLenses :: Name -> DecsQ
makeClassy' :: Name -> DecsQ
makeClassy :: Name -> DecsQ
wrapped' :: (Wrapped s, Profunctor p, Functor f) => p (Unwrapped s) (f (Unwrapped s)) -> p s (f s)
unwrapped' :: (Wrapped s, Profunctor p, Functor f) => p s (f s) -> p (Unwrapped s) (f (Unwrapped s))
wrapping' :: (Wrapped s, Profunctor p, Functor f) => (Unwrapped s -> s) -> p (Unwrapped s) (f (Unwrapped s)) -> p s (f s)
unwrapping' :: (Wrapped s, Profunctor p, Functor f) => (Unwrapped s -> s) -> p s (f s) -> p (Unwrapped s) (f (Unwrapped s))
unwrap' :: (MonadReader s m, Wrapped s) => m (Unwrapped s)
wrap' :: (MonadReader (Unwrapped s) m, Wrapped s) => m s
wrapped :: (Rewrapped s t, Rewrapped t s, Profunctor p, Functor f) => p (Unwrapped s) (f (Unwrapped t)) -> p s (f t)
unwrapped :: (Rewrapped s t, Rewrapped t s, Profunctor p, Functor f) => p t (f s) -> p (Unwrapped t) (f (Unwrapped s))
wrapping :: (Rewrapped s t, Rewrapped t s, Profunctor p, Functor f) => (Unwrapped s -> s) -> p (Unwrapped s) (f (Unwrapped t)) -> p s (f t)
unwrapping :: (Rewrapped s t, Rewrapped t s, Profunctor p, Functor f) => (Unwrapped s -> s) -> p t (f s) -> p (Unwrapped t) (f (Unwrapped s))
_unwrap :: (MonadReader s m, Rewrapped s s) => m (Unwrapped s)
_wrap :: (MonadReader (Unwrapped t) m, Rewrapped t t) => m t
rewrap :: (Rewrapped s t, Rewrapped t s, Unwrapped t ~# Unwrapped s) => s -> t
wrappedM' :: (Functor f, Wrapped b, Wrapped s) => (Unwrapped s -> f (Unwrapped b)) -> s -> f b
wrap :: forall a. Coercible (Unwrapped a) a => Unwrapped a -> a
unwrap :: forall a. Coercible a (Unwrapped a) => a -> Unwrapped a

Documentation

class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where #

Functors representing data structures that can be traversed from left to right.

A definition of traverse must satisfy the following laws:

naturality: t . traverse f = traverse (t . f) for every applicative transformation t
identity: traverse Identity = Identity
composition: traverse (Compose . fmap g . f) = Compose . fmap (traverse g) . traverse f

A definition of sequenceA must satisfy the following laws:

naturality: t . sequenceA = sequenceA . fmap t for every applicative transformation t
identity: sequenceA . fmap Identity = Identity
composition: sequenceA . fmap Compose = Compose . fmap sequenceA . sequenceA

where an applicative transformation is a function

t :: (Applicative f, Applicative g) => f a -> g a

preserving the Applicative operations, i.e.

```
t (pure x) = pure x
```
```
t (x <*> y) = t x <*> t y
```

and the identity functor Identity and composition of functors Compose are defined as

  newtype Identity a = Identity a

  instance Functor Identity where
    fmap f (Identity x) = Identity (f x)

  instance Applicative Identity where
    pure x = Identity x
    Identity f <*> Identity x = Identity (f x)

  newtype Compose f g a = Compose (f (g a))

  instance (Functor f, Functor g) => Functor (Compose f g) where
    fmap f (Compose x) = Compose (fmap (fmap f) x)

  instance (Applicative f, Applicative g) => Applicative (Compose f g) where
    pure x = Compose (pure (pure x))
    Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)

(The naturality law is implied by parametricity.)

Instances are similar to Functor, e.g. given a data type

data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be

instance Traversable Tree where
   traverse f Empty = pure Empty
   traverse f (Leaf x) = Leaf <$> f x
   traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r

This is suitable even for abstract types, as the laws for <*> imply a form of associativity.

The superclass instances should satisfy the following:

In the Functor instance, fmap should be equivalent to traversal with the identity applicative functor (fmapDefault).
In the Foldable instance, foldMap should be equivalent to traversal with a constant applicative functor (foldMapDefault).

Minimal complete definition

traverse | sequenceA

Methods

traverse :: Applicative f => (a -> f b) -> t a -> f (t b) #

Map each element of a structure to an action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see traverse_.

Instances

Traversable []	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> [a] -> f [b] # sequenceA :: Applicative f => [f a] -> f [a] # mapM :: Monad m => (a -> m b) -> [a] -> m [b] # sequence :: Monad m => [m a] -> m [a] #
Traversable Maybe	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) # sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) # mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) # sequence :: Monad m => Maybe (m a) -> m (Maybe a) #
Traversable Par1	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Par1 a -> f (Par1 b) # sequenceA :: Applicative f => Par1 (f a) -> f (Par1 a) # mapM :: Monad m => (a -> m b) -> Par1 a -> m (Par1 b) # sequence :: Monad m => Par1 (m a) -> m (Par1 a) #
Traversable IResult
Instance details Defined in Data.Aeson.Types.Internal Methods traverse :: Applicative f => (a -> f b) -> IResult a -> f (IResult b) # sequenceA :: Applicative f => IResult (f a) -> f (IResult a) # mapM :: Monad m => (a -> m b) -> IResult a -> m (IResult b) # sequence :: Monad m => IResult (m a) -> m (IResult a) #
Traversable Result
Instance details Defined in Data.Aeson.Types.Internal Methods traverse :: Applicative f => (a -> f b) -> Result a -> f (Result b) # sequenceA :: Applicative f => Result (f a) -> f (Result a) # mapM :: Monad m => (a -> m b) -> Result a -> m (Result b) # sequence :: Monad m => Result (m a) -> m (Result a) #
Traversable Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b) # sequenceA :: Applicative f => Complex (f a) -> f (Complex a) # mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b) # sequence :: Monad m => Complex (m a) -> m (Complex a) #
Traversable Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Min a -> f (Min b) # sequenceA :: Applicative f => Min (f a) -> f (Min a) # mapM :: Monad m => (a -> m b) -> Min a -> m (Min b) # sequence :: Monad m => Min (m a) -> m (Min a) #
Traversable Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Max a -> f (Max b) # sequenceA :: Applicative f => Max (f a) -> f (Max a) # mapM :: Monad m => (a -> m b) -> Max a -> m (Max b) # sequence :: Monad m => Max (m a) -> m (Max a) #
Traversable First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) # sequenceA :: Applicative f => First (f a) -> f (First a) # mapM :: Monad m => (a -> m b) -> First a -> m (First b) # sequence :: Monad m => First (m a) -> m (First a) #
Traversable Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) # sequenceA :: Applicative f => Last (f a) -> f (Last a) # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) # sequence :: Monad m => Last (m a) -> m (Last a) #
Traversable Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Option a -> f (Option b) # sequenceA :: Applicative f => Option (f a) -> f (Option a) # mapM :: Monad m => (a -> m b) -> Option a -> m (Option b) # sequence :: Monad m => Option (m a) -> m (Option a) #
Traversable ZipList	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> ZipList a -> f (ZipList b) # sequenceA :: Applicative f => ZipList (f a) -> f (ZipList a) # mapM :: Monad m => (a -> m b) -> ZipList a -> m (ZipList b) # sequence :: Monad m => ZipList (m a) -> m (ZipList a) #
Traversable Identity	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Identity a -> f (Identity b) # sequenceA :: Applicative f => Identity (f a) -> f (Identity a) # mapM :: Monad m => (a -> m b) -> Identity a -> m (Identity b) # sequence :: Monad m => Identity (m a) -> m (Identity a) #
Traversable First	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) # sequenceA :: Applicative f => First (f a) -> f (First a) # mapM :: Monad m => (a -> m b) -> First a -> m (First b) # sequence :: Monad m => First (m a) -> m (First a) #
Traversable Last	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) # sequenceA :: Applicative f => Last (f a) -> f (Last a) # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) # sequence :: Monad m => Last (m a) -> m (Last a) #
Traversable Dual	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) # sequenceA :: Applicative f => Dual (f a) -> f (Dual a) # mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) # sequence :: Monad m => Dual (m a) -> m (Dual a) #
Traversable Sum	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) # sequenceA :: Applicative f => Sum (f a) -> f (Sum a) # mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) # sequence :: Monad m => Sum (m a) -> m (Sum a) #
Traversable Product	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) # sequenceA :: Applicative f => Product (f a) -> f (Product a) # mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) # sequence :: Monad m => Product (m a) -> m (Product a) #
Traversable Down	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Down a -> f (Down b) # sequenceA :: Applicative f => Down (f a) -> f (Down a) # mapM :: Monad m => (a -> m b) -> Down a -> m (Down b) # sequence :: Monad m => Down (m a) -> m (Down a) #
Traversable NonEmpty	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) # sequenceA :: Applicative f => NonEmpty (f a) -> f (NonEmpty a) # mapM :: Monad m => (a -> m b) -> NonEmpty a -> m (NonEmpty b) # sequence :: Monad m => NonEmpty (m a) -> m (NonEmpty a) #
Traversable IntMap
Instance details Defined in Data.IntMap.Internal Methods traverse :: Applicative f => (a -> f b) -> IntMap a -> f (IntMap b) # sequenceA :: Applicative f => IntMap (f a) -> f (IntMap a) # mapM :: Monad m => (a -> m b) -> IntMap a -> m (IntMap b) # sequence :: Monad m => IntMap (m a) -> m (IntMap a) #
Traversable Tree
Instance details Defined in Data.Tree Methods traverse :: Applicative f => (a -> f b) -> Tree a -> f (Tree b) # sequenceA :: Applicative f => Tree (f a) -> f (Tree a) # mapM :: Monad m => (a -> m b) -> Tree a -> m (Tree b) # sequence :: Monad m => Tree (m a) -> m (Tree a) #
Traversable Seq
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Seq a -> f (Seq b) # sequenceA :: Applicative f => Seq (f a) -> f (Seq a) # mapM :: Monad m => (a -> m b) -> Seq a -> m (Seq b) # sequence :: Monad m => Seq (m a) -> m (Seq a) #
Traversable FingerTree
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> FingerTree a -> f (FingerTree b) # sequenceA :: Applicative f => FingerTree (f a) -> f (FingerTree a) # mapM :: Monad m => (a -> m b) -> FingerTree a -> m (FingerTree b) # sequence :: Monad m => FingerTree (m a) -> m (FingerTree a) #
Traversable Digit
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Digit a -> f (Digit b) # sequenceA :: Applicative f => Digit (f a) -> f (Digit a) # mapM :: Monad m => (a -> m b) -> Digit a -> m (Digit b) # sequence :: Monad m => Digit (m a) -> m (Digit a) #
Traversable Node
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Node a -> f (Node b) # sequenceA :: Applicative f => Node (f a) -> f (Node a) # mapM :: Monad m => (a -> m b) -> Node a -> m (Node b) # sequence :: Monad m => Node (m a) -> m (Node a) #
Traversable Elem
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Elem a -> f (Elem b) # sequenceA :: Applicative f => Elem (f a) -> f (Elem a) # mapM :: Monad m => (a -> m b) -> Elem a -> m (Elem b) # sequence :: Monad m => Elem (m a) -> m (Elem a) #
Traversable ViewL
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> ViewL a -> f (ViewL b) # sequenceA :: Applicative f => ViewL (f a) -> f (ViewL a) # mapM :: Monad m => (a -> m b) -> ViewL a -> m (ViewL b) # sequence :: Monad m => ViewL (m a) -> m (ViewL a) #
Traversable ViewR
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> ViewR a -> f (ViewR b) # sequenceA :: Applicative f => ViewR (f a) -> f (ViewR a) # mapM :: Monad m => (a -> m b) -> ViewR a -> m (ViewR b) # sequence :: Monad m => ViewR (m a) -> m (ViewR a) #
Traversable Vector
Instance details Defined in Data.Vector Methods traverse :: Applicative f => (a -> f b) -> Vector a -> f (Vector b) # sequenceA :: Applicative f => Vector (f a) -> f (Vector a) # mapM :: Monad m => (a -> m b) -> Vector a -> m (Vector b) # sequence :: Monad m => Vector (m a) -> m (Vector a) #
Traversable SmallArray
Instance details Defined in Data.Primitive.SmallArray Methods traverse :: Applicative f => (a -> f b) -> SmallArray a -> f (SmallArray b) # sequenceA :: Applicative f => SmallArray (f a) -> f (SmallArray a) # mapM :: Monad m => (a -> m b) -> SmallArray a -> m (SmallArray b) # sequence :: Monad m => SmallArray (m a) -> m (SmallArray a) #
Traversable Array
Instance details Defined in Data.Primitive.Array Methods traverse :: Applicative f => (a -> f b) -> Array a -> f (Array b) # sequenceA :: Applicative f => Array (f a) -> f (Array a) # mapM :: Monad m => (a -> m b) -> Array a -> m (Array b) # sequence :: Monad m => Array (m a) -> m (Array a) #
Traversable (Either a)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) # sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) # mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) # sequence :: Monad m => Either a (m a0) -> m (Either a a0) #
Traversable (V1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> V1 a -> f (V1 b) # sequenceA :: Applicative f => V1 (f a) -> f (V1 a) # mapM :: Monad m => (a -> m b) -> V1 a -> m (V1 b) # sequence :: Monad m => V1 (m a) -> m (V1 a) #
Traversable (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> U1 a -> f (U1 b) # sequenceA :: Applicative f => U1 (f a) -> f (U1 a) # mapM :: Monad m => (a -> m b) -> U1 a -> m (U1 b) # sequence :: Monad m => U1 (m a) -> m (U1 a) #
Traversable ((,) a)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> (a, a0) -> f (a, b) # sequenceA :: Applicative f => (a, f a0) -> f (a, a0) # mapM :: Monad m => (a0 -> m b) -> (a, a0) -> m (a, b) # sequence :: Monad m => (a, m a0) -> m (a, a0) #
Traversable (HashMap k)
Instance details Defined in Data.HashMap.Base Methods traverse :: Applicative f => (a -> f b) -> HashMap k a -> f (HashMap k b) # sequenceA :: Applicative f => HashMap k (f a) -> f (HashMap k a) # mapM :: Monad m => (a -> m b) -> HashMap k a -> m (HashMap k b) # sequence :: Monad m => HashMap k (m a) -> m (HashMap k a) #
Traversable (Map k)
Instance details Defined in Data.Map.Internal Methods traverse :: Applicative f => (a -> f b) -> Map k a -> f (Map k b) # sequenceA :: Applicative f => Map k (f a) -> f (Map k a) # mapM :: Monad m => (a -> m b) -> Map k a -> m (Map k b) # sequence :: Monad m => Map k (m a) -> m (Map k a) #
Ix i => Traversable (Array i)	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Array i a -> f (Array i b) # sequenceA :: Applicative f => Array i (f a) -> f (Array i a) # mapM :: Monad m => (a -> m b) -> Array i a -> m (Array i b) # sequence :: Monad m => Array i (m a) -> m (Array i a) #
Traversable (Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a0 -> f b) -> Arg a a0 -> f (Arg a b) # sequenceA :: Applicative f => Arg a (f a0) -> f (Arg a a0) # mapM :: Monad m => (a0 -> m b) -> Arg a a0 -> m (Arg a b) # sequence :: Monad m => Arg a (m a0) -> m (Arg a a0) #
Traversable (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Proxy a -> f (Proxy b) # sequenceA :: Applicative f => Proxy (f a) -> f (Proxy a) # mapM :: Monad m => (a -> m b) -> Proxy a -> m (Proxy b) # sequence :: Monad m => Proxy (m a) -> m (Proxy a) #
Traversable f => Traversable (MaybeT f)
Instance details Defined in Control.Monad.Trans.Maybe Methods traverse :: Applicative f0 => (a -> f0 b) -> MaybeT f a -> f0 (MaybeT f b) # sequenceA :: Applicative f0 => MaybeT f (f0 a) -> f0 (MaybeT f a) # mapM :: Monad m => (a -> m b) -> MaybeT f a -> m (MaybeT f b) # sequence :: Monad m => MaybeT f (m a) -> m (MaybeT f a) #
(Monad m, Traversable m) => Traversable (CatchT m)
Instance details Defined in Control.Monad.Catch.Pure Methods traverse :: Applicative f => (a -> f b) -> CatchT m a -> f (CatchT m b) # sequenceA :: Applicative f => CatchT m (f a) -> f (CatchT m a) # mapM :: Monad m0 => (a -> m0 b) -> CatchT m a -> m0 (CatchT m b) # sequence :: Monad m0 => CatchT m (m0 a) -> m0 (CatchT m a) #
Traversable f => Traversable (Cofree f)
Instance details Defined in Control.Comonad.Cofree Methods traverse :: Applicative f0 => (a -> f0 b) -> Cofree f a -> f0 (Cofree f b) # sequenceA :: Applicative f0 => Cofree f (f0 a) -> f0 (Cofree f a) # mapM :: Monad m => (a -> m b) -> Cofree f a -> m (Cofree f b) # sequence :: Monad m => Cofree f (m a) -> m (Cofree f a) #
Traversable w => Traversable (CoiterT w)
Instance details Defined in Control.Comonad.Trans.Coiter Methods traverse :: Applicative f => (a -> f b) -> CoiterT w a -> f (CoiterT w b) # sequenceA :: Applicative f => CoiterT w (f a) -> f (CoiterT w a) # mapM :: Monad m => (a -> m b) -> CoiterT w a -> m (CoiterT w b) # sequence :: Monad m => CoiterT w (m a) -> m (CoiterT w a) #
Traversable f => Traversable (Free f)
Instance details Defined in Control.Monad.Free Methods traverse :: Applicative f0 => (a -> f0 b) -> Free f a -> f0 (Free f b) # sequenceA :: Applicative f0 => Free f (f0 a) -> f0 (Free f a) # mapM :: Monad m => (a -> m b) -> Free f a -> m (Free f b) # sequence :: Monad m => Free f (m a) -> m (Free f a) #
(Monad m, Traversable m) => Traversable (IterT m)
Instance details Defined in Control.Monad.Trans.Iter Methods traverse :: Applicative f => (a -> f b) -> IterT m a -> f (IterT m b) # sequenceA :: Applicative f => IterT m (f a) -> f (IterT m a) # mapM :: Monad m0 => (a -> m0 b) -> IterT m a -> m0 (IterT m b) # sequence :: Monad m0 => IterT m (m0 a) -> m0 (IterT m a) #
Traversable f => Traversable (Yoneda f)
Instance details Defined in Data.Functor.Yoneda Methods traverse :: Applicative f0 => (a -> f0 b) -> Yoneda f a -> f0 (Yoneda f b) # sequenceA :: Applicative f0 => Yoneda f (f0 a) -> f0 (Yoneda f a) # mapM :: Monad m => (a -> m b) -> Yoneda f a -> m (Yoneda f b) # sequence :: Monad m => Yoneda f (m a) -> m (Yoneda f a) #
Traversable (Level i)
Instance details Defined in Control.Lens.Internal.Level Methods traverse :: Applicative f => (a -> f b) -> Level i a -> f (Level i b) # sequenceA :: Applicative f => Level i (f a) -> f (Level i a) # mapM :: Monad m => (a -> m b) -> Level i a -> m (Level i b) # sequence :: Monad m => Level i (m a) -> m (Level i a) #
Traversable f => Traversable (ListT f)
Instance details Defined in Control.Monad.Trans.List Methods traverse :: Applicative f0 => (a -> f0 b) -> ListT f a -> f0 (ListT f b) # sequenceA :: Applicative f0 => ListT f (f0 a) -> f0 (ListT f a) # mapM :: Monad m => (a -> m b) -> ListT f a -> m (ListT f b) # sequence :: Monad m => ListT f (m a) -> m (ListT f a) #
Traversable f => Traversable (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Rec1 f a -> f0 (Rec1 f b) # sequenceA :: Applicative f0 => Rec1 f (f0 a) -> f0 (Rec1 f a) # mapM :: Monad m => (a -> m b) -> Rec1 f a -> m (Rec1 f b) # sequence :: Monad m => Rec1 f (m a) -> m (Rec1 f a) #
Traversable (URec Char :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Char a -> f (URec Char b) # sequenceA :: Applicative f => URec Char (f a) -> f (URec Char a) # mapM :: Monad m => (a -> m b) -> URec Char a -> m (URec Char b) # sequence :: Monad m => URec Char (m a) -> m (URec Char a) #
Traversable (URec Double :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Double a -> f (URec Double b) # sequenceA :: Applicative f => URec Double (f a) -> f (URec Double a) # mapM :: Monad m => (a -> m b) -> URec Double a -> m (URec Double b) # sequence :: Monad m => URec Double (m a) -> m (URec Double a) #
Traversable (URec Float :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Float a -> f (URec Float b) # sequenceA :: Applicative f => URec Float (f a) -> f (URec Float a) # mapM :: Monad m => (a -> m b) -> URec Float a -> m (URec Float b) # sequence :: Monad m => URec Float (m a) -> m (URec Float a) #
Traversable (URec Int :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Int a -> f (URec Int b) # sequenceA :: Applicative f => URec Int (f a) -> f (URec Int a) # mapM :: Monad m => (a -> m b) -> URec Int a -> m (URec Int b) # sequence :: Monad m => URec Int (m a) -> m (URec Int a) #
Traversable (URec Word :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Word a -> f (URec Word b) # sequenceA :: Applicative f => URec Word (f a) -> f (URec Word a) # mapM :: Monad m => (a -> m b) -> URec Word a -> m (URec Word b) # sequence :: Monad m => URec Word (m a) -> m (URec Word a) #
Traversable (URec (Ptr ()) :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec (Ptr ()) a -> f (URec (Ptr ()) b) # sequenceA :: Applicative f => URec (Ptr ()) (f a) -> f (URec (Ptr ()) a) # mapM :: Monad m => (a -> m b) -> URec (Ptr ()) a -> m (URec (Ptr ()) b) # sequence :: Monad m => URec (Ptr ()) (m a) -> m (URec (Ptr ()) a) #
Traversable (Const m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b) # sequenceA :: Applicative f => Const m (f a) -> f (Const m a) # mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b) # sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a) #
Traversable f => Traversable (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Ap f a -> f0 (Ap f b) # sequenceA :: Applicative f0 => Ap f (f0 a) -> f0 (Ap f a) # mapM :: Monad m => (a -> m b) -> Ap f a -> m (Ap f b) # sequence :: Monad m => Ap f (m a) -> m (Ap f a) #
Traversable f => Traversable (Alt f)	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Alt f a -> f0 (Alt f b) # sequenceA :: Applicative f0 => Alt f (f0 a) -> f0 (Alt f a) # mapM :: Monad m => (a -> m b) -> Alt f a -> m (Alt f b) # sequence :: Monad m => Alt f (m a) -> m (Alt f a) #
Bitraversable p => Traversable (Join p)
Instance details Defined in Data.Bifunctor.Join Methods traverse :: Applicative f => (a -> f b) -> Join p a -> f (Join p b) # sequenceA :: Applicative f => Join p (f a) -> f (Join p a) # mapM :: Monad m => (a -> m b) -> Join p a -> m (Join p b) # sequence :: Monad m => Join p (m a) -> m (Join p a) #
Bitraversable p => Traversable (Fix p)
Instance details Defined in Data.Bifunctor.Fix Methods traverse :: Applicative f => (a -> f b) -> Fix p a -> f (Fix p b) # sequenceA :: Applicative f => Fix p (f a) -> f (Fix p a) # mapM :: Monad m => (a -> m b) -> Fix p a -> m (Fix p b) # sequence :: Monad m => Fix p (m a) -> m (Fix p a) #
Traversable f => Traversable (IdentityT f)
Instance details Defined in Control.Monad.Trans.Identity Methods traverse :: Applicative f0 => (a -> f0 b) -> IdentityT f a -> f0 (IdentityT f b) # sequenceA :: Applicative f0 => IdentityT f (f0 a) -> f0 (IdentityT f a) # mapM :: Monad m => (a -> m b) -> IdentityT f a -> m (IdentityT f b) # sequence :: Monad m => IdentityT f (m a) -> m (IdentityT f a) #
Traversable f => Traversable (ExceptT e f)
Instance details Defined in Control.Monad.Trans.Except Methods traverse :: Applicative f0 => (a -> f0 b) -> ExceptT e f a -> f0 (ExceptT e f b) # sequenceA :: Applicative f0 => ExceptT e f (f0 a) -> f0 (ExceptT e f a) # mapM :: Monad m => (a -> m b) -> ExceptT e f a -> m (ExceptT e f b) # sequence :: Monad m => ExceptT e f (m a) -> m (ExceptT e f a) #
Traversable f => Traversable (FreeF f a)
Instance details Defined in Control.Monad.Trans.Free Methods traverse :: Applicative f0 => (a0 -> f0 b) -> FreeF f a a0 -> f0 (FreeF f a b) # sequenceA :: Applicative f0 => FreeF f a (f0 a0) -> f0 (FreeF f a a0) # mapM :: Monad m => (a0 -> m b) -> FreeF f a a0 -> m (FreeF f a b) # sequence :: Monad m => FreeF f a (m a0) -> m (FreeF f a a0) #
(Monad m, Traversable m, Traversable f) => Traversable (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods traverse :: Applicative f0 => (a -> f0 b) -> FreeT f m a -> f0 (FreeT f m b) # sequenceA :: Applicative f0 => FreeT f m (f0 a) -> f0 (FreeT f m a) # mapM :: Monad m0 => (a -> m0 b) -> FreeT f m a -> m0 (FreeT f m b) # sequence :: Monad m0 => FreeT f m (m0 a) -> m0 (FreeT f m a) #
Traversable f => Traversable (CofreeF f a)
Instance details Defined in Control.Comonad.Trans.Cofree Methods traverse :: Applicative f0 => (a0 -> f0 b) -> CofreeF f a a0 -> f0 (CofreeF f a b) # sequenceA :: Applicative f0 => CofreeF f a (f0 a0) -> f0 (CofreeF f a a0) # mapM :: Monad m => (a0 -> m b) -> CofreeF f a a0 -> m (CofreeF f a b) # sequence :: Monad m => CofreeF f a (m a0) -> m (CofreeF f a a0) #
(Traversable f, Traversable w) => Traversable (CofreeT f w)
Instance details Defined in Control.Comonad.Trans.Cofree Methods traverse :: Applicative f0 => (a -> f0 b) -> CofreeT f w a -> f0 (CofreeT f w b) # sequenceA :: Applicative f0 => CofreeT f w (f0 a) -> f0 (CofreeT f w a) # mapM :: Monad m => (a -> m b) -> CofreeT f w a -> m (CofreeT f w b) # sequence :: Monad m => CofreeT f w (m a) -> m (CofreeT f w a) #
Traversable f => Traversable (ErrorT e f)
Instance details Defined in Control.Monad.Trans.Error Methods traverse :: Applicative f0 => (a -> f0 b) -> ErrorT e f a -> f0 (ErrorT e f b) # sequenceA :: Applicative f0 => ErrorT e f (f0 a) -> f0 (ErrorT e f a) # mapM :: Monad m => (a -> m b) -> ErrorT e f a -> m (ErrorT e f b) # sequence :: Monad m => ErrorT e f (m a) -> m (ErrorT e f a) #
Traversable f => Traversable (Backwards f)	Derived instance.
Instance details Defined in Control.Applicative.Backwards Methods traverse :: Applicative f0 => (a -> f0 b) -> Backwards f a -> f0 (Backwards f b) # sequenceA :: Applicative f0 => Backwards f (f0 a) -> f0 (Backwards f a) # mapM :: Monad m => (a -> m b) -> Backwards f a -> m (Backwards f b) # sequence :: Monad m => Backwards f (m a) -> m (Backwards f a) #
Traversable f => Traversable (AlongsideLeft f b)
Instance details Defined in Control.Lens.Internal.Getter Methods traverse :: Applicative f0 => (a -> f0 b0) -> AlongsideLeft f b a -> f0 (AlongsideLeft f b b0) # sequenceA :: Applicative f0 => AlongsideLeft f b (f0 a) -> f0 (AlongsideLeft f b a) # mapM :: Monad m => (a -> m b0) -> AlongsideLeft f b a -> m (AlongsideLeft f b b0) # sequence :: Monad m => AlongsideLeft f b (m a) -> m (AlongsideLeft f b a) #
Traversable f => Traversable (AlongsideRight f a)
Instance details Defined in Control.Lens.Internal.Getter Methods traverse :: Applicative f0 => (a0 -> f0 b) -> AlongsideRight f a a0 -> f0 (AlongsideRight f a b) # sequenceA :: Applicative f0 => AlongsideRight f a (f0 a0) -> f0 (AlongsideRight f a a0) # mapM :: Monad m => (a0 -> m b) -> AlongsideRight f a a0 -> m (AlongsideRight f a b) # sequence :: Monad m => AlongsideRight f a (m a0) -> m (AlongsideRight f a a0) #
Traversable f => Traversable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 (WriterT w f b) # sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 (WriterT w f a) # mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b) # sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a) #
Traversable f => Traversable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 (WriterT w f b) # sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 (WriterT w f a) # mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b) # sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a) #
Traversable (Forget r a)
Instance details Defined in Data.Profunctor.Types Methods traverse :: Applicative f => (a0 -> f b) -> Forget r a a0 -> f (Forget r a b) # sequenceA :: Applicative f => Forget r a (f a0) -> f (Forget r a a0) # mapM :: Monad m => (a0 -> m b) -> Forget r a a0 -> m (Forget r a b) # sequence :: Monad m => Forget r a (m a0) -> m (Forget r a a0) #
Traversable (Tagged s)
Instance details Defined in Data.Tagged Methods traverse :: Applicative f => (a -> f b) -> Tagged s a -> f (Tagged s b) # sequenceA :: Applicative f => Tagged s (f a) -> f (Tagged s a) # mapM :: Monad m => (a -> m b) -> Tagged s a -> m (Tagged s b) # sequence :: Monad m => Tagged s (m a) -> m (Tagged s a) #
Traversable f => Traversable (Reverse f)	Traverse from right to left.
Instance details Defined in Data.Functor.Reverse Methods traverse :: Applicative f0 => (a -> f0 b) -> Reverse f a -> f0 (Reverse f b) # sequenceA :: Applicative f0 => Reverse f (f0 a) -> f0 (Reverse f a) # mapM :: Monad m => (a -> m b) -> Reverse f a -> m (Reverse f b) # sequence :: Monad m => Reverse f (m a) -> m (Reverse f a) #
Traversable (Constant a :: Type -> Type)
Instance details Defined in Data.Functor.Constant Methods traverse :: Applicative f => (a0 -> f b) -> Constant a a0 -> f (Constant a b) # sequenceA :: Applicative f => Constant a (f a0) -> f (Constant a a0) # mapM :: Monad m => (a0 -> m b) -> Constant a a0 -> m (Constant a b) # sequence :: Monad m => Constant a (m a0) -> m (Constant a a0) #
Traversable (K1 i c :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> K1 i c a -> f (K1 i c b) # sequenceA :: Applicative f => K1 i c (f a) -> f (K1 i c a) # mapM :: Monad m => (a -> m b) -> K1 i c a -> m (K1 i c b) # sequence :: Monad m => K1 i c (m a) -> m (K1 i c a) #
(Traversable f, Traversable g) => Traversable (f :+: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) # sequenceA :: Applicative f0 => (f :+: g) (f0 a) -> f0 ((f :+: g) a) # mapM :: Monad m => (a -> m b) -> (f :+: g) a -> m ((f :+: g) b) # sequence :: Monad m => (f :+: g) (m a) -> m ((f :+: g) a) #
(Traversable f, Traversable g) => Traversable (f :*: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :: g) a -> f0 ((f :: g) b) # sequenceA :: Applicative f0 => (f :: g) (f0 a) -> f0 ((f :: g) a) # mapM :: Monad m => (a -> m b) -> (f :: g) a -> m ((f :: g) b) # sequence :: Monad m => (f :: g) (m a) -> m ((f :: g) a) #
Traversable (Magma i t b)
Instance details Defined in Control.Lens.Internal.Magma Methods traverse :: Applicative f => (a -> f b0) -> Magma i t b a -> f (Magma i t b b0) # sequenceA :: Applicative f => Magma i t b (f a) -> f (Magma i t b a) # mapM :: Monad m => (a -> m b0) -> Magma i t b a -> m (Magma i t b b0) # sequence :: Monad m => Magma i t b (m a) -> m (Magma i t b a) #
Traversable f => Traversable (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> M1 i c f a -> f0 (M1 i c f b) # sequenceA :: Applicative f0 => M1 i c f (f0 a) -> f0 (M1 i c f a) # mapM :: Monad m => (a -> m b) -> M1 i c f a -> m (M1 i c f b) # sequence :: Monad m => M1 i c f (m a) -> m (M1 i c f a) #
(Traversable f, Traversable g) => Traversable (f :.: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) # sequenceA :: Applicative f0 => (f :.: g) (f0 a) -> f0 ((f :.: g) a) # mapM :: Monad m => (a -> m b) -> (f :.: g) a -> m ((f :.: g) b) # sequence :: Monad m => (f :.: g) (m a) -> m ((f :.: g) a) #
(Traversable f, Traversable g) => Traversable (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods traverse :: Applicative f0 => (a -> f0 b) -> Compose f g a -> f0 (Compose f g b) # sequenceA :: Applicative f0 => Compose f g (f0 a) -> f0 (Compose f g a) # mapM :: Monad m => (a -> m b) -> Compose f g a -> m (Compose f g b) # sequence :: Monad m => Compose f g (m a) -> m (Compose f g a) #
Bitraversable p => Traversable (WrappedBifunctor p a)
Instance details Defined in Data.Bifunctor.Wrapped Methods traverse :: Applicative f => (a0 -> f b) -> WrappedBifunctor p a a0 -> f (WrappedBifunctor p a b) # sequenceA :: Applicative f => WrappedBifunctor p a (f a0) -> f (WrappedBifunctor p a a0) # mapM :: Monad m => (a0 -> m b) -> WrappedBifunctor p a a0 -> m (WrappedBifunctor p a b) # sequence :: Monad m => WrappedBifunctor p a (m a0) -> m (WrappedBifunctor p a a0) #
Traversable g => Traversable (Joker g a)
Instance details Defined in Data.Bifunctor.Joker Methods traverse :: Applicative f => (a0 -> f b) -> Joker g a a0 -> f (Joker g a b) # sequenceA :: Applicative f => Joker g a (f a0) -> f (Joker g a a0) # mapM :: Monad m => (a0 -> m b) -> Joker g a a0 -> m (Joker g a b) # sequence :: Monad m => Joker g a (m a0) -> m (Joker g a a0) #
Bitraversable p => Traversable (Flip p a)
Instance details Defined in Data.Bifunctor.Flip Methods traverse :: Applicative f => (a0 -> f b) -> Flip p a a0 -> f (Flip p a b) # sequenceA :: Applicative f => Flip p a (f a0) -> f (Flip p a a0) # mapM :: Monad m => (a0 -> m b) -> Flip p a a0 -> m (Flip p a b) # sequence :: Monad m => Flip p a (m a0) -> m (Flip p a a0) #
Traversable (Clown f a :: Type -> Type)
Instance details Defined in Data.Bifunctor.Clown Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Clown f a a0 -> f0 (Clown f a b) # sequenceA :: Applicative f0 => Clown f a (f0 a0) -> f0 (Clown f a a0) # mapM :: Monad m => (a0 -> m b) -> Clown f a a0 -> m (Clown f a b) # sequence :: Monad m => Clown f a (m a0) -> m (Clown f a a0) #
(Traversable f, Bitraversable p) => Traversable (Tannen f p a)
Instance details Defined in Data.Bifunctor.Tannen Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Tannen f p a a0 -> f0 (Tannen f p a b) # sequenceA :: Applicative f0 => Tannen f p a (f0 a0) -> f0 (Tannen f p a a0) # mapM :: Monad m => (a0 -> m b) -> Tannen f p a a0 -> m (Tannen f p a b) # sequence :: Monad m => Tannen f p a (m a0) -> m (Tannen f p a a0) #
(Bitraversable p, Traversable g) => Traversable (Biff p f g a)
Instance details Defined in Data.Bifunctor.Biff Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Biff p f g a a0 -> f0 (Biff p f g a b) # sequenceA :: Applicative f0 => Biff p f g a (f0 a0) -> f0 (Biff p f g a a0) # mapM :: Monad m => (a0 -> m b) -> Biff p f g a a0 -> m (Biff p f g a b) # sequence :: Monad m => Biff p f g a (m a0) -> m (Biff p f g a a0) #

class Contravariant (f :: Type -> Type) where #

The class of contravariant functors.

Whereas in Haskell, one can think of a Functor as containing or producing values, a contravariant functor is a functor that can be thought of as consuming values.

As an example, consider the type of predicate functions a -> Bool. One such predicate might be negative x = x < 0, which classifies integers as to whether they are negative. However, given this predicate, we can re-use it in other situations, providing we have a way to map values to integers. For instance, we can use the negative predicate on a person's bank balance to work out if they are currently overdrawn:

newtype Predicate a = Predicate { getPredicate :: a -> Bool }

instance Contravariant Predicate where
  contramap f (Predicate p) = Predicate (p . f)
                                         |   `- First, map the input...
                                         `----- then apply the predicate.

overdrawn :: Predicate Person
overdrawn = contramap personBankBalance negative

Any instance should be subject to the following laws:

contramap id = id
contramap f . contramap g = contramap (g . f)

Note, that the second law follows from the free theorem of the type of contramap and the first law, so you need only check that the former condition holds.

Minimal complete definition

contramap

Methods

contramap :: (a -> b) -> f b -> f a #

(>$) :: b -> f b -> f a infixl 4 #

Replace all locations in the output with the same value. The default definition is contramap . const, but this may be overridden with a more efficient version.

Instances

Contravariant ToJSONKeyFunction
Instance details Defined in Data.Aeson.Types.ToJSON Methods contramap :: (a -> b) -> ToJSONKeyFunction b -> ToJSONKeyFunction a # (>$) :: b -> ToJSONKeyFunction b -> ToJSONKeyFunction a #
Contravariant Predicate	A `Predicate` is a `Contravariant` `Functor`, because `contramap` can apply its function argument to the input of the predicate.
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Predicate b -> Predicate a # (>$) :: b -> Predicate b -> Predicate a #
Contravariant Comparison	A `Comparison` is a `Contravariant` `Functor`, because `contramap` can apply its function argument to each input of the comparison function.
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Comparison b -> Comparison a # (>$) :: b -> Comparison b -> Comparison a #
Contravariant Equivalence	Equivalence relations are `Contravariant`, because you can apply the contramapped function to each input to the equivalence relation.
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Equivalence b -> Equivalence a # (>$) :: b -> Equivalence b -> Equivalence a #
Contravariant (V1 :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> V1 b -> V1 a # (>$) :: b -> V1 b -> V1 a #
Contravariant (U1 :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> U1 b -> U1 a # (>$) :: b -> U1 b -> U1 a #
Contravariant (Op a)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a0 -> b) -> Op a b -> Op a a0 # (>$) :: b -> Op a b -> Op a a0 #
Contravariant (Proxy :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Proxy b -> Proxy a # (>$) :: b -> Proxy b -> Proxy a #
Contravariant m => Contravariant (MaybeT m)
Instance details Defined in Control.Monad.Trans.Maybe Methods contramap :: (a -> b) -> MaybeT m b -> MaybeT m a # (>$) :: b -> MaybeT m b -> MaybeT m a #
Contravariant f => Contravariant (Indexing f)
Instance details Defined in Control.Lens.Internal.Indexed Methods contramap :: (a -> b) -> Indexing f b -> Indexing f a # (>$) :: b -> Indexing f b -> Indexing f a #
Contravariant f => Contravariant (Indexing64 f)
Instance details Defined in Control.Lens.Internal.Indexed Methods contramap :: (a -> b) -> Indexing64 f b -> Indexing64 f a # (>$) :: b -> Indexing64 f b -> Indexing64 f a #
Contravariant m => Contravariant (ListT m)
Instance details Defined in Control.Monad.Trans.List Methods contramap :: (a -> b) -> ListT m b -> ListT m a # (>$) :: b -> ListT m b -> ListT m a #
Contravariant f => Contravariant (Rec1 f)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Rec1 f b -> Rec1 f a # (>$) :: b -> Rec1 f b -> Rec1 f a #
Contravariant (Const a :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a0 -> b) -> Const a b -> Const a a0 # (>$) :: b -> Const a b -> Const a a0 #
Contravariant f => Contravariant (Alt f)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Alt f b -> Alt f a # (>$) :: b -> Alt f b -> Alt f a #
Contravariant f => Contravariant (IdentityT f)
Instance details Defined in Control.Monad.Trans.Identity Methods contramap :: (a -> b) -> IdentityT f b -> IdentityT f a # (>$) :: b -> IdentityT f b -> IdentityT f a #
(Functor f, Contravariant g) => Contravariant (ComposeFC f g)
Instance details Defined in Data.Functor.Contravariant.Compose Methods contramap :: (a -> b) -> ComposeFC f g b -> ComposeFC f g a # (>$) :: b -> ComposeFC f g b -> ComposeFC f g a #
(Contravariant f, Functor g) => Contravariant (ComposeCF f g)
Instance details Defined in Data.Functor.Contravariant.Compose Methods contramap :: (a -> b) -> ComposeCF f g b -> ComposeCF f g a # (>$) :: b -> ComposeCF f g b -> ComposeCF f g a #
Contravariant m => Contravariant (ExceptT e m)
Instance details Defined in Control.Monad.Trans.Except Methods contramap :: (a -> b) -> ExceptT e m b -> ExceptT e m a # (>$) :: b -> ExceptT e m b -> ExceptT e m a #
Contravariant m => Contravariant (ErrorT e m)
Instance details Defined in Control.Monad.Trans.Error Methods contramap :: (a -> b) -> ErrorT e m b -> ErrorT e m a # (>$) :: b -> ErrorT e m b -> ErrorT e m a #
Contravariant m => Contravariant (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods contramap :: (a -> b) -> StateT s m b -> StateT s m a # (>$) :: b -> StateT s m b -> StateT s m a #
Contravariant f => Contravariant (Backwards f)	Derived instance.
Instance details Defined in Control.Applicative.Backwards Methods contramap :: (a -> b) -> Backwards f b -> Backwards f a # (>$) :: b -> Backwards f b -> Backwards f a #
Contravariant f => Contravariant (AlongsideLeft f b)
Instance details Defined in Control.Lens.Internal.Getter Methods contramap :: (a -> b0) -> AlongsideLeft f b b0 -> AlongsideLeft f b a # (>$) :: b0 -> AlongsideLeft f b b0 -> AlongsideLeft f b a #
Contravariant f => Contravariant (AlongsideRight f a)
Instance details Defined in Control.Lens.Internal.Getter Methods contramap :: (a0 -> b) -> AlongsideRight f a b -> AlongsideRight f a a0 # (>$) :: b -> AlongsideRight f a b -> AlongsideRight f a a0 #
Contravariant m => Contravariant (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Lazy Methods contramap :: (a -> b) -> StateT s m b -> StateT s m a # (>$) :: b -> StateT s m b -> StateT s m a #
Contravariant m => Contravariant (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods contramap :: (a -> b) -> WriterT w m b -> WriterT w m a # (>$) :: b -> WriterT w m b -> WriterT w m a #
Contravariant m => Contravariant (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods contramap :: (a -> b) -> WriterT w m b -> WriterT w m a # (>$) :: b -> WriterT w m b -> WriterT w m a #
Contravariant f => Contravariant (Reverse f)	Derived instance.
Instance details Defined in Data.Functor.Reverse Methods contramap :: (a -> b) -> Reverse f b -> Reverse f a # (>$) :: b -> Reverse f b -> Reverse f a #
Contravariant (Constant a :: Type -> Type)
Instance details Defined in Data.Functor.Constant Methods contramap :: (a0 -> b) -> Constant a b -> Constant a a0 # (>$) :: b -> Constant a b -> Constant a a0 #
Contravariant (K1 i c :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> K1 i c b -> K1 i c a # (>$) :: b -> K1 i c b -> K1 i c a #
(Contravariant f, Contravariant g) => Contravariant (f :+: g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> (f :+: g) b -> (f :+: g) a # (>$) :: b -> (f :+: g) b -> (f :+: g) a #
(Contravariant f, Contravariant g) => Contravariant (f :*: g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> (f :: g) b -> (f :: g) a # (>$) :: b -> (f :: g) b -> (f :: g) a #
(Contravariant f, Contravariant g) => Contravariant (Product f g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Product f g b -> Product f g a # (>$) :: b -> Product f g b -> Product f g a #
(Contravariant f, Contravariant g) => Contravariant (Sum f g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Sum f g b -> Sum f g a # (>$) :: b -> Sum f g b -> Sum f g a #
Contravariant m => Contravariant (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods contramap :: (a -> b) -> ReaderT r m b -> ReaderT r m a # (>$) :: b -> ReaderT r m b -> ReaderT r m a #
Contravariant f => Contravariant (M1 i c f)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> M1 i c f b -> M1 i c f a # (>$) :: b -> M1 i c f b -> M1 i c f a #
(Functor f, Contravariant g) => Contravariant (f :.: g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> (f :.: g) b -> (f :.: g) a # (>$) :: b -> (f :.: g) b -> (f :.: g) a #
(Functor f, Contravariant g) => Contravariant (Compose f g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Compose f g b -> Compose f g a # (>$) :: b -> Compose f g b -> Compose f g a #
Contravariant m => Contravariant (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Strict Methods contramap :: (a -> b) -> RWST r w s m b -> RWST r w s m a # (>$) :: b -> RWST r w s m b -> RWST r w s m a #
Contravariant f => Contravariant (TakingWhile p f a b)
Instance details Defined in Control.Lens.Internal.Magma Methods contramap :: (a0 -> b0) -> TakingWhile p f a b b0 -> TakingWhile p f a b a0 # (>$) :: b0 -> TakingWhile p f a b b0 -> TakingWhile p f a b a0 #
(Profunctor p, Contravariant g) => Contravariant (BazaarT p g a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods contramap :: (a0 -> b0) -> BazaarT p g a b b0 -> BazaarT p g a b a0 # (>$) :: b0 -> BazaarT p g a b b0 -> BazaarT p g a b a0 #
(Profunctor p, Contravariant g) => Contravariant (BazaarT1 p g a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods contramap :: (a0 -> b0) -> BazaarT1 p g a b b0 -> BazaarT1 p g a b a0 # (>$) :: b0 -> BazaarT1 p g a b b0 -> BazaarT1 p g a b a0 #
(Profunctor p, Contravariant g) => Contravariant (PretextT p g a b)
Instance details Defined in Control.Lens.Internal.Context Methods contramap :: (a0 -> b0) -> PretextT p g a b b0 -> PretextT p g a b a0 # (>$) :: b0 -> PretextT p g a b b0 -> PretextT p g a b a0 #
Contravariant m => Contravariant (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Lazy Methods contramap :: (a -> b) -> RWST r w s m b -> RWST r w s m a # (>$) :: b -> RWST r w s m b -> RWST r w s m a #

class Bifunctor (p :: Type -> Type -> Type) where #

A bifunctor is a type constructor that takes two type arguments and is a functor in both arguments. That is, unlike with Functor, a type constructor such as Either does not need to be partially applied for a Bifunctor instance, and the methods in this class permit mapping functions over the Left value or the Right value, or both at the same time.

Formally, the class Bifunctor represents a bifunctor from Hask -> Hask.

Intuitively it is a bifunctor where both the first and second arguments are covariant.

You can define a Bifunctor by either defining bimap or by defining both first and second.

If you supply bimap, you should ensure that:

bimap id id ≡ id

If you supply first and second, ensure:

first id ≡ id
second id ≡ id

If you supply both, you should also ensure:

bimap f g ≡ first f . second g

These ensure by parametricity:

bimap  (f . g) (h . i) ≡ bimap f h . bimap g i
first  (f . g) ≡ first  f . first  g
second (f . g) ≡ second f . second g

Since: base-4.8.0.0

Minimal complete definition

bimap | first, second

Methods

bimap :: (a -> b) -> (c -> d) -> p a c -> p b d #

Map over both arguments at the same time.

bimap f g ≡ first f . second g

Examples

Expand

>>> bimap toUpper (+1) ('j', 3)
('J',4)

>>> bimap toUpper (+1) (Left 'j')
Left 'J'

>>> bimap toUpper (+1) (Right 3)
Right 4

Instances

Bifunctor Either	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> Either a c -> Either b d # first :: (a -> b) -> Either a c -> Either b c # second :: (b -> c) -> Either a b -> Either a c #
Bifunctor (,)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (a, c) -> (b, d) # first :: (a -> b) -> (a, c) -> (b, c) # second :: (b -> c) -> (a, b) -> (a, c) #
Bifunctor Arg	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d # first :: (a -> b) -> Arg a c -> Arg b c # second :: (b -> c) -> Arg a b -> Arg a c #
Bifunctor ((,,) x1)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, a, c) -> (x1, b, d) # first :: (a -> b) -> (x1, a, c) -> (x1, b, c) # second :: (b -> c) -> (x1, a, b) -> (x1, a, c) #
Bifunctor (Const :: Type -> Type -> Type)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> Const a c -> Const b d # first :: (a -> b) -> Const a c -> Const b c # second :: (b -> c) -> Const a b -> Const a c #
Functor f => Bifunctor (FreeF f)
Instance details Defined in Control.Monad.Trans.Free Methods bimap :: (a -> b) -> (c -> d) -> FreeF f a c -> FreeF f b d # first :: (a -> b) -> FreeF f a c -> FreeF f b c # second :: (b -> c) -> FreeF f a b -> FreeF f a c #
Functor f => Bifunctor (CofreeF f)
Instance details Defined in Control.Comonad.Trans.Cofree Methods bimap :: (a -> b) -> (c -> d) -> CofreeF f a c -> CofreeF f b d # first :: (a -> b) -> CofreeF f a c -> CofreeF f b c # second :: (b -> c) -> CofreeF f a b -> CofreeF f a c #
Functor f => Bifunctor (AlongsideLeft f)
Instance details Defined in Control.Lens.Internal.Getter Methods bimap :: (a -> b) -> (c -> d) -> AlongsideLeft f a c -> AlongsideLeft f b d # first :: (a -> b) -> AlongsideLeft f a c -> AlongsideLeft f b c # second :: (b -> c) -> AlongsideLeft f a b -> AlongsideLeft f a c #
Functor f => Bifunctor (AlongsideRight f)
Instance details Defined in Control.Lens.Internal.Getter Methods bimap :: (a -> b) -> (c -> d) -> AlongsideRight f a c -> AlongsideRight f b d # first :: (a -> b) -> AlongsideRight f a c -> AlongsideRight f b c # second :: (b -> c) -> AlongsideRight f a b -> AlongsideRight f a c #
Bifunctor (Tagged :: Type -> Type -> Type)
Instance details Defined in Data.Tagged Methods bimap :: (a -> b) -> (c -> d) -> Tagged a c -> Tagged b d # first :: (a -> b) -> Tagged a c -> Tagged b c # second :: (b -> c) -> Tagged a b -> Tagged a c #
Bifunctor (Constant :: Type -> Type -> Type)
Instance details Defined in Data.Functor.Constant Methods bimap :: (a -> b) -> (c -> d) -> Constant a c -> Constant b d # first :: (a -> b) -> Constant a c -> Constant b c # second :: (b -> c) -> Constant a b -> Constant a c #
Bifunctor (K1 i :: Type -> Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> K1 i a c -> K1 i b d # first :: (a -> b) -> K1 i a c -> K1 i b c # second :: (b -> c) -> K1 i a b -> K1 i a c #
Bifunctor ((,,,) x1 x2)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, a, c) -> (x1, x2, b, d) # first :: (a -> b) -> (x1, x2, a, c) -> (x1, x2, b, c) # second :: (b -> c) -> (x1, x2, a, b) -> (x1, x2, a, c) #
Bifunctor ((,,,,) x1 x2 x3)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, d) # first :: (a -> b) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, c) # second :: (b -> c) -> (x1, x2, x3, a, b) -> (x1, x2, x3, a, c) #
Bifunctor p => Bifunctor (WrappedBifunctor p)
Instance details Defined in Data.Bifunctor.Wrapped Methods bimap :: (a -> b) -> (c -> d) -> WrappedBifunctor p a c -> WrappedBifunctor p b d # first :: (a -> b) -> WrappedBifunctor p a c -> WrappedBifunctor p b c # second :: (b -> c) -> WrappedBifunctor p a b -> WrappedBifunctor p a c #
Functor g => Bifunctor (Joker g :: Type -> Type -> Type)
Instance details Defined in Data.Bifunctor.Joker Methods bimap :: (a -> b) -> (c -> d) -> Joker g a c -> Joker g b d # first :: (a -> b) -> Joker g a c -> Joker g b c # second :: (b -> c) -> Joker g a b -> Joker g a c #
Bifunctor p => Bifunctor (Flip p)
Instance details Defined in Data.Bifunctor.Flip Methods bimap :: (a -> b) -> (c -> d) -> Flip p a c -> Flip p b d # first :: (a -> b) -> Flip p a c -> Flip p b c # second :: (b -> c) -> Flip p a b -> Flip p a c #
Functor f => Bifunctor (Clown f :: Type -> Type -> Type)
Instance details Defined in Data.Bifunctor.Clown Methods bimap :: (a -> b) -> (c -> d) -> Clown f a c -> Clown f b d # first :: (a -> b) -> Clown f a c -> Clown f b c # second :: (b -> c) -> Clown f a b -> Clown f a c #
Bifunctor ((,,,,,) x1 x2 x3 x4)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, d) # first :: (a -> b) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, c) # second :: (b -> c) -> (x1, x2, x3, x4, a, b) -> (x1, x2, x3, x4, a, c) #
(Bifunctor p, Bifunctor q) => Bifunctor (Sum p q)
Instance details Defined in Data.Bifunctor.Sum Methods bimap :: (a -> b) -> (c -> d) -> Sum p q a c -> Sum p q b d # first :: (a -> b) -> Sum p q a c -> Sum p q b c # second :: (b -> c) -> Sum p q a b -> Sum p q a c #
(Bifunctor f, Bifunctor g) => Bifunctor (Product f g)
Instance details Defined in Data.Bifunctor.Product Methods bimap :: (a -> b) -> (c -> d) -> Product f g a c -> Product f g b d # first :: (a -> b) -> Product f g a c -> Product f g b c # second :: (b -> c) -> Product f g a b -> Product f g a c #
Bifunctor ((,,,,,,) x1 x2 x3 x4 x5)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, d) # first :: (a -> b) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, c) # second :: (b -> c) -> (x1, x2, x3, x4, x5, a, b) -> (x1, x2, x3, x4, x5, a, c) #
(Functor f, Bifunctor p) => Bifunctor (Tannen f p)
Instance details Defined in Data.Bifunctor.Tannen Methods bimap :: (a -> b) -> (c -> d) -> Tannen f p a c -> Tannen f p b d # first :: (a -> b) -> Tannen f p a c -> Tannen f p b c # second :: (b -> c) -> Tannen f p a b -> Tannen f p a c #
(Bifunctor p, Functor f, Functor g) => Bifunctor (Biff p f g)
Instance details Defined in Data.Bifunctor.Biff Methods bimap :: (a -> b) -> (c -> d) -> Biff p f g a c -> Biff p f g b d # first :: (a -> b) -> Biff p f g a c -> Biff p f g b c # second :: (b -> c) -> Biff p f g a b -> Biff p f g a c #

newtype Identity a #

Identity functor and monad. (a non-strict monad)

Since: base-4.8.0.0

Constructors

Identity
Fields runIdentity :: a

Instances

Monad Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods (>>=) :: Identity a -> (a -> Identity b) -> Identity b # (>>) :: Identity a -> Identity b -> Identity b # return :: a -> Identity a # fail :: String -> Identity a #
Functor Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods fmap :: (a -> b) -> Identity a -> Identity b # (<$) :: a -> Identity b -> Identity a #
MonadFix Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods mfix :: (a -> Identity a) -> Identity a #
Applicative Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods pure :: a -> Identity a # (<>) :: Identity (a -> b) -> Identity a -> Identity b # liftA2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c # (>) :: Identity a -> Identity b -> Identity b # (<*) :: Identity a -> Identity b -> Identity a #
Foldable Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods fold :: Monoid m => Identity m -> m # foldMap :: Monoid m => (a -> m) -> Identity a -> m # foldr :: (a -> b -> b) -> b -> Identity a -> b # foldr' :: (a -> b -> b) -> b -> Identity a -> b # foldl :: (b -> a -> b) -> b -> Identity a -> b # foldl' :: (b -> a -> b) -> b -> Identity a -> b # foldr1 :: (a -> a -> a) -> Identity a -> a # foldl1 :: (a -> a -> a) -> Identity a -> a # toList :: Identity a -> [a] # null :: Identity a -> Bool # length :: Identity a -> Int # elem :: Eq a => a -> Identity a -> Bool # maximum :: Ord a => Identity a -> a # minimum :: Ord a => Identity a -> a # sum :: Num a => Identity a -> a # product :: Num a => Identity a -> a #
Traversable Identity	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Identity a -> f (Identity b) # sequenceA :: Applicative f => Identity (f a) -> f (Identity a) # mapM :: Monad m => (a -> m b) -> Identity a -> m (Identity b) # sequence :: Monad m => Identity (m a) -> m (Identity a) #
Representable Identity
Instance details Defined in Data.Functor.Rep Associated Types type Rep Identity :: Type # Methods tabulate :: (Rep Identity -> a) -> Identity a # index :: Identity a -> Rep Identity -> a #
ToJSON1 Identity
Instance details Defined in Data.Aeson.Types.ToJSON Methods liftToJSON :: (a -> Value) -> ([a] -> Value) -> Identity a -> Value # liftToJSONList :: (a -> Value) -> ([a] -> Value) -> [Identity a] -> Value # liftToEncoding :: (a -> Encoding) -> ([a] -> Encoding) -> Identity a -> Encoding # liftToEncodingList :: (a -> Encoding) -> ([a] -> Encoding) -> [Identity a] -> Encoding #
FromJSON1 Identity
Instance details Defined in Data.Aeson.Types.FromJSON Methods liftParseJSON :: (Value -> Parser a) -> (Value -> Parser [a]) -> Value -> Parser (Identity a) # liftParseJSONList :: (Value -> Parser a) -> (Value -> Parser [a]) -> Value -> Parser [Identity a] #
Eq1 Identity	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq :: (a -> b -> Bool) -> Identity a -> Identity b -> Bool #
Ord1 Identity	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftCompare :: (a -> b -> Ordering) -> Identity a -> Identity b -> Ordering #
Read1 Identity	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Identity a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Identity a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Identity a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Identity a] #
Show1 Identity	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Identity a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Identity a] -> ShowS #
Comonad Identity
Instance details Defined in Control.Comonad Methods extract :: Identity a -> a # duplicate :: Identity a -> Identity (Identity a) # extend :: (Identity a -> b) -> Identity a -> Identity b #
ComonadApply Identity
Instance details Defined in Control.Comonad Methods (<@>) :: Identity (a -> b) -> Identity a -> Identity b # (@>) :: Identity a -> Identity b -> Identity b # (<@) :: Identity a -> Identity b -> Identity a #
Hashable1 Identity
Instance details Defined in Data.Hashable.Class Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> Identity a -> Int #
Apply Identity
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Identity (a -> b) -> Identity a -> Identity b # (.>) :: Identity a -> Identity b -> Identity b # (<.) :: Identity a -> Identity b -> Identity a # liftF2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c #
Settable Identity	So you can pass our `Setter` into combinators from other lens libraries.
Instance details Defined in Control.Lens.Internal.Setter Methods untainted :: Identity a -> a # untaintedDot :: Profunctor p => p a (Identity b) -> p a b # taintedDot :: Profunctor p => p a b -> p a (Identity b) #
Traversable1 Identity
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Identity a -> f (Identity b) # sequence1 :: Apply f => Identity (f b) -> f (Identity b) #
Bind Identity
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Identity a -> (a -> Identity b) -> Identity b # join :: Identity (Identity a) -> Identity a #
FunctorWithIndex () Identity
Instance details Defined in Control.Lens.Indexed Methods imap :: (() -> a -> b) -> Identity a -> Identity b # imapped :: IndexedSetter () (Identity a) (Identity b) a b #
FoldableWithIndex () Identity
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (() -> a -> m) -> Identity a -> m # ifolded :: IndexedFold () (Identity a) a # ifoldr :: (() -> a -> b -> b) -> b -> Identity a -> b # ifoldl :: (() -> b -> a -> b) -> b -> Identity a -> b # ifoldr' :: (() -> a -> b -> b) -> b -> Identity a -> b # ifoldl' :: (() -> b -> a -> b) -> b -> Identity a -> b #
TraversableWithIndex () Identity
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (() -> a -> f b) -> Identity a -> f (Identity b) # itraversed :: IndexedTraversal () (Identity a) (Identity b) a b #
Sieve ReifiedGetter Identity
Instance details Defined in Control.Lens.Reified Methods sieve :: ReifiedGetter a b -> a -> Identity b #
Cosieve ReifiedGetter Identity
Instance details Defined in Control.Lens.Reified Methods cosieve :: ReifiedGetter a b -> Identity a -> b #
Monad m => MonadFree Identity (IterT m)
Instance details Defined in Control.Monad.Trans.Iter Methods wrap :: Identity (IterT m a) -> IterT m a #
Comonad w => ComonadCofree Identity (CoiterT w)
Instance details Defined in Control.Comonad.Trans.Coiter Methods unwrap :: CoiterT w a -> Identity (CoiterT w a) #
Bounded a => Bounded (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods minBound :: Identity a # maxBound :: Identity a #
Enum a => Enum (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods succ :: Identity a -> Identity a # pred :: Identity a -> Identity a # toEnum :: Int -> Identity a # fromEnum :: Identity a -> Int # enumFrom :: Identity a -> [Identity a] # enumFromThen :: Identity a -> Identity a -> [Identity a] # enumFromTo :: Identity a -> Identity a -> [Identity a] # enumFromThenTo :: Identity a -> Identity a -> Identity a -> [Identity a] #
Eq a => Eq (Identity a)	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods (==) :: Identity a -> Identity a -> Bool # (/=) :: Identity a -> Identity a -> Bool #
Floating a => Floating (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods pi :: Identity a # exp :: Identity a -> Identity a # log :: Identity a -> Identity a # sqrt :: Identity a -> Identity a # (**) :: Identity a -> Identity a -> Identity a # logBase :: Identity a -> Identity a -> Identity a # sin :: Identity a -> Identity a # cos :: Identity a -> Identity a # tan :: Identity a -> Identity a # asin :: Identity a -> Identity a # acos :: Identity a -> Identity a # atan :: Identity a -> Identity a # sinh :: Identity a -> Identity a # cosh :: Identity a -> Identity a # tanh :: Identity a -> Identity a # asinh :: Identity a -> Identity a # acosh :: Identity a -> Identity a # atanh :: Identity a -> Identity a # log1p :: Identity a -> Identity a # expm1 :: Identity a -> Identity a # log1pexp :: Identity a -> Identity a # log1mexp :: Identity a -> Identity a #
Fractional a => Fractional (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (/) :: Identity a -> Identity a -> Identity a # recip :: Identity a -> Identity a # fromRational :: Rational -> Identity a #
Integral a => Integral (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods quot :: Identity a -> Identity a -> Identity a # rem :: Identity a -> Identity a -> Identity a # div :: Identity a -> Identity a -> Identity a # mod :: Identity a -> Identity a -> Identity a # quotRem :: Identity a -> Identity a -> (Identity a, Identity a) # divMod :: Identity a -> Identity a -> (Identity a, Identity a) # toInteger :: Identity a -> Integer #
Num a => Num (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (+) :: Identity a -> Identity a -> Identity a # (-) :: Identity a -> Identity a -> Identity a # (*) :: Identity a -> Identity a -> Identity a # negate :: Identity a -> Identity a # abs :: Identity a -> Identity a # signum :: Identity a -> Identity a # fromInteger :: Integer -> Identity a #
Ord a => Ord (Identity a)	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods compare :: Identity a -> Identity a -> Ordering # (<) :: Identity a -> Identity a -> Bool # (<=) :: Identity a -> Identity a -> Bool # (>) :: Identity a -> Identity a -> Bool # (>=) :: Identity a -> Identity a -> Bool # max :: Identity a -> Identity a -> Identity a # min :: Identity a -> Identity a -> Identity a #
Read a => Read (Identity a)	This instance would be equivalent to the derived instances of the `Identity` newtype if the `runIdentity` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods readsPrec :: Int -> ReadS (Identity a) # readList :: ReadS [Identity a] # readPrec :: ReadPrec (Identity a) # readListPrec :: ReadPrec [Identity a] #
Real a => Real (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods toRational :: Identity a -> Rational #
RealFloat a => RealFloat (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods floatRadix :: Identity a -> Integer # floatDigits :: Identity a -> Int # floatRange :: Identity a -> (Int, Int) # decodeFloat :: Identity a -> (Integer, Int) # encodeFloat :: Integer -> Int -> Identity a # exponent :: Identity a -> Int # significand :: Identity a -> Identity a # scaleFloat :: Int -> Identity a -> Identity a # isNaN :: Identity a -> Bool # isInfinite :: Identity a -> Bool # isDenormalized :: Identity a -> Bool # isNegativeZero :: Identity a -> Bool # isIEEE :: Identity a -> Bool # atan2 :: Identity a -> Identity a -> Identity a #
RealFrac a => RealFrac (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods properFraction :: Integral b => Identity a -> (b, Identity a) # truncate :: Integral b => Identity a -> b # round :: Integral b => Identity a -> b # ceiling :: Integral b => Identity a -> b # floor :: Integral b => Identity a -> b #
Show a => Show (Identity a)	This instance would be equivalent to the derived instances of the `Identity` newtype if the `runIdentity` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods showsPrec :: Int -> Identity a -> ShowS # show :: Identity a -> String # showList :: [Identity a] -> ShowS #
Ix a => Ix (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods range :: (Identity a, Identity a) -> [Identity a] # index :: (Identity a, Identity a) -> Identity a -> Int # unsafeIndex :: (Identity a, Identity a) -> Identity a -> Int inRange :: (Identity a, Identity a) -> Identity a -> Bool # rangeSize :: (Identity a, Identity a) -> Int # unsafeRangeSize :: (Identity a, Identity a) -> Int
Generic (Identity a)
Instance details Defined in Data.Functor.Identity Associated Types type Rep (Identity a) :: Type -> Type # Methods from :: Identity a -> Rep (Identity a) x # to :: Rep (Identity a) x -> Identity a #
Semigroup a => Semigroup (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (<>) :: Identity a -> Identity a -> Identity a # sconcat :: NonEmpty (Identity a) -> Identity a # stimes :: Integral b => b -> Identity a -> Identity a #
Monoid a => Monoid (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods mempty :: Identity a # mappend :: Identity a -> Identity a -> Identity a # mconcat :: [Identity a] -> Identity a #
Hashable a => Hashable (Identity a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Identity a -> Int # hash :: Identity a -> Int #
ToJSON a => ToJSON (Identity a)
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSON :: Identity a -> Value # toEncoding :: Identity a -> Encoding # toJSONList :: [Identity a] -> Value # toEncodingList :: [Identity a] -> Encoding #
ToJSONKey a => ToJSONKey (Identity a)
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSONKey :: ToJSONKeyFunction (Identity a) # toJSONKeyList :: ToJSONKeyFunction [Identity a] #
FromJSON a => FromJSON (Identity a)
Instance details Defined in Data.Aeson.Types.FromJSON Methods parseJSON :: Value -> Parser (Identity a) # parseJSONList :: Value -> Parser [Identity a] #
FromJSONKey a => FromJSONKey (Identity a)
Instance details Defined in Data.Aeson.Types.FromJSON Methods fromJSONKey :: FromJSONKeyFunction (Identity a) # fromJSONKeyList :: FromJSONKeyFunction [Identity a] #
Storable a => Storable (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods sizeOf :: Identity a -> Int # alignment :: Identity a -> Int # peekElemOff :: Ptr (Identity a) -> Int -> IO (Identity a) # pokeElemOff :: Ptr (Identity a) -> Int -> Identity a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Identity a) # pokeByteOff :: Ptr b -> Int -> Identity a -> IO () # peek :: Ptr (Identity a) -> IO (Identity a) # poke :: Ptr (Identity a) -> Identity a -> IO () #
Bits a => Bits (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (.&.) :: Identity a -> Identity a -> Identity a # (.\|.) :: Identity a -> Identity a -> Identity a # xor :: Identity a -> Identity a -> Identity a # complement :: Identity a -> Identity a # shift :: Identity a -> Int -> Identity a # rotate :: Identity a -> Int -> Identity a # zeroBits :: Identity a # bit :: Int -> Identity a # setBit :: Identity a -> Int -> Identity a # clearBit :: Identity a -> Int -> Identity a # complementBit :: Identity a -> Int -> Identity a # testBit :: Identity a -> Int -> Bool # bitSizeMaybe :: Identity a -> Maybe Int # bitSize :: Identity a -> Int # isSigned :: Identity a -> Bool # shiftL :: Identity a -> Int -> Identity a # unsafeShiftL :: Identity a -> Int -> Identity a # shiftR :: Identity a -> Int -> Identity a # unsafeShiftR :: Identity a -> Int -> Identity a # rotateL :: Identity a -> Int -> Identity a # rotateR :: Identity a -> Int -> Identity a # popCount :: Identity a -> Int #
FiniteBits a => FiniteBits (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods finiteBitSize :: Identity a -> Int # countLeadingZeros :: Identity a -> Int # countTrailingZeros :: Identity a -> Int #
Ixed (Identity a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Identity a) -> Traversal' (Identity a) (IxValue (Identity a)) #
Wrapped (Identity a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Identity a) :: Type # Methods _Wrapped' :: Iso' (Identity a) (Unwrapped (Identity a)) #
Generic1 Identity
Instance details Defined in Data.Functor.Identity Associated Types type Rep1 Identity :: k -> Type # Methods from1 :: Identity a -> Rep1 Identity a # to1 :: Rep1 Identity a -> Identity a #
t ~ Identity b => Rewrapped (Identity a) t
Instance details Defined in Control.Lens.Wrapped
Each (Identity a) (Identity b) a b	`each` :: `Traversal` (`Identity` a) (`Identity` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Identity a) (Identity b) a b #
Field1 (Identity a) (Identity b) a b
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (Identity a) (Identity b) a b #
type Rep Identity
Instance details Defined in Data.Functor.Rep type Rep Identity = ()
type Rep (Identity a)	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity type Rep (Identity a) = D1 (MetaData "Identity" "Data.Functor.Identity" "base" True) (C1 (MetaCons "Identity" PrefixI True) (S1 (MetaSel (Just "runIdentity") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Index (Identity a)
Instance details Defined in Control.Lens.At type Index (Identity a) = ()
type IxValue (Identity a)
Instance details Defined in Control.Lens.At type IxValue (Identity a) = a
type Unwrapped (Identity a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Identity a) = a
type Rep1 Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity type Rep1 Identity = D1 (MetaData "Identity" "Data.Functor.Identity" "base" True) (C1 (MetaCons "Identity" PrefixI True) (S1 (MetaSel (Just "runIdentity") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Const a (b :: k) :: forall k. Type -> k -> Type #

The Const functor.

Constructors

Const
Fields getConst :: a

Instances

Generic1 (Const a :: k -> Type)
Instance details Defined in Data.Functor.Const Associated Types type Rep1 (Const a) :: k -> Type # Methods from1 :: Const a a0 -> Rep1 (Const a) a0 # to1 :: Rep1 (Const a) a0 -> Const a a0 #
ToJSON2 (Const :: Type -> Type -> Type)
Instance details Defined in Data.Aeson.Types.ToJSON Methods liftToJSON2 :: (a -> Value) -> ([a] -> Value) -> (b -> Value) -> ([b] -> Value) -> Const a b -> Value # liftToJSONList2 :: (a -> Value) -> ([a] -> Value) -> (b -> Value) -> ([b] -> Value) -> [Const a b] -> Value # liftToEncoding2 :: (a -> Encoding) -> ([a] -> Encoding) -> (b -> Encoding) -> ([b] -> Encoding) -> Const a b -> Encoding # liftToEncodingList2 :: (a -> Encoding) -> ([a] -> Encoding) -> (b -> Encoding) -> ([b] -> Encoding) -> [Const a b] -> Encoding #
FromJSON2 (Const :: Type -> Type -> Type)
Instance details Defined in Data.Aeson.Types.FromJSON Methods liftParseJSON2 :: (Value -> Parser a) -> (Value -> Parser [a]) -> (Value -> Parser b) -> (Value -> Parser [b]) -> Value -> Parser (Const a b) # liftParseJSONList2 :: (Value -> Parser a) -> (Value -> Parser [a]) -> (Value -> Parser b) -> (Value -> Parser [b]) -> Value -> Parser [Const a b] #
Bitraversable (Const :: Type -> Type -> Type)	Since: base-4.10.0.0
Instance details Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Const a b -> f (Const c d) #
Bifunctor (Const :: Type -> Type -> Type)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> Const a c -> Const b d # first :: (a -> b) -> Const a c -> Const b c # second :: (b -> c) -> Const a b -> Const a c #
Eq2 (Const :: Type -> Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Const a c -> Const b d -> Bool #
Ord2 (Const :: Type -> Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Const a c -> Const b d -> Ordering #
Read2 (Const :: Type -> Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Const a b) # liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Const a b] # liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Const a b) # liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Const a b] #
Show2 (Const :: Type -> Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Const a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Const a b] -> ShowS #
Biapplicative (Const :: Type -> Type -> Type)
Instance details Defined in Data.Biapplicative Methods bipure :: a -> b -> Const a b # (<<>>) :: Const (a -> b) (c -> d) -> Const a c -> Const b d # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Const a d -> Const b e -> Const c f # (>>) :: Const a b -> Const c d -> Const c d # (<<*) :: Const a b -> Const c d -> Const a b #
Hashable2 (Const :: Type -> Type -> Type)
Instance details Defined in Data.Hashable.Class Methods liftHashWithSalt2 :: (Int -> a -> Int) -> (Int -> b -> Int) -> Int -> Const a b -> Int #
Bitraversable1 (Const :: Type -> Type -> Type)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Const a c -> f (Const b d) # bisequence1 :: Apply f => Const (f a) (f b) -> f (Const a b) #
Biapply (Const :: Type -> Type -> Type)
Instance details Defined in Data.Functor.Bind.Class Methods (<<.>>) :: Const (a -> b) (c -> d) -> Const a c -> Const b d # (.>>) :: Const a b -> Const c d -> Const c d # (<<.) :: Const a b -> Const c d -> Const a b #
Semigroupoid (Const :: Type -> Type -> Type)
Instance details Defined in Data.Semigroupoid Methods o :: Const j k1 -> Const i j -> Const i k1 #
Functor (Const m :: Type -> Type)	Since: base-2.1
Instance details Defined in Data.Functor.Const Methods fmap :: (a -> b) -> Const m a -> Const m b # (<$) :: a -> Const m b -> Const m a #
Monoid m => Applicative (Const m :: Type -> Type)	Since: base-2.0.1
Instance details Defined in Data.Functor.Const Methods pure :: a -> Const m a # (<>) :: Const m (a -> b) -> Const m a -> Const m b # liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c # (>) :: Const m a -> Const m b -> Const m b # (<*) :: Const m a -> Const m b -> Const m a #
Foldable (Const m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldr :: (a -> b -> b) -> b -> Const m a -> b # foldr' :: (a -> b -> b) -> b -> Const m a -> b # foldl :: (b -> a -> b) -> b -> Const m a -> b # foldl' :: (b -> a -> b) -> b -> Const m a -> b # foldr1 :: (a -> a -> a) -> Const m a -> a # foldl1 :: (a -> a -> a) -> Const m a -> a # toList :: Const m a -> [a] # null :: Const m a -> Bool # length :: Const m a -> Int # elem :: Eq a => a -> Const m a -> Bool # maximum :: Ord a => Const m a -> a # minimum :: Ord a => Const m a -> a # sum :: Num a => Const m a -> a # product :: Num a => Const m a -> a #
Traversable (Const m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b) # sequenceA :: Applicative f => Const m (f a) -> f (Const m a) # mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b) # sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a) #
Contravariant (Const a :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a0 -> b) -> Const a b -> Const a a0 # (>$) :: b -> Const a b -> Const a a0 #
ToJSON a => ToJSON1 (Const a :: Type -> Type)
Instance details Defined in Data.Aeson.Types.ToJSON Methods liftToJSON :: (a0 -> Value) -> ([a0] -> Value) -> Const a a0 -> Value # liftToJSONList :: (a0 -> Value) -> ([a0] -> Value) -> [Const a a0] -> Value # liftToEncoding :: (a0 -> Encoding) -> ([a0] -> Encoding) -> Const a a0 -> Encoding # liftToEncodingList :: (a0 -> Encoding) -> ([a0] -> Encoding) -> [Const a a0] -> Encoding #
FromJSON a => FromJSON1 (Const a :: Type -> Type)
Instance details Defined in Data.Aeson.Types.FromJSON Methods liftParseJSON :: (Value -> Parser a0) -> (Value -> Parser [a0]) -> Value -> Parser (Const a a0) # liftParseJSONList :: (Value -> Parser a0) -> (Value -> Parser [a0]) -> Value -> Parser [Const a a0] #
Eq a => Eq1 (Const a :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq :: (a0 -> b -> Bool) -> Const a a0 -> Const a b -> Bool #
Ord a => Ord1 (Const a :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftCompare :: (a0 -> b -> Ordering) -> Const a a0 -> Const a b -> Ordering #
Read a => Read1 (Const a :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Const a a0) # liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Const a a0] # liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Const a a0) # liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Const a a0] #
Show a => Show1 (Const a :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> Const a a0 -> ShowS # liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [Const a a0] -> ShowS #
Hashable a => Hashable1 (Const a :: Type -> Type)
Instance details Defined in Data.Hashable.Class Methods liftHashWithSalt :: (Int -> a0 -> Int) -> Int -> Const a a0 -> Int #
Semigroup m => Apply (Const m :: Type -> Type)
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Const m (a -> b) -> Const m a -> Const m b # (.>) :: Const m a -> Const m b -> Const m b # (<.) :: Const m a -> Const m b -> Const m a # liftF2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c #
Bounded a => Bounded (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods minBound :: Const a b # maxBound :: Const a b #
Enum a => Enum (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods succ :: Const a b -> Const a b # pred :: Const a b -> Const a b # toEnum :: Int -> Const a b # fromEnum :: Const a b -> Int # enumFrom :: Const a b -> [Const a b] # enumFromThen :: Const a b -> Const a b -> [Const a b] # enumFromTo :: Const a b -> Const a b -> [Const a b] # enumFromThenTo :: Const a b -> Const a b -> Const a b -> [Const a b] #
Eq a => Eq (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (==) :: Const a b -> Const a b -> Bool # (/=) :: Const a b -> Const a b -> Bool #
Floating a => Floating (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods pi :: Const a b # exp :: Const a b -> Const a b # log :: Const a b -> Const a b # sqrt :: Const a b -> Const a b # (**) :: Const a b -> Const a b -> Const a b # logBase :: Const a b -> Const a b -> Const a b # sin :: Const a b -> Const a b # cos :: Const a b -> Const a b # tan :: Const a b -> Const a b # asin :: Const a b -> Const a b # acos :: Const a b -> Const a b # atan :: Const a b -> Const a b # sinh :: Const a b -> Const a b # cosh :: Const a b -> Const a b # tanh :: Const a b -> Const a b # asinh :: Const a b -> Const a b # acosh :: Const a b -> Const a b # atanh :: Const a b -> Const a b # log1p :: Const a b -> Const a b # expm1 :: Const a b -> Const a b # log1pexp :: Const a b -> Const a b # log1mexp :: Const a b -> Const a b #
Fractional a => Fractional (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (/) :: Const a b -> Const a b -> Const a b # recip :: Const a b -> Const a b # fromRational :: Rational -> Const a b #
Integral a => Integral (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods quot :: Const a b -> Const a b -> Const a b # rem :: Const a b -> Const a b -> Const a b # div :: Const a b -> Const a b -> Const a b # mod :: Const a b -> Const a b -> Const a b # quotRem :: Const a b -> Const a b -> (Const a b, Const a b) # divMod :: Const a b -> Const a b -> (Const a b, Const a b) # toInteger :: Const a b -> Integer #
Num a => Num (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (+) :: Const a b -> Const a b -> Const a b # (-) :: Const a b -> Const a b -> Const a b # (*) :: Const a b -> Const a b -> Const a b # negate :: Const a b -> Const a b # abs :: Const a b -> Const a b # signum :: Const a b -> Const a b # fromInteger :: Integer -> Const a b #
Ord a => Ord (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods compare :: Const a b -> Const a b -> Ordering # (<) :: Const a b -> Const a b -> Bool # (<=) :: Const a b -> Const a b -> Bool # (>) :: Const a b -> Const a b -> Bool # (>=) :: Const a b -> Const a b -> Bool # max :: Const a b -> Const a b -> Const a b # min :: Const a b -> Const a b -> Const a b #
Read a => Read (Const a b)	This instance would be equivalent to the derived instances of the `Const` newtype if the `runConst` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Const Methods readsPrec :: Int -> ReadS (Const a b) # readList :: ReadS [Const a b] # readPrec :: ReadPrec (Const a b) # readListPrec :: ReadPrec [Const a b] #
Real a => Real (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods toRational :: Const a b -> Rational #
RealFloat a => RealFloat (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods floatRadix :: Const a b -> Integer # floatDigits :: Const a b -> Int # floatRange :: Const a b -> (Int, Int) # decodeFloat :: Const a b -> (Integer, Int) # encodeFloat :: Integer -> Int -> Const a b # exponent :: Const a b -> Int # significand :: Const a b -> Const a b # scaleFloat :: Int -> Const a b -> Const a b # isNaN :: Const a b -> Bool # isInfinite :: Const a b -> Bool # isDenormalized :: Const a b -> Bool # isNegativeZero :: Const a b -> Bool # isIEEE :: Const a b -> Bool # atan2 :: Const a b -> Const a b -> Const a b #
RealFrac a => RealFrac (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods properFraction :: Integral b0 => Const a b -> (b0, Const a b) # truncate :: Integral b0 => Const a b -> b0 # round :: Integral b0 => Const a b -> b0 # ceiling :: Integral b0 => Const a b -> b0 # floor :: Integral b0 => Const a b -> b0 #
Show a => Show (Const a b)	This instance would be equivalent to the derived instances of the `Const` newtype if the `runConst` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Const Methods showsPrec :: Int -> Const a b -> ShowS # show :: Const a b -> String # showList :: [Const a b] -> ShowS #
Ix a => Ix (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods range :: (Const a b, Const a b) -> [Const a b] # index :: (Const a b, Const a b) -> Const a b -> Int # unsafeIndex :: (Const a b, Const a b) -> Const a b -> Int inRange :: (Const a b, Const a b) -> Const a b -> Bool # rangeSize :: (Const a b, Const a b) -> Int # unsafeRangeSize :: (Const a b, Const a b) -> Int
Generic (Const a b)
Instance details Defined in Data.Functor.Const Associated Types type Rep (Const a b) :: Type -> Type # Methods from :: Const a b -> Rep (Const a b) x # to :: Rep (Const a b) x -> Const a b #
Semigroup a => Semigroup (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (<>) :: Const a b -> Const a b -> Const a b # sconcat :: NonEmpty (Const a b) -> Const a b # stimes :: Integral b0 => b0 -> Const a b -> Const a b #
Monoid a => Monoid (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods mempty :: Const a b # mappend :: Const a b -> Const a b -> Const a b # mconcat :: [Const a b] -> Const a b #
Hashable a => Hashable (Const a b)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Const a b -> Int # hash :: Const a b -> Int #
ToJSON a => ToJSON (Const a b)
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSON :: Const a b -> Value # toEncoding :: Const a b -> Encoding # toJSONList :: [Const a b] -> Value # toEncodingList :: [Const a b] -> Encoding #
FromJSON a => FromJSON (Const a b)
Instance details Defined in Data.Aeson.Types.FromJSON Methods parseJSON :: Value -> Parser (Const a b) # parseJSONList :: Value -> Parser [Const a b] #
Storable a => Storable (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods sizeOf :: Const a b -> Int # alignment :: Const a b -> Int # peekElemOff :: Ptr (Const a b) -> Int -> IO (Const a b) # pokeElemOff :: Ptr (Const a b) -> Int -> Const a b -> IO () # peekByteOff :: Ptr b0 -> Int -> IO (Const a b) # pokeByteOff :: Ptr b0 -> Int -> Const a b -> IO () # peek :: Ptr (Const a b) -> IO (Const a b) # poke :: Ptr (Const a b) -> Const a b -> IO () #
Bits a => Bits (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (.&.) :: Const a b -> Const a b -> Const a b # (.\|.) :: Const a b -> Const a b -> Const a b # xor :: Const a b -> Const a b -> Const a b # complement :: Const a b -> Const a b # shift :: Const a b -> Int -> Const a b # rotate :: Const a b -> Int -> Const a b # zeroBits :: Const a b # bit :: Int -> Const a b # setBit :: Const a b -> Int -> Const a b # clearBit :: Const a b -> Int -> Const a b # complementBit :: Const a b -> Int -> Const a b # testBit :: Const a b -> Int -> Bool # bitSizeMaybe :: Const a b -> Maybe Int # bitSize :: Const a b -> Int # isSigned :: Const a b -> Bool # shiftL :: Const a b -> Int -> Const a b # unsafeShiftL :: Const a b -> Int -> Const a b # shiftR :: Const a b -> Int -> Const a b # unsafeShiftR :: Const a b -> Int -> Const a b # rotateL :: Const a b -> Int -> Const a b # rotateR :: Const a b -> Int -> Const a b # popCount :: Const a b -> Int #
FiniteBits a => FiniteBits (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods finiteBitSize :: Const a b -> Int # countLeadingZeros :: Const a b -> Int # countTrailingZeros :: Const a b -> Int #
Wrapped (Const a x)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Const a x) :: Type # Methods _Wrapped' :: Iso' (Const a x) (Unwrapped (Const a x)) #
t ~ Const a' x' => Rewrapped (Const a x) t
Instance details Defined in Control.Lens.Wrapped
type Rep1 (Const a :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const type Rep1 (Const a :: k -> Type) = D1 (MetaData "Const" "Data.Functor.Const" "base" True) (C1 (MetaCons "Const" PrefixI True) (S1 (MetaSel (Just "getConst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const type Rep (Const a b) = D1 (MetaData "Const" "Data.Functor.Const" "base" True) (C1 (MetaCons "Const" PrefixI True) (S1 (MetaSel (Just "getConst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Unwrapped (Const a x)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Const a x) = a

(&) :: a -> (a -> b) -> b infixl 1 #

& is a reverse application operator. This provides notational convenience. Its precedence is one higher than that of the forward application operator $, which allows & to be nested in $.

>>> 5 & (+1) & show
"6"

Since: base-4.8.0.0

(<&>) :: Functor f => f a -> (a -> b) -> f b infixl 1 #

Flipped version of <$>.

(<&>) = flip fmap

Examples

Expand

Apply (+1) to a list, a Just and a Right:

>>> Just 2 <&> (+1)
Just 3

>>> [1,2,3] <&> (+1)
[2,3,4]

>>> Right 3 <&> (+1)
Right 4

Since: base-4.11.0.0

class Profunctor (p :: Type -> Type -> Type) where #

Formally, the class Profunctor represents a profunctor from Hask -> Hask.

Intuitively it is a bifunctor where the first argument is contravariant and the second argument is covariant.

You can define a Profunctor by either defining dimap or by defining both lmap and rmap.

If you supply dimap, you should ensure that:

dimap id id ≡ id

If you supply lmap and rmap, ensure:

lmap id ≡ id
rmap id ≡ id

If you supply both, you should also ensure:

dimap f g ≡ lmap f . rmap g

These ensure by parametricity:

dimap (f . g) (h . i) ≡ dimap g h . dimap f i
lmap (f . g) ≡ lmap g . lmap f
rmap (f . g) ≡ rmap f . rmap g

Minimal complete definition

dimap | lmap, rmap

Methods

dimap :: (a -> b) -> (c -> d) -> p b c -> p a d #

Map over both arguments at the same time.

dimap f g ≡ lmap f . rmap g

lmap :: (a -> b) -> p b c -> p a c #

Map the first argument contravariantly.

lmap f ≡ dimap f id

rmap :: (b -> c) -> p a b -> p a c #

Map the second argument covariantly.

rmap ≡ dimap id

Instances

Profunctor ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedGetter b c -> ReifiedGetter a d # lmap :: (a -> b) -> ReifiedGetter b c -> ReifiedGetter a c # rmap :: (b -> c) -> ReifiedGetter a b -> ReifiedGetter a c # (#.) :: Coercible c b => q b c -> ReifiedGetter a b -> ReifiedGetter a c # (.#) :: Coercible b a => ReifiedGetter b c -> q a b -> ReifiedGetter a c #
Profunctor ReifiedFold
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedFold b c -> ReifiedFold a d # lmap :: (a -> b) -> ReifiedFold b c -> ReifiedFold a c # rmap :: (b -> c) -> ReifiedFold a b -> ReifiedFold a c # (#.) :: Coercible c b => q b c -> ReifiedFold a b -> ReifiedFold a c # (.#) :: Coercible b a => ReifiedFold b c -> q a b -> ReifiedFold a c #
Monad m => Profunctor (Kleisli m)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Kleisli m b c -> Kleisli m a d # lmap :: (a -> b) -> Kleisli m b c -> Kleisli m a c # rmap :: (b -> c) -> Kleisli m a b -> Kleisli m a c # (#.) :: Coercible c b => q b c -> Kleisli m a b -> Kleisli m a c # (.#) :: Coercible b a => Kleisli m b c -> q a b -> Kleisli m a c #
Profunctor (ReifiedIndexedGetter i)
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedIndexedGetter i b c -> ReifiedIndexedGetter i a d # lmap :: (a -> b) -> ReifiedIndexedGetter i b c -> ReifiedIndexedGetter i a c # rmap :: (b -> c) -> ReifiedIndexedGetter i a b -> ReifiedIndexedGetter i a c # (#.) :: Coercible c b => q b c -> ReifiedIndexedGetter i a b -> ReifiedIndexedGetter i a c # (.#) :: Coercible b a => ReifiedIndexedGetter i b c -> q a b -> ReifiedIndexedGetter i a c #
Profunctor (ReifiedIndexedFold i)
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedIndexedFold i b c -> ReifiedIndexedFold i a d # lmap :: (a -> b) -> ReifiedIndexedFold i b c -> ReifiedIndexedFold i a c # rmap :: (b -> c) -> ReifiedIndexedFold i a b -> ReifiedIndexedFold i a c # (#.) :: Coercible c b => q b c -> ReifiedIndexedFold i a b -> ReifiedIndexedFold i a c # (.#) :: Coercible b a => ReifiedIndexedFold i b c -> q a b -> ReifiedIndexedFold i a c #
Profunctor (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods dimap :: (a -> b) -> (c -> d) -> Indexed i b c -> Indexed i a d # lmap :: (a -> b) -> Indexed i b c -> Indexed i a c # rmap :: (b -> c) -> Indexed i a b -> Indexed i a c # (#.) :: Coercible c b => q b c -> Indexed i a b -> Indexed i a c # (.#) :: Coercible b a => Indexed i b c -> q a b -> Indexed i a c #
Profunctor p => Profunctor (TambaraSum p)
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> TambaraSum p b c -> TambaraSum p a d # lmap :: (a -> b) -> TambaraSum p b c -> TambaraSum p a c # rmap :: (b -> c) -> TambaraSum p a b -> TambaraSum p a c # (#.) :: Coercible c b => q b c -> TambaraSum p a b -> TambaraSum p a c # (.#) :: Coercible b a => TambaraSum p b c -> q a b -> TambaraSum p a c #
Profunctor (PastroSum p)
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> PastroSum p b c -> PastroSum p a d # lmap :: (a -> b) -> PastroSum p b c -> PastroSum p a c # rmap :: (b -> c) -> PastroSum p a b -> PastroSum p a c # (#.) :: Coercible c b => q b c -> PastroSum p a b -> PastroSum p a c # (.#) :: Coercible b a => PastroSum p b c -> q a b -> PastroSum p a c #
Profunctor (CotambaraSum p)
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> CotambaraSum p b c -> CotambaraSum p a d # lmap :: (a -> b) -> CotambaraSum p b c -> CotambaraSum p a c # rmap :: (b -> c) -> CotambaraSum p a b -> CotambaraSum p a c # (#.) :: Coercible c b => q b c -> CotambaraSum p a b -> CotambaraSum p a c # (.#) :: Coercible b a => CotambaraSum p b c -> q a b -> CotambaraSum p a c #
Profunctor (CopastroSum p)
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> CopastroSum p b c -> CopastroSum p a d # lmap :: (a -> b) -> CopastroSum p b c -> CopastroSum p a c # rmap :: (b -> c) -> CopastroSum p a b -> CopastroSum p a c # (#.) :: Coercible c b => q b c -> CopastroSum p a b -> CopastroSum p a c # (.#) :: Coercible b a => CopastroSum p b c -> q a b -> CopastroSum p a c #
Profunctor p => Profunctor (Tambara p)
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Tambara p b c -> Tambara p a d # lmap :: (a -> b) -> Tambara p b c -> Tambara p a c # rmap :: (b -> c) -> Tambara p a b -> Tambara p a c # (#.) :: Coercible c b => q b c -> Tambara p a b -> Tambara p a c # (.#) :: Coercible b a => Tambara p b c -> q a b -> Tambara p a c #
Profunctor (Pastro p)
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Pastro p b c -> Pastro p a d # lmap :: (a -> b) -> Pastro p b c -> Pastro p a c # rmap :: (b -> c) -> Pastro p a b -> Pastro p a c # (#.) :: Coercible c b => q b c -> Pastro p a b -> Pastro p a c # (.#) :: Coercible b a => Pastro p b c -> q a b -> Pastro p a c #
Profunctor (Cotambara p)
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Cotambara p b c -> Cotambara p a d # lmap :: (a -> b) -> Cotambara p b c -> Cotambara p a c # rmap :: (b -> c) -> Cotambara p a b -> Cotambara p a c # (#.) :: Coercible c b => q b c -> Cotambara p a b -> Cotambara p a c # (.#) :: Coercible b a => Cotambara p b c -> q a b -> Cotambara p a c #
Profunctor (Copastro p)
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Copastro p b c -> Copastro p a d # lmap :: (a -> b) -> Copastro p b c -> Copastro p a c # rmap :: (b -> c) -> Copastro p a b -> Copastro p a c # (#.) :: Coercible c b => q b c -> Copastro p a b -> Copastro p a c # (.#) :: Coercible b a => Copastro p b c -> q a b -> Copastro p a c #
Functor f => Profunctor (Star f)
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Star f b c -> Star f a d # lmap :: (a -> b) -> Star f b c -> Star f a c # rmap :: (b -> c) -> Star f a b -> Star f a c # (#.) :: Coercible c b => q b c -> Star f a b -> Star f a c # (.#) :: Coercible b a => Star f b c -> q a b -> Star f a c #
Functor f => Profunctor (Costar f)
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Costar f b c -> Costar f a d # lmap :: (a -> b) -> Costar f b c -> Costar f a c # rmap :: (b -> c) -> Costar f a b -> Costar f a c # (#.) :: Coercible c b => q b c -> Costar f a b -> Costar f a c # (.#) :: Coercible b a => Costar f b c -> q a b -> Costar f a c #
Arrow p => Profunctor (WrappedArrow p)
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> WrappedArrow p b c -> WrappedArrow p a d # lmap :: (a -> b) -> WrappedArrow p b c -> WrappedArrow p a c # rmap :: (b -> c) -> WrappedArrow p a b -> WrappedArrow p a c # (#.) :: Coercible c b => q b c -> WrappedArrow p a b -> WrappedArrow p a c # (.#) :: Coercible b a => WrappedArrow p b c -> q a b -> WrappedArrow p a c #
Profunctor (Forget r)
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Forget r b c -> Forget r a d # lmap :: (a -> b) -> Forget r b c -> Forget r a c # rmap :: (b -> c) -> Forget r a b -> Forget r a c # (#.) :: Coercible c b => q b c -> Forget r a b -> Forget r a c # (.#) :: Coercible b a => Forget r b c -> q a b -> Forget r a c #
Profunctor (Tagged :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Tagged b c -> Tagged a d # lmap :: (a -> b) -> Tagged b c -> Tagged a c # rmap :: (b -> c) -> Tagged a b -> Tagged a c # (#.) :: Coercible c b => q b c -> Tagged a b -> Tagged a c # (.#) :: Coercible b a => Tagged b c -> q a b -> Tagged a c #
Profunctor ((->) :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> (b -> c) -> a -> d # lmap :: (a -> b) -> (b -> c) -> a -> c # rmap :: (b -> c) -> (a -> b) -> a -> c # (#.) :: Coercible c b => q b c -> (a -> b) -> a -> c # (.#) :: Coercible b a => (b -> c) -> q a b -> a -> c #
Functor w => Profunctor (Cokleisli w)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Cokleisli w b c -> Cokleisli w a d # lmap :: (a -> b) -> Cokleisli w b c -> Cokleisli w a c # rmap :: (b -> c) -> Cokleisli w a b -> Cokleisli w a c # (#.) :: Coercible c b => q b c -> Cokleisli w a b -> Cokleisli w a c # (.#) :: Coercible b a => Cokleisli w b c -> q a b -> Cokleisli w a c #
Profunctor (Market a b)
Instance details Defined in Control.Lens.Internal.Prism Methods dimap :: (a0 -> b0) -> (c -> d) -> Market a b b0 c -> Market a b a0 d # lmap :: (a0 -> b0) -> Market a b b0 c -> Market a b a0 c # rmap :: (b0 -> c) -> Market a b a0 b0 -> Market a b a0 c # (#.) :: Coercible c b0 => q b0 c -> Market a b a0 b0 -> Market a b a0 c # (.#) :: Coercible b0 a0 => Market a b b0 c -> q a0 b0 -> Market a b a0 c #
Profunctor (Exchange a b)
Instance details Defined in Control.Lens.Internal.Iso Methods dimap :: (a0 -> b0) -> (c -> d) -> Exchange a b b0 c -> Exchange a b a0 d # lmap :: (a0 -> b0) -> Exchange a b b0 c -> Exchange a b a0 c # rmap :: (b0 -> c) -> Exchange a b a0 b0 -> Exchange a b a0 c # (#.) :: Coercible c b0 => q b0 c -> Exchange a b a0 b0 -> Exchange a b a0 c # (.#) :: Coercible b0 a0 => Exchange a b b0 c -> q a0 b0 -> Exchange a b a0 c #
(Functor f, Profunctor p) => Profunctor (Cayley f p)
Instance details Defined in Data.Profunctor.Cayley Methods dimap :: (a -> b) -> (c -> d) -> Cayley f p b c -> Cayley f p a d # lmap :: (a -> b) -> Cayley f p b c -> Cayley f p a c # rmap :: (b -> c) -> Cayley f p a b -> Cayley f p a c # (#.) :: Coercible c b => q b c -> Cayley f p a b -> Cayley f p a c # (.#) :: Coercible b a => Cayley f p b c -> q a b -> Cayley f p a c #
(Profunctor p, Profunctor q) => Profunctor (Procompose p q)
Instance details Defined in Data.Profunctor.Composition Methods dimap :: (a -> b) -> (c -> d) -> Procompose p q b c -> Procompose p q a d # lmap :: (a -> b) -> Procompose p q b c -> Procompose p q a c # rmap :: (b -> c) -> Procompose p q a b -> Procompose p q a c # (#.) :: Coercible c b => q0 b c -> Procompose p q a b -> Procompose p q a c # (.#) :: Coercible b a => Procompose p q b c -> q0 a b -> Procompose p q a c #
(Profunctor p, Profunctor q) => Profunctor (Rift p q)
Instance details Defined in Data.Profunctor.Composition Methods dimap :: (a -> b) -> (c -> d) -> Rift p q b c -> Rift p q a d # lmap :: (a -> b) -> Rift p q b c -> Rift p q a c # rmap :: (b -> c) -> Rift p q a b -> Rift p q a c # (#.) :: Coercible c b => q0 b c -> Rift p q a b -> Rift p q a c # (.#) :: Coercible b a => Rift p q b c -> q0 a b -> Rift p q a c #
Functor f => Profunctor (Joker f :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Joker f b c -> Joker f a d # lmap :: (a -> b) -> Joker f b c -> Joker f a c # rmap :: (b -> c) -> Joker f a b -> Joker f a c # (#.) :: Coercible c b => q b c -> Joker f a b -> Joker f a c # (.#) :: Coercible b a => Joker f b c -> q a b -> Joker f a c #
Contravariant f => Profunctor (Clown f :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Clown f b c -> Clown f a d # lmap :: (a -> b) -> Clown f b c -> Clown f a c # rmap :: (b -> c) -> Clown f a b -> Clown f a c # (#.) :: Coercible c b => q b c -> Clown f a b -> Clown f a c # (.#) :: Coercible b a => Clown f b c -> q a b -> Clown f a c #
(Profunctor p, Profunctor q) => Profunctor (Sum p q)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Sum p q b c -> Sum p q a d # lmap :: (a -> b) -> Sum p q b c -> Sum p q a c # rmap :: (b -> c) -> Sum p q a b -> Sum p q a c # (#.) :: Coercible c b => q0 b c -> Sum p q a b -> Sum p q a c # (.#) :: Coercible b a => Sum p q b c -> q0 a b -> Sum p q a c #
(Profunctor p, Profunctor q) => Profunctor (Product p q)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Product p q b c -> Product p q a d # lmap :: (a -> b) -> Product p q b c -> Product p q a c # rmap :: (b -> c) -> Product p q a b -> Product p q a c # (#.) :: Coercible c b => q0 b c -> Product p q a b -> Product p q a c # (.#) :: Coercible b a => Product p q b c -> q0 a b -> Product p q a c #
(Functor f, Profunctor p) => Profunctor (Tannen f p)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Tannen f p b c -> Tannen f p a d # lmap :: (a -> b) -> Tannen f p b c -> Tannen f p a c # rmap :: (b -> c) -> Tannen f p a b -> Tannen f p a c # (#.) :: Coercible c b => q b c -> Tannen f p a b -> Tannen f p a c # (.#) :: Coercible b a => Tannen f p b c -> q a b -> Tannen f p a c #
(Profunctor p, Functor f, Functor g) => Profunctor (Biff p f g)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Biff p f g b c -> Biff p f g a d # lmap :: (a -> b) -> Biff p f g b c -> Biff p f g a c # rmap :: (b -> c) -> Biff p f g a b -> Biff p f g a c # (#.) :: Coercible c b => q b c -> Biff p f g a b -> Biff p f g a c # (.#) :: Coercible b a => Biff p f g b c -> q a b -> Biff p f g a c #

defaultFieldRules :: LensRules #

makeFieldsNoPrefix :: Name -> DecsQ #

Generate overloaded field accessors based on field names which are only prefixed with an underscore (e.g. _name), not additionally with the type name (e.g. _fooName).

This might be the desired behaviour in case the DuplicateRecordFields language extension is used in order to get rid of the necessity to prefix each field name with the type name.

As an example:

data Foo a  = Foo { _x :: Int, _y :: a }
newtype Bar = Bar { _x :: Char }
makeFieldsNoPrefix ''Foo
makeFieldsNoPrefix ''Bar

will create classes

class HasX s a | s -> a where
  x :: Lens' s a
class HasY s a | s -> a where
  y :: Lens' s a

together with instances

instance HasX (Foo a) Int
instance HasY (Foo a) a where
instance HasX Bar Char where

For details, see classUnderscoreNoPrefixFields.

makeFieldsNoPrefix = makeLensesWith classUnderscoreNoPrefixFields

makeFields :: Name -> DecsQ #

Generate overloaded field accessors.

e.g

data Foo a = Foo { _fooX :: Int, _fooY :: a }
newtype Bar = Bar { _barX :: Char }
makeFields ''Foo
makeFields ''Bar

will create

_fooXLens :: Lens' (Foo a) Int
_fooYLens :: Lens (Foo a) (Foo b) a b
class HasX s a | s -> a where
  x :: Lens' s a
instance HasX (Foo a) Int where
  x = _fooXLens
class HasY s a | s -> a where
  y :: Lens' s a
instance HasY (Foo a) a where
  y = _fooYLens
_barXLens :: Iso' Bar Char
instance HasX Bar Char where
  x = _barXLens

For details, see camelCaseFields.

makeFields = makeLensesWith defaultFieldRules

abbreviatedNamer :: FieldNamer #

A FieldNamer for abbreviatedFields.

abbreviatedFields :: LensRules #

Field rules fields in the form prefixFieldname or _prefixFieldname If you want all fields to be lensed, then there is no reason to use an _ before the prefix. If any of the record fields leads with an _ then it is assume a field without an _ should not have a lens created.

Note that prefix may be any string of characters that are not uppercase letters. (In particular, it may be arbitrary string of lowercase letters and numbers) This is the behavior that defaultFieldRules had in lens 4.4 and earlier.

classUnderscoreNoPrefixNamer :: FieldNamer #

A FieldNamer for classUnderscoreNoPrefixFields.

classUnderscoreNoPrefixFields :: LensRules #

Field rules for fields in the form _fieldname (the leading underscore is mandatory).

Note: The primary difference to camelCaseFields is that for classUnderscoreNoPrefixFields the field names are not expected to be prefixed with the type name. This might be the desired behaviour when the DuplicateRecordFields extension is enabled.

camelCaseNamer :: FieldNamer #

A FieldNamer for camelCaseFields.

camelCaseFields :: LensRules #

Field rules for fields in the form prefixFieldname or _prefixFieldname If you want all fields to be lensed, then there is no reason to use an _ before the prefix. If any of the record fields leads with an _ then it is assume a field without an _ should not have a lens created.

Note: The prefix must be the same as the typename (with the first letter lowercased). This is a change from lens versions before lens 4.5. If you want the old behaviour, use makeLensesWith abbreviatedFields

underscoreNamer :: FieldNamer #

A FieldNamer for underscoreFields.

underscoreFields :: LensRules #

Field rules for fields in the form _prefix_fieldname

makeWrapped :: Name -> DecsQ #

Build Wrapped instance for a given newtype

declareLensesWith :: LensRules -> DecsQ -> DecsQ #

Declare lenses for each records in the given declarations, using the specified LensRules. Any record syntax in the input will be stripped off.

declareFields :: DecsQ -> DecsQ #

 declareFields = declareLensesWith defaultFieldRules

declareWrapped :: DecsQ -> DecsQ #

Build Wrapped instance for each newtype.

declarePrisms :: DecsQ -> DecsQ #

Generate a Prism for each constructor of each data type.

e.g.

declarePrisms [d|
  data Exp = Lit Int | Var String | Lambda{ bound::String, body::Exp }
  |]

will create

data Exp = Lit Int | Var String | Lambda { bound::String, body::Exp }
_Lit :: Prism' Exp Int
_Var :: Prism' Exp String
_Lambda :: Prism' Exp (String, Exp)

declareClassyFor :: [(String, (String, String))] -> [(String, String)] -> DecsQ -> DecsQ #

Similar to makeClassyFor, but takes a declaration quote.

declareClassy :: DecsQ -> DecsQ #

For each record in the declaration quote, make lenses and traversals for it, and create a class when the type has no arguments. All record syntax in the input will be stripped off.

e.g.

declareClassy [d|
  data Foo = Foo { fooX, fooY :: Int }
    deriving Show
  |]

will create

data Foo = Foo Int Int deriving Show
class HasFoo t where
  foo :: Lens' t Foo
instance HasFoo Foo where foo = id
fooX, fooY :: HasFoo t => Lens' t Int

declareLensesFor :: [(String, String)] -> DecsQ -> DecsQ #

Similar to makeLensesFor, but takes a declaration quote.

declareLenses :: DecsQ -> DecsQ #

Make lenses for all records in the given declaration quote. All record syntax in the input will be stripped off.

e.g.

declareLenses [d|
  data Foo = Foo { fooX, fooY :: Int }
    deriving Show
  |]

will create

data Foo = Foo Int Int deriving Show
fooX, fooY :: Lens' Foo Int

makeLensesWith :: LensRules -> Name -> DecsQ #

Build lenses with a custom configuration.

makeClassyFor :: String -> String -> [(String, String)] -> Name -> DecsQ #

Derive lenses and traversals, using a named wrapper class, and specifying explicit pairings of (fieldName, traversalName).

Example usage:

makeClassyFor "HasFoo" "foo" [("_foo", "fooLens"), ("bar", "lbar")] ''Foo

makeLensesFor :: [(String, String)] -> Name -> DecsQ #

Derive lenses and traversals, specifying explicit pairings of (fieldName, lensName).

If you map multiple names to the same label, and it is present in the same constructor then this will generate a Traversal.

e.g.

makeLensesFor [("_foo", "fooLens"), ("baz", "lbaz")] ''Foo
makeLensesFor [("_barX", "bar"), ("_barY", "bar")] ''Bar

makeClassy_ :: Name -> DecsQ #

Make lenses and traversals for a type, and create a class when the type has no arguments. Works the same as makeClassy except that (a) it expects that record field names do not begin with an underscore, (b) all record fields are made into lenses, and (c) the resulting lens is prefixed with an underscore.

classyRules_ :: LensRules #

A LensRules used by makeClassy_.

classyRules :: LensRules #

Rules for making lenses and traversals that precompose another Lens.

mappingNamer #

Arguments

:: (String -> [String])	A function that maps a `fieldName` to `lensName`s.
-> FieldNamer

Create a FieldNamer from a mapping function. If the function returns [], it creates no lens for the field.

lookingupNamer :: [(String, String)] -> FieldNamer #

Create a FieldNamer from explicit pairings of (fieldName, lensName).

lensRulesFor #

Arguments

:: [(String, String)]	(Field Name, Definition Name)
-> LensRules

Construct a LensRules value for generating top-level definitions using the given map from field names to definition names.

underscoreNoPrefixNamer :: FieldNamer #

A FieldNamer that strips the _ off of the field name, lowercases the name, and skips the field if it doesn't start with an '_'.

lensRules :: LensRules #

Rules for making fairly simple partial lenses, ignoring the special cases for isomorphisms and traversals, and not making any classes. It uses underscoreNoPrefixNamer.

lensClass :: Lens' LensRules ClassyNamer #

Lens' to access the option for naming "classy" lenses.

lensField :: Lens' LensRules FieldNamer #

Lens' to access the convention for naming fields in our LensRules.

createClass :: Lens' LensRules Bool #

Create the class if the constructor is Simple and the lensClass rule matches.

generateLazyPatterns :: Lens' LensRules Bool #

Generate optics using lazy pattern matches. This can allow fields of an undefined value to be initialized with lenses:

data Foo = Foo {_x :: Int, _y :: Bool}
  deriving Show

makeLensesWith (lensRules & generateLazyPatterns .~ True) ''Foo

> undefined & x .~ 8 & y .~ True
Foo {_x = 8, _y = True}

The downside of this flag is that it can lead to space-leaks and code-size/compile-time increases when generated for large records. By default this flag is turned off, and strict optics are generated.

When using lazy optics the strict optic can be recovered by composing with $!:

strictOptic = ($!) . lazyOptic

generateUpdateableOptics :: Lens' LensRules Bool #

Generate "updateable" optics when True. When False, Folds will be generated instead of Traversals and Getters will be generated instead of Lenses. This mode is intended to be used for types with invariants which must be maintained by "smart" constructors.

generateSignatures :: Lens' LensRules Bool #

Indicate whether or not to supply the signatures for the generated lenses.

Disabling this can be useful if you want to provide a more restricted type signature or if you want to supply hand-written haddocks.

simpleLenses :: Lens' LensRules Bool #

Generate "simple" optics even when type-changing optics are possible. (e.g. Lens' instead of Lens)

data LensRules #

Rules to construct lenses for data fields.

type FieldNamer #

Arguments

= Name	Name of the data type that lenses are being generated for.
-> [Name]	Names of all fields (including the field being named) in the data type.
-> Name	Name of the field being named.
-> [DefName]	Name(s) of the lens functions. If empty, no lens is created for that field.

The rule to create function names of lenses for data fields.

Although it's sometimes useful, you won't need the first two arguments most of the time.

data DefName #

Name to give to generated field optics.

Constructors

TopName Name	Simple top-level definiton name
MethodName Name Name	makeFields-style class name and method name

Instances

Eq DefName
Instance details Defined in Control.Lens.Internal.FieldTH Methods (==) :: DefName -> DefName -> Bool # (/=) :: DefName -> DefName -> Bool #
Ord DefName
Instance details Defined in Control.Lens.Internal.FieldTH Methods compare :: DefName -> DefName -> Ordering # (<) :: DefName -> DefName -> Bool # (<=) :: DefName -> DefName -> Bool # (>) :: DefName -> DefName -> Bool # (>=) :: DefName -> DefName -> Bool # max :: DefName -> DefName -> DefName # min :: DefName -> DefName -> DefName #
Show DefName
Instance details Defined in Control.Lens.Internal.FieldTH Methods showsPrec :: Int -> DefName -> ShowS # show :: DefName -> String # showList :: [DefName] -> ShowS #

type ClassyNamer #

Arguments

= Name	Name of the data type that lenses are being generated for.
-> Maybe (Name, Name)	Names of the class and the main method it generates, respectively.

The optional rule to create a class and method around a monomorphic data type. If this naming convention is provided, it generates a "classy" lens.

makeClassyPrisms #

Arguments

:: Name	Type constructor name
-> DecsQ

Generate a Prism for each constructor of a data type and combine them into a single class. No Isos are created. Reviews are created for constructors with existentially quantified constructors and GADTs.

e.g.

data FooBarBaz a
  = Foo Int
  | Bar a
  | Baz Int Char
makeClassyPrisms ''FooBarBaz

will create

class AsFooBarBaz s a | s -> a where
  _FooBarBaz :: Prism' s (FooBarBaz a)
  _Foo :: Prism' s Int
  _Bar :: Prism' s a
  _Baz :: Prism' s (Int,Char)

  _Foo = _FooBarBaz . _Foo
  _Bar = _FooBarBaz . _Bar
  _Baz = _FooBarBaz . _Baz

instance AsFooBarBaz (FooBarBaz a) a

Generate an As class of prisms. Names are selected by prefixing the constructor name with an underscore. Constructors with multiple fields will construct Prisms to tuples of those fields.

makePrisms #

Arguments

:: Name	Type constructor name
-> DecsQ

Generate a Prism for each constructor of a data type. Isos generated when possible. Reviews are created for constructors with existentially quantified constructors and GADTs.

e.g.

data FooBarBaz a
  = Foo Int
  | Bar a
  | Baz Int Char
makePrisms ''FooBarBaz

will create

_Foo :: Prism' (FooBarBaz a) Int
_Bar :: Prism (FooBarBaz a) (FooBarBaz b) a b
_Baz :: Prism' (FooBarBaz a) (Int, Char)

iat :: At m => Index m -> IndexedLens' (Index m) m (Maybe (IxValue m)) #

An indexed version of at.

>>> Map.fromList [(1,"world")] ^@. iat 1
(1,Just "world")

>>> iat 1 %@~ (\i x -> if odd i then Just "hello" else Nothing) $ Map.empty
fromList [(1,"hello")]

>>> iat 2 %@~ (\i x -> if odd i then Just "hello" else Nothing) $ Map.empty
fromList []

sans :: At m => Index m -> m -> m #

Delete the value associated with a key in a Map-like container

sans k = at k .~ Nothing

ixAt :: At m => Index m -> Traversal' m (IxValue m) #

A definition of ix for types with an At instance. This is the default if you don't specify a definition for ix.

iix :: Ixed m => Index m -> IndexedTraversal' (Index m) m (IxValue m) #

An indexed version of ix.

>>> Seq.fromList [a,b,c,d] & iix 2 %@~ f'
fromList [a,b,f' 2 c,d]

>>> Seq.fromList [a,b,c,d] & iix 2 .@~ h
fromList [a,b,h 2,d]

>>> Seq.fromList [a,b,c,d] ^@? iix 2
Just (2,c)

>>> Seq.fromList [] ^@? iix 2
Nothing

icontains :: Contains m => Index m -> IndexedLens' (Index m) m Bool #

An indexed version of contains.

>>> IntSet.fromList [1,2,3,4] ^@. icontains 3
(3,True)

>>> IntSet.fromList [1,2,3,4] ^@. icontains 5
(5,False)

>>> IntSet.fromList [1,2,3,4] & icontains 3 %@~ \i x -> if odd i then not x else x
fromList [1,2,4]

>>> IntSet.fromList [1,2,3,4] & icontains 3 %@~ \i x -> if even i then not x else x
fromList [1,2,3,4]

type family Index s :: Type #

Instances

type Index ByteString
Instance details Defined in Control.Lens.At type Index ByteString = Int
type Index ByteString
Instance details Defined in Control.Lens.At type Index ByteString = Int64
type Index Text
Instance details Defined in Control.Lens.At type Index Text = Int
type Index Text
Instance details Defined in Control.Lens.At type Index Text = Int64
type Index IntSet
Instance details Defined in Control.Lens.At type Index IntSet = Int
type Index [a]
Instance details Defined in Control.Lens.At type Index [a] = Int
type Index (Maybe a)
Instance details Defined in Control.Lens.At type Index (Maybe a) = ()
type Index (Complex a)
Instance details Defined in Control.Lens.At type Index (Complex a) = Int
type Index (Identity a)
Instance details Defined in Control.Lens.At type Index (Identity a) = ()
type Index (NonEmpty a)
Instance details Defined in Control.Lens.At type Index (NonEmpty a) = Int
type Index (IntMap a)
Instance details Defined in Control.Lens.At type Index (IntMap a) = Int
type Index (Tree a)
Instance details Defined in Control.Lens.At type Index (Tree a) = [Int]
type Index (Seq a)
Instance details Defined in Control.Lens.At type Index (Seq a) = Int
type Index (Set a)
Instance details Defined in Control.Lens.At type Index (Set a) = a
type Index (Vector a)
Instance details Defined in Control.Lens.At type Index (Vector a) = Int
type Index (Vector a)
Instance details Defined in Control.Lens.At type Index (Vector a) = Int
type Index (Vector a)
Instance details Defined in Control.Lens.At type Index (Vector a) = Int
type Index (HashSet a)
Instance details Defined in Control.Lens.At type Index (HashSet a) = a
type Index (Vector a)
Instance details Defined in Control.Lens.At type Index (Vector a) = Int
type Index (e -> a)
Instance details Defined in Control.Lens.At type Index (e -> a) = e
type Index (a, b)
Instance details Defined in Control.Lens.At type Index (a, b) = Int
type Index (HashMap k a)
Instance details Defined in Control.Lens.At type Index (HashMap k a) = k
type Index (Map k a)
Instance details Defined in Control.Lens.At type Index (Map k a) = k
type Index (UArray i e)
Instance details Defined in Control.Lens.At type Index (UArray i e) = i
type Index (Array i e)
Instance details Defined in Control.Lens.At type Index (Array i e) = i
type Index (a, b, c)
Instance details Defined in Control.Lens.At type Index (a, b, c) = Int
type Index (a, b, c, d)
Instance details Defined in Control.Lens.At type Index (a, b, c, d) = Int
type Index (a, b, c, d, e)
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e) = Int
type Index (a, b, c, d, e, f)
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e, f) = Int
type Index (a, b, c, d, e, f, g)
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e, f, g) = Int
type Index (a, b, c, d, e, f, g, h)
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e, f, g, h) = Int
type Index (a, b, c, d, e, f, g, h, i)
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e, f, g, h, i) = Int

class Contains m where #

This class provides a simple Lens that lets you view (and modify) information about whether or not a container contains a given Index.

Methods

contains :: Index m -> Lens' m Bool #

>>> IntSet.fromList [1,2,3,4] ^. contains 3
True

>>> IntSet.fromList [1,2,3,4] ^. contains 5
False

>>> IntSet.fromList [1,2,3,4] & contains 3 .~ False
fromList [1,2,4]

Instances

Contains IntSet
Instance details Defined in Control.Lens.At Methods contains :: Index IntSet -> Lens' IntSet Bool #
Ord a => Contains (Set a)
Instance details Defined in Control.Lens.At Methods contains :: Index (Set a) -> Lens' (Set a) Bool #
(Eq a, Hashable a) => Contains (HashSet a)
Instance details Defined in Control.Lens.At Methods contains :: Index (HashSet a) -> Lens' (HashSet a) Bool #

type family IxValue m :: Type #

This provides a common notion of a value at an index that is shared by both Ixed and At.

Instances

type IxValue ByteString
Instance details Defined in Control.Lens.At type IxValue ByteString = Word8
type IxValue ByteString
Instance details Defined in Control.Lens.At type IxValue ByteString = Word8
type IxValue Text
Instance details Defined in Control.Lens.At type IxValue Text = Char
type IxValue Text
Instance details Defined in Control.Lens.At type IxValue Text = Char
type IxValue IntSet
Instance details Defined in Control.Lens.At type IxValue IntSet = ()
type IxValue [a]
Instance details Defined in Control.Lens.At type IxValue [a] = a
type IxValue (Maybe a)
Instance details Defined in Control.Lens.At type IxValue (Maybe a) = a
type IxValue (Identity a)
Instance details Defined in Control.Lens.At type IxValue (Identity a) = a
type IxValue (NonEmpty a)
Instance details Defined in Control.Lens.At type IxValue (NonEmpty a) = a
type IxValue (IntMap a)
Instance details Defined in Control.Lens.At type IxValue (IntMap a) = a
type IxValue (Tree a)
Instance details Defined in Control.Lens.At type IxValue (Tree a) = a
type IxValue (Seq a)
Instance details Defined in Control.Lens.At type IxValue (Seq a) = a
type IxValue (Set k)
Instance details Defined in Control.Lens.At type IxValue (Set k) = ()
type IxValue (Vector a)
Instance details Defined in Control.Lens.At type IxValue (Vector a) = a
type IxValue (Vector a)
Instance details Defined in Control.Lens.At type IxValue (Vector a) = a
type IxValue (Vector a)
Instance details Defined in Control.Lens.At type IxValue (Vector a) = a
type IxValue (HashSet k)
Instance details Defined in Control.Lens.At type IxValue (HashSet k) = ()
type IxValue (Vector a)
Instance details Defined in Control.Lens.At type IxValue (Vector a) = a
type IxValue (e -> a)
Instance details Defined in Control.Lens.At type IxValue (e -> a) = a
type IxValue (a, a2)	`ix` :: `Int` -> `Traversal'` (a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2) = a
type IxValue (HashMap k a)
Instance details Defined in Control.Lens.At type IxValue (HashMap k a) = a
type IxValue (Map k a)
Instance details Defined in Control.Lens.At type IxValue (Map k a) = a
type IxValue (UArray i e)
Instance details Defined in Control.Lens.At type IxValue (UArray i e) = e
type IxValue (Array i e)
Instance details Defined in Control.Lens.At type IxValue (Array i e) = e
type IxValue (a, a2, a3)	`ix` :: `Int` -> `Traversal'` (a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3) = a
type IxValue (a, a2, a3, a4)	`ix` :: `Int` -> `Traversal'` (a,a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4) = a
type IxValue (a, a2, a3, a4, a5)	`ix` :: `Int` -> `Traversal'` (a,a,a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5) = a
type IxValue (a, a2, a3, a4, a5, a6)	`ix` :: `Int` -> `Traversal'` (a,a,a,a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5, a6) = a
type IxValue (a, a2, a3, a4, a5, a6, a7)	`ix` :: `Int` -> `Traversal'` (a,a,a,a,a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5, a6, a7) = a
type IxValue (a, a2, a3, a4, a5, a6, a7, a8)	`ix` :: `Int` -> `Traversal'` (a,a,a,a,a,a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5, a6, a7, a8) = a
type IxValue (a, a2, a3, a4, a5, a6, a7, a8, a9)	`ix` :: `Int` -> `Traversal'` (a,a,a,a,a,a,a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5, a6, a7, a8, a9) = a

class Ixed m where #

Provides a simple Traversal lets you traverse the value at a given key in a Map or element at an ordinal position in a list or Seq.

Minimal complete definition

Nothing

Methods

ix :: Index m -> Traversal' m (IxValue m) #

NB: Setting the value of this Traversal will only set the value in at if it is already present.

If you want to be able to insert missing values, you want at.

>>> Seq.fromList [a,b,c,d] & ix 2 %~ f
fromList [a,b,f c,d]

>>> Seq.fromList [a,b,c,d] & ix 2 .~ e
fromList [a,b,e,d]

>>> Seq.fromList [a,b,c,d] ^? ix 2
Just c

>>> Seq.fromList [] ^? ix 2
Nothing

Instances

Ixed ByteString
Instance details Defined in Control.Lens.At Methods ix :: Index ByteString -> Traversal' ByteString (IxValue ByteString) #
Ixed ByteString
Instance details Defined in Control.Lens.At Methods ix :: Index ByteString -> Traversal' ByteString (IxValue ByteString) #
Ixed Text
Instance details Defined in Control.Lens.At Methods ix :: Index Text -> Traversal' Text (IxValue Text) #
Ixed Text
Instance details Defined in Control.Lens.At Methods ix :: Index Text -> Traversal' Text (IxValue Text) #
Ixed IntSet
Instance details Defined in Control.Lens.At Methods ix :: Index IntSet -> Traversal' IntSet (IxValue IntSet) #
Ixed [a]
Instance details Defined in Control.Lens.At Methods ix :: Index [a] -> Traversal' [a] (IxValue [a]) #
Ixed (Maybe a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Maybe a) -> Traversal' (Maybe a) (IxValue (Maybe a)) #
Ixed (Identity a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Identity a) -> Traversal' (Identity a) (IxValue (Identity a)) #
Ixed (NonEmpty a)
Instance details Defined in Control.Lens.At Methods ix :: Index (NonEmpty a) -> Traversal' (NonEmpty a) (IxValue (NonEmpty a)) #
Ixed (IntMap a)
Instance details Defined in Control.Lens.At Methods ix :: Index (IntMap a) -> Traversal' (IntMap a) (IxValue (IntMap a)) #
Ixed (Tree a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Tree a) -> Traversal' (Tree a) (IxValue (Tree a)) #
Ixed (Seq a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Seq a) -> Traversal' (Seq a) (IxValue (Seq a)) #
Ord k => Ixed (Set k)
Instance details Defined in Control.Lens.At Methods ix :: Index (Set k) -> Traversal' (Set k) (IxValue (Set k)) #
Prim a => Ixed (Vector a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Vector a) -> Traversal' (Vector a) (IxValue (Vector a)) #
Storable a => Ixed (Vector a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Vector a) -> Traversal' (Vector a) (IxValue (Vector a)) #
Unbox a => Ixed (Vector a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Vector a) -> Traversal' (Vector a) (IxValue (Vector a)) #
(Eq k, Hashable k) => Ixed (HashSet k)
Instance details Defined in Control.Lens.At Methods ix :: Index (HashSet k) -> Traversal' (HashSet k) (IxValue (HashSet k)) #
Ixed (Vector a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Vector a) -> Traversal' (Vector a) (IxValue (Vector a)) #
Eq e => Ixed (e -> a)
Instance details Defined in Control.Lens.At Methods ix :: Index (e -> a) -> Traversal' (e -> a) (IxValue (e -> a)) #
a ~ a2 => Ixed (a, a2)
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2) -> Traversal' (a, a2) (IxValue (a, a2)) #
(Eq k, Hashable k) => Ixed (HashMap k a)
Instance details Defined in Control.Lens.At Methods ix :: Index (HashMap k a) -> Traversal' (HashMap k a) (IxValue (HashMap k a)) #
Ord k => Ixed (Map k a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Map k a) -> Traversal' (Map k a) (IxValue (Map k a)) #
(IArray UArray e, Ix i) => Ixed (UArray i e)	arr `!` i ≡ arr `^.` `ix` i arr `//` [(i,e)] ≡ `ix` i `.~` e `$` arr
Instance details Defined in Control.Lens.At Methods ix :: Index (UArray i e) -> Traversal' (UArray i e) (IxValue (UArray i e)) #
Ix i => Ixed (Array i e)	arr `!` i ≡ arr `^.` `ix` i arr `//` [(i,e)] ≡ `ix` i `.~` e `$` arr
Instance details Defined in Control.Lens.At Methods ix :: Index (Array i e) -> Traversal' (Array i e) (IxValue (Array i e)) #
(a ~ a2, a ~ a3) => Ixed (a, a2, a3)
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3) -> Traversal' (a, a2, a3) (IxValue (a, a2, a3)) #
(a ~ a2, a ~ a3, a ~ a4) => Ixed (a, a2, a3, a4)
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3, a4) -> Traversal' (a, a2, a3, a4) (IxValue (a, a2, a3, a4)) #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5) => Ixed (a, a2, a3, a4, a5)
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3, a4, a5) -> Traversal' (a, a2, a3, a4, a5) (IxValue (a, a2, a3, a4, a5)) #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6) => Ixed (a, a2, a3, a4, a5, a6)
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3, a4, a5, a6) -> Traversal' (a, a2, a3, a4, a5, a6) (IxValue (a, a2, a3, a4, a5, a6)) #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7) => Ixed (a, a2, a3, a4, a5, a6, a7)
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3, a4, a5, a6, a7) -> Traversal' (a, a2, a3, a4, a5, a6, a7) (IxValue (a, a2, a3, a4, a5, a6, a7)) #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7, a ~ a8) => Ixed (a, a2, a3, a4, a5, a6, a7, a8)
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3, a4, a5, a6, a7, a8) -> Traversal' (a, a2, a3, a4, a5, a6, a7, a8) (IxValue (a, a2, a3, a4, a5, a6, a7, a8)) #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7, a ~ a8, a ~ a9) => Ixed (a, a2, a3, a4, a5, a6, a7, a8, a9)
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3, a4, a5, a6, a7, a8, a9) -> Traversal' (a, a2, a3, a4, a5, a6, a7, a8, a9) (IxValue (a, a2, a3, a4, a5, a6, a7, a8, a9)) #

class Ixed m => At m where #

At provides a Lens that can be used to read, write or delete the value associated with a key in a Map-like container on an ad hoc basis.

An instance of At should satisfy:

ix k ≡ at k . traverse

Methods

at :: Index m -> Lens' m (Maybe (IxValue m)) #

>>> Map.fromList [(1,"world")] ^.at 1
Just "world"

>>> at 1 ?~ "hello" $ Map.empty
fromList [(1,"hello")]

Note: Map-like containers form a reasonable instance, but not Array-like ones, where you cannot satisfy the Lens laws.

Instances

At IntSet
Instance details Defined in Control.Lens.At Methods at :: Index IntSet -> Lens' IntSet (Maybe (IxValue IntSet)) #
At (Maybe a)
Instance details Defined in Control.Lens.At Methods at :: Index (Maybe a) -> Lens' (Maybe a) (Maybe (IxValue (Maybe a))) #
At (IntMap a)
Instance details Defined in Control.Lens.At Methods at :: Index (IntMap a) -> Lens' (IntMap a) (Maybe (IxValue (IntMap a))) #
Ord k => At (Set k)
Instance details Defined in Control.Lens.At Methods at :: Index (Set k) -> Lens' (Set k) (Maybe (IxValue (Set k))) #
(Eq k, Hashable k) => At (HashSet k)
Instance details Defined in Control.Lens.At Methods at :: Index (HashSet k) -> Lens' (HashSet k) (Maybe (IxValue (HashSet k))) #
(Eq k, Hashable k) => At (HashMap k a)
Instance details Defined in Control.Lens.At Methods at :: Index (HashMap k a) -> Lens' (HashMap k a) (Maybe (IxValue (HashMap k a))) #
Ord k => At (Map k a)
Instance details Defined in Control.Lens.At Methods at :: Index (Map k a) -> Lens' (Map k a) (Maybe (IxValue (Map k a))) #

class Each s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Extract each element of a (potentially monomorphic) container.

Notably, when applied to a tuple, this generalizes both to arbitrary homogeneous tuples.

>>> (1,2,3) & each *~ 10
(10,20,30)

It can also be used on monomorphic containers like Text or ByteString.

>>> over each Char.toUpper ("hello"^.Text.packed)
"HELLO"

>>> ("hello","world") & each.each %~ Char.toUpper
("HELLO","WORLD")

Minimal complete definition

Nothing

Methods

each :: Traversal s t a b #

Instances

(a ~ Word8, b ~ Word8) => Each ByteString ByteString a b	`each` :: `Traversal` `ByteString` `ByteString` `Word8` `Word8`
Instance details Defined in Control.Lens.Each Methods each :: Traversal ByteString ByteString a b #
(a ~ Word8, b ~ Word8) => Each ByteString ByteString a b	`each` :: `Traversal` `ByteString` `ByteString` `Word8` `Word8`
Instance details Defined in Control.Lens.Each Methods each :: Traversal ByteString ByteString a b #
(a ~ Char, b ~ Char) => Each Text Text a b	`each` :: `Traversal` `Text` `Text` `Char` `Char`
Instance details Defined in Control.Lens.Each Methods each :: Traversal Text Text a b #
(a ~ Char, b ~ Char) => Each Text Text a b	`each` :: `Traversal` `Text` `Text` `Char` `Char`
Instance details Defined in Control.Lens.Each Methods each :: Traversal Text Text a b #
Each [a] [b] a b	`each` :: `Traversal` [a] [b] a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal [a] [b] a b #
Each (Maybe a) (Maybe b) a b	`each` :: `Traversal` (`Maybe` a) (`Maybe` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Maybe a) (Maybe b) a b #
Each (Complex a) (Complex b) a b	`each` :: (`RealFloat` a, `RealFloat` b) => `Traversal` (`Complex` a) (`Complex` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Complex a) (Complex b) a b #
Each (Identity a) (Identity b) a b	`each` :: `Traversal` (`Identity` a) (`Identity` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Identity a) (Identity b) a b #
Each (NonEmpty a) (NonEmpty b) a b	`each` :: `Traversal` (NonEmpty a) (NonEmpty b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (NonEmpty a) (NonEmpty b) a b #
Each (IntMap a) (IntMap b) a b	`each` :: `Traversal` (`Map` c a) (`Map` c b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (IntMap a) (IntMap b) a b #
Each (Tree a) (Tree b) a b	`each` :: `Traversal` (`Tree` a) (`Tree` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Tree a) (Tree b) a b #
Each (Seq a) (Seq b) a b	`each` :: `Traversal` (`Seq` a) (`Seq` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Seq a) (Seq b) a b #
(Prim a, Prim b) => Each (Vector a) (Vector b) a b	`each` :: (`Prim` a, `Prim` b) => `Traversal` (`Vector` a) (`Vector` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Vector a) (Vector b) a b #
(Storable a, Storable b) => Each (Vector a) (Vector b) a b	`each` :: (`Storable` a, `Storable` b) => `Traversal` (`Vector` a) (`Vector` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Vector a) (Vector b) a b #
(Unbox a, Unbox b) => Each (Vector a) (Vector b) a b	`each` :: (`Unbox` a, `Unbox` b) => `Traversal` (`Vector` a) (`Vector` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Vector a) (Vector b) a b #
Each (Vector a) (Vector b) a b	`each` :: `Traversal` (`Vector` a) (`Vector` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Vector a) (Vector b) a b #
(a ~ a', b ~ b') => Each (a, a') (b, b') a b	`each` :: `Traversal` (a,a) (b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a') (b, b') a b #
c ~ d => Each (HashMap c a) (HashMap d b) a b	`each` :: `Traversal` (`HashMap` c a) (`HashMap` c b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (HashMap c a) (HashMap d b) a b #
c ~ d => Each (Map c a) (Map d b) a b	`each` :: `Traversal` (`Map` c a) (`Map` c b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Map c a) (Map d b) a b #
(Ix i, IArray UArray a, IArray UArray b, i ~ j) => Each (UArray i a) (UArray j b) a b	`each` :: (`Ix` i, `IArray` `UArray` a, `IArray` `UArray` b) => `Traversal` (`Array` i a) (`Array` i b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (UArray i a) (UArray j b) a b #
(Ix i, i ~ j) => Each (Array i a) (Array j b) a b	`each` :: `Ix` i => `Traversal` (`Array` i a) (`Array` i b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Array i a) (Array j b) a b #
(a ~ a2, a ~ a3, b ~ b2, b ~ b3) => Each (a, a2, a3) (b, b2, b3) a b	`each` :: `Traversal` (a,a,a) (b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3) (b, b2, b3) a b #
(a ~ a2, a ~ a3, a ~ a4, b ~ b2, b ~ b3, b ~ b4) => Each (a, a2, a3, a4) (b, b2, b3, b4) a b	`each` :: `Traversal` (a,a,a,a) (b,b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3, a4) (b, b2, b3, b4) a b #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, b ~ b2, b ~ b3, b ~ b4, b ~ b5) => Each (a, a2, a3, a4, a5) (b, b2, b3, b4, b5) a b	`each` :: `Traversal` (a,a,a,a,a) (b,b,b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3, a4, a5) (b, b2, b3, b4, b5) a b #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, b ~ b2, b ~ b3, b ~ b4, b ~ b5, b ~ b6) => Each (a, a2, a3, a4, a5, a6) (b, b2, b3, b4, b5, b6) a b	`each` :: `Traversal` (a,a,a,a,a,a) (b,b,b,b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3, a4, a5, a6) (b, b2, b3, b4, b5, b6) a b #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7, b ~ b2, b ~ b3, b ~ b4, b ~ b5, b ~ b6, b ~ b7) => Each (a, a2, a3, a4, a5, a6, a7) (b, b2, b3, b4, b5, b6, b7) a b	`each` :: `Traversal` (a,a,a,a,a,a,a) (b,b,b,b,b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3, a4, a5, a6, a7) (b, b2, b3, b4, b5, b6, b7) a b #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7, a ~ a8, b ~ b2, b ~ b3, b ~ b4, b ~ b5, b ~ b6, b ~ b7, b ~ b8) => Each (a, a2, a3, a4, a5, a6, a7, a8) (b, b2, b3, b4, b5, b6, b7, b8) a b	`each` :: `Traversal` (a,a,a,a,a,a,a,a) (b,b,b,b,b,b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3, a4, a5, a6, a7, a8) (b, b2, b3, b4, b5, b6, b7, b8) a b #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7, a ~ a8, a ~ a9, b ~ b2, b ~ b3, b ~ b4, b ~ b5, b ~ b6, b ~ b7, b ~ b8, b ~ b9) => Each (a, a2, a3, a4, a5, a6, a7, a8, a9) (b, b2, b3, b4, b5, b6, b7, b8, b9) a b	`each` :: `Traversal` (a,a,a,a,a,a,a,a,a) (b,b,b,b,b,b,b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3, a4, a5, a6, a7, a8, a9) (b, b2, b3, b4, b5, b6, b7, b8, b9) a b #

gplate :: (Generic a, GPlated a (Rep a)) => Traversal' a a #

Implement plate operation for a type using its Generic instance.

parts :: Plated a => Lens' a [a] #

The original uniplate combinator, implemented in terms of Plated as a Lens.

parts ≡ partsOf plate

The resulting Lens is safer to use as it ignores 'over-application' and deals gracefully with under-application, but it is only a proper Lens if you don't change the list length!

composOpFold :: Plated a => b -> (b -> b -> b) -> (a -> b) -> a -> b #

Fold the immediate children of a Plated container.

composOpFold z c f = foldrOf plate (c . f) z

para :: Plated a => (a -> [r] -> r) -> a -> r #

Perform a fold-like computation on each value, technically a paramorphism.

para ≡ paraOf plate

paraOf :: Getting (Endo [a]) a a -> (a -> [r] -> r) -> a -> r #

Perform a fold-like computation on each value, technically a paramorphism.

paraOf :: Fold a a -> (a -> [r] -> r) -> a -> r

holesOnOf :: Conjoined p => LensLike (Bazaar p r r) s t a b -> Over p (Bazaar p r r) a b r r -> s -> [Pretext p r r t] #

Extract one level of holes from a container in a region specified by one Traversal, using another.

holesOnOf b l ≡ holesOf (b . l)

holesOnOf :: Iso' s a       -> Iso' a a                -> s -> [Pretext (->) a a s]
holesOnOf :: Lens' s a      -> Lens' a a               -> s -> [Pretext (->) a a s]
holesOnOf :: Traversal' s a -> Traversal' a a          -> s -> [Pretext (->) a a s]
holesOnOf :: Lens' s a      -> IndexedLens' i a a      -> s -> [Pretext (Indexed i) a a s]
holesOnOf :: Traversal' s a -> IndexedTraversal' i a a -> s -> [Pretext (Indexed i) a a s]

holesOn :: Conjoined p => Over p (Bazaar p a a) s t a a -> s -> [Pretext p a a t] #

An alias for holesOf, provided for consistency with the other combinators.

holesOn ≡ holesOf

holesOn :: Iso' s a                -> s -> [Pretext (->) a a s]
holesOn :: Lens' s a               -> s -> [Pretext (->) a a s]
holesOn :: Traversal' s a          -> s -> [Pretext (->) a a s]
holesOn :: IndexedLens' i s a      -> s -> [Pretext (Indexed i) a a s]
holesOn :: IndexedTraversal' i s a -> s -> [Pretext (Indexed i) a a s]

holes :: Plated a => a -> [Pretext ((->) :: Type -> Type -> Type) a a a] #

The one-level version of context. This extracts a list of the immediate children as editable contexts.

Given a context you can use pos to see the values, peek at what the structure would be like with an edited result, or simply extract the original structure.

propChildren x = children l x == map pos (holes l x)
propId x = all (== x) [extract w | w <- holes l x]

holes = holesOf plate

contextsOnOf :: ATraversal s t a a -> ATraversal' a a -> s -> [Context a a t] #

Return a list of all of the editable contexts for every location in the structure in an areas indicated by a user supplied Traversal, recursively using another user-supplied Traversal to walk each layer.

contextsOnOf :: Traversal' s a -> Traversal' a a -> s -> [Context a a s]

contextsOn :: Plated a => ATraversal s t a a -> s -> [Context a a t] #

Return a list of all of the editable contexts for every location in the structure in an areas indicated by a user supplied Traversal, recursively using plate.

contextsOn b ≡ contextsOnOf b plate

contextsOn :: Plated a => Traversal' s a -> s -> [Context a a s]

contextsOf :: ATraversal' a a -> a -> [Context a a a] #

Return a list of all of the editable contexts for every location in the structure, recursively, using a user-specified Traversal to walk each layer.

propUniverse l x = universeOf l x == map pos (contextsOf l x)
propId l x = all (== x) [extract w | w <- contextsOf l x]

contextsOf :: Traversal' a a -> a -> [Context a a a]

contexts :: Plated a => a -> [Context a a a] #

Return a list of all of the editable contexts for every location in the structure, recursively.

propUniverse x = universe x == map pos (contexts x)
propId x = all (== x) [extract w | w <- contexts x]

contexts ≡ contextsOf plate

transformMOnOf :: Monad m => LensLike (WrappedMonad m) s t a b -> LensLike (WrappedMonad m) a b a b -> (b -> m b) -> s -> m t #

Transform every element in a tree that lies in a region indicated by a supplied Traversal, walking with a user supplied Traversal in a bottom-up manner with a monadic effect.

transformMOnOf :: Monad m => Traversal' s a -> Traversal' a a -> (a -> m a) -> s -> m s

transformMOf :: Monad m => LensLike (WrappedMonad m) a b a b -> (b -> m b) -> a -> m b #

Transform every element in a tree using a user supplied Traversal in a bottom-up manner with a monadic effect.

transformMOf :: Monad m => Traversal' a a -> (a -> m a) -> a -> m a

transformMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m a) -> s -> m t #

Transform every element in the tree in a region indicated by a supplied Traversal, in a bottom-up manner, monadically.

transformMOn :: (Monad m, Plated a) => Traversal' s a -> (a -> m a) -> s -> m s

transformM :: (Monad m, Plated a) => (a -> m a) -> a -> m a #

Transform every element in the tree, in a bottom-up manner, monadically.

transformOnOf :: ASetter s t a b -> ASetter a b a b -> (b -> b) -> s -> t #

Transform every element in a region indicated by a Setter by recursively applying another Setter in a bottom-up manner.

transformOnOf :: Setter' s a -> Traversal' a a -> (a -> a) -> s -> s
transformOnOf :: Setter' s a -> Setter' a a    -> (a -> a) -> s -> s

transformOf :: ASetter a b a b -> (b -> b) -> a -> b #

Transform every element by recursively applying a given Setter in a bottom-up manner.

transformOf :: Traversal' a a -> (a -> a) -> a -> a
transformOf :: Setter' a a    -> (a -> a) -> a -> a

transformOn :: Plated a => ASetter s t a a -> (a -> a) -> s -> t #

Transform every element in the tree in a bottom-up manner over a region indicated by a Setter.

transformOn :: Plated a => Traversal' s a -> (a -> a) -> s -> s
transformOn :: Plated a => Setter' s a    -> (a -> a) -> s -> s

transform :: Plated a => (a -> a) -> a -> a #

Transform every element in the tree, in a bottom-up manner.

For example, replacing negative literals with literals:

negLits = transform $ \x -> case x of
  Neg (Lit i) -> Lit (negate i)
  _           -> x

cosmosOnOf :: (Applicative f, Contravariant f) => LensLike' f s a -> LensLike' f a a -> LensLike' f s a #

Given a Fold that knows how to locate immediate children, fold all of the transitive descendants of a node, including itself that lie in a region indicated by another Fold.

cosmosOnOf :: Fold s a -> Fold a a -> Fold s a

cosmosOn :: (Applicative f, Contravariant f, Plated a) => LensLike' f s a -> LensLike' f s a #

Given a Fold that knows how to find Plated parts of a container fold them and all of their descendants, recursively.

cosmosOn :: Plated a => Fold s a -> Fold s a

cosmosOf :: (Applicative f, Contravariant f) => LensLike' f a a -> LensLike' f a a #

Given a Fold that knows how to locate immediate children, fold all of the transitive descendants of a node, including itself.

cosmosOf :: Fold a a -> Fold a a

cosmos :: Plated a => Fold a a #

Fold over all transitive descendants of a Plated container, including itself.

universeOnOf :: Getting [a] s a -> Getting [a] a a -> s -> [a] #

Given a Fold that knows how to locate immediate children, retrieve all of the transitive descendants of a node, including itself that lie in a region indicated by another Fold.

toListOf l ≡ universeOnOf l ignored

universeOn :: Plated a => Getting [a] s a -> s -> [a] #

Given a Fold that knows how to find Plated parts of a container retrieve them and all of their descendants, recursively.

universeOf :: Getting [a] a a -> a -> [a] #

Given a Fold that knows how to locate immediate children, retrieve all of the transitive descendants of a node, including itself.

universeOf :: Fold a a -> a -> [a]

universe :: Plated a => a -> [a] #

Retrieve all of the transitive descendants of a Plated container, including itself.

rewriteMOnOf :: Monad m => LensLike (WrappedMonad m) s t a b -> LensLike (WrappedMonad m) a b a b -> (b -> m (Maybe a)) -> s -> m t #

Rewrite by applying a monadic rule everywhere inside of a structure located by a user-specified Traversal, using a user-specified Traversal for recursion. Ensures that the rule cannot be applied anywhere in the result.

rewriteMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m (Maybe a)) -> s -> m t #

Rewrite by applying a monadic rule everywhere inside of a structure located by a user-specified Traversal. Ensures that the rule cannot be applied anywhere in the result.

rewriteMOf :: Monad m => LensLike (WrappedMonad m) a b a b -> (b -> m (Maybe a)) -> a -> m b #

Rewrite by applying a monadic rule everywhere you recursing with a user-specified Traversal. Ensures that the rule cannot be applied anywhere in the result.

rewriteM :: (Monad m, Plated a) => (a -> m (Maybe a)) -> a -> m a #

Rewrite by applying a monadic rule everywhere you can. Ensures that the rule cannot be applied anywhere in the result.

rewriteOnOf :: ASetter s t a b -> ASetter a b a b -> (b -> Maybe a) -> s -> t #

Rewrite recursively over part of a larger structure using a specified Setter.

rewriteOnOf :: Iso' s a       -> Iso' a a       -> (a -> Maybe a) -> s -> s
rewriteOnOf :: Lens' s a      -> Lens' a a      -> (a -> Maybe a) -> s -> s
rewriteOnOf :: Traversal' s a -> Traversal' a a -> (a -> Maybe a) -> s -> s
rewriteOnOf :: Setter' s a    -> Setter' a a    -> (a -> Maybe a) -> s -> s

rewriteOn :: Plated a => ASetter s t a a -> (a -> Maybe a) -> s -> t #

Rewrite recursively over part of a larger structure.

rewriteOn :: Plated a => Iso' s a       -> (a -> Maybe a) -> s -> s
rewriteOn :: Plated a => Lens' s a      -> (a -> Maybe a) -> s -> s
rewriteOn :: Plated a => Traversal' s a -> (a -> Maybe a) -> s -> s
rewriteOn :: Plated a => ASetter' s a   -> (a -> Maybe a) -> s -> s

rewriteOf :: ASetter a b a b -> (b -> Maybe a) -> a -> b #

Rewrite by applying a rule everywhere you can. Ensures that the rule cannot be applied anywhere in the result:

propRewriteOf l r x = all (isNothing . r) (universeOf l (rewriteOf l r x))

Usually transformOf is more appropriate, but rewriteOf can give better compositionality. Given two single transformations f and g, you can construct a -> f a mplus g a which performs both rewrites until a fixed point.

rewriteOf :: Iso' a a       -> (a -> Maybe a) -> a -> a
rewriteOf :: Lens' a a      -> (a -> Maybe a) -> a -> a
rewriteOf :: Traversal' a a -> (a -> Maybe a) -> a -> a
rewriteOf :: Setter' a a    -> (a -> Maybe a) -> a -> a

rewrite :: Plated a => (a -> Maybe a) -> a -> a #

Rewrite by applying a rule everywhere you can. Ensures that the rule cannot be applied anywhere in the result:

propRewrite r x = all (isNothing . r) (universe (rewrite r x))

Usually transform is more appropriate, but rewrite can give better compositionality. Given two single transformations f and g, you can construct a -> f a mplus g a which performs both rewrites until a fixed point.

children :: Plated a => a -> [a] #

Extract the immediate descendants of a Plated container.

children ≡ toListOf plate

deep :: (Conjoined p, Applicative f, Plated s) => Traversing p f s s a b -> Over p f s s a b #

Try to apply a traversal to all transitive descendants of a Plated container, but do not recurse through matching descendants.

deep :: Plated s => Fold s a                 -> Fold s a
deep :: Plated s => IndexedFold s a          -> IndexedFold s a
deep :: Plated s => Traversal s s a b        -> Traversal s s a b
deep :: Plated s => IndexedTraversal s s a b -> IndexedTraversal s s a b

(...) :: (Applicative f, Plated c) => LensLike f s t c c -> Over p f c c a b -> Over p f s t a b infixr 9 #

Compose through a plate

class Plated a where #

A Plated type is one where we know how to extract its immediate self-similar children.

Example 1:

import Control.Applicative
import Control.Lens
import Control.Lens.Plated
import Data.Data
import Data.Data.Lens (uniplate)

data Expr
  = Val Int
  | Neg Expr
  | Add Expr Expr
  deriving (Eq,Ord,Show,Read,Data,Typeable)

instance Plated Expr where
  plate f (Neg e) = Neg <$> f e
  plate f (Add a b) = Add <$> f a <*> f b
  plate _ a = pure a

or

instance Plated Expr where
  plate = uniplate

Example 2:

import Control.Applicative
import Control.Lens
import Control.Lens.Plated
import Data.Data
import Data.Data.Lens (uniplate)

data Tree a
  = Bin (Tree a) (Tree a)
  | Tip a
  deriving (Eq,Ord,Show,Read,Data,Typeable)

instance Plated (Tree a) where
  plate f (Bin l r) = Bin <$> f l <*> f r
  plate _ t = pure t

or

instance Data a => Plated (Tree a) where
  plate = uniplate

Note the big distinction between these two implementations.

The former will only treat children directly in this tree as descendents, the latter will treat trees contained in the values under the tips also as descendants!

When in doubt, pick a Traversal and just use the various ...Of combinators rather than pollute Plated with orphan instances!

If you want to find something unplated and non-recursive with biplate use the ...OnOf variant with ignored, though those usecases are much better served in most cases by using the existing Lens combinators! e.g.

toListOf biplate ≡ universeOnOf biplate ignored

This same ability to explicitly pass the Traversal in question is why there is no analogue to uniplate's Biplate.

Moreover, since we can allow custom traversals, we implement reasonable defaults for polymorphic data types, that only traverse into themselves, and not their polymorphic arguments.

Minimal complete definition

Nothing

Methods

plate :: Traversal' a a #

Traversal of the immediate children of this structure.

If you're using GHC 7.2 or newer and your type has a Data instance, plate will default to uniplate and you can choose to not override it with your own definition.

Instances

Plated Exp
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' Exp Exp #
Plated Pat
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' Pat Pat #
Plated Type
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' Type Type #
Plated Dec
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' Dec Dec #
Plated Con
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' Con Con #
Plated Stmt
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' Stmt Stmt #
Plated [a]
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' [a] [a] #
Plated (Tree a)
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' (Tree a) (Tree a) #
Traversable f => Plated (Cofree f a)
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' (Cofree f a) (Cofree f a) #
Traversable f => Plated (F f a)
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' (F f a) (F f a) #
Traversable f => Plated (Free f a)
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' (Free f a) (Free f a) #
(Traversable f, Traversable m) => Plated (FreeT f m a)
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' (FreeT f m a) (FreeT f m a) #
(Traversable f, Traversable w) => Plated (CofreeT f w a)
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' (CofreeT f w a) (CofreeT f w a) #

class GPlated a (g :: Type -> Type) #

Minimal complete definition

gplate'

Instances

GPlated a (V1 :: Type -> Type)
Instance details Defined in Control.Lens.Plated Methods gplate' :: Traversal' (V1 p) a
GPlated a (U1 :: Type -> Type)
Instance details Defined in Control.Lens.Plated Methods gplate' :: Traversal' (U1 p) a
GPlated a (K1 i a :: Type -> Type)
Instance details Defined in Control.Lens.Plated Methods gplate' :: Traversal' (K1 i a p) a
GPlated a (K1 i b :: Type -> Type)
Instance details Defined in Control.Lens.Plated Methods gplate' :: Traversal' (K1 i b p) a
(GPlated a f, GPlated a g) => GPlated a (f :+: g)
Instance details Defined in Control.Lens.Plated Methods gplate' :: Traversal' ((f :+: g) p) a
(GPlated a f, GPlated a g) => GPlated a (f :*: g)
Instance details Defined in Control.Lens.Plated Methods gplate' :: Traversal' ((f :*: g) p) a
GPlated a f => GPlated a (M1 i c f)
Instance details Defined in Control.Lens.Plated Methods gplate' :: Traversal' (M1 i c f p) a

type family Zoomed (m :: Type -> Type) :: Type -> Type -> Type #

This type family is used by Zoom to describe the common effect type.

Instances

type Zoomed (MaybeT m)
Instance details Defined in Control.Lens.Zoom type Zoomed (MaybeT m) = FocusingMay (Zoomed m)
type Zoomed (ListT m)
Instance details Defined in Control.Lens.Zoom type Zoomed (ListT m) = FocusingOn [] (Zoomed m)
type Zoomed (IdentityT m)
Instance details Defined in Control.Lens.Zoom type Zoomed (IdentityT m) = Zoomed m
type Zoomed (ExceptT e m)
Instance details Defined in Control.Lens.Zoom type Zoomed (ExceptT e m) = FocusingErr e (Zoomed m)
type Zoomed (FreeT f m)
Instance details Defined in Control.Lens.Zoom type Zoomed (FreeT f m) = FocusingFree f m (Zoomed m)
type Zoomed (ErrorT e m)
Instance details Defined in Control.Lens.Zoom type Zoomed (ErrorT e m) = FocusingErr e (Zoomed m)
type Zoomed (StateT s z)
Instance details Defined in Control.Lens.Zoom type Zoomed (StateT s z) = Focusing z
type Zoomed (StateT s z)
Instance details Defined in Control.Lens.Zoom type Zoomed (StateT s z) = Focusing z
type Zoomed (WriterT w m)
Instance details Defined in Control.Lens.Zoom type Zoomed (WriterT w m) = FocusingPlus w (Zoomed m)
type Zoomed (WriterT w m)
Instance details Defined in Control.Lens.Zoom type Zoomed (WriterT w m) = FocusingPlus w (Zoomed m)
type Zoomed (ReaderT e m)
Instance details Defined in Control.Lens.Zoom type Zoomed (ReaderT e m) = Zoomed m
type Zoomed (RWST r w s z)
Instance details Defined in Control.Lens.Zoom type Zoomed (RWST r w s z) = FocusingWith w z
type Zoomed (RWST r w s z)
Instance details Defined in Control.Lens.Zoom type Zoomed (RWST r w s z) = FocusingWith w z

type family Magnified (m :: Type -> Type) :: Type -> Type -> Type #

This type family is used by Magnify to describe the common effect type.

Instances

type Magnified (IdentityT m)
Instance details Defined in Control.Lens.Zoom type Magnified (IdentityT m) = Magnified m
type Magnified ((->) b :: Type -> Type)
Instance details Defined in Control.Lens.Zoom type Magnified ((->) b :: Type -> Type) = (Const :: Type -> Type -> Type)
type Magnified (ReaderT b m)
Instance details Defined in Control.Lens.Zoom type Magnified (ReaderT b m) = Effect m
type Magnified (RWST a w s m)
Instance details Defined in Control.Lens.Zoom type Magnified (RWST a w s m) = EffectRWS w s m
type Magnified (RWST a w s m)
Instance details Defined in Control.Lens.Zoom type Magnified (RWST a w s m) = EffectRWS w s m

class (MonadState s m, MonadState t n) => Zoom (m :: Type -> Type) (n :: Type -> Type) s t | m -> s, n -> t, m t -> n, n s -> m where #

This class allows us to use zoom in, changing the State supplied by many different Monad transformers, potentially quite deep in a Monad transformer stack.

Methods

zoom :: LensLike' (Zoomed m c) t s -> m c -> n c infixr 2 #

Run a monadic action in a larger State than it was defined in, using a Lens' or Traversal'.

This is commonly used to lift actions in a simpler State Monad into a State Monad with a larger State type.

When applied to a Traversal' over multiple values, the actions for each target are executed sequentially and the results are aggregated.

This can be used to edit pretty much any Monad transformer stack with a State in it!

>>> flip State.evalState (a,b) $ zoom _1 $ use id
a

>>> flip State.execState (a,b) $ zoom _1 $ id .= c
(c,b)

>>> flip State.execState [(a,b),(c,d)] $ zoom traverse $ _2 %= f
[(a,f b),(c,f d)]

>>> flip State.runState [(a,b),(c,d)] $ zoom traverse $ _2 <%= f
(f b <> f d <> mempty,[(a,f b),(c,f d)])

>>> flip State.evalState (a,b) $ zoom both (use id)
a <> b

zoom :: Monad m             => Lens' s t      -> StateT t m a -> StateT s m a
zoom :: (Monad m, Monoid c) => Traversal' s t -> StateT t m c -> StateT s m c
zoom :: (Monad m, Monoid w)             => Lens' s t      -> RWST r w t m c -> RWST r w s m c
zoom :: (Monad m, Monoid w, Monoid c) => Traversal' s t -> RWST r w t m c -> RWST r w s m c
zoom :: (Monad m, Monoid w, Error e)  => Lens' s t      -> ErrorT e (RWST r w t m) c -> ErrorT e (RWST r w s m) c
zoom :: (Monad m, Monoid w, Monoid c, Error e) => Traversal' s t -> ErrorT e (RWST r w t m) c -> ErrorT e (RWST r w s m) c
...

Instances

Zoom m n s t => Zoom (MaybeT m) (MaybeT n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (MaybeT m) c) t s -> MaybeT m c -> MaybeT n c #
Zoom m n s t => Zoom (ListT m) (ListT n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (ListT m) c) t s -> ListT m c -> ListT n c #
Zoom m n s t => Zoom (IdentityT m) (IdentityT n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (IdentityT m) c) t s -> IdentityT m c -> IdentityT n c #
Zoom m n s t => Zoom (ExceptT e m) (ExceptT e n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (ExceptT e m) c) t s -> ExceptT e m c -> ExceptT e n c #
(Functor f, Zoom m n s t) => Zoom (FreeT f m) (FreeT f n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (FreeT f m) c) t s -> FreeT f m c -> FreeT f n c #
(Error e, Zoom m n s t) => Zoom (ErrorT e m) (ErrorT e n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (ErrorT e m) c) t s -> ErrorT e m c -> ErrorT e n c #
Monad z => Zoom (StateT s z) (StateT t z) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (StateT s z) c) t s -> StateT s z c -> StateT t z c #
Monad z => Zoom (StateT s z) (StateT t z) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (StateT s z) c) t s -> StateT s z c -> StateT t z c #
(Monoid w, Zoom m n s t) => Zoom (WriterT w m) (WriterT w n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (WriterT w m) c) t s -> WriterT w m c -> WriterT w n c #
(Monoid w, Zoom m n s t) => Zoom (WriterT w m) (WriterT w n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (WriterT w m) c) t s -> WriterT w m c -> WriterT w n c #
Zoom m n s t => Zoom (ReaderT e m) (ReaderT e n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (ReaderT e m) c) t s -> ReaderT e m c -> ReaderT e n c #
(Monoid w, Monad z) => Zoom (RWST r w s z) (RWST r w t z) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (RWST r w s z) c) t s -> RWST r w s z c -> RWST r w t z c #
(Monoid w, Monad z) => Zoom (RWST r w s z) (RWST r w t z) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (RWST r w s z) c) t s -> RWST r w s z c -> RWST r w t z c #

class (Magnified m ~ Magnified n, MonadReader b m, MonadReader a n) => Magnify (m :: Type -> Type) (n :: Type -> Type) b a | m -> b, n -> a, m a -> n, n b -> m where #

This class allows us to use magnify part of the environment, changing the environment supplied by many different Monad transformers. Unlike zoom this can change the environment of a deeply nested Monad transformer.

Also, unlike zoom, this can be used with any valid Getter, but cannot be used with a Traversal or Fold.

Methods

magnify :: LensLike' (Magnified m c) a b -> m c -> n c infixr 2 #

Run a monadic action in a larger environment than it was defined in, using a Getter.

This acts like local, but can in many cases change the type of the environment as well.

This is commonly used to lift actions in a simpler Reader Monad into a Monad with a larger environment type.

This can be used to edit pretty much any Monad transformer stack with an environment in it:

>>> (1,2) & magnify _2 (+1)
3

>>> flip Reader.runReader (1,2) $ magnify _1 Reader.ask
1

>>> flip Reader.runReader (1,2,[10..20]) $ magnify (_3._tail) Reader.ask
[11,12,13,14,15,16,17,18,19,20]

magnify :: Getter s a -> (a -> r) -> s -> r
magnify :: Monoid r => Fold s a   -> (a -> r) -> s -> r

magnify :: Monoid w                 => Getter s t -> RWS t w st c -> RWS s w st c
magnify :: (Monoid w, Monoid c) => Fold s a   -> RWS a w st c -> RWS s w st c
...

Instances

Magnify m n b a => Magnify (IdentityT m) (IdentityT n) b a
Instance details Defined in Control.Lens.Zoom Methods magnify :: LensLike' (Magnified (IdentityT m) c) a b -> IdentityT m c -> IdentityT n c #
Magnify ((->) b :: Type -> Type) ((->) a :: Type -> Type) b a	`magnify` = `views`
Instance details Defined in Control.Lens.Zoom Methods magnify :: LensLike' (Magnified ((->) b) c) a b -> (b -> c) -> a -> c #
Monad m => Magnify (ReaderT b m) (ReaderT a m) b a
Instance details Defined in Control.Lens.Zoom Methods magnify :: LensLike' (Magnified (ReaderT b m) c) a b -> ReaderT b m c -> ReaderT a m c #
(Monad m, Monoid w) => Magnify (RWST b w s m) (RWST a w s m) b a
Instance details Defined in Control.Lens.Zoom Methods magnify :: LensLike' (Magnified (RWST b w s m) c) a b -> RWST b w s m c -> RWST a w s m c #
(Monad m, Monoid w) => Magnify (RWST b w s m) (RWST a w s m) b a
Instance details Defined in Control.Lens.Zoom Methods magnify :: LensLike' (Magnified (RWST b w s m) c) a b -> RWST b w s m c -> RWST a w s m c #

alaf :: (Functor f, Functor g, Rewrapping s t) => (Unwrapped s -> s) -> (f t -> g s) -> f (Unwrapped t) -> g (Unwrapped s) #

This combinator is based on ala' from Conor McBride's work on Epigram.

As with _Wrapping, the user supplied function for the newtype is ignored.

alaf :: Rewrapping s t => (Unwrapped s -> s) -> ((r ->  t) -> e -> s) -> (r -> Unwrapped t) -> e -> Unwrapped s

>>> alaf Sum foldMap Prelude.length ["hello","world"]
10

ala :: (Functor f, Rewrapping s t) => (Unwrapped s -> s) -> ((Unwrapped t -> t) -> f s) -> f (Unwrapped s) #

This combinator is based on ala from Conor McBride's work on Epigram.

As with _Wrapping, the user supplied function for the newtype is ignored.

>>> ala Sum foldMap [1,2,3,4]
10

>>> ala All foldMap [True,True]
True

>>> ala All foldMap [True,False]
False

>>> ala Any foldMap [False,False]
False

>>> ala Any foldMap [True,False]
True

>>> ala Product foldMap [1,2,3,4]
24

You may want to think of this combinator as having the following, simpler, type.

ala :: Rewrapping s t => (Unwrapped s -> s) -> ((Unwrapped t -> t) -> e -> s) -> e -> Unwrapped s

_Unwrapping :: Rewrapping s t => (Unwrapped s -> s) -> Iso (Unwrapped t) (Unwrapped s) t s #

This is a convenient version of _Unwrapped with an argument that's ignored.

The user supplied function is ignored, merely its types are used.

_Wrapping :: Rewrapping s t => (Unwrapped s -> s) -> Iso s t (Unwrapped s) (Unwrapped t) #

This is a convenient version of _Wrapped with an argument that's ignored.

The user supplied function is ignored, merely its types are used.

_Unwrapping' :: Wrapped s => (Unwrapped s -> s) -> Iso' (Unwrapped s) s #

This is a convenient version of _Wrapped with an argument that's ignored.

The user supplied function is ignored, merely its type is used.

_Wrapping' :: Wrapped s => (Unwrapped s -> s) -> Iso' s (Unwrapped s) #

This is a convenient version of _Wrapped with an argument that's ignored.

The user supplied function is ignored, merely its type is used.

op :: Wrapped s => (Unwrapped s -> s) -> s -> Unwrapped s #

Given the constructor for a Wrapped type, return a deconstructor that is its inverse.

Assuming the Wrapped instance is legal, these laws hold:

op f . f ≡ id
f . op f ≡ id

>>> op Identity (Identity 4)
4

>>> op Const (Const "hello")
"hello"

_Unwrapped :: Rewrapping s t => Iso (Unwrapped t) (Unwrapped s) t s #

_Wrapped :: Rewrapping s t => Iso s t (Unwrapped s) (Unwrapped t) #

Work under a newtype wrapper.

>>> Const "hello" & _Wrapped %~ Prelude.length & getConst
5

_Wrapped   ≡ from _Unwrapped
_Unwrapped ≡ from _Wrapped

_Unwrapped' :: Wrapped s => Iso' (Unwrapped s) s #

_GWrapped' :: (Generic s, D1 d (C1 c (S1 s' (Rec0 a))) ~ Rep s, Unwrapped s ~ GUnwrapped (Rep s)) => Iso' s (Unwrapped s) #

Implement the _Wrapped operation for a type using its Generic instance.

pattern Wrapped :: forall s. Rewrapped s s => Unwrapped s -> s #

pattern Unwrapped :: forall t. Rewrapped t t => t -> Unwrapped t #

class Wrapped s where #

Wrapped provides isomorphisms to wrap and unwrap newtypes or data types with one constructor.

Minimal complete definition

Nothing

Associated Types

type Unwrapped s :: Type #

Methods

_Wrapped' :: Iso' s (Unwrapped s) #

An isomorphism between s and a.

If your type has a Generic instance, _Wrapped' will default to _GWrapped', and you can choose to not override it with your own definition.

Instances

Wrapped PatternMatchFail
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped PatternMatchFail :: Type # Methods _Wrapped' :: Iso' PatternMatchFail (Unwrapped PatternMatchFail) #
Wrapped RecSelError
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped RecSelError :: Type # Methods _Wrapped' :: Iso' RecSelError (Unwrapped RecSelError) #
Wrapped RecConError
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped RecConError :: Type # Methods _Wrapped' :: Iso' RecConError (Unwrapped RecConError) #
Wrapped RecUpdError
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped RecUpdError :: Type # Methods _Wrapped' :: Iso' RecUpdError (Unwrapped RecUpdError) #
Wrapped NoMethodError
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped NoMethodError :: Type # Methods _Wrapped' :: Iso' NoMethodError (Unwrapped NoMethodError) #
Wrapped TypeError
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped TypeError :: Type # Methods _Wrapped' :: Iso' TypeError (Unwrapped TypeError) #
Wrapped CDev
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CDev :: Type # Methods _Wrapped' :: Iso' CDev (Unwrapped CDev) #
Wrapped CIno
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CIno :: Type # Methods _Wrapped' :: Iso' CIno (Unwrapped CIno) #
Wrapped CMode
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CMode :: Type # Methods _Wrapped' :: Iso' CMode (Unwrapped CMode) #
Wrapped COff
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped COff :: Type # Methods _Wrapped' :: Iso' COff (Unwrapped COff) #
Wrapped CPid
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CPid :: Type # Methods _Wrapped' :: Iso' CPid (Unwrapped CPid) #
Wrapped CSsize
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CSsize :: Type # Methods _Wrapped' :: Iso' CSsize (Unwrapped CSsize) #
Wrapped CGid
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CGid :: Type # Methods _Wrapped' :: Iso' CGid (Unwrapped CGid) #
Wrapped CNlink
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CNlink :: Type # Methods _Wrapped' :: Iso' CNlink (Unwrapped CNlink) #
Wrapped CUid
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUid :: Type # Methods _Wrapped' :: Iso' CUid (Unwrapped CUid) #
Wrapped CCc
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CCc :: Type # Methods _Wrapped' :: Iso' CCc (Unwrapped CCc) #
Wrapped CSpeed
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CSpeed :: Type # Methods _Wrapped' :: Iso' CSpeed (Unwrapped CSpeed) #
Wrapped CTcflag
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CTcflag :: Type # Methods _Wrapped' :: Iso' CTcflag (Unwrapped CTcflag) #
Wrapped CRLim
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CRLim :: Type # Methods _Wrapped' :: Iso' CRLim (Unwrapped CRLim) #
Wrapped CBlkSize
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CBlkSize :: Type # Methods _Wrapped' :: Iso' CBlkSize (Unwrapped CBlkSize) #
Wrapped CBlkCnt
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CBlkCnt :: Type # Methods _Wrapped' :: Iso' CBlkCnt (Unwrapped CBlkCnt) #
Wrapped CClockId
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CClockId :: Type # Methods _Wrapped' :: Iso' CClockId (Unwrapped CClockId) #
Wrapped CFsBlkCnt
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CFsBlkCnt :: Type # Methods _Wrapped' :: Iso' CFsBlkCnt (Unwrapped CFsBlkCnt) #
Wrapped CFsFilCnt
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CFsFilCnt :: Type # Methods _Wrapped' :: Iso' CFsFilCnt (Unwrapped CFsFilCnt) #
Wrapped CId
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CId :: Type # Methods _Wrapped' :: Iso' CId (Unwrapped CId) #
Wrapped CKey
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CKey :: Type # Methods _Wrapped' :: Iso' CKey (Unwrapped CKey) #
Wrapped CTimer
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CTimer :: Type # Methods _Wrapped' :: Iso' CTimer (Unwrapped CTimer) #
Wrapped Fd
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped Fd :: Type # Methods _Wrapped' :: Iso' Fd (Unwrapped Fd) #
Wrapped Errno
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped Errno :: Type # Methods _Wrapped' :: Iso' Errno (Unwrapped Errno) #
Wrapped CompactionFailed
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CompactionFailed :: Type # Methods _Wrapped' :: Iso' CompactionFailed (Unwrapped CompactionFailed) #
Wrapped AssertionFailed
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped AssertionFailed :: Type # Methods _Wrapped' :: Iso' AssertionFailed (Unwrapped AssertionFailed) #
Wrapped ErrorCall
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped ErrorCall :: Type # Methods _Wrapped' :: Iso' ErrorCall (Unwrapped ErrorCall) #
Wrapped All
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped All :: Type # Methods _Wrapped' :: Iso' All (Unwrapped All) #
Wrapped Any
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped Any :: Type # Methods _Wrapped' :: Iso' Any (Unwrapped Any) #
Wrapped CChar
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CChar :: Type # Methods _Wrapped' :: Iso' CChar (Unwrapped CChar) #
Wrapped CSChar
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CSChar :: Type # Methods _Wrapped' :: Iso' CSChar (Unwrapped CSChar) #
Wrapped CUChar
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUChar :: Type # Methods _Wrapped' :: Iso' CUChar (Unwrapped CUChar) #
Wrapped CShort
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CShort :: Type # Methods _Wrapped' :: Iso' CShort (Unwrapped CShort) #
Wrapped CUShort
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUShort :: Type # Methods _Wrapped' :: Iso' CUShort (Unwrapped CUShort) #
Wrapped CInt
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CInt :: Type # Methods _Wrapped' :: Iso' CInt (Unwrapped CInt) #
Wrapped CUInt
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUInt :: Type # Methods _Wrapped' :: Iso' CUInt (Unwrapped CUInt) #
Wrapped CLong
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CLong :: Type # Methods _Wrapped' :: Iso' CLong (Unwrapped CLong) #
Wrapped CULong
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CULong :: Type # Methods _Wrapped' :: Iso' CULong (Unwrapped CULong) #
Wrapped CLLong
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CLLong :: Type # Methods _Wrapped' :: Iso' CLLong (Unwrapped CLLong) #
Wrapped CULLong
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CULLong :: Type # Methods _Wrapped' :: Iso' CULLong (Unwrapped CULLong) #
Wrapped CBool
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CBool :: Type # Methods _Wrapped' :: Iso' CBool (Unwrapped CBool) #
Wrapped CFloat
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CFloat :: Type # Methods _Wrapped' :: Iso' CFloat (Unwrapped CFloat) #
Wrapped CDouble
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CDouble :: Type # Methods _Wrapped' :: Iso' CDouble (Unwrapped CDouble) #
Wrapped CPtrdiff
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CPtrdiff :: Type # Methods _Wrapped' :: Iso' CPtrdiff (Unwrapped CPtrdiff) #
Wrapped CSize
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CSize :: Type # Methods _Wrapped' :: Iso' CSize (Unwrapped CSize) #
Wrapped CWchar
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CWchar :: Type # Methods _Wrapped' :: Iso' CWchar (Unwrapped CWchar) #
Wrapped CSigAtomic
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CSigAtomic :: Type # Methods _Wrapped' :: Iso' CSigAtomic (Unwrapped CSigAtomic) #
Wrapped CClock
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CClock :: Type # Methods _Wrapped' :: Iso' CClock (Unwrapped CClock) #
Wrapped CTime
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CTime :: Type # Methods _Wrapped' :: Iso' CTime (Unwrapped CTime) #
Wrapped CUSeconds
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUSeconds :: Type # Methods _Wrapped' :: Iso' CUSeconds (Unwrapped CUSeconds) #
Wrapped CSUSeconds
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CSUSeconds :: Type # Methods _Wrapped' :: Iso' CSUSeconds (Unwrapped CSUSeconds) #
Wrapped CIntPtr
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CIntPtr :: Type # Methods _Wrapped' :: Iso' CIntPtr (Unwrapped CIntPtr) #
Wrapped CUIntPtr
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUIntPtr :: Type # Methods _Wrapped' :: Iso' CUIntPtr (Unwrapped CUIntPtr) #
Wrapped CIntMax
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CIntMax :: Type # Methods _Wrapped' :: Iso' CIntMax (Unwrapped CIntMax) #
Wrapped CUIntMax
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUIntMax :: Type # Methods _Wrapped' :: Iso' CUIntMax (Unwrapped CUIntMax) #
Wrapped IntSet
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped IntSet :: Type # Methods _Wrapped' :: Iso' IntSet (Unwrapped IntSet) #
Wrapped (Par1 p)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Par1 p) :: Type # Methods _Wrapped' :: Iso' (Par1 p) (Unwrapped (Par1 p)) #
Wrapped (Predicate a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Predicate a) :: Type # Methods _Wrapped' :: Iso' (Predicate a) (Unwrapped (Predicate a)) #
Wrapped (Comparison a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Comparison a) :: Type # Methods _Wrapped' :: Iso' (Comparison a) (Unwrapped (Comparison a)) #
Wrapped (Equivalence a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Equivalence a) :: Type # Methods _Wrapped' :: Iso' (Equivalence a) (Unwrapped (Equivalence a)) #
Wrapped (Min a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Min a) :: Type # Methods _Wrapped' :: Iso' (Min a) (Unwrapped (Min a)) #
Wrapped (Max a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Max a) :: Type # Methods _Wrapped' :: Iso' (Max a) (Unwrapped (Max a)) #
Wrapped (First a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (First a) :: Type # Methods _Wrapped' :: Iso' (First a) (Unwrapped (First a)) #
Wrapped (Last a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Last a) :: Type # Methods _Wrapped' :: Iso' (Last a) (Unwrapped (Last a)) #
Wrapped (WrappedMonoid a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedMonoid a) :: Type # Methods _Wrapped' :: Iso' (WrappedMonoid a) (Unwrapped (WrappedMonoid a)) #
Wrapped (Option a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Option a) :: Type # Methods _Wrapped' :: Iso' (Option a) (Unwrapped (Option a)) #
Wrapped (ZipList a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ZipList a) :: Type # Methods _Wrapped' :: Iso' (ZipList a) (Unwrapped (ZipList a)) #
Wrapped (Identity a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Identity a) :: Type # Methods _Wrapped' :: Iso' (Identity a) (Unwrapped (Identity a)) #
Wrapped (First a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (First a) :: Type # Methods _Wrapped' :: Iso' (First a) (Unwrapped (First a)) #
Wrapped (Last a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Last a) :: Type # Methods _Wrapped' :: Iso' (Last a) (Unwrapped (Last a)) #
Wrapped (Dual a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Dual a) :: Type # Methods _Wrapped' :: Iso' (Dual a) (Unwrapped (Dual a)) #
Wrapped (Endo a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Endo a) :: Type # Methods _Wrapped' :: Iso' (Endo a) (Unwrapped (Endo a)) #
Wrapped (Sum a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Sum a) :: Type # Methods _Wrapped' :: Iso' (Sum a) (Unwrapped (Sum a)) #
Wrapped (Product a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Product a) :: Type # Methods _Wrapped' :: Iso' (Product a) (Unwrapped (Product a)) #
Wrapped (Down a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Down a) :: Type # Methods _Wrapped' :: Iso' (Down a) (Unwrapped (Down a)) #
Wrapped (NonEmpty a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (NonEmpty a) :: Type # Methods _Wrapped' :: Iso' (NonEmpty a) (Unwrapped (NonEmpty a)) #
Wrapped (IntMap a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (IntMap a) :: Type # Methods _Wrapped' :: Iso' (IntMap a) (Unwrapped (IntMap a)) #
Wrapped (Seq a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Seq a) :: Type # Methods _Wrapped' :: Iso' (Seq a) (Unwrapped (Seq a)) #
Ord a => Wrapped (Set a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Set a) :: Type # Methods _Wrapped' :: Iso' (Set a) (Unwrapped (Set a)) #
Prim a => Wrapped (Vector a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Vector a) :: Type # Methods _Wrapped' :: Iso' (Vector a) (Unwrapped (Vector a)) #
Storable a => Wrapped (Vector a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Vector a) :: Type # Methods _Wrapped' :: Iso' (Vector a) (Unwrapped (Vector a)) #
Unbox a => Wrapped (Vector a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Vector a) :: Type # Methods _Wrapped' :: Iso' (Vector a) (Unwrapped (Vector a)) #
(Hashable a, Eq a) => Wrapped (HashSet a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (HashSet a) :: Type # Methods _Wrapped' :: Iso' (HashSet a) (Unwrapped (HashSet a)) #
Wrapped (Vector a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Vector a) :: Type # Methods _Wrapped' :: Iso' (Vector a) (Unwrapped (Vector a)) #
Wrapped (Op a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Op a b) :: Type # Methods _Wrapped' :: Iso' (Op a b) (Unwrapped (Op a b)) #
(Hashable k, Eq k) => Wrapped (HashMap k a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (HashMap k a) :: Type # Methods _Wrapped' :: Iso' (HashMap k a) (Unwrapped (HashMap k a)) #
Ord k => Wrapped (Map k a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Map k a) :: Type # Methods _Wrapped' :: Iso' (Map k a) (Unwrapped (Map k a)) #
Wrapped (WrappedMonad m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedMonad m a) :: Type # Methods _Wrapped' :: Iso' (WrappedMonad m a) (Unwrapped (WrappedMonad m a)) #
Wrapped (ArrowMonad m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ArrowMonad m a) :: Type # Methods _Wrapped' :: Iso' (ArrowMonad m a) (Unwrapped (ArrowMonad m a)) #
Wrapped (MaybeT m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (MaybeT m a) :: Type # Methods _Wrapped' :: Iso' (MaybeT m a) (Unwrapped (MaybeT m a)) #
Wrapped (CatchT m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (CatchT m a) :: Type # Methods _Wrapped' :: Iso' (CatchT m a) (Unwrapped (CatchT m a)) #
Wrapped (CoiterT w a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (CoiterT w a) :: Type # Methods _Wrapped' :: Iso' (CoiterT w a) (Unwrapped (CoiterT w a)) #
Wrapped (IterT m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (IterT m a) :: Type # Methods _Wrapped' :: Iso' (IterT m a) (Unwrapped (IterT m a)) #
Wrapped (Alt f a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Alt f a) :: Type # Methods _Wrapped' :: Iso' (Alt f a) (Unwrapped (Alt f a)) #
Wrapped (ListT m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ListT m a) :: Type # Methods _Wrapped' :: Iso' (ListT m a) (Unwrapped (ListT m a)) #
Wrapped (WrappedApplicative f a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedApplicative f a) :: Type # Methods _Wrapped' :: Iso' (WrappedApplicative f a) (Unwrapped (WrappedApplicative f a)) #
Wrapped (MaybeApply f a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (MaybeApply f a) :: Type # Methods _Wrapped' :: Iso' (MaybeApply f a) (Unwrapped (MaybeApply f a)) #
Wrapped (Rec1 f p)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Rec1 f p) :: Type # Methods _Wrapped' :: Iso' (Rec1 f p) (Unwrapped (Rec1 f p)) #
Wrapped (WrappedArrow a b c)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedArrow a b c) :: Type # Methods _Wrapped' :: Iso' (WrappedArrow a b c) (Unwrapped (WrappedArrow a b c)) #
Wrapped (Kleisli m a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Kleisli m a b) :: Type # Methods _Wrapped' :: Iso' (Kleisli m a b) (Unwrapped (Kleisli m a b)) #
Wrapped (Const a x)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Const a x) :: Type # Methods _Wrapped' :: Iso' (Const a x) (Unwrapped (Const a x)) #
Wrapped (Alt f a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Alt f a) :: Type # Methods _Wrapped' :: Iso' (Alt f a) (Unwrapped (Alt f a)) #
Wrapped (Join p a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Join p a) :: Type # Methods _Wrapped' :: Iso' (Join p a) (Unwrapped (Join p a)) #
Wrapped (Fix p a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Fix p a) :: Type # Methods _Wrapped' :: Iso' (Fix p a) (Unwrapped (Fix p a)) #
Wrapped (TracedT m w a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (TracedT m w a) :: Type # Methods _Wrapped' :: Iso' (TracedT m w a) (Unwrapped (TracedT m w a)) #
Wrapped (IdentityT m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (IdentityT m a) :: Type # Methods _Wrapped' :: Iso' (IdentityT m a) (Unwrapped (IdentityT m a)) #
Wrapped (Compose f g a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Compose f g a) :: Type # Methods _Wrapped' :: Iso' (Compose f g a) (Unwrapped (Compose f g a)) #
Wrapped (ComposeFC f g a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ComposeFC f g a) :: Type # Methods _Wrapped' :: Iso' (ComposeFC f g a) (Unwrapped (ComposeFC f g a)) #
Wrapped (ComposeCF f g a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ComposeCF f g a) :: Type # Methods _Wrapped' :: Iso' (ComposeCF f g a) (Unwrapped (ComposeCF f g a)) #
Wrapped (ExceptT e m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ExceptT e m a) :: Type # Methods _Wrapped' :: Iso' (ExceptT e m a) (Unwrapped (ExceptT e m a)) #
Wrapped (FreeT f m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (FreeT f m a) :: Type # Methods _Wrapped' :: Iso' (FreeT f m a) (Unwrapped (FreeT f m a)) #
Wrapped (CofreeT f w a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (CofreeT f w a) :: Type # Methods _Wrapped' :: Iso' (CofreeT f w a) (Unwrapped (CofreeT f w a)) #
Wrapped (ApT f g a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ApT f g a) :: Type # Methods _Wrapped' :: Iso' (ApT f g a) (Unwrapped (ApT f g a)) #
Wrapped (ErrorT e m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ErrorT e m a) :: Type # Methods _Wrapped' :: Iso' (ErrorT e m a) (Unwrapped (ErrorT e m a)) #
Wrapped (StateT s m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (StateT s m a) :: Type # Methods _Wrapped' :: Iso' (StateT s m a) (Unwrapped (StateT s m a)) #
Wrapped (Backwards f a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Backwards f a) :: Type # Methods _Wrapped' :: Iso' (Backwards f a) (Unwrapped (Backwards f a)) #
Wrapped (StateT s m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (StateT s m a) :: Type # Methods _Wrapped' :: Iso' (StateT s m a) (Unwrapped (StateT s m a)) #
Wrapped (WriterT w m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WriterT w m a) :: Type # Methods _Wrapped' :: Iso' (WriterT w m a) (Unwrapped (WriterT w m a)) #
Wrapped (WriterT w m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WriterT w m a) :: Type # Methods _Wrapped' :: Iso' (WriterT w m a) (Unwrapped (WriterT w m a)) #
Wrapped (Star f d c)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Star f d c) :: Type # Methods _Wrapped' :: Iso' (Star f d c) (Unwrapped (Star f d c)) #
Wrapped (Costar f d c)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Costar f d c) :: Type # Methods _Wrapped' :: Iso' (Costar f d c) (Unwrapped (Costar f d c)) #
Wrapped (WrappedArrow p a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedArrow p a b) :: Type # Methods _Wrapped' :: Iso' (WrappedArrow p a b) (Unwrapped (WrappedArrow p a b)) #
Wrapped (Forget r a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Forget r a b) :: Type # Methods _Wrapped' :: Iso' (Forget r a b) (Unwrapped (Forget r a b)) #
Wrapped (Static f a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Static f a b) :: Type # Methods _Wrapped' :: Iso' (Static f a b) (Unwrapped (Static f a b)) #
Wrapped (Tagged s a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Tagged s a) :: Type # Methods _Wrapped' :: Iso' (Tagged s a) (Unwrapped (Tagged s a)) #
Wrapped (Reverse f a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Reverse f a) :: Type # Methods _Wrapped' :: Iso' (Reverse f a) (Unwrapped (Reverse f a)) #
Wrapped (Constant a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Constant a b) :: Type # Methods _Wrapped' :: Iso' (Constant a b) (Unwrapped (Constant a b)) #
Wrapped (K1 i c p)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (K1 i c p) :: Type # Methods _Wrapped' :: Iso' (K1 i c p) (Unwrapped (K1 i c p)) #
Wrapped (ContT r m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ContT r m a) :: Type # Methods _Wrapped' :: Iso' (ContT r m a) (Unwrapped (ContT r m a)) #
Wrapped (ReaderT r m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ReaderT r m a) :: Type # Methods _Wrapped' :: Iso' (ReaderT r m a) (Unwrapped (ReaderT r m a)) #
Wrapped (Cayley f p a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Cayley f p a b) :: Type # Methods _Wrapped' :: Iso' (Cayley f p a b) (Unwrapped (Cayley f p a b)) #
Wrapped (M1 i c f p)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (M1 i c f p) :: Type # Methods _Wrapped' :: Iso' (M1 i c f p) (Unwrapped (M1 i c f p)) #
Wrapped ((f :.: g) p)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped ((f :.: g) p) :: Type # Methods _Wrapped' :: Iso' ((f :.: g) p) (Unwrapped ((f :.: g) p)) #
Wrapped (Compose f g a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Compose f g a) :: Type # Methods _Wrapped' :: Iso' (Compose f g a) (Unwrapped (Compose f g a)) #
Wrapped (WrappedBifunctor p a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedBifunctor p a b) :: Type # Methods _Wrapped' :: Iso' (WrappedBifunctor p a b) (Unwrapped (WrappedBifunctor p a b)) #
Wrapped (Joker g a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Joker g a b) :: Type # Methods _Wrapped' :: Iso' (Joker g a b) (Unwrapped (Joker g a b)) #
Wrapped (Flip p a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Flip p a b) :: Type # Methods _Wrapped' :: Iso' (Flip p a b) (Unwrapped (Flip p a b)) #
Wrapped (Clown f a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Clown f a b) :: Type # Methods _Wrapped' :: Iso' (Clown f a b) (Unwrapped (Clown f a b)) #
Wrapped (RWST r w s m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (RWST r w s m a) :: Type # Methods _Wrapped' :: Iso' (RWST r w s m a) (Unwrapped (RWST r w s m a)) #
Wrapped (RWST r w s m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (RWST r w s m a) :: Type # Methods _Wrapped' :: Iso' (RWST r w s m a) (Unwrapped (RWST r w s m a)) #
Wrapped (Dual k3 a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Dual k3 a b) :: Type # Methods _Wrapped' :: Iso' (Dual k3 a b) (Unwrapped (Dual k3 a b)) #
Wrapped (WrappedCategory k3 a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedCategory k3 a b) :: Type # Methods _Wrapped' :: Iso' (WrappedCategory k3 a b) (Unwrapped (WrappedCategory k3 a b)) #
Wrapped (Semi m a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Semi m a b) :: Type # Methods _Wrapped' :: Iso' (Semi m a b) (Unwrapped (Semi m a b)) #
Wrapped (Tannen f p a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Tannen f p a b) :: Type # Methods _Wrapped' :: Iso' (Tannen f p a b) (Unwrapped (Tannen f p a b)) #
Wrapped (Biff p f g a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Biff p f g a b) :: Type # Methods _Wrapped' :: Iso' (Biff p f g a b) (Unwrapped (Biff p f g a b)) #

class Wrapped s => Rewrapped s t #

Instances

t ~ PatternMatchFail => Rewrapped PatternMatchFail t
Instance details Defined in Control.Lens.Wrapped
t ~ RecSelError => Rewrapped RecSelError t
Instance details Defined in Control.Lens.Wrapped
t ~ RecConError => Rewrapped RecConError t
Instance details Defined in Control.Lens.Wrapped
t ~ RecUpdError => Rewrapped RecUpdError t
Instance details Defined in Control.Lens.Wrapped
t ~ NoMethodError => Rewrapped NoMethodError t
Instance details Defined in Control.Lens.Wrapped
t ~ TypeError => Rewrapped TypeError t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CDev t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CIno t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CMode t
Instance details Defined in Control.Lens.Wrapped
Rewrapped COff t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CPid t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CSsize t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CGid t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CNlink t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUid t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CCc t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CSpeed t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CTcflag t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CRLim t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CBlkSize t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CBlkCnt t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CClockId t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CFsBlkCnt t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CFsFilCnt t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CId t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CKey t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CTimer t
Instance details Defined in Control.Lens.Wrapped
Rewrapped Fd t
Instance details Defined in Control.Lens.Wrapped
Rewrapped Errno t
Instance details Defined in Control.Lens.Wrapped
t ~ CompactionFailed => Rewrapped CompactionFailed t
Instance details Defined in Control.Lens.Wrapped
t ~ AssertionFailed => Rewrapped AssertionFailed t
Instance details Defined in Control.Lens.Wrapped
t ~ ErrorCall => Rewrapped ErrorCall t
Instance details Defined in Control.Lens.Wrapped
t ~ All => Rewrapped All t
Instance details Defined in Control.Lens.Wrapped
t ~ Any => Rewrapped Any t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CChar t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CSChar t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUChar t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CShort t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUShort t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CInt t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUInt t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CLong t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CULong t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CLLong t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CULLong t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CBool t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CFloat t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CDouble t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CPtrdiff t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CSize t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CWchar t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CSigAtomic t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CClock t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CTime t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUSeconds t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CSUSeconds t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CIntPtr t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUIntPtr t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CIntMax t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUIntMax t
Instance details Defined in Control.Lens.Wrapped
t ~ IntSet => Rewrapped IntSet t	Use `wrapping fromList`. unwrapping returns a sorted list.
Instance details Defined in Control.Lens.Wrapped
t ~ Par1 p' => Rewrapped (Par1 p) t
Instance details Defined in Control.Lens.Wrapped
t ~ Predicate b => Rewrapped (Predicate a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Comparison b => Rewrapped (Comparison a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Equivalence b => Rewrapped (Equivalence a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Min b => Rewrapped (Min a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Max b => Rewrapped (Max a) t
Instance details Defined in Control.Lens.Wrapped
t ~ First b => Rewrapped (First a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Last b => Rewrapped (Last a) t
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedMonoid b => Rewrapped (WrappedMonoid a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Option b => Rewrapped (Option a) t
Instance details Defined in Control.Lens.Wrapped
t ~ ZipList b => Rewrapped (ZipList a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Identity b => Rewrapped (Identity a) t
Instance details Defined in Control.Lens.Wrapped
t ~ First b => Rewrapped (First a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Last b => Rewrapped (Last a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Dual b => Rewrapped (Dual a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Endo b => Rewrapped (Endo a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Sum b => Rewrapped (Sum a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Product b => Rewrapped (Product a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Down b => Rewrapped (Down a) t
Instance details Defined in Control.Lens.Wrapped
t ~ NonEmpty b => Rewrapped (NonEmpty a) t
Instance details Defined in Control.Lens.Wrapped
t ~ IntMap a' => Rewrapped (IntMap a) t	Use `wrapping fromList`. unwrapping returns a sorted list.
Instance details Defined in Control.Lens.Wrapped
t ~ Seq a' => Rewrapped (Seq a) t
Instance details Defined in Control.Lens.Wrapped
(t ~ Set a', Ord a) => Rewrapped (Set a) t	Use `wrapping fromList`. unwrapping returns a sorted list.
Instance details Defined in Control.Lens.Wrapped
(Prim a, t ~ Vector a') => Rewrapped (Vector a) t
Instance details Defined in Control.Lens.Wrapped
(Storable a, t ~ Vector a') => Rewrapped (Vector a) t
Instance details Defined in Control.Lens.Wrapped
(Unbox a, t ~ Vector a') => Rewrapped (Vector a) t
Instance details Defined in Control.Lens.Wrapped
(t ~ HashSet a', Hashable a, Eq a) => Rewrapped (HashSet a) t	Use `wrapping fromList`. Unwrapping returns some permutation of the list.
Instance details Defined in Control.Lens.Wrapped
t ~ Vector a' => Rewrapped (Vector a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Op a' b' => Rewrapped (Op a b) t
Instance details Defined in Control.Lens.Wrapped
(t ~ HashMap k' a', Hashable k, Eq k) => Rewrapped (HashMap k a) t	Use `wrapping fromList`. Unwrapping returns some permutation of the list.
Instance details Defined in Control.Lens.Wrapped
(t ~ Map k' a', Ord k) => Rewrapped (Map k a) t	Use `wrapping fromList`. unwrapping returns a sorted list.
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedMonad m' a' => Rewrapped (WrappedMonad m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ ArrowMonad m' a' => Rewrapped (ArrowMonad m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ MaybeT n b => Rewrapped (MaybeT m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ CatchT m' a' => Rewrapped (CatchT m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ CoiterT w' a' => Rewrapped (CoiterT w a) t
Instance details Defined in Control.Lens.Wrapped
t ~ IterT m' a' => Rewrapped (IterT m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Alt f' a' => Rewrapped (Alt f a) t
Instance details Defined in Control.Lens.Wrapped
t ~ ListT n b => Rewrapped (ListT m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedApplicative f' a' => Rewrapped (WrappedApplicative f a) t
Instance details Defined in Control.Lens.Wrapped
t ~ MaybeApply f' a' => Rewrapped (MaybeApply f a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Rec1 f' p' => Rewrapped (Rec1 f p) t
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedArrow a' b' c' => Rewrapped (WrappedArrow a b c) t
Instance details Defined in Control.Lens.Wrapped
t ~ Kleisli m' a' b' => Rewrapped (Kleisli m a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Const a' x' => Rewrapped (Const a x) t
Instance details Defined in Control.Lens.Wrapped
t ~ Alt g b => Rewrapped (Alt f a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Join p' a' => Rewrapped (Join p a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Fix p' a' => Rewrapped (Fix p a) t
Instance details Defined in Control.Lens.Wrapped
t ~ TracedT m' w' a' => Rewrapped (TracedT m w a) t
Instance details Defined in Control.Lens.Wrapped
t ~ IdentityT n b => Rewrapped (IdentityT m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Compose f' g' a' => Rewrapped (Compose f g a) t
Instance details Defined in Control.Lens.Wrapped
t ~ ComposeFC f' g' a' => Rewrapped (ComposeFC f g a) t
Instance details Defined in Control.Lens.Wrapped
t ~ ComposeCF f' g' a' => Rewrapped (ComposeCF f g a) t
Instance details Defined in Control.Lens.Wrapped
t ~ ExceptT e' m' a' => Rewrapped (ExceptT e m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ FreeT f' m' a' => Rewrapped (FreeT f m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ CofreeT f' w' a' => Rewrapped (CofreeT f w a) t
Instance details Defined in Control.Lens.Wrapped
t ~ ApT f' g' a' => Rewrapped (ApT f g a) t
Instance details Defined in Control.Lens.Wrapped
t ~ ErrorT e' m' a' => Rewrapped (ErrorT e m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ StateT s' m' a' => Rewrapped (StateT s m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Backwards g b => Rewrapped (Backwards f a) t
Instance details Defined in Control.Lens.Wrapped
t ~ StateT s' m' a' => Rewrapped (StateT s m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ WriterT w' m' a' => Rewrapped (WriterT w m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ WriterT w' m' a' => Rewrapped (WriterT w m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Star f' d' c' => Rewrapped (Star f d c) t
Instance details Defined in Control.Lens.Wrapped
t ~ Costar f' d' c' => Rewrapped (Costar f d c) t
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedArrow p' a' b' => Rewrapped (WrappedArrow p a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Forget r' a' b' => Rewrapped (Forget r a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Static f' a' b' => Rewrapped (Static f a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Tagged s' a' => Rewrapped (Tagged s a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Reverse g b => Rewrapped (Reverse f a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Constant a' b' => Rewrapped (Constant a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ K1 i' c' p' => Rewrapped (K1 i c p) t
Instance details Defined in Control.Lens.Wrapped
t ~ ContT r' m' a' => Rewrapped (ContT r m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ ReaderT s n b => Rewrapped (ReaderT r m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Cayley f' p' a' b' => Rewrapped (Cayley f p a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ M1 i' c' f' p' => Rewrapped (M1 i c f p) t
Instance details Defined in Control.Lens.Wrapped
t ~ (f' :.: g') p' => Rewrapped ((f :.: g) p) t
Instance details Defined in Control.Lens.Wrapped
t ~ Compose f' g' a' => Rewrapped (Compose f g a) t
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedBifunctor p' a' b' => Rewrapped (WrappedBifunctor p a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Joker g' a' b' => Rewrapped (Joker g a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Flip p' a' b' => Rewrapped (Flip p a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Clown f' a' b' => Rewrapped (Clown f a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ RWST r' w' s' m' a' => Rewrapped (RWST r w s m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ RWST r' w' s' m' a' => Rewrapped (RWST r w s m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Dual k' a' b' => Rewrapped (Dual k6 a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedCategory k' a' b' => Rewrapped (WrappedCategory k6 a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Semi m' a' b' => Rewrapped (Semi m a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Tannen f' p' a' b' => Rewrapped (Tannen f p a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Biff p' f' g' a' b' => Rewrapped (Biff p f g a b) t
Instance details Defined in Control.Lens.Wrapped

class (Rewrapped s t, Rewrapped t s) => Rewrapping s t #

Instances

(Rewrapped s t, Rewrapped t s) => Rewrapping s t
Instance details Defined in Control.Lens.Wrapped

unsnoc :: Snoc s s a a => s -> Maybe (s, a) #

Attempt to extract the right-most element from a container, and a version of the container without that element.

>>> unsnoc (LazyT.pack "hello!")
Just ("hello",'!')

>>> unsnoc (LazyT.pack "")
Nothing

>>> unsnoc (Seq.fromList [b,c,a])
Just (fromList [b,c],a)

>>> unsnoc (Seq.fromList [])
Nothing

snoc :: Snoc s s a a => s -> a -> s infixl 5 #

snoc an element onto the end of a container.

>>> snoc (Seq.fromList []) a
fromList [a]

>>> snoc (Seq.fromList [b, c]) a
fromList [b,c,a]

>>> snoc (LazyT.pack "hello") '!'
"hello!"

(|>) :: Snoc s s a a => s -> a -> s infixl 5 #

snoc an element onto the end of a container.

This is an infix alias for snoc.

>>> Seq.fromList [] |> a
fromList [a]

>>> Seq.fromList [b, c] |> a
fromList [b,c,a]

>>> LazyT.pack "hello" |> '!'
"hello!"

_last :: Snoc s s a a => Traversal' s a #

A Traversal reading and writing to the last element of a non-empty container.

>>> [a,b,c]^?!_last
c

>>> []^?_last
Nothing

>>> [a,b,c] & _last %~ f
[a,b,f c]

>>> [1,2]^?_last
Just 2

>>> [] & _last .~ 1
[]

>>> [0] & _last .~ 2
[2]

>>> [0,1] & _last .~ 2
[0,2]

This Traversal is not limited to lists, however. We can also work with other containers, such as a Vector.

>>> Vector.fromList "abcde" ^? _last
Just 'e'

>>> Vector.empty ^? _last
Nothing

>>> (Vector.fromList "abcde" & _last .~ 'Q') == Vector.fromList "abcdQ"
True

_last :: Traversal' [a] a
_last :: Traversal' (Seq a) a
_last :: Traversal' (Vector a) a

_init :: Snoc s s a a => Traversal' s s #

A Traversal reading and replacing all but the a last element of a non-empty container.

>>> [a,b,c,d]^?_init
Just [a,b,c]

>>> []^?_init
Nothing

>>> [a,b] & _init .~ [c,d,e]
[c,d,e,b]

>>> [] & _init .~ [a,b]
[]

>>> [a,b,c,d] & _init.traverse %~ f
[f a,f b,f c,d]

>>> [1,2,3]^?_init
Just [1,2]

>>> [1,2,3,4]^?!_init
[1,2,3]

>>> "hello"^._init
"hell"

>>> ""^._init
""

_init :: Traversal' [a] [a]
_init :: Traversal' (Seq a) (Seq a)
_init :: Traversal' (Vector a) (Vector a)

_tail :: Cons s s a a => Traversal' s s #

A Traversal reading and writing to the tail of a non-empty container.

>>> [a,b] & _tail .~ [c,d,e]
[a,c,d,e]

>>> [] & _tail .~ [a,b]
[]

>>> [a,b,c,d,e] & _tail.traverse %~ f
[a,f b,f c,f d,f e]

>>> [1,2] & _tail .~ [3,4,5]
[1,3,4,5]

>>> [] & _tail .~ [1,2]
[]

>>> [a,b,c]^?_tail
Just [b,c]

>>> [1,2]^?!_tail
[2]

>>> "hello"^._tail
"ello"

>>> ""^._tail
""

This isn't limited to lists. For instance you can also traverse the tail of a Seq.

>>> Seq.fromList [a,b] & _tail .~ Seq.fromList [c,d,e]
fromList [a,c,d,e]

>>> Seq.fromList [a,b,c] ^? _tail
Just (fromList [b,c])

>>> Seq.fromList [] ^? _tail
Nothing

_tail :: Traversal' [a] [a]
_tail :: Traversal' (Seq a) (Seq a)
_tail :: Traversal' (Vector a) (Vector a)

_head :: Cons s s a a => Traversal' s a #

A Traversal reading and writing to the head of a non-empty container.

>>> [a,b,c]^? _head
Just a

>>> [a,b,c] & _head .~ d
[d,b,c]

>>> [a,b,c] & _head %~ f
[f a,b,c]

>>> [] & _head %~ f
[]

>>> [1,2,3]^?!_head
1

>>> []^?_head
Nothing

>>> [1,2]^?_head
Just 1

>>> [] & _head .~ 1
[]

>>> [0] & _head .~ 2
[2]

>>> [0,1] & _head .~ 2
[2,1]

This isn't limited to lists.

For instance you can also traverse the head of a Seq:

>>> Seq.fromList [a,b,c,d] & _head %~ f
fromList [f a,b,c,d]

>>> Seq.fromList [] ^? _head
Nothing

>>> Seq.fromList [a,b,c,d] ^? _head
Just a

_head :: Traversal' [a] a
_head :: Traversal' (Seq a) a
_head :: Traversal' (Vector a) a

uncons :: Cons s s a a => s -> Maybe (a, s) #

Attempt to extract the left-most element from a container, and a version of the container without that element.

>>> uncons []
Nothing

>>> uncons [a, b, c]
Just (a,[b,c])

cons :: Cons s s a a => a -> s -> s infixr 5 #

cons an element onto a container.

>>> cons a []
[a]

>>> cons a [b, c]
[a,b,c]

>>> cons a (Seq.fromList [])
fromList [a]

>>> cons a (Seq.fromList [b, c])
fromList [a,b,c]

(<|) :: Cons s s a a => a -> s -> s infixr 5 #

cons an element onto a container.

This is an infix alias for cons.

>>> a <| []
[a]

>>> a <| [b, c]
[a,b,c]

>>> a <| Seq.fromList []
fromList [a]

>>> a <| Seq.fromList [b, c]
fromList [a,b,c]

pattern (:<) :: forall b a. Cons b b a a => a -> b -> b infixr 5 #

pattern (:>) :: forall a b. Snoc a a b b => a -> b -> a infixl 5 #

class Cons s t a b | s -> a, t -> b, s b -> t, t a -> s where #

This class provides a way to attach or detach elements on the left side of a structure in a flexible manner.

Methods

_Cons :: Prism s t (a, s) (b, t) #

_Cons :: Prism [a] [b] (a, [a]) (b, [b])
_Cons :: Prism (Seq a) (Seq b) (a, Seq a) (b, Seq b)
_Cons :: Prism (Vector a) (Vector b) (a, Vector a) (b, Vector b)
_Cons :: Prism' String (Char, String)
_Cons :: Prism' Text (Char, Text)
_Cons :: Prism' ByteString (Word8, ByteString)

Instances

Cons ByteString ByteString Word8 Word8
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism ByteString ByteString (Word8, ByteString) (Word8, ByteString) #
Cons ByteString ByteString Word8 Word8
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism ByteString ByteString (Word8, ByteString) (Word8, ByteString) #
Cons Text Text Char Char
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism Text Text (Char, Text) (Char, Text) #
Cons Text Text Char Char
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism Text Text (Char, Text) (Char, Text) #
Cons [a] [b] a b
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism [a] [b] (a, [a]) (b, [b]) #
Cons (ZipList a) (ZipList b) a b
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (ZipList a) (ZipList b) (a, ZipList a) (b, ZipList b) #
Cons (Seq a) (Seq b) a b
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (Seq a) (Seq b) (a, Seq a) (b, Seq b) #
(Prim a, Prim b) => Cons (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (Vector a) (Vector b) (a, Vector a) (b, Vector b) #
(Storable a, Storable b) => Cons (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (Vector a) (Vector b) (a, Vector a) (b, Vector b) #
(Unbox a, Unbox b) => Cons (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (Vector a) (Vector b) (a, Vector a) (b, Vector b) #
Cons (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (Vector a) (Vector b) (a, Vector a) (b, Vector b) #

class Snoc s t a b | s -> a, t -> b, s b -> t, t a -> s where #

This class provides a way to attach or detach elements on the right side of a structure in a flexible manner.

Methods

_Snoc :: Prism s t (s, a) (t, b) #

_Snoc :: Prism [a] [b] ([a], a) ([b], b)
_Snoc :: Prism (Seq a) (Seq b) (Seq a, a) (Seq b, b)
_Snoc :: Prism (Vector a) (Vector b) (Vector a, a) (Vector b, b)
_Snoc :: Prism' String (String, Char)
_Snoc :: Prism' Text (Text, Char)
_Snoc :: Prism' ByteString (ByteString, Word8)

Instances

Snoc ByteString ByteString Word8 Word8
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism ByteString ByteString (ByteString, Word8) (ByteString, Word8) #
Snoc ByteString ByteString Word8 Word8
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism ByteString ByteString (ByteString, Word8) (ByteString, Word8) #
Snoc Text Text Char Char
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism Text Text (Text, Char) (Text, Char) #
Snoc Text Text Char Char
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism Text Text (Text, Char) (Text, Char) #
Snoc [a] [b] a b
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism [a] [b] ([a], a) ([b], b) #
Snoc (ZipList a) (ZipList b) a b
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (ZipList a) (ZipList b) (ZipList a, a) (ZipList b, b) #
Snoc (Seq a) (Seq b) a b
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (Seq a) (Seq b) (Seq a, a) (Seq b, b) #
(Prim a, Prim b) => Snoc (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (Vector a) (Vector b) (Vector a, a) (Vector b, b) #
(Storable a, Storable b) => Snoc (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (Vector a) (Vector b) (Vector a, a) (Vector b, b) #
(Unbox a, Unbox b) => Snoc (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (Vector a) (Vector b) (Vector a, a) (Vector b, b) #
Snoc (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (Vector a) (Vector b) (Vector a, a) (Vector b, b) #

pattern Empty :: forall s. AsEmpty s => s #

class AsEmpty a where #

Minimal complete definition

Nothing

Methods

_Empty :: Prism' a () #

>>> isn't _Empty [1,2,3]
True

Instances

AsEmpty Ordering
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' Ordering () #
AsEmpty ()
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' () () #
AsEmpty ByteString
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' ByteString () #
AsEmpty ByteString
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' ByteString () #
AsEmpty Text
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' Text () #
AsEmpty Text
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' Text () #
AsEmpty Event
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' Event () #
AsEmpty All
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' All () #
AsEmpty Any
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' Any () #
AsEmpty IntSet
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' IntSet () #
AsEmpty [a]
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' [a] () #
AsEmpty (Maybe a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Maybe a) () #
AsEmpty (ZipList a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (ZipList a) () #
AsEmpty (First a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (First a) () #
AsEmpty (Last a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Last a) () #
AsEmpty a => AsEmpty (Dual a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Dual a) () #
(Eq a, Num a) => AsEmpty (Sum a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Sum a) () #
(Eq a, Num a) => AsEmpty (Product a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Product a) () #
AsEmpty (IntMap a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (IntMap a) () #
AsEmpty (Seq a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Seq a) () #
AsEmpty (Set a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Set a) () #
Storable a => AsEmpty (Vector a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Vector a) () #
Unbox a => AsEmpty (Vector a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Vector a) () #
AsEmpty (HashSet a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (HashSet a) () #
AsEmpty (Vector a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Vector a) () #
(AsEmpty a, AsEmpty b) => AsEmpty (a, b)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (a, b) () #
AsEmpty (HashMap k a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (HashMap k a) () #
AsEmpty (Map k a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Map k a) () #
(AsEmpty a, AsEmpty b, AsEmpty c) => AsEmpty (a, b, c)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (a, b, c) () #

coerced :: (Coercible s a, Coercible t b) => Iso s t a b #

Data types that are representationally equal are isomorphic.

This is only available on GHC 7.8+

Since: lens-4.13

seconding :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> Iso (f x s) (g y t) (f x a) (g y b) #

Lift an Iso into the second argument of a Bifunctor. This is essentially the same as mapping, but it takes a 'Bifunctor p' constraint instead of a 'Functor (p a)' one.

seconding :: Bifunctor p => Iso s t a b -> Iso (p x s) (p y t) (p x a) (p y b)
seconding :: Bifunctor p => Iso' s a -> Iso' (p x s) (p x a)

firsting :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> Iso (f s x) (g t y) (f a x) (g b y) #

Lift an Iso into the first argument of a Bifunctor.

firsting :: Bifunctor p => Iso s t a b -> Iso (p s x) (p t y) (p a x) (p b y)
firsting :: Bifunctor p => Iso' s a -> Iso' (p s x) (p a x)

bimapping :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> AnIso s' t' a' b' -> Iso (f s s') (g t t') (f a a') (g b b') #

Lift two Isos into both arguments of a Bifunctor.

bimapping :: Bifunctor p => Iso s t a b -> Iso s' t' a' b' -> Iso (p s s') (p t t') (p a a') (p b b')
bimapping :: Bifunctor p => Iso' s a -> Iso' s' a' -> Iso' (p s s') (p a a')

rmapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> Iso (p x s) (q y t) (p x a) (q y b) #

Lift an Iso covariantly into the right argument of a Profunctor.

rmapping :: Profunctor p => Iso s t a b -> Iso (p x s) (p y t) (p x a) (p y b)
rmapping :: Profunctor p => Iso' s a -> Iso' (p x s) (p x a)

lmapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> Iso (p a x) (q b y) (p s x) (q t y) #

Lift an Iso contravariantly into the left argument of a Profunctor.

lmapping :: Profunctor p => Iso s t a b -> Iso (p a x) (p b y) (p s x) (p t y)
lmapping :: Profunctor p => Iso' s a -> Iso' (p a x) (p s x)

dimapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> AnIso s' t' a' b' -> Iso (p a s') (q b t') (p s a') (q t b') #

Lift two Isos into both arguments of a Profunctor simultaneously.

dimapping :: Profunctor p => Iso s t a b -> Iso s' t' a' b' -> Iso (p a s') (p b t') (p s a') (p t b')
dimapping :: Profunctor p => Iso' s a -> Iso' s' a' -> Iso' (p a s') (p s a')

contramapping :: Contravariant f => AnIso s t a b -> Iso (f a) (f b) (f s) (f t) #

Lift an Iso into a Contravariant functor.

contramapping :: Contravariant f => Iso s t a b -> Iso (f a) (f b) (f s) (f t)
contramapping :: Contravariant f => Iso' s a -> Iso' (f a) (f s)

imagma :: Over (Indexed i) (Molten i a b) s t a b -> Iso s t' (Magma i t b a) (Magma j t' c c) #

This isomorphism can be used to inspect an IndexedTraversal to see how it associates the structure and it can also be used to bake the IndexedTraversal into a Magma so that you can traverse over it multiple times with access to the original indices.

magma :: LensLike (Mafic a b) s t a b -> Iso s u (Magma Int t b a) (Magma j u c c) #

This isomorphism can be used to inspect a Traversal to see how it associates the structure and it can also be used to bake the Traversal into a Magma so that you can traverse over it multiple times.

involuted :: (a -> a) -> Iso' a a #

Given a function that is its own inverse, this gives you an Iso using it in both directions.

involuted ≡ join iso

>>> "live" ^. involuted reverse
"evil"

>>> "live" & involuted reverse %~ ('d':)
"lived"

reversed :: Reversing a => Iso' a a #

An Iso between a list, ByteString, Text fragment, etc. and its reversal.

>>> "live" ^. reversed
"evil"

>>> "live" & reversed %~ ('d':)
"lived"

lazy :: Strict lazy strict => Iso' strict lazy #

An Iso between the strict variant of a structure and its lazy counterpart.

lazy = from strict

See http://hackage.haskell.org/package/strict-base-types for an example use.

flipped :: Iso (a -> b -> c) (a' -> b' -> c') (b -> a -> c) (b' -> a' -> c') #

The isomorphism for flipping a function.

>>> ((,)^.flipped) 1 2
(2,1)

uncurried :: Iso (a -> b -> c) (d -> e -> f) ((a, b) -> c) ((d, e) -> f) #

The canonical isomorphism for uncurrying and currying a function.

uncurried = iso uncurry curry

uncurried = from curried

>>> ((+)^.uncurried) (1,2)
3

curried :: Iso ((a, b) -> c) ((d, e) -> f) (a -> b -> c) (d -> e -> f) #

The canonical isomorphism for currying and uncurrying a function.

curried = iso curry uncurry

>>> (fst^.curried) 3 4
3

>>> view curried fst 3 4
3

anon :: a -> (a -> Bool) -> Iso' (Maybe a) a #

anon a p generalizes non a to take any value and a predicate.

This function assumes that p a holds True and generates an isomorphism between Maybe (a | not (p a)) and a.

>>> Map.empty & at "hello" . anon Map.empty Map.null . at "world" ?~ "!!!"
fromList [("hello",fromList [("world","!!!")])]

>>> fromList [("hello",fromList [("world","!!!")])] & at "hello" . anon Map.empty Map.null . at "world" .~ Nothing
fromList []

non' :: APrism' a () -> Iso' (Maybe a) a #

non' p generalizes non (p # ()) to take any unit Prism

This function generates an isomorphism between Maybe (a | isn't p a) and a.

>>> Map.singleton "hello" Map.empty & at "hello" . non' _Empty . at "world" ?~ "!!!"
fromList [("hello",fromList [("world","!!!")])]

>>> fromList [("hello",fromList [("world","!!!")])] & at "hello" . non' _Empty . at "world" .~ Nothing
fromList []

non :: Eq a => a -> Iso' (Maybe a) a #

If v is an element of a type a, and a' is a sans the element v, then non v is an isomorphism from Maybe a' to a.

non ≡ non' . only

Keep in mind this is only a real isomorphism if you treat the domain as being Maybe (a sans v).

This is practically quite useful when you want to have a Map where all the entries should have non-zero values.

>>> Map.fromList [("hello",1)] & at "hello" . non 0 +~ 2
fromList [("hello",3)]

>>> Map.fromList [("hello",1)] & at "hello" . non 0 -~ 1
fromList []

>>> Map.fromList [("hello",1)] ^. at "hello" . non 0
1

>>> Map.fromList [] ^. at "hello" . non 0
0

This combinator is also particularly useful when working with nested maps.

e.g. When you want to create the nested Map when it is missing:

>>> Map.empty & at "hello" . non Map.empty . at "world" ?~ "!!!"
fromList [("hello",fromList [("world","!!!")])]

and when have deleting the last entry from the nested Map mean that we should delete its entry from the surrounding one:

>>> fromList [("hello",fromList [("world","!!!")])] & at "hello" . non Map.empty . at "world" .~ Nothing
fromList []

It can also be used in reverse to exclude a given value:

>>> non 0 # rem 10 4
Just 2

>>> non 0 # rem 10 5
Nothing

mapping :: (Functor f, Functor g) => AnIso s t a b -> Iso (f s) (g t) (f a) (g b) #

This can be used to lift any Iso into an arbitrary Functor.

enum :: Enum a => Iso' Int a #

This isomorphism can be used to convert to or from an instance of Enum.

>>> LT^.from enum
0

>>> 97^.enum :: Char
'a'

Note: this is only an isomorphism from the numeric range actually used and it is a bit of a pleasant fiction, since there are questionable Enum instances for Double, and Float that exist solely for [1.0 .. 4.0] sugar and the instances for those and Integer don't cover all values in their range.

under :: AnIso s t a b -> (t -> s) -> b -> a #

The opposite of working over a Setter is working under an isomorphism.

under ≡ over . from

under :: Iso s t a b -> (t -> s) -> b -> a

auf :: Optic (Costar f) g s t a b -> (f a -> g b) -> f s -> g t #

Based on ala' from Conor McBride's work on Epigram.

This version is generalized to accept any Iso, not just a newtype.

For a version you pass the name of the newtype constructor to, see alaf.

>>> auf (_Unwrapping Sum) (foldMapOf both) Prelude.length ("hello","world")
10

Mnemonically, the German auf plays a similar role to à la, and the combinator is au with an extra function argument:

auf :: Iso s t a b -> ((r ->  a) -> e -> b) -> (r -> s) -> e -> t

but the signature is general.

au :: Functor f => AnIso s t a b -> ((b -> t) -> f s) -> f a #

Based on ala from Conor McBride's work on Epigram.

This version is generalized to accept any Iso, not just a newtype.

>>> au (_Wrapping Sum) foldMap [1,2,3,4]
10

You may want to think of this combinator as having the following, simpler type:

au :: AnIso s t a b -> ((b -> t) -> e -> s) -> e -> a

cloneIso :: AnIso s t a b -> Iso s t a b #

Convert from AnIso back to any Iso.

This is useful when you need to store an isomorphism as a data type inside a container and later reconstitute it as an overloaded function.

See cloneLens or cloneTraversal for more information on why you might want to do this.

withIso :: AnIso s t a b -> ((s -> a) -> (b -> t) -> r) -> r #

Extract the two functions, one from s -> a and one from b -> t that characterize an Iso.

from :: AnIso s t a b -> Iso b a t s #

Invert an isomorphism.

from (from l) ≡ l

iso :: (s -> a) -> (b -> t) -> Iso s t a b #

Build a simple isomorphism from a pair of inverse functions.

view (iso f g) ≡ f
view (from (iso f g)) ≡ g
over (iso f g) h ≡ g . h . f
over (from (iso f g)) h ≡ f . h . g

pattern Strict :: forall s t. Strict s t => t -> s #

pattern Lazy :: forall t s. Strict t s => t -> s #

pattern Swapped :: forall (p :: Type -> Type -> Type) c d. Swapped p => p d c -> p c d #

pattern Reversed :: forall t. Reversing t => t -> t #

pattern List :: forall l. IsList l => [Item l] -> l #

type AnIso s t a b = Exchange a b a (Identity b) -> Exchange a b s (Identity t) #

When you see this as an argument to a function, it expects an Iso.

type AnIso' s a = AnIso s s a a #

A Simple AnIso.

class Bifunctor p => Swapped (p :: Type -> Type -> Type) where #

This class provides for symmetric bifunctors.

Methods

swapped :: Iso (p a b) (p c d) (p b a) (p d c) #

swapped . swapped ≡ id
first f . swapped = swapped . second f
second g . swapped = swapped . first g
bimap f g . swapped = swapped . bimap g f

>>> (1,2)^.swapped
(2,1)

Instances

Swapped Either
Instance details Defined in Control.Lens.Iso Methods swapped :: Iso (Either a b) (Either c d) (Either b a) (Either d c) #
Swapped (,)
Instance details Defined in Control.Lens.Iso Methods swapped :: Iso (a, b) (c, d) (b, a) (d, c) #

class Strict lazy strict | lazy -> strict, strict -> lazy where #

Ad hoc conversion between "strict" and "lazy" versions of a structure, such as Text or ByteString.

Methods

strict :: Iso' lazy strict #

Instances

Strict ByteString ByteString
Instance details Defined in Control.Lens.Iso Methods strict :: Iso' ByteString ByteString0 #
Strict Text Text
Instance details Defined in Control.Lens.Iso Methods strict :: Iso' Text Text0 #
Strict (ST s a) (ST s a)
Instance details Defined in Control.Lens.Iso Methods strict :: Iso' (ST s a) (ST0 s a) #
Strict (StateT s m a) (StateT s m a)
Instance details Defined in Control.Lens.Iso Methods strict :: Iso' (StateT s m a) (StateT0 s m a) #
Strict (WriterT w m a) (WriterT w m a)
Instance details Defined in Control.Lens.Iso Methods strict :: Iso' (WriterT0 w m a) (WriterT w m a) #
Strict (RWST r w s m a) (RWST r w s m a)
Instance details Defined in Control.Lens.Iso Methods strict :: Iso' (RWST r w s m a) (RWST0 r w s m a) #

simple :: Equality' a a #

Composition with this isomorphism is occasionally useful when your Lens, Traversal or Iso has a constraint on an unused argument to force that argument to agree with the type of a used argument and avoid ScopedTypeVariables or other ugliness.

simply :: (Optic' p f s a -> r) -> Optic' p f s a -> r #

This is an adverb that can be used to modify many other Lens combinators to make them require simple lenses, simple traversals, simple prisms or simple isos as input.

fromEq :: AnEquality s t a b -> Equality b a t s #

Equality is symmetric.

mapEq :: AnEquality s t a b -> f s -> f a #

We can use Equality to do substitution into anything.

substEq :: AnEquality s t a b -> ((s ~ a) -> (t ~ b) -> r) -> r #

Substituting types with Equality.

runEq :: AnEquality s t a b -> Identical s t a b #

Extract a witness of type Equality.

data Identical (a :: k) (b :: k1) (s :: k) (t :: k1) :: forall k k1. k -> k1 -> k -> k1 -> Type where #

Provides witness that (s ~ a, b ~ t) holds.

Constructors

Identical :: forall k k1 (a :: k) (b :: k1) (s :: k) (t :: k1). Identical a b a b

type AnEquality (s :: k1) (t :: k2) (a :: k1) (b :: k2) = Identical a (Proxy b) a (Proxy b) -> Identical a (Proxy b) s (Proxy t) #

When you see this as an argument to a function, it expects an Equality.

type AnEquality' (s :: k2) (a :: k2) = AnEquality s s a a #

A Simple AnEquality.

itraverseByOf :: IndexedTraversal i s t a b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> s -> f t #

itraverseBy :: TraversableWithIndex i t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> t a -> f (t b) #

ifoldMapByOf :: IndexedFold i t a -> (r -> r -> r) -> r -> (i -> a -> r) -> t -> r #

ifoldMapBy :: FoldableWithIndex i t => (r -> r -> r) -> r -> (i -> a -> r) -> t a -> r #

imapAccumL :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b) #

Generalizes mapAccumL to add access to the index.

imapAccumLOf accumulates state from left to right.

mapAccumLOf ≡ imapAccumL . const

imapAccumR :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b) #

Generalizes mapAccumR to add access to the index.

imapAccumROf accumulates state from right to left.

mapAccumR ≡ imapAccumR . const

iforM :: (TraversableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m (t b) #

Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results, with access its position (and the arguments flipped).

forM a ≡ iforM a . const
iforM ≡ flip imapM

imapM :: (TraversableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m (t b) #

Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results, with access the index.

When you don't need access to the index mapM is more liberal in what it can accept.

mapM ≡ imapM . const

ifor :: (TraversableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f (t b) #

Traverse with an index (and the arguments flipped).

for a ≡ ifor a . const
ifor ≡ flip itraverse

itoList :: FoldableWithIndex i f => f a -> [(i, a)] #

Extract the key-value pairs from a structure.

When you don't need access to the indices in the result, then toList is more flexible in what it accepts.

toList ≡ map snd . itoList

ifoldlM :: (FoldableWithIndex i f, Monad m) => (i -> b -> a -> m b) -> b -> f a -> m b #

Monadic fold over the elements of a structure with an index, associating to the left.

When you don't need access to the index then foldlM is more flexible in what it accepts.

foldlM ≡ ifoldlM . const

ifoldrM :: (FoldableWithIndex i f, Monad m) => (i -> a -> b -> m b) -> b -> f a -> m b #

Monadic fold right over the elements of a structure with an index.

When you don't need access to the index then foldrM is more flexible in what it accepts.

foldrM ≡ ifoldrM . const

ifind :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Maybe (i, a) #

Searches a container with a predicate that is also supplied the index, returning the left-most element of the structure matching the predicate, or Nothing if there is no such element.

When you don't need access to the index then find is more flexible in what it accepts.

find ≡ ifind . const

iconcatMap :: FoldableWithIndex i f => (i -> a -> [b]) -> f a -> [b] #

Concatenate the results of a function of the elements of an indexed container with access to the index.

When you don't need access to the index then concatMap is more flexible in what it accepts.

concatMap ≡ iconcatMap . const
iconcatMap ≡ ifoldMap

iforM_ :: (FoldableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m () #

Run monadic actions for each target of an IndexedFold or IndexedTraversal with access to the index, discarding the results (with the arguments flipped).

iforM_ ≡ flip imapM_

When you don't need access to the index then forMOf_ is more flexible in what it accepts.

forMOf_ l a ≡ iforMOf l a . const

imapM_ :: (FoldableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m () #

Run monadic actions for each target of an IndexedFold or IndexedTraversal with access to the index, discarding the results.

When you don't need access to the index then mapMOf_ is more flexible in what it accepts.

mapM_ ≡ imapM . const

ifor_ :: (FoldableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f () #

Traverse elements with access to the index i, discarding the results (with the arguments flipped).

ifor_ ≡ flip itraverse_

When you don't need access to the index then for_ is more flexible in what it accepts.

for_ a ≡ ifor_ a . const

itraverse_ :: (FoldableWithIndex i t, Applicative f) => (i -> a -> f b) -> t a -> f () #

Traverse elements with access to the index i, discarding the results.

When you don't need access to the index then traverse_ is more flexible in what it accepts.

traverse_ l = itraverse . const

none :: Foldable f => (a -> Bool) -> f a -> Bool #

Determines whether no elements of the structure satisfy the predicate.

none f ≡ not . any f

inone :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool #

Return whether or not none of the elements in a container satisfy a predicate, with access to the index i.

When you don't need access to the index then none is more flexible in what it accepts.

none ≡ inone . const
inone f ≡ not . iany f

iall :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool #

Return whether or not all elements in a container satisfy a predicate, with access to the index i.

When you don't need access to the index then all is more flexible in what it accepts.

all ≡ iall . const

iany :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool #

Return whether or not any element in a container satisfies a predicate, with access to the index i.

When you don't need access to the index then any is more flexible in what it accepts.

any ≡ iany . const

index :: (Indexable i p, Eq i, Applicative f) => i -> Optical' p (Indexed i) f a a #

This allows you to filter an IndexedFold, IndexedGetter, IndexedTraversal or IndexedLens based on an index.

>>> ["hello","the","world","!!!"]^?traversed.index 2
Just "world"

indices :: (Indexable i p, Applicative f) => (i -> Bool) -> Optical' p (Indexed i) f a a #

This allows you to filter an IndexedFold, IndexedGetter, IndexedTraversal or IndexedLens based on a predicate on the indices.

>>> ["hello","the","world","!!!"]^..traversed.indices even
["hello","world"]

>>> over (traversed.indices (>0)) Prelude.reverse $ ["He","was","stressed","o_O"]
["He","saw","desserts","O_o"]

icompose :: Indexable p c => (i -> j -> p) -> (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> c a b -> r #

Composition of Indexed functions with a user supplied function for combining indices.

(<.>) :: Indexable (i, j) p => (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> p a b -> r infixr 9 #

Composition of Indexed functions.

Mnemonically, the < and > points to the fact that we want to preserve the indices.

>>> let nestedMap = (fmap Map.fromList . Map.fromList) [(1, [(10, "one,ten"), (20, "one,twenty")]), (2, [(30, "two,thirty"), (40,"two,forty")])]
>>> nestedMap^..(itraversed<.>itraversed).withIndex
[((1,10),"one,ten"),((1,20),"one,twenty"),((2,30),"two,thirty"),((2,40),"two,forty")]

reindexed :: Indexable j p => (i -> j) -> (Indexed i a b -> r) -> p a b -> r #

Remap the index.

selfIndex :: Indexable a p => p a fb -> a -> fb #

Use a value itself as its own index. This is essentially an indexed version of id.

Note: When used to modify the value, this can break the index requirements assumed by indices and similar, so this is only properly an IndexedGetter, but it can be used as more.

selfIndex :: IndexedGetter a a b

(.>) :: (st -> r) -> (kab -> st) -> kab -> r infixr 9 #

Compose a non-indexed function with an Indexed function.

Mnemonically, the > points to the indexing we want to preserve.

This is the same as (.).

f . g (and f .> g) gives you the index of g unless g is index-preserving, like a Prism, Iso or Equality, in which case it'll pass through the index of f.

>>> let nestedMap = (fmap Map.fromList . Map.fromList) [(1, [(10, "one,ten"), (20, "one,twenty")]), (2, [(30, "two,thirty"), (40,"two,forty")])]
>>> nestedMap^..(itraversed.>itraversed).withIndex
[(10,"one,ten"),(20,"one,twenty"),(30,"two,thirty"),(40,"two,forty")]

(<.) :: Indexable i p => (Indexed i s t -> r) -> ((a -> b) -> s -> t) -> p a b -> r infixr 9 #

Compose an Indexed function with a non-indexed function.

Mnemonically, the < points to the indexing we want to preserve.

>>> let nestedMap = (fmap Map.fromList . Map.fromList) [(1, [(10, "one,ten"), (20, "one,twenty")]), (2, [(30, "two,thirty"), (40,"two,forty")])]
>>> nestedMap^..(itraversed<.itraversed).withIndex
[(1,"one,ten"),(1,"one,twenty"),(2,"two,thirty"),(2,"two,forty")]

class Functor f => FunctorWithIndex i (f :: Type -> Type) | f -> i where #

A Functor with an additional index.

Instances must satisfy a modified form of the Functor laws:

imap f . imap g ≡ imap (\i -> f i . g i)
imap (\_ a -> a) ≡ id

Minimal complete definition

Nothing

Methods

imap :: (i -> a -> b) -> f a -> f b #

Map with access to the index.

imapped :: IndexedSetter i (f a) (f b) a b #

The IndexedSetter for a FunctorWithIndex.

If you don't need access to the index, then mapped is more flexible in what it accepts.

Instances

FunctorWithIndex Int []	The position in the list is available as the index.
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> [a] -> [b] # imapped :: IndexedSetter Int [a] [b] a b #
FunctorWithIndex Int ZipList	Same instance as for `[]`.
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> ZipList a -> ZipList b # imapped :: IndexedSetter Int (ZipList a) (ZipList b) a b #
FunctorWithIndex Int NonEmpty
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> NonEmpty a -> NonEmpty b # imapped :: IndexedSetter Int (NonEmpty a) (NonEmpty b) a b #
FunctorWithIndex Int IntMap
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> IntMap a -> IntMap b # imapped :: IndexedSetter Int (IntMap a) (IntMap b) a b #
FunctorWithIndex Int Seq	The position in the `Seq` is available as the index.
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> Seq a -> Seq b # imapped :: IndexedSetter Int (Seq a) (Seq b) a b #
FunctorWithIndex Int Vector
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> Vector a -> Vector b # imapped :: IndexedSetter Int (Vector a) (Vector b) a b #
FunctorWithIndex () Maybe
Instance details Defined in Control.Lens.Indexed Methods imap :: (() -> a -> b) -> Maybe a -> Maybe b # imapped :: IndexedSetter () (Maybe a) (Maybe b) a b #
FunctorWithIndex () Par1
Instance details Defined in Control.Lens.Indexed Methods imap :: (() -> a -> b) -> Par1 a -> Par1 b # imapped :: IndexedSetter () (Par1 a) (Par1 b) a b #
FunctorWithIndex () Identity
Instance details Defined in Control.Lens.Indexed Methods imap :: (() -> a -> b) -> Identity a -> Identity b # imapped :: IndexedSetter () (Identity a) (Identity b) a b #
FunctorWithIndex k (Map k)
Instance details Defined in Control.Lens.Indexed Methods imap :: (k -> a -> b) -> Map k a -> Map k b # imapped :: IndexedSetter k (Map k a) (Map k b) a b #
FunctorWithIndex k (HashMap k)
Instance details Defined in Control.Lens.Indexed Methods imap :: (k -> a -> b) -> HashMap k a -> HashMap k b # imapped :: IndexedSetter k (HashMap k a) (HashMap k b) a b #
FunctorWithIndex k ((,) k)
Instance details Defined in Control.Lens.Indexed Methods imap :: (k -> a -> b) -> (k, a) -> (k, b) # imapped :: IndexedSetter k (k, a) (k, b) a b #
FunctorWithIndex i (Level i)
Instance details Defined in Control.Lens.Indexed Methods imap :: (i -> a -> b) -> Level i a -> Level i b # imapped :: IndexedSetter i (Level i a) (Level i b) a b #
Ix i => FunctorWithIndex i (Array i)
Instance details Defined in Control.Lens.Indexed Methods imap :: (i -> a -> b) -> Array i a -> Array i b # imapped :: IndexedSetter i (Array i a) (Array i b) a b #
FunctorWithIndex Void (V1 :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Void -> a -> b) -> V1 a -> V1 b # imapped :: IndexedSetter Void (V1 a) (V1 b) a b #
FunctorWithIndex Void (U1 :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Void -> a -> b) -> U1 a -> U1 b # imapped :: IndexedSetter Void (U1 a) (U1 b) a b #
FunctorWithIndex Void (Proxy :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Void -> a -> b) -> Proxy a -> Proxy b # imapped :: IndexedSetter Void (Proxy a) (Proxy b) a b #
FunctorWithIndex () (Tagged a)
Instance details Defined in Control.Lens.Indexed Methods imap :: (() -> a0 -> b) -> Tagged a a0 -> Tagged a b # imapped :: IndexedSetter () (Tagged a a0) (Tagged a b) a0 b #
FunctorWithIndex i f => FunctorWithIndex i (Reverse f)
Instance details Defined in Control.Lens.Indexed Methods imap :: (i -> a -> b) -> Reverse f a -> Reverse f b # imapped :: IndexedSetter i (Reverse f a) (Reverse f b) a b #
FunctorWithIndex i f => FunctorWithIndex i (Rec1 f)
Instance details Defined in Control.Lens.Indexed Methods imap :: (i -> a -> b) -> Rec1 f a -> Rec1 f b # imapped :: IndexedSetter i (Rec1 f a) (Rec1 f b) a b #
FunctorWithIndex i m => FunctorWithIndex i (IdentityT m)
Instance details Defined in Control.Lens.Indexed Methods imap :: (i -> a -> b) -> IdentityT m a -> IdentityT m b # imapped :: IndexedSetter i (IdentityT m a) (IdentityT m b) a b #
FunctorWithIndex i f => FunctorWithIndex i (Backwards f)
Instance details Defined in Control.Lens.Indexed Methods imap :: (i -> a -> b) -> Backwards f a -> Backwards f b # imapped :: IndexedSetter i (Backwards f a) (Backwards f b) a b #
FunctorWithIndex r ((->) r :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods imap :: (r -> a -> b) -> (r -> a) -> r -> b # imapped :: IndexedSetter r (r -> a) (r -> b) a b #
FunctorWithIndex i (Magma i t b)
Instance details Defined in Control.Lens.Indexed Methods imap :: (i -> a -> b0) -> Magma i t b a -> Magma i t b b0 # imapped :: IndexedSetter i (Magma i t b a) (Magma i t b b0) a b0 #
FunctorWithIndex Void (K1 i c :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Void -> a -> b) -> K1 i c a -> K1 i c b # imapped :: IndexedSetter Void (K1 i c a) (K1 i c b) a b #
FunctorWithIndex [Int] Tree
Instance details Defined in Control.Lens.Indexed Methods imap :: ([Int] -> a -> b) -> Tree a -> Tree b # imapped :: IndexedSetter [Int] (Tree a) (Tree b) a b #
FunctorWithIndex i f => FunctorWithIndex [i] (Free f)
Instance details Defined in Control.Lens.Indexed Methods imap :: ([i] -> a -> b) -> Free f a -> Free f b # imapped :: IndexedSetter [i] (Free f a) (Free f b) a b #
FunctorWithIndex i f => FunctorWithIndex [i] (Cofree f)
Instance details Defined in Control.Lens.Indexed Methods imap :: ([i] -> a -> b) -> Cofree f a -> Cofree f b # imapped :: IndexedSetter [i] (Cofree f a) (Cofree f b) a b #
FunctorWithIndex i w => FunctorWithIndex (s, i) (TracedT s w)
Instance details Defined in Control.Lens.Indexed Methods imap :: ((s, i) -> a -> b) -> TracedT s w a -> TracedT s w b # imapped :: IndexedSetter (s, i) (TracedT s w a) (TracedT s w b) a b #
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (Sum f g)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Either i j -> a -> b) -> Sum f g a -> Sum f g b # imapped :: IndexedSetter (Either i j) (Sum f g a) (Sum f g b) a b #
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (Product f g)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Either i j -> a -> b) -> Product f g a -> Product f g b # imapped :: IndexedSetter (Either i j) (Product f g a) (Product f g b) a b #
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (f :+: g)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Either i j -> a -> b) -> (f :+: g) a -> (f :+: g) b # imapped :: IndexedSetter (Either i j) ((f :+: g) a) ((f :+: g) b) a b #
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (f :*: g)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Either i j -> a -> b) -> (f :: g) a -> (f :: g) b # imapped :: IndexedSetter (Either i j) ((f :: g) a) ((f :: g) b) a b #
FunctorWithIndex i m => FunctorWithIndex (e, i) (ReaderT e m)
Instance details Defined in Control.Lens.Indexed Methods imap :: ((e, i) -> a -> b) -> ReaderT e m a -> ReaderT e m b # imapped :: IndexedSetter (e, i) (ReaderT e m a) (ReaderT e m b) a b #
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (i, j) (Compose f g)
Instance details Defined in Control.Lens.Indexed Methods imap :: ((i, j) -> a -> b) -> Compose f g a -> Compose f g b # imapped :: IndexedSetter (i, j) (Compose f g a) (Compose f g b) a b #
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (i, j) (f :.: g)
Instance details Defined in Control.Lens.Indexed Methods imap :: ((i, j) -> a -> b) -> (f :.: g) a -> (f :.: g) b # imapped :: IndexedSetter (i, j) ((f :.: g) a) ((f :.: g) b) a b #

class Foldable f => FoldableWithIndex i (f :: Type -> Type) | f -> i where #

A container that supports folding with an additional index.

Minimal complete definition

Nothing

Methods

ifoldMap :: Monoid m => (i -> a -> m) -> f a -> m #

Fold a container by mapping value to an arbitrary Monoid with access to the index i.

When you don't need access to the index then foldMap is more flexible in what it accepts.

foldMap ≡ ifoldMap . const

ifolded :: IndexedFold i (f a) a #

The IndexedFold of a FoldableWithIndex container.

ifolded . asIndex is a fold over the keys of a FoldableWithIndex.

>>> Data.Map.fromList [(2, "hello"), (1, "world")]^..ifolded.asIndex
[1,2]

ifoldr :: (i -> a -> b -> b) -> b -> f a -> b #

Right-associative fold of an indexed container with access to the index i.

When you don't need access to the index then foldr is more flexible in what it accepts.

foldr ≡ ifoldr . const

ifoldl :: (i -> b -> a -> b) -> b -> f a -> b #

Left-associative fold of an indexed container with access to the index i.

When you don't need access to the index then foldl is more flexible in what it accepts.

foldl ≡ ifoldl . const

ifoldr' :: (i -> a -> b -> b) -> b -> f a -> b #

Strictly fold right over the elements of a structure with access to the index i.

When you don't need access to the index then Foldable is more flexible in what it accepts.

Foldable ≡ ifoldr' . const

ifoldl' :: (i -> b -> a -> b) -> b -> f a -> b #

Fold over the elements of a structure with an index, associating to the left, but strictly.

When you don't need access to the index then foldlOf' is more flexible in what it accepts.

foldlOf' l ≡ ifoldlOf' l . const

Instances

FoldableWithIndex Int []
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> [a] -> m # ifolded :: IndexedFold Int [a] a # ifoldr :: (Int -> a -> b -> b) -> b -> [a] -> b # ifoldl :: (Int -> b -> a -> b) -> b -> [a] -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> [a] -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> [a] -> b #
FoldableWithIndex Int ZipList
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> ZipList a -> m # ifolded :: IndexedFold Int (ZipList a) a # ifoldr :: (Int -> a -> b -> b) -> b -> ZipList a -> b # ifoldl :: (Int -> b -> a -> b) -> b -> ZipList a -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> ZipList a -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> ZipList a -> b #
FoldableWithIndex Int NonEmpty
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> NonEmpty a -> m # ifolded :: IndexedFold Int (NonEmpty a) a # ifoldr :: (Int -> a -> b -> b) -> b -> NonEmpty a -> b # ifoldl :: (Int -> b -> a -> b) -> b -> NonEmpty a -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> NonEmpty a -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> NonEmpty a -> b #
FoldableWithIndex Int IntMap
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> IntMap a -> m # ifolded :: IndexedFold Int (IntMap a) a # ifoldr :: (Int -> a -> b -> b) -> b -> IntMap a -> b # ifoldl :: (Int -> b -> a -> b) -> b -> IntMap a -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> IntMap a -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> IntMap a -> b #
FoldableWithIndex Int Seq
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> Seq a -> m # ifolded :: IndexedFold Int (Seq a) a # ifoldr :: (Int -> a -> b -> b) -> b -> Seq a -> b # ifoldl :: (Int -> b -> a -> b) -> b -> Seq a -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> Seq a -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> Seq a -> b #
FoldableWithIndex Int Vector
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> Vector a -> m # ifolded :: IndexedFold Int (Vector a) a # ifoldr :: (Int -> a -> b -> b) -> b -> Vector a -> b # ifoldl :: (Int -> b -> a -> b) -> b -> Vector a -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> Vector a -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> Vector a -> b #
FoldableWithIndex () Maybe
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (() -> a -> m) -> Maybe a -> m # ifolded :: IndexedFold () (Maybe a) a # ifoldr :: (() -> a -> b -> b) -> b -> Maybe a -> b # ifoldl :: (() -> b -> a -> b) -> b -> Maybe a -> b # ifoldr' :: (() -> a -> b -> b) -> b -> Maybe a -> b # ifoldl' :: (() -> b -> a -> b) -> b -> Maybe a -> b #
FoldableWithIndex () Par1
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (() -> a -> m) -> Par1 a -> m # ifolded :: IndexedFold () (Par1 a) a # ifoldr :: (() -> a -> b -> b) -> b -> Par1 a -> b # ifoldl :: (() -> b -> a -> b) -> b -> Par1 a -> b # ifoldr' :: (() -> a -> b -> b) -> b -> Par1 a -> b # ifoldl' :: (() -> b -> a -> b) -> b -> Par1 a -> b #
FoldableWithIndex () Identity
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (() -> a -> m) -> Identity a -> m # ifolded :: IndexedFold () (Identity a) a # ifoldr :: (() -> a -> b -> b) -> b -> Identity a -> b # ifoldl :: (() -> b -> a -> b) -> b -> Identity a -> b # ifoldr' :: (() -> a -> b -> b) -> b -> Identity a -> b # ifoldl' :: (() -> b -> a -> b) -> b -> Identity a -> b #
FoldableWithIndex k (Map k)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (k -> a -> m) -> Map k a -> m # ifolded :: IndexedFold k (Map k a) a # ifoldr :: (k -> a -> b -> b) -> b -> Map k a -> b # ifoldl :: (k -> b -> a -> b) -> b -> Map k a -> b # ifoldr' :: (k -> a -> b -> b) -> b -> Map k a -> b # ifoldl' :: (k -> b -> a -> b) -> b -> Map k a -> b #
FoldableWithIndex k (HashMap k)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (k -> a -> m) -> HashMap k a -> m # ifolded :: IndexedFold k (HashMap k a) a # ifoldr :: (k -> a -> b -> b) -> b -> HashMap k a -> b # ifoldl :: (k -> b -> a -> b) -> b -> HashMap k a -> b # ifoldr' :: (k -> a -> b -> b) -> b -> HashMap k a -> b # ifoldl' :: (k -> b -> a -> b) -> b -> HashMap k a -> b #
FoldableWithIndex k ((,) k)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (k -> a -> m) -> (k, a) -> m # ifolded :: IndexedFold k (k, a) a # ifoldr :: (k -> a -> b -> b) -> b -> (k, a) -> b # ifoldl :: (k -> b -> a -> b) -> b -> (k, a) -> b # ifoldr' :: (k -> a -> b -> b) -> b -> (k, a) -> b # ifoldl' :: (k -> b -> a -> b) -> b -> (k, a) -> b #
FoldableWithIndex i (Level i)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (i -> a -> m) -> Level i a -> m # ifolded :: IndexedFold i (Level i a) a # ifoldr :: (i -> a -> b -> b) -> b -> Level i a -> b # ifoldl :: (i -> b -> a -> b) -> b -> Level i a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> Level i a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> Level i a -> b #
Ix i => FoldableWithIndex i (Array i)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (i -> a -> m) -> Array i a -> m # ifolded :: IndexedFold i (Array i a) a # ifoldr :: (i -> a -> b -> b) -> b -> Array i a -> b # ifoldl :: (i -> b -> a -> b) -> b -> Array i a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> Array i a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> Array i a -> b #
FoldableWithIndex Void (V1 :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Void -> a -> m) -> V1 a -> m # ifolded :: IndexedFold Void (V1 a) a # ifoldr :: (Void -> a -> b -> b) -> b -> V1 a -> b # ifoldl :: (Void -> b -> a -> b) -> b -> V1 a -> b # ifoldr' :: (Void -> a -> b -> b) -> b -> V1 a -> b # ifoldl' :: (Void -> b -> a -> b) -> b -> V1 a -> b #
FoldableWithIndex Void (U1 :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Void -> a -> m) -> U1 a -> m # ifolded :: IndexedFold Void (U1 a) a # ifoldr :: (Void -> a -> b -> b) -> b -> U1 a -> b # ifoldl :: (Void -> b -> a -> b) -> b -> U1 a -> b # ifoldr' :: (Void -> a -> b -> b) -> b -> U1 a -> b # ifoldl' :: (Void -> b -> a -> b) -> b -> U1 a -> b #
FoldableWithIndex Void (Proxy :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Void -> a -> m) -> Proxy a -> m # ifolded :: IndexedFold Void (Proxy a) a # ifoldr :: (Void -> a -> b -> b) -> b -> Proxy a -> b # ifoldl :: (Void -> b -> a -> b) -> b -> Proxy a -> b # ifoldr' :: (Void -> a -> b -> b) -> b -> Proxy a -> b # ifoldl' :: (Void -> b -> a -> b) -> b -> Proxy a -> b #
FoldableWithIndex () (Tagged a)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (() -> a0 -> m) -> Tagged a a0 -> m # ifolded :: IndexedFold () (Tagged a a0) a0 # ifoldr :: (() -> a0 -> b -> b) -> b -> Tagged a a0 -> b # ifoldl :: (() -> b -> a0 -> b) -> b -> Tagged a a0 -> b # ifoldr' :: (() -> a0 -> b -> b) -> b -> Tagged a a0 -> b # ifoldl' :: (() -> b -> a0 -> b) -> b -> Tagged a a0 -> b #
FoldableWithIndex i f => FoldableWithIndex i (Reverse f)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (i -> a -> m) -> Reverse f a -> m # ifolded :: IndexedFold i (Reverse f a) a # ifoldr :: (i -> a -> b -> b) -> b -> Reverse f a -> b # ifoldl :: (i -> b -> a -> b) -> b -> Reverse f a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> Reverse f a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> Reverse f a -> b #
FoldableWithIndex i f => FoldableWithIndex i (Rec1 f)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (i -> a -> m) -> Rec1 f a -> m # ifolded :: IndexedFold i (Rec1 f a) a # ifoldr :: (i -> a -> b -> b) -> b -> Rec1 f a -> b # ifoldl :: (i -> b -> a -> b) -> b -> Rec1 f a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> Rec1 f a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> Rec1 f a -> b #
FoldableWithIndex i m => FoldableWithIndex i (IdentityT m)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m0 => (i -> a -> m0) -> IdentityT m a -> m0 # ifolded :: IndexedFold i (IdentityT m a) a # ifoldr :: (i -> a -> b -> b) -> b -> IdentityT m a -> b # ifoldl :: (i -> b -> a -> b) -> b -> IdentityT m a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> IdentityT m a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> IdentityT m a -> b #
FoldableWithIndex i f => FoldableWithIndex i (Backwards f)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (i -> a -> m) -> Backwards f a -> m # ifolded :: IndexedFold i (Backwards f a) a # ifoldr :: (i -> a -> b -> b) -> b -> Backwards f a -> b # ifoldl :: (i -> b -> a -> b) -> b -> Backwards f a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> Backwards f a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> Backwards f a -> b #
FoldableWithIndex i (Magma i t b)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (i -> a -> m) -> Magma i t b a -> m # ifolded :: IndexedFold i (Magma i t b a) a # ifoldr :: (i -> a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # ifoldl :: (i -> b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 # ifoldr' :: (i -> a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # ifoldl' :: (i -> b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 #
FoldableWithIndex Void (K1 i c :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Void -> a -> m) -> K1 i c a -> m # ifolded :: IndexedFold Void (K1 i c a) a # ifoldr :: (Void -> a -> b -> b) -> b -> K1 i c a -> b # ifoldl :: (Void -> b -> a -> b) -> b -> K1 i c a -> b # ifoldr' :: (Void -> a -> b -> b) -> b -> K1 i c a -> b # ifoldl' :: (Void -> b -> a -> b) -> b -> K1 i c a -> b #
FoldableWithIndex [Int] Tree
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => ([Int] -> a -> m) -> Tree a -> m # ifolded :: IndexedFold [Int] (Tree a) a # ifoldr :: ([Int] -> a -> b -> b) -> b -> Tree a -> b # ifoldl :: ([Int] -> b -> a -> b) -> b -> Tree a -> b # ifoldr' :: ([Int] -> a -> b -> b) -> b -> Tree a -> b # ifoldl' :: ([Int] -> b -> a -> b) -> b -> Tree a -> b #
FoldableWithIndex i f => FoldableWithIndex [i] (Free f)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => ([i] -> a -> m) -> Free f a -> m # ifolded :: IndexedFold [i] (Free f a) a # ifoldr :: ([i] -> a -> b -> b) -> b -> Free f a -> b # ifoldl :: ([i] -> b -> a -> b) -> b -> Free f a -> b # ifoldr' :: ([i] -> a -> b -> b) -> b -> Free f a -> b # ifoldl' :: ([i] -> b -> a -> b) -> b -> Free f a -> b #
FoldableWithIndex i f => FoldableWithIndex [i] (Cofree f)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => ([i] -> a -> m) -> Cofree f a -> m # ifolded :: IndexedFold [i] (Cofree f a) a # ifoldr :: ([i] -> a -> b -> b) -> b -> Cofree f a -> b # ifoldl :: ([i] -> b -> a -> b) -> b -> Cofree f a -> b # ifoldr' :: ([i] -> a -> b -> b) -> b -> Cofree f a -> b # ifoldl' :: ([i] -> b -> a -> b) -> b -> Cofree f a -> b #
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (Sum f g)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Either i j -> a -> m) -> Sum f g a -> m # ifolded :: IndexedFold (Either i j) (Sum f g a) a # ifoldr :: (Either i j -> a -> b -> b) -> b -> Sum f g a -> b # ifoldl :: (Either i j -> b -> a -> b) -> b -> Sum f g a -> b # ifoldr' :: (Either i j -> a -> b -> b) -> b -> Sum f g a -> b # ifoldl' :: (Either i j -> b -> a -> b) -> b -> Sum f g a -> b #
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (Product f g)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Either i j -> a -> m) -> Product f g a -> m # ifolded :: IndexedFold (Either i j) (Product f g a) a # ifoldr :: (Either i j -> a -> b -> b) -> b -> Product f g a -> b # ifoldl :: (Either i j -> b -> a -> b) -> b -> Product f g a -> b # ifoldr' :: (Either i j -> a -> b -> b) -> b -> Product f g a -> b # ifoldl' :: (Either i j -> b -> a -> b) -> b -> Product f g a -> b #
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (f :+: g)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Either i j -> a -> m) -> (f :+: g) a -> m # ifolded :: IndexedFold (Either i j) ((f :+: g) a) a # ifoldr :: (Either i j -> a -> b -> b) -> b -> (f :+: g) a -> b # ifoldl :: (Either i j -> b -> a -> b) -> b -> (f :+: g) a -> b # ifoldr' :: (Either i j -> a -> b -> b) -> b -> (f :+: g) a -> b # ifoldl' :: (Either i j -> b -> a -> b) -> b -> (f :+: g) a -> b #
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (f :*: g)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Either i j -> a -> m) -> (f :: g) a -> m # ifolded :: IndexedFold (Either i j) ((f :: g) a) a # ifoldr :: (Either i j -> a -> b -> b) -> b -> (f :: g) a -> b # ifoldl :: (Either i j -> b -> a -> b) -> b -> (f :: g) a -> b # ifoldr' :: (Either i j -> a -> b -> b) -> b -> (f :: g) a -> b # ifoldl' :: (Either i j -> b -> a -> b) -> b -> (f :: g) a -> b #
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (i, j) (Compose f g)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => ((i, j) -> a -> m) -> Compose f g a -> m # ifolded :: IndexedFold (i, j) (Compose f g a) a # ifoldr :: ((i, j) -> a -> b -> b) -> b -> Compose f g a -> b # ifoldl :: ((i, j) -> b -> a -> b) -> b -> Compose f g a -> b # ifoldr' :: ((i, j) -> a -> b -> b) -> b -> Compose f g a -> b # ifoldl' :: ((i, j) -> b -> a -> b) -> b -> Compose f g a -> b #
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (i, j) (f :.: g)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => ((i, j) -> a -> m) -> (f :.: g) a -> m # ifolded :: IndexedFold (i, j) ((f :.: g) a) a # ifoldr :: ((i, j) -> a -> b -> b) -> b -> (f :.: g) a -> b # ifoldl :: ((i, j) -> b -> a -> b) -> b -> (f :.: g) a -> b # ifoldr' :: ((i, j) -> a -> b -> b) -> b -> (f :.: g) a -> b # ifoldl' :: ((i, j) -> b -> a -> b) -> b -> (f :.: g) a -> b #

class (FunctorWithIndex i t, FoldableWithIndex i t, Traversable t) => TraversableWithIndex i (t :: Type -> Type) | t -> i where #

A Traversable with an additional index.

An instance must satisfy a (modified) form of the Traversable laws:

itraverse (const Identity) ≡ Identity
fmap (itraverse f) . itraverse g ≡ getCompose . itraverse (\i -> Compose . fmap (f i) . g i)

Minimal complete definition

Nothing

Methods

itraverse :: Applicative f => (i -> a -> f b) -> t a -> f (t b) #

Traverse an indexed container.

itraverse ≡ itraverseOf itraversed

itraversed :: IndexedTraversal i (t a) (t b) a b #

The IndexedTraversal of a TraversableWithIndex container.

Instances

TraversableWithIndex Int []
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> [a] -> f [b] # itraversed :: IndexedTraversal Int [a] [b] a b #
TraversableWithIndex Int ZipList
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> ZipList a -> f (ZipList b) # itraversed :: IndexedTraversal Int (ZipList a) (ZipList b) a b #
TraversableWithIndex Int NonEmpty
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> NonEmpty a -> f (NonEmpty b) # itraversed :: IndexedTraversal Int (NonEmpty a) (NonEmpty b) a b #
TraversableWithIndex Int IntMap
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> IntMap a -> f (IntMap b) # itraversed :: IndexedTraversal Int (IntMap a) (IntMap b) a b #
TraversableWithIndex Int Seq
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> Seq a -> f (Seq b) # itraversed :: IndexedTraversal Int (Seq a) (Seq b) a b #
TraversableWithIndex Int Vector
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> Vector a -> f (Vector b) # itraversed :: IndexedTraversal Int (Vector a) (Vector b) a b #
TraversableWithIndex () Maybe
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (() -> a -> f b) -> Maybe a -> f (Maybe b) # itraversed :: IndexedTraversal () (Maybe a) (Maybe b) a b #
TraversableWithIndex () Par1
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (() -> a -> f b) -> Par1 a -> f (Par1 b) # itraversed :: IndexedTraversal () (Par1 a) (Par1 b) a b #
TraversableWithIndex () Identity
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (() -> a -> f b) -> Identity a -> f (Identity b) # itraversed :: IndexedTraversal () (Identity a) (Identity b) a b #
TraversableWithIndex k (Map k)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (k -> a -> f b) -> Map k a -> f (Map k b) # itraversed :: IndexedTraversal k (Map k a) (Map k b) a b #
TraversableWithIndex k (HashMap k)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (k -> a -> f b) -> HashMap k a -> f (HashMap k b) # itraversed :: IndexedTraversal k (HashMap k a) (HashMap k b) a b #
TraversableWithIndex k ((,) k)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (k -> a -> f b) -> (k, a) -> f (k, b) # itraversed :: IndexedTraversal k (k, a) (k, b) a b #
TraversableWithIndex i (Level i)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (i -> a -> f b) -> Level i a -> f (Level i b) # itraversed :: IndexedTraversal i (Level i a) (Level i b) a b #
Ix i => TraversableWithIndex i (Array i)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (i -> a -> f b) -> Array i a -> f (Array i b) # itraversed :: IndexedTraversal i (Array i a) (Array i b) a b #
TraversableWithIndex Void (V1 :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Void -> a -> f b) -> V1 a -> f (V1 b) # itraversed :: IndexedTraversal Void (V1 a) (V1 b) a b #
TraversableWithIndex Void (U1 :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Void -> a -> f b) -> U1 a -> f (U1 b) # itraversed :: IndexedTraversal Void (U1 a) (U1 b) a b #
TraversableWithIndex Void (Proxy :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Void -> a -> f b) -> Proxy a -> f (Proxy b) # itraversed :: IndexedTraversal Void (Proxy a) (Proxy b) a b #
TraversableWithIndex () (Tagged a)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (() -> a0 -> f b) -> Tagged a a0 -> f (Tagged a b) # itraversed :: IndexedTraversal () (Tagged a a0) (Tagged a b) a0 b #
TraversableWithIndex i f => TraversableWithIndex i (Reverse f)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => (i -> a -> f0 b) -> Reverse f a -> f0 (Reverse f b) # itraversed :: IndexedTraversal i (Reverse f a) (Reverse f b) a b #
TraversableWithIndex i f => TraversableWithIndex i (Rec1 f)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => (i -> a -> f0 b) -> Rec1 f a -> f0 (Rec1 f b) # itraversed :: IndexedTraversal i (Rec1 f a) (Rec1 f b) a b #
TraversableWithIndex i m => TraversableWithIndex i (IdentityT m)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (i -> a -> f b) -> IdentityT m a -> f (IdentityT m b) # itraversed :: IndexedTraversal i (IdentityT m a) (IdentityT m b) a b #
TraversableWithIndex i f => TraversableWithIndex i (Backwards f)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => (i -> a -> f0 b) -> Backwards f a -> f0 (Backwards f b) # itraversed :: IndexedTraversal i (Backwards f a) (Backwards f b) a b #
TraversableWithIndex i (Magma i t b)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (i -> a -> f b0) -> Magma i t b a -> f (Magma i t b b0) # itraversed :: IndexedTraversal i (Magma i t b a) (Magma i t b b0) a b0 #
TraversableWithIndex Void (K1 i c :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Void -> a -> f b) -> K1 i c a -> f (K1 i c b) # itraversed :: IndexedTraversal Void (K1 i c a) (K1 i c b) a b #
TraversableWithIndex [Int] Tree
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => ([Int] -> a -> f b) -> Tree a -> f (Tree b) # itraversed :: IndexedTraversal [Int] (Tree a) (Tree b) a b #
TraversableWithIndex i f => TraversableWithIndex [i] (Free f)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => ([i] -> a -> f0 b) -> Free f a -> f0 (Free f b) # itraversed :: IndexedTraversal [i] (Free f a) (Free f b) a b #
TraversableWithIndex i f => TraversableWithIndex [i] (Cofree f)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => ([i] -> a -> f0 b) -> Cofree f a -> f0 (Cofree f b) # itraversed :: IndexedTraversal [i] (Cofree f a) (Cofree f b) a b #
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (Sum f g)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> Sum f g a -> f0 (Sum f g b) # itraversed :: IndexedTraversal (Either i j) (Sum f g a) (Sum f g b) a b #
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (Product f g)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> Product f g a -> f0 (Product f g b) # itraversed :: IndexedTraversal (Either i j) (Product f g a) (Product f g b) a b #
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (f :+: g)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) # itraversed :: IndexedTraversal (Either i j) ((f :+: g) a) ((f :+: g) b) a b #
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (f :*: g)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> (f :: g) a -> f0 ((f :: g) b) # itraversed :: IndexedTraversal (Either i j) ((f :: g) a) ((f :: g) b) a b #
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (i, j) (Compose f g)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => ((i, j) -> a -> f0 b) -> Compose f g a -> f0 (Compose f g b) # itraversed :: IndexedTraversal (i, j) (Compose f g a) (Compose f g b) a b #
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (i, j) (f :.: g)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => ((i, j) -> a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) # itraversed :: IndexedTraversal (i, j) ((f :.: g) a) ((f :.: g) b) a b #

newtype ReifiedLens s t a b #

Reify a ReifiedLens so it can be stored safely in a container.

Constructors

Lens
Fields runLens :: Lens s t a b

type ReifiedLens' s a = ReifiedLens s s a a #

type ReifiedLens' = Simple ReifiedLens

newtype ReifiedIndexedLens i s t a b #

Reify an ReifiedIndexedLens so it can be stored safely in a container.

Constructors

IndexedLens
Fields runIndexedLens :: IndexedLens i s t a b

type ReifiedIndexedLens' i s a = ReifiedIndexedLens i s s a a #

type ReifiedIndexedLens' i = Simple (ReifiedIndexedLens i)

newtype ReifiedIndexedTraversal i s t a b #

Reify an ReifiedIndexedTraversal so it can be stored safely in a container.

Constructors

IndexedTraversal
Fields runIndexedTraversal :: IndexedTraversal i s t a b

type ReifiedIndexedTraversal' i s a = ReifiedIndexedTraversal i s s a a #

type ReifiedIndexedTraversal' i = Simple (ReifiedIndexedTraversal i)

newtype ReifiedTraversal s t a b #

A form of ReifiedTraversal that can be stored monomorphically in a container.

Constructors

Traversal
Fields runTraversal :: Traversal s t a b

type ReifiedTraversal' s a = ReifiedTraversal s s a a #

type ReifiedTraversal' = Simple ReifiedTraversal

newtype ReifiedGetter s a #

Reify a ReifiedGetter so it can be stored safely in a container.

This can also be useful when combining getters in novel ways, as ReifiedGetter is isomorphic to '(->)' and provides similar instances.

>>> ("hello","world","!!!")^.runGetter ((,) <$> Getter _2 <*> Getter (_1.to length))
("world",5)

Constructors

Getter
Fields runGetter :: Getter s a

Instances

Arrow ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods arr :: (b -> c) -> ReifiedGetter b c # first :: ReifiedGetter b c -> ReifiedGetter (b, d) (c, d) # second :: ReifiedGetter b c -> ReifiedGetter (d, b) (d, c) # (***) :: ReifiedGetter b c -> ReifiedGetter b' c' -> ReifiedGetter (b, b') (c, c') # (&&&) :: ReifiedGetter b c -> ReifiedGetter b c' -> ReifiedGetter b (c, c') #
ArrowChoice ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods left :: ReifiedGetter b c -> ReifiedGetter (Either b d) (Either c d) # right :: ReifiedGetter b c -> ReifiedGetter (Either d b) (Either d c) # (+++) :: ReifiedGetter b c -> ReifiedGetter b' c' -> ReifiedGetter (Either b b') (Either c c') # (\|\|\|) :: ReifiedGetter b d -> ReifiedGetter c d -> ReifiedGetter (Either b c) d #
ArrowApply ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods app :: ReifiedGetter (ReifiedGetter b c, b) c #
ArrowLoop ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods loop :: ReifiedGetter (b, d) (c, d) -> ReifiedGetter b c #
Profunctor ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedGetter b c -> ReifiedGetter a d # lmap :: (a -> b) -> ReifiedGetter b c -> ReifiedGetter a c # rmap :: (b -> c) -> ReifiedGetter a b -> ReifiedGetter a c # (#.) :: Coercible c b => q b c -> ReifiedGetter a b -> ReifiedGetter a c # (.#) :: Coercible b a => ReifiedGetter b c -> q a b -> ReifiedGetter a c #
Representable ReifiedGetter
Instance details Defined in Control.Lens.Reified Associated Types type Rep ReifiedGetter :: Type -> Type # Methods tabulate :: (d -> Rep ReifiedGetter c) -> ReifiedGetter d c #
Corepresentable ReifiedGetter
Instance details Defined in Control.Lens.Reified Associated Types type Corep ReifiedGetter :: Type -> Type # Methods cotabulate :: (Corep ReifiedGetter d -> c) -> ReifiedGetter d c #
Conjoined ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods distrib :: Functor f => ReifiedGetter a b -> ReifiedGetter (f a) (f b) # conjoined :: ((ReifiedGetter ~ (->)) -> q (a -> b) r) -> q (ReifiedGetter a b) r -> q (ReifiedGetter a b) r #
Choice ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods left' :: ReifiedGetter a b -> ReifiedGetter (Either a c) (Either b c) # right' :: ReifiedGetter a b -> ReifiedGetter (Either c a) (Either c b) #
Closed ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods closed :: ReifiedGetter a b -> ReifiedGetter (x -> a) (x -> b) #
Strong ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods first' :: ReifiedGetter a b -> ReifiedGetter (a, c) (b, c) # second' :: ReifiedGetter a b -> ReifiedGetter (c, a) (c, b) #
Costrong ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods unfirst :: ReifiedGetter (a, d) (b, d) -> ReifiedGetter a b # unsecond :: ReifiedGetter (d, a) (d, b) -> ReifiedGetter a b #
Sieve ReifiedGetter Identity
Instance details Defined in Control.Lens.Reified Methods sieve :: ReifiedGetter a b -> a -> Identity b #
Cosieve ReifiedGetter Identity
Instance details Defined in Control.Lens.Reified Methods cosieve :: ReifiedGetter a b -> Identity a -> b #
MonadReader s (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods ask :: ReifiedGetter s s # local :: (s -> s) -> ReifiedGetter s a -> ReifiedGetter s a # reader :: (s -> a) -> ReifiedGetter s a #
Monad (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods (>>=) :: ReifiedGetter s a -> (a -> ReifiedGetter s b) -> ReifiedGetter s b # (>>) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s b # return :: a -> ReifiedGetter s a # fail :: String -> ReifiedGetter s a #
Functor (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods fmap :: (a -> b) -> ReifiedGetter s a -> ReifiedGetter s b # (<$) :: a -> ReifiedGetter s b -> ReifiedGetter s a #
Applicative (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods pure :: a -> ReifiedGetter s a # (<>) :: ReifiedGetter s (a -> b) -> ReifiedGetter s a -> ReifiedGetter s b # liftA2 :: (a -> b -> c) -> ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s c # (>) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s b # (<*) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s a #
Distributive (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods distribute :: Functor f => f (ReifiedGetter s a) -> ReifiedGetter s (f a) # collect :: Functor f => (a -> ReifiedGetter s b) -> f a -> ReifiedGetter s (f b) # distributeM :: Monad m => m (ReifiedGetter s a) -> ReifiedGetter s (m a) # collectM :: Monad m => (a -> ReifiedGetter s b) -> m a -> ReifiedGetter s (m b) #
Monoid s => Comonad (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods extract :: ReifiedGetter s a -> a # duplicate :: ReifiedGetter s a -> ReifiedGetter s (ReifiedGetter s a) # extend :: (ReifiedGetter s a -> b) -> ReifiedGetter s a -> ReifiedGetter s b #
Monoid s => ComonadApply (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods (<@>) :: ReifiedGetter s (a -> b) -> ReifiedGetter s a -> ReifiedGetter s b # (@>) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s b # (<@) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s a #
Apply (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods (<.>) :: ReifiedGetter s (a -> b) -> ReifiedGetter s a -> ReifiedGetter s b # (.>) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s b # (<.) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s a # liftF2 :: (a -> b -> c) -> ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s c #
Bind (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods (>>-) :: ReifiedGetter s a -> (a -> ReifiedGetter s b) -> ReifiedGetter s b # join :: ReifiedGetter s (ReifiedGetter s a) -> ReifiedGetter s a #
Semigroup s => Extend (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods duplicated :: ReifiedGetter s a -> ReifiedGetter s (ReifiedGetter s a) # extended :: (ReifiedGetter s a -> b) -> ReifiedGetter s a -> ReifiedGetter s b #
Category ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods id :: ReifiedGetter a a # (.) :: ReifiedGetter b c -> ReifiedGetter a b -> ReifiedGetter a c #
type Rep ReifiedGetter
Instance details Defined in Control.Lens.Reified type Rep ReifiedGetter = Identity
type Corep ReifiedGetter
Instance details Defined in Control.Lens.Reified type Corep ReifiedGetter = Identity

newtype ReifiedIndexedGetter i s a #

Reify an ReifiedIndexedGetter so it can be stored safely in a container.

Constructors

IndexedGetter
Fields runIndexedGetter :: IndexedGetter i s a

Instances

Profunctor (ReifiedIndexedGetter i)
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedIndexedGetter i b c -> ReifiedIndexedGetter i a d # lmap :: (a -> b) -> ReifiedIndexedGetter i b c -> ReifiedIndexedGetter i a c # rmap :: (b -> c) -> ReifiedIndexedGetter i a b -> ReifiedIndexedGetter i a c # (#.) :: Coercible c b => q b c -> ReifiedIndexedGetter i a b -> ReifiedIndexedGetter i a c # (.#) :: Coercible b a => ReifiedIndexedGetter i b c -> q a b -> ReifiedIndexedGetter i a c #
Representable (ReifiedIndexedGetter i)
Instance details Defined in Control.Lens.Reified Associated Types type Rep (ReifiedIndexedGetter i) :: Type -> Type # Methods tabulate :: (d -> Rep (ReifiedIndexedGetter i) c) -> ReifiedIndexedGetter i d c #
Strong (ReifiedIndexedGetter i)
Instance details Defined in Control.Lens.Reified Methods first' :: ReifiedIndexedGetter i a b -> ReifiedIndexedGetter i (a, c) (b, c) # second' :: ReifiedIndexedGetter i a b -> ReifiedIndexedGetter i (c, a) (c, b) #
Sieve (ReifiedIndexedGetter i) ((,) i)
Instance details Defined in Control.Lens.Reified Methods sieve :: ReifiedIndexedGetter i a b -> a -> (i, b) #
Functor (ReifiedIndexedGetter i s)
Instance details Defined in Control.Lens.Reified Methods fmap :: (a -> b) -> ReifiedIndexedGetter i s a -> ReifiedIndexedGetter i s b # (<$) :: a -> ReifiedIndexedGetter i s b -> ReifiedIndexedGetter i s a #
Semigroup i => Apply (ReifiedIndexedGetter i s)
Instance details Defined in Control.Lens.Reified Methods (<.>) :: ReifiedIndexedGetter i s (a -> b) -> ReifiedIndexedGetter i s a -> ReifiedIndexedGetter i s b # (.>) :: ReifiedIndexedGetter i s a -> ReifiedIndexedGetter i s b -> ReifiedIndexedGetter i s b # (<.) :: ReifiedIndexedGetter i s a -> ReifiedIndexedGetter i s b -> ReifiedIndexedGetter i s a # liftF2 :: (a -> b -> c) -> ReifiedIndexedGetter i s a -> ReifiedIndexedGetter i s b -> ReifiedIndexedGetter i s c #
type Rep (ReifiedIndexedGetter i)
Instance details Defined in Control.Lens.Reified type Rep (ReifiedIndexedGetter i) = (,) i

newtype ReifiedFold s a #

Reify a ReifiedFold so it can be stored safely in a container.

This can also be useful for creatively combining folds as ReifiedFold s is isomorphic to ReaderT s [] and provides similar instances.

>>> ("hello","world")^..runFold ((,) <$> Fold _2 <*> Fold both)
[("world","hello"),("world","world")]

Constructors

Fold
Fields runFold :: Fold s a

Instances

Arrow ReifiedFold
Instance details Defined in Control.Lens.Reified Methods arr :: (b -> c) -> ReifiedFold b c # first :: ReifiedFold b c -> ReifiedFold (b, d) (c, d) # second :: ReifiedFold b c -> ReifiedFold (d, b) (d, c) # (***) :: ReifiedFold b c -> ReifiedFold b' c' -> ReifiedFold (b, b') (c, c') # (&&&) :: ReifiedFold b c -> ReifiedFold b c' -> ReifiedFold b (c, c') #
ArrowChoice ReifiedFold
Instance details Defined in Control.Lens.Reified Methods left :: ReifiedFold b c -> ReifiedFold (Either b d) (Either c d) # right :: ReifiedFold b c -> ReifiedFold (Either d b) (Either d c) # (+++) :: ReifiedFold b c -> ReifiedFold b' c' -> ReifiedFold (Either b b') (Either c c') # (\|\|\|) :: ReifiedFold b d -> ReifiedFold c d -> ReifiedFold (Either b c) d #
ArrowApply ReifiedFold
Instance details Defined in Control.Lens.Reified Methods app :: ReifiedFold (ReifiedFold b c, b) c #
Profunctor ReifiedFold
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedFold b c -> ReifiedFold a d # lmap :: (a -> b) -> ReifiedFold b c -> ReifiedFold a c # rmap :: (b -> c) -> ReifiedFold a b -> ReifiedFold a c # (#.) :: Coercible c b => q b c -> ReifiedFold a b -> ReifiedFold a c # (.#) :: Coercible b a => ReifiedFold b c -> q a b -> ReifiedFold a c #
Representable ReifiedFold
Instance details Defined in Control.Lens.Reified Associated Types type Rep ReifiedFold :: Type -> Type # Methods tabulate :: (d -> Rep ReifiedFold c) -> ReifiedFold d c #
Choice ReifiedFold
Instance details Defined in Control.Lens.Reified Methods left' :: ReifiedFold a b -> ReifiedFold (Either a c) (Either b c) # right' :: ReifiedFold a b -> ReifiedFold (Either c a) (Either c b) #
Strong ReifiedFold
Instance details Defined in Control.Lens.Reified Methods first' :: ReifiedFold a b -> ReifiedFold (a, c) (b, c) # second' :: ReifiedFold a b -> ReifiedFold (c, a) (c, b) #
Sieve ReifiedFold []
Instance details Defined in Control.Lens.Reified Methods sieve :: ReifiedFold a b -> a -> [b] #
MonadReader s (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods ask :: ReifiedFold s s # local :: (s -> s) -> ReifiedFold s a -> ReifiedFold s a # reader :: (s -> a) -> ReifiedFold s a #
Monad (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods (>>=) :: ReifiedFold s a -> (a -> ReifiedFold s b) -> ReifiedFold s b # (>>) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s b # return :: a -> ReifiedFold s a # fail :: String -> ReifiedFold s a #
Functor (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods fmap :: (a -> b) -> ReifiedFold s a -> ReifiedFold s b # (<$) :: a -> ReifiedFold s b -> ReifiedFold s a #
Applicative (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods pure :: a -> ReifiedFold s a # (<>) :: ReifiedFold s (a -> b) -> ReifiedFold s a -> ReifiedFold s b # liftA2 :: (a -> b -> c) -> ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s c # (>) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s b # (<*) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s a #
Alternative (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods empty :: ReifiedFold s a # (<\|>) :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a # some :: ReifiedFold s a -> ReifiedFold s [a] # many :: ReifiedFold s a -> ReifiedFold s [a] #
MonadPlus (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods mzero :: ReifiedFold s a # mplus :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a #
Apply (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods (<.>) :: ReifiedFold s (a -> b) -> ReifiedFold s a -> ReifiedFold s b # (.>) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s b # (<.) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s a # liftF2 :: (a -> b -> c) -> ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s c #
Plus (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods zero :: ReifiedFold s a #
Alt (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods (<!>) :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a # some :: Applicative (ReifiedFold s) => ReifiedFold s a -> ReifiedFold s [a] # many :: Applicative (ReifiedFold s) => ReifiedFold s a -> ReifiedFold s [a] #
Bind (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods (>>-) :: ReifiedFold s a -> (a -> ReifiedFold s b) -> ReifiedFold s b # join :: ReifiedFold s (ReifiedFold s a) -> ReifiedFold s a #
Category ReifiedFold
Instance details Defined in Control.Lens.Reified Methods id :: ReifiedFold a a # (.) :: ReifiedFold b c -> ReifiedFold a b -> ReifiedFold a c #
Semigroup (ReifiedFold s a)
Instance details Defined in Control.Lens.Reified Methods (<>) :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a # sconcat :: NonEmpty (ReifiedFold s a) -> ReifiedFold s a # stimes :: Integral b => b -> ReifiedFold s a -> ReifiedFold s a #
Monoid (ReifiedFold s a)
Instance details Defined in Control.Lens.Reified Methods mempty :: ReifiedFold s a # mappend :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a # mconcat :: [ReifiedFold s a] -> ReifiedFold s a #
type Rep ReifiedFold
Instance details Defined in Control.Lens.Reified type Rep ReifiedFold = []

newtype ReifiedIndexedFold i s a #

Constructors

IndexedFold
Fields runIndexedFold :: IndexedFold i s a

Instances

Profunctor (ReifiedIndexedFold i)
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedIndexedFold i b c -> ReifiedIndexedFold i a d # lmap :: (a -> b) -> ReifiedIndexedFold i b c -> ReifiedIndexedFold i a c # rmap :: (b -> c) -> ReifiedIndexedFold i a b -> ReifiedIndexedFold i a c # (#.) :: Coercible c b => q b c -> ReifiedIndexedFold i a b -> ReifiedIndexedFold i a c # (.#) :: Coercible b a => ReifiedIndexedFold i b c -> q a b -> ReifiedIndexedFold i a c #
Representable (ReifiedIndexedFold i)
Instance details Defined in Control.Lens.Reified Associated Types type Rep (ReifiedIndexedFold i) :: Type -> Type # Methods tabulate :: (d -> Rep (ReifiedIndexedFold i) c) -> ReifiedIndexedFold i d c #
Strong (ReifiedIndexedFold i)
Instance details Defined in Control.Lens.Reified Methods first' :: ReifiedIndexedFold i a b -> ReifiedIndexedFold i (a, c) (b, c) # second' :: ReifiedIndexedFold i a b -> ReifiedIndexedFold i (c, a) (c, b) #
Sieve (ReifiedIndexedFold i) (Compose [] ((,) i))
Instance details Defined in Control.Lens.Reified Methods sieve :: ReifiedIndexedFold i a b -> a -> Compose [] ((,) i) b #
Functor (ReifiedIndexedFold i s)
Instance details Defined in Control.Lens.Reified Methods fmap :: (a -> b) -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s b # (<$) :: a -> ReifiedIndexedFold i s b -> ReifiedIndexedFold i s a #
Plus (ReifiedIndexedFold i s)
Instance details Defined in Control.Lens.Reified Methods zero :: ReifiedIndexedFold i s a #
Alt (ReifiedIndexedFold i s)
Instance details Defined in Control.Lens.Reified Methods (<!>) :: ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a # some :: Applicative (ReifiedIndexedFold i s) => ReifiedIndexedFold i s a -> ReifiedIndexedFold i s [a] # many :: Applicative (ReifiedIndexedFold i s) => ReifiedIndexedFold i s a -> ReifiedIndexedFold i s [a] #
Semigroup (ReifiedIndexedFold i s a)
Instance details Defined in Control.Lens.Reified Methods (<>) :: ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a # sconcat :: NonEmpty (ReifiedIndexedFold i s a) -> ReifiedIndexedFold i s a # stimes :: Integral b => b -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a #
Monoid (ReifiedIndexedFold i s a)
Instance details Defined in Control.Lens.Reified Methods mempty :: ReifiedIndexedFold i s a # mappend :: ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a # mconcat :: [ReifiedIndexedFold i s a] -> ReifiedIndexedFold i s a #
type Rep (ReifiedIndexedFold i)
Instance details Defined in Control.Lens.Reified type Rep (ReifiedIndexedFold i) = Compose [] ((,) i)

newtype ReifiedSetter s t a b #

Reify a ReifiedSetter so it can be stored safely in a container.

Constructors

Setter
Fields runSetter :: Setter s t a b

type ReifiedSetter' s a = ReifiedSetter s s a a #

type ReifiedSetter' = Simple ReifiedSetter

newtype ReifiedIndexedSetter i s t a b #

Reify an ReifiedIndexedSetter so it can be stored safely in a container.

Constructors

IndexedSetter
Fields runIndexedSetter :: IndexedSetter i s t a b

type ReifiedIndexedSetter' i s a = ReifiedIndexedSetter i s s a a #

type ReifiedIndexedSetter' i = Simple (ReifiedIndexedSetter i)

newtype ReifiedIso s t a b #

Reify an ReifiedIso so it can be stored safely in a container.

Constructors

Iso
Fields runIso :: Iso s t a b

type ReifiedIso' s a = ReifiedIso s s a a #

type ReifiedIso' = Simple ReifiedIso

newtype ReifiedPrism s t a b #

Reify a ReifiedPrism so it can be stored safely in a container.

Constructors

Prism
Fields runPrism :: Prism s t a b

type ReifiedPrism' s a = ReifiedPrism s s a a #

type ReifiedPrism' = Simple ReifiedPrism

ilevels :: Applicative f => Traversing (Indexed i) f s t a b -> IndexedLensLike Int f s t (Level i a) (Level j b) #

This provides a breadth-first Traversal or Fold of the individual levels of any other Traversal or Fold via iterative deepening depth-first search. The levels are returned to you in a compressed format.

This is similar to levels, but retains the index of the original IndexedTraversal, so you can access it when traversing the levels later on.

>>> ["dog","cat"]^@..ilevels (traversed<.>traversed).itraversed
[((0,0),'d'),((0,1),'o'),((1,0),'c'),((0,2),'g'),((1,1),'a'),((1,2),'t')]

The resulting Traversal of the levels which is indexed by the depth of each Level.

>>> ["dog","cat"]^@..ilevels (traversed<.>traversed)<.>itraversed
[((2,(0,0)),'d'),((3,(0,1)),'o'),((3,(1,0)),'c'),((4,(0,2)),'g'),((4,(1,1)),'a'),((5,(1,2)),'t')]

ilevels :: IndexedTraversal i s t a b      -> IndexedTraversal Int s t (Level i a) (Level i b)
ilevels :: IndexedFold i s a               -> IndexedFold Int s (Level i a)

Note: Internally this is implemented by using an illegal Applicative, as it extracts information in an order that violates the Applicative laws.

levels :: Applicative f => Traversing ((->) :: Type -> Type -> Type) f s t a b -> IndexedLensLike Int f s t (Level () a) (Level () b) #

This provides a breadth-first Traversal or Fold of the individual levels of any other Traversal or Fold via iterative deepening depth-first search. The levels are returned to you in a compressed format.

This can permit us to extract the levels directly:

>>> ["hello","world"]^..levels (traverse.traverse)
[Zero,Zero,One () 'h',Two 0 (One () 'e') (One () 'w'),Two 0 (One () 'l') (One () 'o'),Two 0 (One () 'l') (One () 'r'),Two 0 (One () 'o') (One () 'l'),One () 'd']

But we can also traverse them in turn:

>>> ["hello","world"]^..levels (traverse.traverse).traverse
"hewlolrold"

We can use this to traverse to a fixed depth in the tree of (<*>) used in the Traversal:

>>> ["hello","world"] & taking 4 (levels (traverse.traverse)).traverse %~ toUpper
["HEllo","World"]

Or we can use it to traverse the first n elements in found in that Traversal regardless of the depth at which they were found.

>>> ["hello","world"] & taking 4 (levels (traverse.traverse).traverse) %~ toUpper
["HELlo","World"]

The resulting Traversal of the levels which is indexed by the depth of each Level.

>>> ["dog","cat"]^@..levels (traverse.traverse) <. traverse
[(2,'d'),(3,'o'),(3,'c'),(4,'g'),(4,'a'),(5,'t')]

levels :: Traversal s t a b      -> IndexedTraversal Int s t (Level () a) (Level () b)
levels :: Fold s a               -> IndexedFold Int s (Level () a)

Note: Internally this is implemented by using an illegal Applicative, as it extracts information in an order that violates the Applicative laws.

sequenceByOf :: Traversal s t (f b) b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> s -> f t #

Sequence a container using a specified Applicative.

This is like traverseBy where the Traversable instance can be specified by any Traversal

sequenceByOf traverse ≡ sequenceBy

traverseByOf :: Traversal s t a b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (a -> f b) -> s -> f t #

Traverse a container using a specified Applicative.

This is like traverseBy where the Traversable instance can be specified by any Traversal

traverseByOf traverse ≡ traverseBy

confusing :: Applicative f => LensLike (Curried (Yoneda f) (Yoneda f)) s t a b -> LensLike f s t a b #

Fuse a Traversal by reassociating all of the (<*>) operations to the left and fusing all of the fmap calls into one. This is particularly useful when constructing a Traversal using operations from GHC.Generics.

Given a pair of Traversals foo and bar,

confusing (foo.bar) = foo.bar

However, foo and bar are each going to use the Applicative they are given.

confusing exploits the Yoneda lemma to merge their separate uses of fmap into a single fmap. and it further exploits an interesting property of the right Kan lift (or Curried) to left associate all of the uses of (<*>) to make it possible to fuse together more fmaps.

This is particularly effective when the choice of functor f is unknown at compile time or when the Traversal foo.bar in the above description is recursive or complex enough to prevent inlining.

fusing is a version of this combinator suitable for fusing lenses.

confusing :: Traversal s t a b -> Traversal s t a b

deepOf :: (Conjoined p, Applicative f) => LensLike f s t s t -> Traversing p f s t a b -> Over p f s t a b #

Try the second traversal. If it returns no entries, try again with all entries from the first traversal, recursively.

deepOf :: Fold s s          -> Fold s a                   -> Fold s a
deepOf :: Traversal' s s    -> Traversal' s a             -> Traversal' s a
deepOf :: Traversal s t s t -> Traversal s t a b          -> Traversal s t a b
deepOf :: Fold s s          -> IndexedFold i s a          -> IndexedFold i s a
deepOf :: Traversal s t s t -> IndexedTraversal i s t a b -> IndexedTraversal i s t a b

failing :: (Conjoined p, Applicative f) => Traversing p f s t a b -> Over p f s t a b -> Over p f s t a b infixl 5 #

Try the first Traversal (or Fold), falling back on the second Traversal (or Fold) if it returns no entries.

This is only a valid Traversal if the second Traversal is disjoint from the result of the first or returns exactly the same results. These conditions are trivially met when given a Lens, Iso, Getter, Prism or "affine" Traversal -- one that has 0 or 1 target.

Mutatis mutandis for Fold.

>>> [0,1,2,3] ^? failing (ix 1) (ix 2)
Just 1

>>> [0,1,2,3] ^? failing (ix 42) (ix 2)
Just 2

failing :: Traversal s t a b -> Traversal s t a b -> Traversal s t a b
failing :: Prism s t a b     -> Prism s t a b     -> Traversal s t a b
failing :: Fold s a          -> Fold s a          -> Fold s a

These cases are also supported, trivially, but are boring, because the left hand side always succeeds.

failing :: Lens s t a b      -> Traversal s t a b -> Traversal s t a b
failing :: Iso s t a b       -> Traversal s t a b -> Traversal s t a b
failing :: Equality s t a b  -> Traversal s t a b -> Traversal s t a b
failing :: Getter s a        -> Fold s a          -> Fold s a

If both of the inputs are indexed, the result is also indexed, so you can apply this to a pair of indexed traversals or indexed folds, obtaining an indexed traversal or indexed fold.

failing :: IndexedTraversal i s t a b -> IndexedTraversal i s t a b -> IndexedTraversal i s t a b
failing :: IndexedFold i s a          -> IndexedFold i s a          -> IndexedFold i s a

These cases are also supported, trivially, but are boring, because the left hand side always succeeds.

failing :: IndexedLens i s t a b      -> IndexedTraversal i s t a b -> IndexedTraversal i s t a b
failing :: IndexedGetter i s a        -> IndexedGetter i s a        -> IndexedFold i s a

ifailover :: Alternative m => Over (Indexed i) ((,) Any) s t a b -> (i -> a -> b) -> s -> m t #

Try to map a function which uses the index over this IndexedTraversal, failing if the IndexedTraversal has no targets.

ifailover :: Alternative m => IndexedTraversal i s t a b -> (i -> a -> b) -> s -> m t

failover :: Alternative m => LensLike ((,) Any) s t a b -> (a -> b) -> s -> m t #

Try to map a function over this Traversal, failing if the Traversal has no targets.

>>> failover (element 3) (*2) [1,2] :: Maybe [Int]
Nothing

>>> failover _Left (*2) (Right 4) :: Maybe (Either Int Int)
Nothing

>>> failover _Right (*2) (Right 4) :: Maybe (Either Int Int)
Just (Right 8)

failover :: Alternative m => Traversal s t a b -> (a -> b) -> s -> m t

elements :: Traversable t => (Int -> Bool) -> IndexedTraversal' Int (t a) a #

Traverse elements of a Traversable container where their ordinal positions match a predicate.

elements ≡ elementsOf traverse

elementsOf :: Applicative f => LensLike (Indexing f) s t a a -> (Int -> Bool) -> IndexedLensLike Int f s t a a #

Traverse (or fold) selected elements of a Traversal (or Fold) where their ordinal positions match a predicate.

elementsOf :: Traversal' s a -> (Int -> Bool) -> IndexedTraversal' Int s a
elementsOf :: Fold s a       -> (Int -> Bool) -> IndexedFold Int s a

element :: Traversable t => Int -> IndexedTraversal' Int (t a) a #

Traverse the nth element of a Traversable container.

element ≡ elementOf traverse

elementOf :: Applicative f => LensLike (Indexing f) s t a a -> Int -> IndexedLensLike Int f s t a a #

Traverse the nth elementOf a Traversal, Lens or Iso if it exists.

>>> [[1],[3,4]] & elementOf (traverse.traverse) 1 .~ 5
[[1],[5,4]]

>>> [[1],[3,4]] ^? elementOf (folded.folded) 1
Just 3

>>> timingOut $ ['a'..] ^?! elementOf folded 5
'f'

>>> timingOut $ take 10 $ elementOf traverse 3 .~ 16 $ [0..]
[0,1,2,16,4,5,6,7,8,9]

elementOf :: Traversal' s a -> Int -> IndexedTraversal' Int s a
elementOf :: Fold s a       -> Int -> IndexedFold Int s a

ignored :: Applicative f => pafb -> s -> f s #

This is the trivial empty Traversal.

ignored :: IndexedTraversal i s s a b

ignored ≡ const pure

>>> 6 & ignored %~ absurd
6

traversed64 :: Traversable f => IndexedTraversal Int64 (f a) (f b) a b #

Traverse any Traversable container. This is an IndexedTraversal that is indexed by ordinal position.

traversed1 :: Traversable1 f => IndexedTraversal1 Int (f a) (f b) a b #

Traverse any Traversable1 container. This is an IndexedTraversal1 that is indexed by ordinal position.

traversed :: Traversable f => IndexedTraversal Int (f a) (f b) a b #

Traverse any Traversable container. This is an IndexedTraversal that is indexed by ordinal position.

imapAccumLOf :: Over (Indexed i) (State acc) s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t) #

Generalizes mapAccumL to an arbitrary IndexedTraversal with access to the index.

imapAccumLOf accumulates state from left to right.

mapAccumLOf l ≡ imapAccumLOf l . const

imapAccumLOf :: IndexedLens i s t a b      -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
imapAccumLOf :: IndexedTraversal i s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)

imapAccumROf :: Over (Indexed i) (Backwards (State acc)) s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t) #

Generalizes mapAccumR to an arbitrary IndexedTraversal with access to the index.

imapAccumROf accumulates state from right to left.

mapAccumROf l ≡ imapAccumROf l . const

imapAccumROf :: IndexedLens i s t a b      -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
imapAccumROf :: IndexedTraversal i s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)

iforMOf :: (Indexed i a (WrappedMonad m b) -> s -> WrappedMonad m t) -> s -> (i -> a -> m b) -> m t #

Map each element of a structure targeted by a Lens to a monadic action, evaluate these actions from left to right, and collect the results, with access its position (and the arguments flipped).

forMOf l a ≡ iforMOf l a . const
iforMOf ≡ flip . imapMOf

iforMOf :: Monad m => IndexedLens i s t a b      -> s -> (i -> a -> m b) -> m t
iforMOf :: Monad m => IndexedTraversal i s t a b -> s -> (i -> a -> m b) -> m t

imapMOf :: Over (Indexed i) (WrappedMonad m) s t a b -> (i -> a -> m b) -> s -> m t #

Map each element of a structure targeted by a Lens to a monadic action, evaluate these actions from left to right, and collect the results, with access its position.

When you don't need access to the index mapMOf is more liberal in what it can accept.

mapMOf l ≡ imapMOf l . const

imapMOf :: Monad m => IndexedLens       i s t a b -> (i -> a -> m b) -> s -> m t
imapMOf :: Monad m => IndexedTraversal  i s t a b -> (i -> a -> m b) -> s -> m t
imapMOf :: Bind  m => IndexedTraversal1 i s t a b -> (i -> a -> m b) -> s -> m t

iforOf :: (Indexed i a (f b) -> s -> f t) -> s -> (i -> a -> f b) -> f t #

Traverse with an index (and the arguments flipped).

forOf l a ≡ iforOf l a . const
iforOf ≡ flip . itraverseOf

iforOf :: Functor f     => IndexedLens i s t a b       -> s -> (i -> a -> f b) -> f t
iforOf :: Applicative f => IndexedTraversal i s t a b  -> s -> (i -> a -> f b) -> f t
iforOf :: Apply f       => IndexedTraversal1 i s t a b -> s -> (i -> a -> f b) -> f t

itraverseOf :: (Indexed i a (f b) -> s -> f t) -> (i -> a -> f b) -> s -> f t #

Traversal with an index.

NB: When you don't need access to the index then you can just apply your IndexedTraversal directly as a function!

itraverseOf ≡ withIndex
traverseOf l = itraverseOf l . const = id

itraverseOf :: Functor f     => IndexedLens i s t a b       -> (i -> a -> f b) -> s -> f t
itraverseOf :: Applicative f => IndexedTraversal i s t a b  -> (i -> a -> f b) -> s -> f t
itraverseOf :: Apply f       => IndexedTraversal1 i s t a b -> (i -> a -> f b) -> s -> f t

cloneIndexedTraversal1 :: AnIndexedTraversal1 i s t a b -> IndexedTraversal1 i s t a b #

Clone an IndexedTraversal1 yielding an IndexedTraversal1 with the same index.

cloneIndexPreservingTraversal1 :: ATraversal1 s t a b -> IndexPreservingTraversal1 s t a b #

Clone a Traversal1 yielding an IndexPreservingTraversal1 that passes through whatever index it is composed with.

cloneTraversal1 :: ATraversal1 s t a b -> Traversal1 s t a b #

A Traversal1 is completely characterized by its behavior on a Bazaar1.

cloneIndexedTraversal :: AnIndexedTraversal i s t a b -> IndexedTraversal i s t a b #

Clone an IndexedTraversal yielding an IndexedTraversal with the same index.

cloneIndexPreservingTraversal :: ATraversal s t a b -> IndexPreservingTraversal s t a b #

Clone a Traversal yielding an IndexPreservingTraversal that passes through whatever index it is composed with.

cloneTraversal :: ATraversal s t a b -> Traversal s t a b #

A Traversal is completely characterized by its behavior on a Bazaar.

Cloning a Traversal is one way to make sure you aren't given something weaker, such as a Fold and can be used as a way to pass around traversals that have to be monomorphic in f.

Note: This only accepts a proper Traversal (or Lens). To clone a Lens as such, use cloneLens.

Note: It is usually better to use ReifiedTraversal and runTraversal than to cloneTraversal. The former can execute at full speed, while the latter needs to round trip through the Bazaar.

>>> let foo l a = (view (getting (cloneTraversal l)) a, set (cloneTraversal l) 10 a)
>>> foo both ("hello","world")
("helloworld",(10,10))

cloneTraversal :: LensLike (Bazaar (->) a b) s t a b -> Traversal s t a b

dropping :: (Conjoined p, Applicative f) => Int -> Over p (Indexing f) s t a a -> Over p f s t a a #

Visit all but the first n targets of a Traversal, Fold, Getter or Lens.

>>> ("hello","world") ^? dropping 1 both
Just "world"

Dropping works on infinite traversals as well:

>>> [1..] ^? dropping 1 folded
Just 2

dropping :: Int -> Traversal' s a                   -> Traversal' s a
dropping :: Int -> Lens' s a                        -> Traversal' s a
dropping :: Int -> Iso' s a                         -> Traversal' s a
dropping :: Int -> Prism' s a                       -> Traversal' s a
dropping :: Int -> Getter s a                       -> Fold s a
dropping :: Int -> Fold s a                         -> Fold s a
dropping :: Int -> IndexedTraversal' i s a          -> IndexedTraversal' i s a
dropping :: Int -> IndexedLens' i s a               -> IndexedTraversal' i s a
dropping :: Int -> IndexedGetter i s a              -> IndexedFold i s a
dropping :: Int -> IndexedFold i s a                -> IndexedFold i s a

taking :: (Conjoined p, Applicative f) => Int -> Traversing p f s t a a -> Over p f s t a a #

Visit the first n targets of a Traversal, Fold, Getter or Lens.

>>> [("hello","world"),("!!!","!!!")]^.. taking 2 (traverse.both)
["hello","world"]

>>> timingOut $ [1..] ^.. taking 3 traverse
[1,2,3]

>>> over (taking 5 traverse) succ "hello world"
"ifmmp world"

taking :: Int -> Traversal' s a                   -> Traversal' s a
taking :: Int -> Lens' s a                        -> Traversal' s a
taking :: Int -> Iso' s a                         -> Traversal' s a
taking :: Int -> Prism' s a                       -> Traversal' s a
taking :: Int -> Getter s a                       -> Fold s a
taking :: Int -> Fold s a                         -> Fold s a
taking :: Int -> IndexedTraversal' i s a          -> IndexedTraversal' i s a
taking :: Int -> IndexedLens' i s a               -> IndexedTraversal' i s a
taking :: Int -> IndexedGetter i s a              -> IndexedFold i s a
taking :: Int -> IndexedFold i s a                -> IndexedFold i s a

beside :: (Representable q, Applicative (Rep q), Applicative f, Bitraversable r) => Optical p q f s t a b -> Optical p q f s' t' a b -> Optical p q f (r s s') (r t t') a b #

Apply a different Traversal or Fold to each side of a Bitraversable container.

beside :: Traversal s t a b                -> Traversal s' t' a b                -> Traversal (r s s') (r t t') a b
beside :: IndexedTraversal i s t a b       -> IndexedTraversal i s' t' a b       -> IndexedTraversal i (r s s') (r t t') a b
beside :: IndexPreservingTraversal s t a b -> IndexPreservingTraversal s' t' a b -> IndexPreservingTraversal (r s s') (r t t') a b

beside :: Traversal s t a b                -> Traversal s' t' a b                -> Traversal (s,s') (t,t') a b
beside :: Lens s t a b                     -> Lens s' t' a b                     -> Traversal (s,s') (t,t') a b
beside :: Fold s a                         -> Fold s' a                          -> Fold (s,s') a
beside :: Getter s a                       -> Getter s' a                        -> Fold (s,s') a

beside :: IndexedTraversal i s t a b       -> IndexedTraversal i s' t' a b       -> IndexedTraversal i (s,s') (t,t') a b
beside :: IndexedLens i s t a b            -> IndexedLens i s' t' a b            -> IndexedTraversal i (s,s') (t,t') a b
beside :: IndexedFold i s a                -> IndexedFold i s' a                 -> IndexedFold i (s,s') a
beside :: IndexedGetter i s a              -> IndexedGetter i s' a               -> IndexedFold i (s,s') a

beside :: IndexPreservingTraversal s t a b -> IndexPreservingTraversal s' t' a b -> IndexPreservingTraversal (s,s') (t,t') a b
beside :: IndexPreservingLens s t a b      -> IndexPreservingLens s' t' a b      -> IndexPreservingTraversal (s,s') (t,t') a b
beside :: IndexPreservingFold s a          -> IndexPreservingFold s' a           -> IndexPreservingFold (s,s') a
beside :: IndexPreservingGetter s a        -> IndexPreservingGetter s' a         -> IndexPreservingFold (s,s') a

>>> ("hello",["world","!!!"])^..beside id traverse
["hello","world","!!!"]

both1 :: Bitraversable1 r => Traversal1 (r a a) (r b b) a b #

Traverse both parts of a Bitraversable1 container with matching types.

Usually that type will be a pair.

both1 :: Traversal1 (a, a)       (b, b)       a b
both1 :: Traversal1 (Either a a) (Either b b) a b

both :: Bitraversable r => Traversal (r a a) (r b b) a b #

Traverse both parts of a Bitraversable container with matching types.

Usually that type will be a pair.

>>> (1,2) & both *~ 10
(10,20)

>>> over both length ("hello","world")
(5,5)

>>> ("hello","world")^.both
"helloworld"

both :: Traversal (a, a)       (b, b)       a b
both :: Traversal (Either a a) (Either b b) a b

holesOf :: Conjoined p => Over p (Bazaar p a a) s t a a -> s -> [Pretext p a a t] #

The one-level version of contextsOf. This extracts a list of the immediate children according to a given Traversal as editable contexts.

Given a context you can use pos to see the values, peek at what the structure would be like with an edited result, or simply extract the original structure.

propChildren l x = toListOf l x == map pos (holesOf l x)
propId l x = all (== x) [extract w | w <- holesOf l x]

holesOf :: Iso' s a                -> s -> [Pretext' (->) a s]
holesOf :: Lens' s a               -> s -> [Pretext' (->) a s]
holesOf :: Traversal' s a          -> s -> [Pretext' (->) a s]
holesOf :: IndexedLens' i s a      -> s -> [Pretext' (Indexed i) a s]
holesOf :: IndexedTraversal' i s a -> s -> [Pretext' (Indexed i) a s]

unsafeSingular :: (HasCallStack, Conjoined p, Functor f) => Traversing p f s t a b -> Over p f s t a b #

This converts a Traversal that you "know" will target only one element to a Lens. It can also be used to transform a Fold into a Getter.

The resulting Lens or Getter will be partial if the Traversal targets nothing or more than one element.

>>> Left (ErrorCall "unsafeSingular: empty traversal") <- try (evaluate ([] & unsafeSingular traverse .~ 0)) :: IO (Either ErrorCall [Integer])

unsafeSingular :: Traversal s t a b          -> Lens s t a b
unsafeSingular :: Fold s a                   -> Getter s a
unsafeSingular :: IndexedTraversal i s t a b -> IndexedLens i s t a b
unsafeSingular :: IndexedFold i s a          -> IndexedGetter i s a

singular :: (HasCallStack, Conjoined p, Functor f) => Traversing p f s t a a -> Over p f s t a a #

This converts a Traversal that you "know" will target one or more elements to a Lens. It can also be used to transform a non-empty Fold into a Getter.

The resulting Lens or Getter will be partial if the supplied Traversal returns no results.

>>> [1,2,3] ^. singular _head
1

>>> Left (ErrorCall "singular: empty traversal") <- try (evaluate ([] ^. singular _head)) :: IO (Either ErrorCall ())

>>> Left 4 ^. singular _Left
4

>>> [1..10] ^. singular (ix 7)
8

>>> [] & singular traverse .~ 0
[]

singular :: Traversal s t a a          -> Lens s t a a
singular :: Fold s a                   -> Getter s a
singular :: IndexedTraversal i s t a a -> IndexedLens i s t a a
singular :: IndexedFold i s a          -> IndexedGetter i s a

iunsafePartsOf' :: Over (Indexed i) (Bazaar (Indexed i) a b) s t a b -> IndexedLens [i] s t [a] [b] #

unsafePartsOf' :: ATraversal s t a b -> Lens s t [a] [b] #

iunsafePartsOf :: (Indexable [i] p, Functor f) => Traversing (Indexed i) f s t a b -> Over p f s t [a] [b] #

An indexed version of unsafePartsOf that receives the entire list of indices as its index.

unsafePartsOf :: Functor f => Traversing ((->) :: Type -> Type -> Type) f s t a b -> LensLike f s t [a] [b] #

unsafePartsOf turns a Traversal into a uniplate (or biplate) family.

If you do not need the types of s and t to be different, it is recommended that you use partsOf.

It is generally safer to traverse with the Bazaar rather than use this combinator. However, it is sometimes convenient.

This is unsafe because if you don't supply at least as many b's as you were given a's, then the reconstruction of t will result in an error!

When applied to a Fold the result is merely a Getter (and becomes safe).

unsafePartsOf :: Iso s t a b       -> Lens s t [a] [b]
unsafePartsOf :: Lens s t a b      -> Lens s t [a] [b]
unsafePartsOf :: Traversal s t a b -> Lens s t [a] [b]
unsafePartsOf :: Fold s a          -> Getter s [a]
unsafePartsOf :: Getter s a        -> Getter s [a]

ipartsOf' :: (Indexable [i] p, Functor f) => Over (Indexed i) (Bazaar' (Indexed i) a) s t a a -> Over p f s t [a] [a] #

A type-restricted version of ipartsOf that can only be used with an IndexedTraversal.

partsOf' :: ATraversal s t a a -> Lens s t [a] [a] #

A type-restricted version of partsOf that can only be used with a Traversal.

ipartsOf :: (Indexable [i] p, Functor f) => Traversing (Indexed i) f s t a a -> Over p f s t [a] [a] #

An indexed version of partsOf that receives the entire list of indices as its index.

partsOf :: Functor f => Traversing ((->) :: Type -> Type -> Type) f s t a a -> LensLike f s t [a] [a] #

partsOf turns a Traversal into a Lens that resembles an early version of the uniplate (or biplate) type.

Note: You should really try to maintain the invariant of the number of children in the list.

>>> (a,b,c) & partsOf each .~ [x,y,z]
(x,y,z)

Any extras will be lost. If you do not supply enough, then the remainder will come from the original structure.

>>> (a,b,c) & partsOf each .~ [w,x,y,z]
(w,x,y)

>>> (a,b,c) & partsOf each .~ [x,y]
(x,y,c)

>>> ('b', 'a', 'd', 'c') & partsOf each %~ sort
('a','b','c','d')

So technically, this is only a Lens if you do not change the number of results it returns.

When applied to a Fold the result is merely a Getter.

partsOf :: Iso' s a       -> Lens' s [a]
partsOf :: Lens' s a      -> Lens' s [a]
partsOf :: Traversal' s a -> Lens' s [a]
partsOf :: Fold s a       -> Getter s [a]
partsOf :: Getter s a     -> Getter s [a]

iloci :: IndexedTraversal i (Bazaar (Indexed i) a c s) (Bazaar (Indexed i) b c s) a b #

This IndexedTraversal allows you to traverse the individual stores in a Bazaar with access to their indices.

loci :: Traversal (Bazaar ((->) :: Type -> Type -> Type) a c s) (Bazaar ((->) :: Type -> Type -> Type) b c s) a b #

This Traversal allows you to traverse the individual stores in a Bazaar.

scanl1Of :: LensLike (State (Maybe a)) s t a a -> (a -> a -> a) -> s -> t #

This permits the use of scanl1 over an arbitrary Traversal or Lens.

scanl1 ≡ scanl1Of traverse

scanl1Of :: Iso s t a a       -> (a -> a -> a) -> s -> t
scanl1Of :: Lens s t a a      -> (a -> a -> a) -> s -> t
scanl1Of :: Traversal s t a a -> (a -> a -> a) -> s -> t

scanr1Of :: LensLike (Backwards (State (Maybe a))) s t a a -> (a -> a -> a) -> s -> t #

This permits the use of scanr1 over an arbitrary Traversal or Lens.

scanr1 ≡ scanr1Of traverse

scanr1Of :: Iso s t a a       -> (a -> a -> a) -> s -> t
scanr1Of :: Lens s t a a      -> (a -> a -> a) -> s -> t
scanr1Of :: Traversal s t a a -> (a -> a -> a) -> s -> t

mapAccumLOf :: LensLike (State acc) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t) #

This generalizes mapAccumL to an arbitrary Traversal.

mapAccumL ≡ mapAccumLOf traverse

mapAccumLOf accumulates State from left to right.

mapAccumLOf :: Iso s t a b       -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumLOf :: Lens s t a b      -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumLOf :: Traversal s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)

mapAccumLOf :: LensLike (State acc) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumLOf l f acc0 s = swap (runState (l (a -> state (acc -> swap (f acc a))) s) acc0)

mapAccumROf :: LensLike (Backwards (State acc)) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t) #

This generalizes mapAccumR to an arbitrary Traversal.

mapAccumR ≡ mapAccumROf traverse

mapAccumROf accumulates State from right to left.

mapAccumROf :: Iso s t a b       -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumROf :: Lens s t a b      -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumROf :: Traversal s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)

mapAccumROf :: LensLike (Backwards (State acc)) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)

transposeOf :: LensLike ZipList s t [a] a -> s -> [t] #

This generalizes transpose to an arbitrary Traversal.

Note: transpose handles ragged inputs more intelligently, but for non-ragged inputs:

>>> transposeOf traverse [[1,2,3],[4,5,6]]
[[1,4],[2,5],[3,6]]

transpose ≡ transposeOf traverse

Since every Lens is a Traversal, we can use this as a form of monadic strength as well:

transposeOf _2 :: (b, [a]) -> [(b, a)]

sequenceOf :: LensLike (WrappedMonad m) s t (m b) b -> s -> m t #

Sequence the (monadic) effects targeted by a Lens in a container from left to right.

>>> sequenceOf each ([1,2],[3,4],[5,6])
[(1,3,5),(1,3,6),(1,4,5),(1,4,6),(2,3,5),(2,3,6),(2,4,5),(2,4,6)]

sequence ≡ sequenceOf traverse
sequenceOf l ≡ mapMOf l id
sequenceOf l ≡ unwrapMonad . l WrapMonad

sequenceOf :: Monad m => Iso s t (m b) b       -> s -> m t
sequenceOf :: Monad m => Lens s t (m b) b      -> s -> m t
sequenceOf :: Monad m => Traversal s t (m b) b -> s -> m t

forMOf :: LensLike (WrappedMonad m) s t a b -> s -> (a -> m b) -> m t #

forMOf is a flipped version of mapMOf, consistent with the definition of forM.

>>> forMOf both (1,3) $ \x -> [x, x + 1]
[(1,3),(1,4),(2,3),(2,4)]

forM ≡ forMOf traverse
forMOf l ≡ flip (mapMOf l)
iforMOf l s ≡ forM l s . Indexed

forMOf :: Monad m => Iso s t a b       -> s -> (a -> m b) -> m t
forMOf :: Monad m => Lens s t a b      -> s -> (a -> m b) -> m t
forMOf :: Monad m => Traversal s t a b -> s -> (a -> m b) -> m t

mapMOf :: LensLike (WrappedMonad m) s t a b -> (a -> m b) -> s -> m t #

Map each element of a structure targeted by a Lens to a monadic action, evaluate these actions from left to right, and collect the results.

>>> mapMOf both (\x -> [x, x + 1]) (1,3)
[(1,3),(1,4),(2,3),(2,4)]

mapM ≡ mapMOf traverse
imapMOf l ≡ forM l . Indexed

mapMOf :: Monad m => Iso s t a b       -> (a -> m b) -> s -> m t
mapMOf :: Monad m => Lens s t a b      -> (a -> m b) -> s -> m t
mapMOf :: Monad m => Traversal s t a b -> (a -> m b) -> s -> m t

sequenceAOf :: LensLike f s t (f b) b -> s -> f t #

Evaluate each action in the structure from left to right, and collect the results.

>>> sequenceAOf both ([1,2],[3,4])
[(1,3),(1,4),(2,3),(2,4)]

sequenceA ≡ sequenceAOf traverse ≡ traverse id
sequenceAOf l ≡ traverseOf l id ≡ l id

sequenceAOf :: Functor f => Iso s t (f b) b       -> s -> f t
sequenceAOf :: Functor f => Lens s t (f b) b      -> s -> f t
sequenceAOf :: Applicative f => Traversal s t (f b) b -> s -> f t

forOf :: LensLike f s t a b -> s -> (a -> f b) -> f t #

A version of traverseOf with the arguments flipped, such that:

>>> forOf each (1,2,3) print
1
2
3
((),(),())

This function is only provided for consistency, flip is strictly more general.

forOf ≡ flip
forOf ≡ flip . traverseOf

for ≡ forOf traverse
ifor l s ≡ for l s . Indexed

forOf :: Functor f => Iso s t a b -> s -> (a -> f b) -> f t
forOf :: Functor f => Lens s t a b -> s -> (a -> f b) -> f t
forOf :: Applicative f => Traversal s t a b -> s -> (a -> f b) -> f t

traverseOf :: LensLike f s t a b -> (a -> f b) -> s -> f t #

Map each element of a structure targeted by a Lens or Traversal, evaluate these actions from left to right, and collect the results.

This function is only provided for consistency, id is strictly more general.

>>> traverseOf each print (1,2,3)
1
2
3
((),(),())

traverseOf ≡ id
itraverseOf l ≡ traverseOf l . Indexed
itraverseOf itraversed ≡ itraverse

This yields the obvious law:

traverse ≡ traverseOf traverse

traverseOf :: Functor f     => Iso s t a b        -> (a -> f b) -> s -> f t
traverseOf :: Functor f     => Lens s t a b       -> (a -> f b) -> s -> f t
traverseOf :: Apply f       => Traversal1 s t a b -> (a -> f b) -> s -> f t
traverseOf :: Applicative f => Traversal s t a b  -> (a -> f b) -> s -> f t

type ATraversal s t a b = LensLike (Bazaar ((->) :: Type -> Type -> Type) a b) s t a b #

When you see this as an argument to a function, it expects a Traversal.

type ATraversal' s a = ATraversal s s a a #

type ATraversal' = Simple ATraversal

type ATraversal1 s t a b = LensLike (Bazaar1 ((->) :: Type -> Type -> Type) a b) s t a b #

When you see this as an argument to a function, it expects a Traversal1.

type ATraversal1' s a = ATraversal1 s s a a #

type ATraversal1' = Simple ATraversal1

type AnIndexedTraversal i s t a b = Over (Indexed i) (Bazaar (Indexed i) a b) s t a b #

When you see this as an argument to a function, it expects an IndexedTraversal.

type AnIndexedTraversal1 i s t a b = Over (Indexed i) (Bazaar1 (Indexed i) a b) s t a b #

When you see this as an argument to a function, it expects an IndexedTraversal1.

type AnIndexedTraversal' i s a = AnIndexedTraversal i s s a a #

type AnIndexedTraversal' = Simple (AnIndexedTraversal i)

type AnIndexedTraversal1' i s a = AnIndexedTraversal1 i s s a a #

type AnIndexedTraversal1' = Simple (AnIndexedTraversal1 i)

type Traversing (p :: Type -> Type -> Type) (f :: Type -> Type) s t a b = Over p (BazaarT p f a b) s t a b #

When you see this as an argument to a function, it expects

to be indexed if p is an instance of Indexed i,
to be unindexed if p is (->),
a Traversal if f is Applicative,
a Getter if f is only a Functor and Contravariant,
a Lens if f is only a Functor,
a Fold if f is Applicative and Contravariant.

type Traversing1 (p :: Type -> Type -> Type) (f :: Type -> Type) s t a b = Over p (BazaarT1 p f a b) s t a b #

type Traversing' (p :: Type -> Type -> Type) (f :: Type -> Type) s a = Traversing p f s s a a #

type Traversing' f = Simple (Traversing f)

type Traversing1' (p :: Type -> Type -> Type) (f :: Type -> Type) s a = Traversing1 p f s s a a #

class Ord k => TraverseMin k (m :: Type -> Type) | m -> k where #

Allows IndexedTraversal the value at the smallest index.

Methods

traverseMin :: IndexedTraversal' k (m v) v #

IndexedTraversal of the element with the smallest index.

Instances

TraverseMin Int IntMap
Instance details Defined in Control.Lens.Traversal Methods traverseMin :: IndexedTraversal' Int (IntMap v) v #
Ord k => TraverseMin k (Map k)
Instance details Defined in Control.Lens.Traversal Methods traverseMin :: IndexedTraversal' k (Map k v) v #

class Ord k => TraverseMax k (m :: Type -> Type) | m -> k where #

Allows IndexedTraversal of the value at the largest index.

Methods

traverseMax :: IndexedTraversal' k (m v) v #

IndexedTraversal of the element at the largest index.

Instances

TraverseMax Int IntMap
Instance details Defined in Control.Lens.Traversal Methods traverseMax :: IndexedTraversal' Int (IntMap v) v #
Ord k => TraverseMax k (Map k)
Instance details Defined in Control.Lens.Traversal Methods traverseMax :: IndexedTraversal' k (Map k v) v #

foldMapByOf :: Fold s a -> (r -> r -> r) -> r -> (a -> r) -> s -> r #

Fold a value using a specified Fold and Monoid operations. This is like foldMapBy where the Foldable instance can be manually specified.

foldMapByOf folded ≡ foldMapBy

foldMapByOf :: Getter s a     -> (r -> r -> r) -> r -> (a -> r) -> s -> r
foldMapByOf :: Fold s a       -> (r -> r -> r) -> r -> (a -> r) -> s -> r
foldMapByOf :: Traversal' s a -> (r -> r -> r) -> r -> (a -> r) -> s -> r
foldMapByOf :: Lens' s a      -> (r -> r -> r) -> r -> (a -> r) -> s -> r
foldMapByOf :: Iso' s a       -> (r -> r -> r) -> r -> (a -> r) -> s -> r

>>> foldMapByOf both (+) 0 length ("hello","world")
10

foldByOf :: Fold s a -> (a -> a -> a) -> a -> s -> a #

Fold a value using a specified Fold and Monoid operations. This is like foldBy where the Foldable instance can be manually specified.

foldByOf folded ≡ foldBy

foldByOf :: Getter s a     -> (a -> a -> a) -> a -> s -> a
foldByOf :: Fold s a       -> (a -> a -> a) -> a -> s -> a
foldByOf :: Lens' s a      -> (a -> a -> a) -> a -> s -> a
foldByOf :: Traversal' s a -> (a -> a -> a) -> a -> s -> a
foldByOf :: Iso' s a       -> (a -> a -> a) -> a -> s -> a

>>> foldByOf both (++) [] ("hello","world")
"helloworld"

idroppingWhile :: (Indexable i p, Profunctor q, Applicative f) => (i -> a -> Bool) -> Optical (Indexed i) q (Compose (State Bool) f) s t a a -> Optical p q f s t a a #

Obtain an IndexedFold by dropping elements from another IndexedFold, IndexedLens, IndexedGetter or IndexedTraversal while a predicate holds.

idroppingWhile :: (i -> a -> Bool) -> IndexedFold i s a          -> IndexedFold i s a
idroppingWhile :: (i -> a -> Bool) -> IndexedTraversal' i s a    -> IndexedFold i s a -- see notes
idroppingWhile :: (i -> a -> Bool) -> IndexedLens' i s a         -> IndexedFold i s a -- see notes
idroppingWhile :: (i -> a -> Bool) -> IndexedGetter i s a        -> IndexedFold i s a

Note: As with droppingWhile applying idroppingWhile to an IndexedLens or IndexedTraversal will still allow you to use it as a pseudo-IndexedTraversal, but if you change the value of the first target to one where the predicate returns True, then you will break the Traversal laws and Traversal fusion will no longer be sound.

itakingWhile :: (Indexable i p, Profunctor q, Contravariant f, Applicative f) => (i -> a -> Bool) -> Optical' (Indexed i) q (Const (Endo (f s)) :: Type -> Type) s a -> Optical' p q f s a #

Obtain an IndexedFold by taking elements from another IndexedFold, IndexedLens, IndexedGetter or IndexedTraversal while a predicate holds.

itakingWhile :: (i -> a -> Bool) -> IndexedFold i s a          -> IndexedFold i s a
itakingWhile :: (i -> a -> Bool) -> IndexedTraversal' i s a    -> IndexedFold i s a
itakingWhile :: (i -> a -> Bool) -> IndexedLens' i s a         -> IndexedFold i s a
itakingWhile :: (i -> a -> Bool) -> IndexedGetter i s a        -> IndexedFold i s a

Note: Applying itakingWhile to an IndexedLens or IndexedTraversal will still allow you to use it as a pseudo-IndexedTraversal, but if you change the value of any target to one where the predicate returns False, then you will break the Traversal laws and Traversal fusion will no longer be sound.

ifiltered :: (Indexable i p, Applicative f) => (i -> a -> Bool) -> Optical' p (Indexed i) f a a #

Filter an IndexedFold or IndexedGetter, obtaining an IndexedFold.

>>> [0,0,0,5,5,5]^..traversed.ifiltered (\i a -> i <= a)
[0,5,5,5]

Compose with ifiltered to filter another IndexedLens, IndexedIso, IndexedGetter, IndexedFold (or IndexedTraversal) with access to both the value and the index.

Note: As with filtered, this is not a legal IndexedTraversal, unless you are very careful not to invalidate the predicate on the target!

findIndicesOf :: IndexedGetting i (Endo [i]) s a -> (a -> Bool) -> s -> [i] #

Retrieve the indices of the values targeted by a IndexedFold or IndexedTraversal which satisfy a predicate.

findIndices ≡ findIndicesOf folded

findIndicesOf :: IndexedFold i s a       -> (a -> Bool) -> s -> [i]
findIndicesOf :: IndexedTraversal' i s a -> (a -> Bool) -> s -> [i]

findIndexOf :: IndexedGetting i (First i) s a -> (a -> Bool) -> s -> Maybe i #

Retrieve the index of the first value targeted by a IndexedFold or IndexedTraversal which satisfies a predicate.

findIndex ≡ findIndexOf folded

findIndexOf :: IndexedFold i s a       -> (a -> Bool) -> s -> Maybe i
findIndexOf :: IndexedTraversal' i s a -> (a -> Bool) -> s -> Maybe i

elemIndicesOf :: Eq a => IndexedGetting i (Endo [i]) s a -> a -> s -> [i] #

Retrieve the indices of the values targeted by a IndexedFold or IndexedTraversal which are equal to a given value.

elemIndices ≡ elemIndicesOf folded

elemIndicesOf :: Eq a => IndexedFold i s a       -> a -> s -> [i]
elemIndicesOf :: Eq a => IndexedTraversal' i s a -> a -> s -> [i]

elemIndexOf :: Eq a => IndexedGetting i (First i) s a -> a -> s -> Maybe i #

Retrieve the index of the first value targeted by a IndexedFold or IndexedTraversal which is equal to a given value.

elemIndex ≡ elemIndexOf folded

elemIndexOf :: Eq a => IndexedFold i s a       -> a -> s -> Maybe i
elemIndexOf :: Eq a => IndexedTraversal' i s a -> a -> s -> Maybe i

(^@?!) :: HasCallStack => s -> IndexedGetting i (Endo (i, a)) s a -> (i, a) infixl 8 #

Perform an *UNSAFE* head (with index) of an IndexedFold or IndexedTraversal assuming that it is there.

(^@?!) :: s -> IndexedGetter i s a     -> (i, a)
(^@?!) :: s -> IndexedFold i s a       -> (i, a)
(^@?!) :: s -> IndexedLens' i s a      -> (i, a)
(^@?!) :: s -> IndexedTraversal' i s a -> (i, a)

(^@?) :: s -> IndexedGetting i (Endo (Maybe (i, a))) s a -> Maybe (i, a) infixl 8 #

Perform a safe head (with index) of an IndexedFold or IndexedTraversal or retrieve Just the index and result from an IndexedGetter or IndexedLens.

When using a IndexedTraversal as a partial IndexedLens, or an IndexedFold as a partial IndexedGetter this can be a convenient way to extract the optional value.

(^@?) :: s -> IndexedGetter i s a     -> Maybe (i, a)
(^@?) :: s -> IndexedFold i s a       -> Maybe (i, a)
(^@?) :: s -> IndexedLens' i s a      -> Maybe (i, a)
(^@?) :: s -> IndexedTraversal' i s a -> Maybe (i, a)

(^@..) :: s -> IndexedGetting i (Endo [(i, a)]) s a -> [(i, a)] infixl 8 #

An infix version of itoListOf.

itoListOf :: IndexedGetting i (Endo [(i, a)]) s a -> s -> [(i, a)] #

Extract the key-value pairs from a structure.

When you don't need access to the indices in the result, then toListOf is more flexible in what it accepts.

toListOf l ≡ map snd . itoListOf l

itoListOf :: IndexedGetter i s a     -> s -> [(i,a)]
itoListOf :: IndexedFold i s a       -> s -> [(i,a)]
itoListOf :: IndexedLens' i s a      -> s -> [(i,a)]
itoListOf :: IndexedTraversal' i s a -> s -> [(i,a)]

ifoldlMOf :: Monad m => IndexedGetting i (Endo (r -> m r)) s a -> (i -> r -> a -> m r) -> r -> s -> m r #

Monadic fold over the elements of a structure with an index, associating to the left.

When you don't need access to the index then foldlMOf is more flexible in what it accepts.

foldlMOf l ≡ ifoldlMOf l . const

ifoldlMOf :: Monad m => IndexedGetter i s a     -> (i -> r -> a -> m r) -> r -> s -> m r
ifoldlMOf :: Monad m => IndexedFold i s a       -> (i -> r -> a -> m r) -> r -> s -> m r
ifoldlMOf :: Monad m => IndexedLens' i s a      -> (i -> r -> a -> m r) -> r -> s -> m r
ifoldlMOf :: Monad m => IndexedTraversal' i s a -> (i -> r -> a -> m r) -> r -> s -> m r

ifoldrMOf :: Monad m => IndexedGetting i (Dual (Endo (r -> m r))) s a -> (i -> a -> r -> m r) -> r -> s -> m r #

Monadic fold right over the elements of a structure with an index.

When you don't need access to the index then foldrMOf is more flexible in what it accepts.

foldrMOf l ≡ ifoldrMOf l . const

ifoldrMOf :: Monad m => IndexedGetter i s a     -> (i -> a -> r -> m r) -> r -> s -> m r
ifoldrMOf :: Monad m => IndexedFold i s a       -> (i -> a -> r -> m r) -> r -> s -> m r
ifoldrMOf :: Monad m => IndexedLens' i s a      -> (i -> a -> r -> m r) -> r -> s -> m r
ifoldrMOf :: Monad m => IndexedTraversal' i s a -> (i -> a -> r -> m r) -> r -> s -> m r

ifoldlOf' :: IndexedGetting i (Endo (r -> r)) s a -> (i -> r -> a -> r) -> r -> s -> r #

Fold over the elements of a structure with an index, associating to the left, but strictly.

When you don't need access to the index then foldlOf' is more flexible in what it accepts.

foldlOf' l ≡ ifoldlOf' l . const

ifoldlOf' :: IndexedGetter i s a       -> (i -> r -> a -> r) -> r -> s -> r
ifoldlOf' :: IndexedFold i s a         -> (i -> r -> a -> r) -> r -> s -> r
ifoldlOf' :: IndexedLens' i s a        -> (i -> r -> a -> r) -> r -> s -> r
ifoldlOf' :: IndexedTraversal' i s a   -> (i -> r -> a -> r) -> r -> s -> r

ifoldrOf' :: IndexedGetting i (Dual (Endo (r -> r))) s a -> (i -> a -> r -> r) -> r -> s -> r #

Strictly fold right over the elements of a structure with an index.

When you don't need access to the index then foldrOf' is more flexible in what it accepts.

foldrOf' l ≡ ifoldrOf' l . const

ifoldrOf' :: IndexedGetter i s a     -> (i -> a -> r -> r) -> r -> s -> r
ifoldrOf' :: IndexedFold i s a       -> (i -> a -> r -> r) -> r -> s -> r
ifoldrOf' :: IndexedLens' i s a      -> (i -> a -> r -> r) -> r -> s -> r
ifoldrOf' :: IndexedTraversal' i s a -> (i -> a -> r -> r) -> r -> s -> r

ifindMOf :: Monad m => IndexedGetting i (Endo (m (Maybe a))) s a -> (i -> a -> m Bool) -> s -> m (Maybe a) #

The ifindMOf function takes an IndexedFold or IndexedTraversal, a monadic predicate that is also supplied the index, a structure and returns in the monad the left-most element of the structure matching the predicate, or Nothing if there is no such element.

When you don't need access to the index then findMOf is more flexible in what it accepts.

findMOf l ≡ ifindMOf l . const

ifindMOf :: Monad m => IndexedGetter i s a     -> (i -> a -> m Bool) -> s -> m (Maybe a)
ifindMOf :: Monad m => IndexedFold i s a       -> (i -> a -> m Bool) -> s -> m (Maybe a)
ifindMOf :: Monad m => IndexedLens' i s a      -> (i -> a -> m Bool) -> s -> m (Maybe a)
ifindMOf :: Monad m => IndexedTraversal' i s a -> (i -> a -> m Bool) -> s -> m (Maybe a)

ifindOf :: IndexedGetting i (Endo (Maybe a)) s a -> (i -> a -> Bool) -> s -> Maybe a #

The ifindOf function takes an IndexedFold or IndexedTraversal, a predicate that is also supplied the index, a structure and returns the left-most element of the structure matching the predicate, or Nothing if there is no such element.

When you don't need access to the index then findOf is more flexible in what it accepts.

findOf l ≡ ifindOf l . const

ifindOf :: IndexedGetter i s a     -> (i -> a -> Bool) -> s -> Maybe a
ifindOf :: IndexedFold i s a       -> (i -> a -> Bool) -> s -> Maybe a
ifindOf :: IndexedLens' i s a      -> (i -> a -> Bool) -> s -> Maybe a
ifindOf :: IndexedTraversal' i s a -> (i -> a -> Bool) -> s -> Maybe a

iconcatMapOf :: IndexedGetting i [r] s a -> (i -> a -> [r]) -> s -> [r] #

Concatenate the results of a function of the elements of an IndexedFold or IndexedTraversal with access to the index.

When you don't need access to the index then concatMapOf is more flexible in what it accepts.

concatMapOf l ≡ iconcatMapOf l . const
iconcatMapOf ≡ ifoldMapOf

iconcatMapOf :: IndexedGetter i s a     -> (i -> a -> [r]) -> s -> [r]
iconcatMapOf :: IndexedFold i s a       -> (i -> a -> [r]) -> s -> [r]
iconcatMapOf :: IndexedLens' i s a      -> (i -> a -> [r]) -> s -> [r]
iconcatMapOf :: IndexedTraversal' i s a -> (i -> a -> [r]) -> s -> [r]

iforMOf_ :: Monad m => IndexedGetting i (Sequenced r m) s a -> s -> (i -> a -> m r) -> m () #

Run monadic actions for each target of an IndexedFold or IndexedTraversal with access to the index, discarding the results (with the arguments flipped).

iforMOf_ ≡ flip . imapMOf_

When you don't need access to the index then forMOf_ is more flexible in what it accepts.

forMOf_ l a ≡ iforMOf l a . const

iforMOf_ :: Monad m => IndexedGetter i s a     -> s -> (i -> a -> m r) -> m ()
iforMOf_ :: Monad m => IndexedFold i s a       -> s -> (i -> a -> m r) -> m ()
iforMOf_ :: Monad m => IndexedLens' i s a      -> s -> (i -> a -> m r) -> m ()
iforMOf_ :: Monad m => IndexedTraversal' i s a -> s -> (i -> a -> m r) -> m ()

imapMOf_ :: Monad m => IndexedGetting i (Sequenced r m) s a -> (i -> a -> m r) -> s -> m () #

Run monadic actions for each target of an IndexedFold or IndexedTraversal with access to the index, discarding the results.

When you don't need access to the index then mapMOf_ is more flexible in what it accepts.

mapMOf_ l ≡ imapMOf l . const

imapMOf_ :: Monad m => IndexedGetter i s a     -> (i -> a -> m r) -> s -> m ()
imapMOf_ :: Monad m => IndexedFold i s a       -> (i -> a -> m r) -> s -> m ()
imapMOf_ :: Monad m => IndexedLens' i s a      -> (i -> a -> m r) -> s -> m ()
imapMOf_ :: Monad m => IndexedTraversal' i s a -> (i -> a -> m r) -> s -> m ()

iforOf_ :: Functor f => IndexedGetting i (Traversed r f) s a -> s -> (i -> a -> f r) -> f () #

Traverse the targets of an IndexedFold or IndexedTraversal with access to the index, discarding the results (with the arguments flipped).

iforOf_ ≡ flip . itraverseOf_

When you don't need access to the index then forOf_ is more flexible in what it accepts.

forOf_ l a ≡ iforOf_ l a . const

iforOf_ :: Functor f     => IndexedGetter i s a     -> s -> (i -> a -> f r) -> f ()
iforOf_ :: Applicative f => IndexedFold i s a       -> s -> (i -> a -> f r) -> f ()
iforOf_ :: Functor f     => IndexedLens' i s a      -> s -> (i -> a -> f r) -> f ()
iforOf_ :: Applicative f => IndexedTraversal' i s a -> s -> (i -> a -> f r) -> f ()

itraverseOf_ :: Functor f => IndexedGetting i (Traversed r f) s a -> (i -> a -> f r) -> s -> f () #

Traverse the targets of an IndexedFold or IndexedTraversal with access to the i, discarding the results.

When you don't need access to the index then traverseOf_ is more flexible in what it accepts.

traverseOf_ l ≡ itraverseOf l . const

itraverseOf_ :: Functor f     => IndexedGetter i s a     -> (i -> a -> f r) -> s -> f ()
itraverseOf_ :: Applicative f => IndexedFold i s a       -> (i -> a -> f r) -> s -> f ()
itraverseOf_ :: Functor f     => IndexedLens' i s a      -> (i -> a -> f r) -> s -> f ()
itraverseOf_ :: Applicative f => IndexedTraversal' i s a -> (i -> a -> f r) -> s -> f ()

inoneOf :: IndexedGetting i Any s a -> (i -> a -> Bool) -> s -> Bool #

Return whether or not none of the elements viewed through an IndexedFold or IndexedTraversal satisfy a predicate, with access to the i.

When you don't need access to the index then noneOf is more flexible in what it accepts.

noneOf l ≡ inoneOf l . const

inoneOf :: IndexedGetter i s a     -> (i -> a -> Bool) -> s -> Bool
inoneOf :: IndexedFold i s a       -> (i -> a -> Bool) -> s -> Bool
inoneOf :: IndexedLens' i s a      -> (i -> a -> Bool) -> s -> Bool
inoneOf :: IndexedTraversal' i s a -> (i -> a -> Bool) -> s -> Bool

iallOf :: IndexedGetting i All s a -> (i -> a -> Bool) -> s -> Bool #

Return whether or not all elements viewed through an IndexedFold or IndexedTraversal satisfy a predicate, with access to the i.

When you don't need access to the index then allOf is more flexible in what it accepts.

allOf l ≡ iallOf l . const

iallOf :: IndexedGetter i s a     -> (i -> a -> Bool) -> s -> Bool
iallOf :: IndexedFold i s a       -> (i -> a -> Bool) -> s -> Bool
iallOf :: IndexedLens' i s a      -> (i -> a -> Bool) -> s -> Bool
iallOf :: IndexedTraversal' i s a -> (i -> a -> Bool) -> s -> Bool

ianyOf :: IndexedGetting i Any s a -> (i -> a -> Bool) -> s -> Bool #

Return whether or not any element viewed through an IndexedFold or IndexedTraversal satisfy a predicate, with access to the i.

When you don't need access to the index then anyOf is more flexible in what it accepts.

anyOf l ≡ ianyOf l . const

ianyOf :: IndexedGetter i s a     -> (i -> a -> Bool) -> s -> Bool
ianyOf :: IndexedFold i s a       -> (i -> a -> Bool) -> s -> Bool
ianyOf :: IndexedLens' i s a      -> (i -> a -> Bool) -> s -> Bool
ianyOf :: IndexedTraversal' i s a -> (i -> a -> Bool) -> s -> Bool

ifoldlOf :: IndexedGetting i (Dual (Endo r)) s a -> (i -> r -> a -> r) -> r -> s -> r #

Left-associative fold of the parts of a structure that are viewed through an IndexedFold or IndexedTraversal with access to the i.

When you don't need access to the index then foldlOf is more flexible in what it accepts.

foldlOf l ≡ ifoldlOf l . const

ifoldlOf :: IndexedGetter i s a     -> (i -> r -> a -> r) -> r -> s -> r
ifoldlOf :: IndexedFold i s a       -> (i -> r -> a -> r) -> r -> s -> r
ifoldlOf :: IndexedLens' i s a      -> (i -> r -> a -> r) -> r -> s -> r
ifoldlOf :: IndexedTraversal' i s a -> (i -> r -> a -> r) -> r -> s -> r

ifoldrOf :: IndexedGetting i (Endo r) s a -> (i -> a -> r -> r) -> r -> s -> r #

Right-associative fold of parts of a structure that are viewed through an IndexedFold or IndexedTraversal with access to the i.

When you don't need access to the index then foldrOf is more flexible in what it accepts.

foldrOf l ≡ ifoldrOf l . const

ifoldrOf :: IndexedGetter i s a     -> (i -> a -> r -> r) -> r -> s -> r
ifoldrOf :: IndexedFold i s a       -> (i -> a -> r -> r) -> r -> s -> r
ifoldrOf :: IndexedLens' i s a      -> (i -> a -> r -> r) -> r -> s -> r
ifoldrOf :: IndexedTraversal' i s a -> (i -> a -> r -> r) -> r -> s -> r

ifoldMapOf :: IndexedGetting i m s a -> (i -> a -> m) -> s -> m #

Fold an IndexedFold or IndexedTraversal by mapping indices and values to an arbitrary Monoid with access to the i.

When you don't need access to the index then foldMapOf is more flexible in what it accepts.

foldMapOf l ≡ ifoldMapOf l . const

ifoldMapOf ::             IndexedGetter i s a     -> (i -> a -> m) -> s -> m
ifoldMapOf :: Monoid m => IndexedFold i s a       -> (i -> a -> m) -> s -> m
ifoldMapOf ::             IndexedLens' i s a      -> (i -> a -> m) -> s -> m
ifoldMapOf :: Monoid m => IndexedTraversal' i s a -> (i -> a -> m) -> s -> m

backwards :: (Profunctor p, Profunctor q) => Optical p q (Backwards f) s t a b -> Optical p q f s t a b #

This allows you to traverse the elements of a pretty much any LensLike construction in the opposite order.

This will preserve indexes on Indexed types and will give you the elements of a (finite) Fold or Traversal in the opposite order.

This has no practical impact on a Getter, Setter, Lens or Iso.

NB: To write back through an Iso, you want to use from. Similarly, to write back through an Prism, you want to use re.

ipreuses :: MonadState s m => IndexedGetting i (First r) s a -> (i -> a -> r) -> m (Maybe r) #

Retrieve a function of the first index and value targeted by an IndexedFold or IndexedTraversal (or a function of Just the index and result from an IndexedGetter or IndexedLens) into the current state.

ipreuses = uses . ipre

ipreuses :: MonadState s m => IndexedGetter i s a     -> (i -> a -> r) -> m (Maybe r)
ipreuses :: MonadState s m => IndexedFold i s a       -> (i -> a -> r) -> m (Maybe r)
ipreuses :: MonadState s m => IndexedLens' i s a      -> (i -> a -> r) -> m (Maybe r)
ipreuses :: MonadState s m => IndexedTraversal' i s a -> (i -> a -> r) -> m (Maybe r)

preuses :: MonadState s m => Getting (First r) s a -> (a -> r) -> m (Maybe r) #

Retrieve a function of the first value targeted by a Fold or Traversal (or Just the result from a Getter or Lens) into the current state.

preuses = uses . pre

preuses :: MonadState s m => Getter s a     -> (a -> r) -> m (Maybe r)
preuses :: MonadState s m => Fold s a       -> (a -> r) -> m (Maybe r)
preuses :: MonadState s m => Lens' s a      -> (a -> r) -> m (Maybe r)
preuses :: MonadState s m => Iso' s a       -> (a -> r) -> m (Maybe r)
preuses :: MonadState s m => Traversal' s a -> (a -> r) -> m (Maybe r)

ipreuse :: MonadState s m => IndexedGetting i (First (i, a)) s a -> m (Maybe (i, a)) #

Retrieve the first index and value targeted by an IndexedFold or IndexedTraversal (or Just the index and result from an IndexedGetter or IndexedLens) into the current state.

ipreuse = use . ipre

ipreuse :: MonadState s m => IndexedGetter i s a     -> m (Maybe (i, a))
ipreuse :: MonadState s m => IndexedFold i s a       -> m (Maybe (i, a))
ipreuse :: MonadState s m => IndexedLens' i s a      -> m (Maybe (i, a))
ipreuse :: MonadState s m => IndexedTraversal' i s a -> m (Maybe (i, a))

preuse :: MonadState s m => Getting (First a) s a -> m (Maybe a) #

Retrieve the first value targeted by a Fold or Traversal (or Just the result from a Getter or Lens) into the current state.

preuse = use . pre

preuse :: MonadState s m => Getter s a     -> m (Maybe a)
preuse :: MonadState s m => Fold s a       -> m (Maybe a)
preuse :: MonadState s m => Lens' s a      -> m (Maybe a)
preuse :: MonadState s m => Iso' s a       -> m (Maybe a)
preuse :: MonadState s m => Traversal' s a -> m (Maybe a)

ipreviews :: MonadReader s m => IndexedGetting i (First r) s a -> (i -> a -> r) -> m (Maybe r) #

Retrieve a function of the first index and value targeted by an IndexedFold or IndexedTraversal (or Just the result from an IndexedGetter or IndexedLens). See also (^@?).

ipreviews = views . ipre

This is usually applied in the Reader Monad (->) s.

ipreviews :: IndexedGetter i s a     -> (i -> a -> r) -> s -> Maybe r
ipreviews :: IndexedFold i s a       -> (i -> a -> r) -> s -> Maybe r
ipreviews :: IndexedLens' i s a      -> (i -> a -> r) -> s -> Maybe r
ipreviews :: IndexedTraversal' i s a -> (i -> a -> r) -> s -> Maybe r

However, it may be useful to think of its full generality when working with a Monad transformer stack:

ipreviews :: MonadReader s m => IndexedGetter i s a     -> (i -> a -> r) -> m (Maybe r)
ipreviews :: MonadReader s m => IndexedFold i s a       -> (i -> a -> r) -> m (Maybe r)
ipreviews :: MonadReader s m => IndexedLens' i s a      -> (i -> a -> r) -> m (Maybe r)
ipreviews :: MonadReader s m => IndexedTraversal' i s a -> (i -> a -> r) -> m (Maybe r)

previews :: MonadReader s m => Getting (First r) s a -> (a -> r) -> m (Maybe r) #

Retrieve a function of the first value targeted by a Fold or Traversal (or Just the result from a Getter or Lens).

This is usually applied in the Reader Monad (->) s.

ipreview :: MonadReader s m => IndexedGetting i (First (i, a)) s a -> m (Maybe (i, a)) #

Retrieve the first index and value targeted by a Fold or Traversal (or Just the result from a Getter or Lens). See also (^@?).

ipreview = view . ipre

This is usually applied in the Reader Monad (->) s.

ipreview :: IndexedGetter i s a     -> s -> Maybe (i, a)
ipreview :: IndexedFold i s a       -> s -> Maybe (i, a)
ipreview :: IndexedLens' i s a      -> s -> Maybe (i, a)
ipreview :: IndexedTraversal' i s a -> s -> Maybe (i, a)

However, it may be useful to think of its full generality when working with a Monad transformer stack:

ipreview :: MonadReader s m => IndexedGetter s a     -> m (Maybe (i, a))
ipreview :: MonadReader s m => IndexedFold s a       -> m (Maybe (i, a))
ipreview :: MonadReader s m => IndexedLens' s a      -> m (Maybe (i, a))
ipreview :: MonadReader s m => IndexedTraversal' s a -> m (Maybe (i, a))

preview :: MonadReader s m => Getting (First a) s a -> m (Maybe a) #

Retrieve the first value targeted by a Fold or Traversal (or Just the result from a Getter or Lens). See also (^?).

listToMaybe . toList ≡ preview folded

This is usually applied in the Reader Monad (->) s.

preview = view . pre

preview :: Getter s a     -> s -> Maybe a
preview :: Fold s a       -> s -> Maybe a
preview :: Lens' s a      -> s -> Maybe a
preview :: Iso' s a       -> s -> Maybe a
preview :: Traversal' s a -> s -> Maybe a

However, it may be useful to think of its full generality when working with a Monad transformer stack:

preview :: MonadReader s m => Getter s a     -> m (Maybe a)
preview :: MonadReader s m => Fold s a       -> m (Maybe a)
preview :: MonadReader s m => Lens' s a      -> m (Maybe a)
preview :: MonadReader s m => Iso' s a       -> m (Maybe a)
preview :: MonadReader s m => Traversal' s a -> m (Maybe a)

ipre :: IndexedGetting i (First (i, a)) s a -> IndexPreservingGetter s (Maybe (i, a)) #

This converts an IndexedFold to an IndexPreservingGetter that returns the first index and element, if they exist, as a Maybe.

ipre :: IndexedGetter i s a     -> IndexPreservingGetter s (Maybe (i, a))
ipre :: IndexedFold i s a       -> IndexPreservingGetter s (Maybe (i, a))
ipre :: IndexedTraversal' i s a -> IndexPreservingGetter s (Maybe (i, a))
ipre :: IndexedLens' i s a      -> IndexPreservingGetter s (Maybe (i, a))

pre :: Getting (First a) s a -> IndexPreservingGetter s (Maybe a) #

This converts a Fold to a IndexPreservingGetter that returns the first element, if it exists, as a Maybe.

pre :: Getter s a     -> IndexPreservingGetter s (Maybe a)
pre :: Fold s a       -> IndexPreservingGetter s (Maybe a)
pre :: Traversal' s a -> IndexPreservingGetter s (Maybe a)
pre :: Lens' s a      -> IndexPreservingGetter s (Maybe a)
pre :: Iso' s a       -> IndexPreservingGetter s (Maybe a)
pre :: Prism' s a     -> IndexPreservingGetter s (Maybe a)

hasn't :: Getting All s a -> s -> Bool #

Check to see if this Fold or Traversal has no matches.

>>> hasn't _Left (Right 12)
True

>>> hasn't _Left (Left 12)
False

has :: Getting Any s a -> s -> Bool #

Check to see if this Fold or Traversal matches 1 or more entries.

>>> has (element 0) []
False

>>> has _Left (Left 12)
True

>>> has _Right (Left 12)
False

This will always return True for a Lens or Getter.

>>> has _1 ("hello","world")
True

has :: Getter s a     -> s -> Bool
has :: Fold s a       -> s -> Bool
has :: Iso' s a       -> s -> Bool
has :: Lens' s a      -> s -> Bool
has :: Traversal' s a -> s -> Bool

foldlMOf :: Monad m => Getting (Endo (r -> m r)) s a -> (r -> a -> m r) -> r -> s -> m r #

Monadic fold over the elements of a structure, associating to the left, i.e. from left to right.

foldlM ≡ foldlMOf folded

foldlMOf :: Monad m => Getter s a     -> (r -> a -> m r) -> r -> s -> m r
foldlMOf :: Monad m => Fold s a       -> (r -> a -> m r) -> r -> s -> m r
foldlMOf :: Monad m => Iso' s a       -> (r -> a -> m r) -> r -> s -> m r
foldlMOf :: Monad m => Lens' s a      -> (r -> a -> m r) -> r -> s -> m r
foldlMOf :: Monad m => Traversal' s a -> (r -> a -> m r) -> r -> s -> m r

foldrMOf :: Monad m => Getting (Dual (Endo (r -> m r))) s a -> (a -> r -> m r) -> r -> s -> m r #

Monadic fold over the elements of a structure, associating to the right, i.e. from right to left.

foldrM ≡ foldrMOf folded

foldrMOf :: Monad m => Getter s a     -> (a -> r -> m r) -> r -> s -> m r
foldrMOf :: Monad m => Fold s a       -> (a -> r -> m r) -> r -> s -> m r
foldrMOf :: Monad m => Iso' s a       -> (a -> r -> m r) -> r -> s -> m r
foldrMOf :: Monad m => Lens' s a      -> (a -> r -> m r) -> r -> s -> m r
foldrMOf :: Monad m => Traversal' s a -> (a -> r -> m r) -> r -> s -> m r

foldl1Of' :: HasCallStack => Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> a) -> s -> a #

A variant of foldlOf' that has no base case and thus may only be applied to folds and structures such that the fold views at least one element of the structure.

foldl1Of' l f ≡ foldl1' f . toListOf l

foldl1Of' :: Getter s a     -> (a -> a -> a) -> s -> a
foldl1Of' :: Fold s a       -> (a -> a -> a) -> s -> a
foldl1Of' :: Iso' s a       -> (a -> a -> a) -> s -> a
foldl1Of' :: Lens' s a      -> (a -> a -> a) -> s -> a
foldl1Of' :: Traversal' s a -> (a -> a -> a) -> s -> a

foldr1Of' :: HasCallStack => Getting (Dual (Endo (Endo (Maybe a)))) s a -> (a -> a -> a) -> s -> a #

A variant of foldrOf' that has no base case and thus may only be applied to folds and structures such that the fold views at least one element of the structure.

foldr1Of l f ≡ foldr1 f . toListOf l

foldr1Of' :: Getter s a     -> (a -> a -> a) -> s -> a
foldr1Of' :: Fold s a       -> (a -> a -> a) -> s -> a
foldr1Of' :: Iso' s a       -> (a -> a -> a) -> s -> a
foldr1Of' :: Lens' s a      -> (a -> a -> a) -> s -> a
foldr1Of' :: Traversal' s a -> (a -> a -> a) -> s -> a

foldlOf' :: Getting (Endo (Endo r)) s a -> (r -> a -> r) -> r -> s -> r #

Fold over the elements of a structure, associating to the left, but strictly.

foldl' ≡ foldlOf' folded

foldlOf' :: Getter s a     -> (r -> a -> r) -> r -> s -> r
foldlOf' :: Fold s a       -> (r -> a -> r) -> r -> s -> r
foldlOf' :: Iso' s a       -> (r -> a -> r) -> r -> s -> r
foldlOf' :: Lens' s a      -> (r -> a -> r) -> r -> s -> r
foldlOf' :: Traversal' s a -> (r -> a -> r) -> r -> s -> r

foldrOf' :: Getting (Dual (Endo (Endo r))) s a -> (a -> r -> r) -> r -> s -> r #

Strictly fold right over the elements of a structure.

foldr' ≡ foldrOf' folded

foldrOf' :: Getter s a     -> (a -> r -> r) -> r -> s -> r
foldrOf' :: Fold s a       -> (a -> r -> r) -> r -> s -> r
foldrOf' :: Iso' s a       -> (a -> r -> r) -> r -> s -> r
foldrOf' :: Lens' s a      -> (a -> r -> r) -> r -> s -> r
foldrOf' :: Traversal' s a -> (a -> r -> r) -> r -> s -> r

foldl1Of :: HasCallStack => Getting (Dual (Endo (Maybe a))) s a -> (a -> a -> a) -> s -> a #

A variant of foldlOf that has no base case and thus may only be applied to lenses and structures such that the Lens views at least one element of the structure.

>>> foldl1Of each (+) (1,2,3,4)
10

foldl1Of l f ≡ foldl1 f . toListOf l
foldl1 ≡ foldl1Of folded

foldl1Of :: Getter s a     -> (a -> a -> a) -> s -> a
foldl1Of :: Fold s a       -> (a -> a -> a) -> s -> a
foldl1Of :: Iso' s a       -> (a -> a -> a) -> s -> a
foldl1Of :: Lens' s a      -> (a -> a -> a) -> s -> a
foldl1Of :: Traversal' s a -> (a -> a -> a) -> s -> a

foldr1Of :: HasCallStack => Getting (Endo (Maybe a)) s a -> (a -> a -> a) -> s -> a #

A variant of foldrOf that has no base case and thus may only be applied to lenses and structures such that the Lens views at least one element of the structure.

>>> foldr1Of each (+) (1,2,3,4)
10

foldr1Of l f ≡ foldr1 f . toListOf l
foldr1 ≡ foldr1Of folded

foldr1Of :: Getter s a     -> (a -> a -> a) -> s -> a
foldr1Of :: Fold s a       -> (a -> a -> a) -> s -> a
foldr1Of :: Iso' s a       -> (a -> a -> a) -> s -> a
foldr1Of :: Lens' s a      -> (a -> a -> a) -> s -> a
foldr1Of :: Traversal' s a -> (a -> a -> a) -> s -> a

lookupOf :: Eq k => Getting (Endo (Maybe v)) s (k, v) -> k -> s -> Maybe v #

The lookupOf function takes a Fold (or Getter, Traversal, Lens, Iso, etc.), a key, and a structure containing key/value pairs. It returns the first value corresponding to the given key. This function generalizes lookup to work on an arbitrary Fold instead of lists.

>>> lookupOf folded 4 [(2, 'a'), (4, 'b'), (4, 'c')]
Just 'b'

>>> lookupOf each 2 [(2, 'a'), (4, 'b'), (4, 'c')]
Just 'a'

lookupOf :: Eq k => Fold s (k,v) -> k -> s -> Maybe v

findMOf :: Monad m => Getting (Endo (m (Maybe a))) s a -> (a -> m Bool) -> s -> m (Maybe a) #

The findMOf function takes a Lens (or Getter, Iso, Fold, or Traversal), a monadic predicate and a structure and returns in the monad the leftmost element of the structure matching the predicate, or Nothing if there is no such element.

>>> findMOf each ( \x -> print ("Checking " ++ show x) >> return (even x)) (1,3,4,6)
"Checking 1"
"Checking 3"
"Checking 4"
Just 4

>>> findMOf each ( \x -> print ("Checking " ++ show x) >> return (even x)) (1,3,5,7)
"Checking 1"
"Checking 3"
"Checking 5"
"Checking 7"
Nothing

findMOf :: (Monad m, Getter s a)     -> (a -> m Bool) -> s -> m (Maybe a)
findMOf :: (Monad m, Fold s a)       -> (a -> m Bool) -> s -> m (Maybe a)
findMOf :: (Monad m, Iso' s a)       -> (a -> m Bool) -> s -> m (Maybe a)
findMOf :: (Monad m, Lens' s a)      -> (a -> m Bool) -> s -> m (Maybe a)
findMOf :: (Monad m, Traversal' s a) -> (a -> m Bool) -> s -> m (Maybe a)

findMOf folded :: (Monad m, Foldable f) => (a -> m Bool) -> f a -> m (Maybe a)
ifindMOf l ≡ findMOf l . Indexed

A simpler version that didn't permit indexing, would be:

findMOf :: Monad m => Getting (Endo (m (Maybe a))) s a -> (a -> m Bool) -> s -> m (Maybe a)
findMOf l p = foldrOf l (a y -> p a >>= x -> if x then return (Just a) else y) $ return Nothing

findOf :: Getting (Endo (Maybe a)) s a -> (a -> Bool) -> s -> Maybe a #

The findOf function takes a Lens (or Getter, Iso, Fold, or Traversal), a predicate and a structure and returns the leftmost element of the structure matching the predicate, or Nothing if there is no such element.

>>> findOf each even (1,3,4,6)
Just 4

>>> findOf folded even [1,3,5,7]
Nothing

findOf :: Getter s a     -> (a -> Bool) -> s -> Maybe a
findOf :: Fold s a       -> (a -> Bool) -> s -> Maybe a
findOf :: Iso' s a       -> (a -> Bool) -> s -> Maybe a
findOf :: Lens' s a      -> (a -> Bool) -> s -> Maybe a
findOf :: Traversal' s a -> (a -> Bool) -> s -> Maybe a

find ≡ findOf folded
ifindOf l ≡ findOf l . Indexed

A simpler version that didn't permit indexing, would be:

findOf :: Getting (Endo (Maybe a)) s a -> (a -> Bool) -> s -> Maybe a
findOf l p = foldrOf l (a y -> if p a then Just a else y) Nothing

minimumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a #

Obtain the minimum element (if any) targeted by a Fold, Traversal, Lens, Iso or Getter according to a user supplied Ordering.

In the interest of efficiency, This operation has semantics more strict than strictly necessary.

>>> minimumByOf traverse (compare `on` length) ["mustard","relish","ham"]
Just "ham"

minimumBy cmp ≡ fromMaybe (error "empty") . minimumByOf folded cmp

minimumByOf :: Getter s a     -> (a -> a -> Ordering) -> s -> Maybe a
minimumByOf :: Fold s a       -> (a -> a -> Ordering) -> s -> Maybe a
minimumByOf :: Iso' s a       -> (a -> a -> Ordering) -> s -> Maybe a
minimumByOf :: Lens' s a      -> (a -> a -> Ordering) -> s -> Maybe a
minimumByOf :: Traversal' s a -> (a -> a -> Ordering) -> s -> Maybe a

maximumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a #

Obtain the maximum element (if any) targeted by a Fold, Traversal, Lens, Iso, or Getter according to a user supplied Ordering.

>>> maximumByOf traverse (compare `on` length) ["mustard","relish","ham"]
Just "mustard"

In the interest of efficiency, This operation has semantics more strict than strictly necessary.

maximumBy cmp ≡ fromMaybe (error "empty") . maximumByOf folded cmp

maximumByOf :: Getter s a     -> (a -> a -> Ordering) -> s -> Maybe a
maximumByOf :: Fold s a       -> (a -> a -> Ordering) -> s -> Maybe a
maximumByOf :: Iso' s a       -> (a -> a -> Ordering) -> s -> Maybe a
maximumByOf :: Lens' s a      -> (a -> a -> Ordering) -> s -> Maybe a
maximumByOf :: Traversal' s a -> (a -> a -> Ordering) -> s -> Maybe a

minimum1Of :: Ord a => Getting (Min a) s a -> s -> a #

Obtain the minimum element targeted by a Fold1 or Traversal1.

>>> minimum1Of traverse1 (1 :| [2..10])
1

minimum1Of :: Ord a => Getter s a      -> s -> a
minimum1Of :: Ord a => Fold1 s a       -> s -> a
minimum1Of :: Ord a => Iso' s a        -> s -> a
minimum1Of :: Ord a => Lens' s a       -> s -> a
minimum1Of :: Ord a => Traversal1' s a -> s -> a

minimumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a #

Obtain the minimum element (if any) targeted by a Fold or Traversal safely.

Note: minimumOf on a valid Iso, Lens or Getter will always return Just a value.

>>> minimumOf traverse [1..10]
Just 1

>>> minimumOf traverse []
Nothing

>>> minimumOf (folded.filtered even) [1,4,3,6,7,9,2]
Just 2

minimum ≡ fromMaybe (error "empty") . minimumOf folded

In the interest of efficiency, This operation has semantics more strict than strictly necessary. rmap getMin (foldMapOf l Min) has lazier semantics but could leak memory.

minimumOf :: Ord a => Getter s a     -> s -> Maybe a
minimumOf :: Ord a => Fold s a       -> s -> Maybe a
minimumOf :: Ord a => Iso' s a       -> s -> Maybe a
minimumOf :: Ord a => Lens' s a      -> s -> Maybe a
minimumOf :: Ord a => Traversal' s a -> s -> Maybe a

maximum1Of :: Ord a => Getting (Max a) s a -> s -> a #

Obtain the maximum element targeted by a Fold1 or Traversal1.

>>> maximum1Of traverse1 (1 :| [2..10])
10

maximum1Of :: Ord a => Getter s a      -> s -> a
maximum1Of :: Ord a => Fold1 s a       -> s -> a
maximum1Of :: Ord a => Iso' s a        -> s -> a
maximum1Of :: Ord a => Lens' s a       -> s -> a
maximum1Of :: Ord a => Traversal1' s a -> s -> a

maximumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a #

Obtain the maximum element (if any) targeted by a Fold or Traversal safely.

Note: maximumOf on a valid Iso, Lens or Getter will always return Just a value.

>>> maximumOf traverse [1..10]
Just 10

>>> maximumOf traverse []
Nothing

>>> maximumOf (folded.filtered even) [1,4,3,6,7,9,2]
Just 6

maximum ≡ fromMaybe (error "empty") . maximumOf folded

In the interest of efficiency, This operation has semantics more strict than strictly necessary. rmap getMax (foldMapOf l Max) has lazier semantics but could leak memory.

maximumOf :: Ord a => Getter s a     -> s -> Maybe a
maximumOf :: Ord a => Fold s a       -> s -> Maybe a
maximumOf :: Ord a => Iso' s a       -> s -> Maybe a
maximumOf :: Ord a => Lens' s a      -> s -> Maybe a
maximumOf :: Ord a => Traversal' s a -> s -> Maybe a

notNullOf :: Getting Any s a -> s -> Bool #

Returns True if this Fold or Traversal has any targets in the given container.

A more "conversational" alias for this combinator is has.

Note: notNullOf on a valid Iso, Lens or Getter should always return True.

not . null ≡ notNullOf folded

This may be rather inefficient compared to the not . null check of many containers.

>>> notNullOf _1 (1,2)
True

>>> notNullOf traverse [1..10]
True

>>> notNullOf folded []
False

>>> notNullOf (element 20) [1..10]
False

notNullOf (folded . _1 . folded) :: (Foldable f, Foldable g) => f (g a, b) -> Bool

notNullOf :: Getter s a     -> s -> Bool
notNullOf :: Fold s a       -> s -> Bool
notNullOf :: Iso' s a       -> s -> Bool
notNullOf :: Lens' s a      -> s -> Bool
notNullOf :: Traversal' s a -> s -> Bool

nullOf :: Getting All s a -> s -> Bool #

Returns True if this Fold or Traversal has no targets in the given container.

Note: nullOf on a valid Iso, Lens or Getter should always return False.

null ≡ nullOf folded

This may be rather inefficient compared to the null check of many containers.

>>> nullOf _1 (1,2)
False

>>> nullOf ignored ()
True

>>> nullOf traverse []
True

>>> nullOf (element 20) [1..10]
True

nullOf (folded . _1 . folded) :: (Foldable f, Foldable g) => f (g a, b) -> Bool

nullOf :: Getter s a     -> s -> Bool
nullOf :: Fold s a       -> s -> Bool
nullOf :: Iso' s a       -> s -> Bool
nullOf :: Lens' s a      -> s -> Bool
nullOf :: Traversal' s a -> s -> Bool

last1Of :: Getting (Last a) s a -> s -> a #

Retrieve the Last entry of a Fold1 or Traversal1 or retrieve the result from a Getter or Lens.o

>>> last1Of traverse1 (1 :| [2..10])
10

>>> last1Of both1 (1,2)
2

last1Of :: Getter s a      -> s -> Maybe a
last1Of :: Fold1 s a       -> s -> Maybe a
last1Of :: Lens' s a       -> s -> Maybe a
last1Of :: Iso' s a        -> s -> Maybe a
last1Of :: Traversal1' s a -> s -> Maybe a

lastOf :: Getting (Rightmost a) s a -> s -> Maybe a #

Retrieve the Last entry of a Fold or Traversal or retrieve Just the result from a Getter or Lens.

The answer is computed in a manner that leaks space less than ala Last . foldMapOf and gives you back access to the outermost Just constructor more quickly, but may have worse constant factors.

>>> lastOf traverse [1..10]
Just 10

>>> lastOf both (1,2)
Just 2

>>> lastOf ignored ()
Nothing

lastOf :: Getter s a     -> s -> Maybe a
lastOf :: Fold s a       -> s -> Maybe a
lastOf :: Lens' s a      -> s -> Maybe a
lastOf :: Iso' s a       -> s -> Maybe a
lastOf :: Traversal' s a -> s -> Maybe a

first1Of :: Getting (First a) s a -> s -> a #

Retrieve the First entry of a Fold1 or Traversal1 or the result from a Getter or Lens.

>>> first1Of traverse1 (1 :| [2..10])
1

>>> first1Of both1 (1,2)
1

Note: this is different from ^..

>>> first1Of traverse1 ([1,2] :| [[3,4],[5,6]])
[1,2]

>>> ([1,2] :| [[3,4],[5,6]]) ^. traverse1
[1,2,3,4,5,6]

first1Of :: Getter s a      -> s -> a
first1Of :: Fold1 s a       -> s -> a
first1Of :: Lens' s a       -> s -> a
first1Of :: Iso' s a        -> s -> a
first1Of :: Traversal1' s a -> s -> a

firstOf :: Getting (Leftmost a) s a -> s -> Maybe a #

Retrieve the First entry of a Fold or Traversal or retrieve Just the result from a Getter or Lens.

The answer is computed in a manner that leaks space less than ala First . foldMapOf and gives you back access to the outermost Just constructor more quickly, but may have worse constant factors.

Note: this could been named headOf.

>>> firstOf traverse [1..10]
Just 1

>>> firstOf both (1,2)
Just 1

>>> firstOf ignored ()
Nothing

firstOf :: Getter s a     -> s -> Maybe a
firstOf :: Fold s a       -> s -> Maybe a
firstOf :: Lens' s a      -> s -> Maybe a
firstOf :: Iso' s a       -> s -> Maybe a
firstOf :: Traversal' s a -> s -> Maybe a

(^?!) :: HasCallStack => s -> Getting (Endo a) s a -> a infixl 8 #

Perform an *UNSAFE* head of a Fold or Traversal assuming that it is there.

>>> Left 4 ^?! _Left
4

>>> "world" ^?! ix 3
'l'

(^?!) :: s -> Getter s a     -> a
(^?!) :: s -> Fold s a       -> a
(^?!) :: s -> Lens' s a      -> a
(^?!) :: s -> Iso' s a       -> a
(^?!) :: s -> Traversal' s a -> a

(^?) :: s -> Getting (First a) s a -> Maybe a infixl 8 #

Perform a safe head of a Fold or Traversal or retrieve Just the result from a Getter or Lens.

When using a Traversal as a partial Lens, or a Fold as a partial Getter this can be a convenient way to extract the optional value.

Note: if you get stack overflows due to this, you may want to use firstOf instead, which can deal more gracefully with heavily left-biased trees.

>>> Left 4 ^?_Left
Just 4

>>> Right 4 ^?_Left
Nothing

>>> "world" ^? ix 3
Just 'l'

>>> "world" ^? ix 20
Nothing

(^?) ≡ flip preview

(^?) :: s -> Getter s a     -> Maybe a
(^?) :: s -> Fold s a       -> Maybe a
(^?) :: s -> Lens' s a      -> Maybe a
(^?) :: s -> Iso' s a       -> Maybe a
(^?) :: s -> Traversal' s a -> Maybe a

lengthOf :: Getting (Endo (Endo Int)) s a -> s -> Int #

Calculate the number of targets there are for a Fold in a given container.

Note: This can be rather inefficient for large containers and just like length, this will not terminate for infinite folds.

length ≡ lengthOf folded

>>> lengthOf _1 ("hello",())
1

>>> lengthOf traverse [1..10]
10

>>> lengthOf (traverse.traverse) [[1,2],[3,4],[5,6]]
6

lengthOf (folded . folded) :: (Foldable f, Foldable g) => f (g a) -> Int

lengthOf :: Getter s a     -> s -> Int
lengthOf :: Fold s a       -> s -> Int
lengthOf :: Lens' s a      -> s -> Int
lengthOf :: Iso' s a       -> s -> Int
lengthOf :: Traversal' s a -> s -> Int

concatOf :: Getting [r] s [r] -> s -> [r] #

Concatenate all of the lists targeted by a Fold into a longer list.

>>> concatOf both ("pan","ama")
"panama"

concat ≡ concatOf folded
concatOf ≡ view

concatOf :: Getter s [r]     -> s -> [r]
concatOf :: Fold s [r]       -> s -> [r]
concatOf :: Iso' s [r]       -> s -> [r]
concatOf :: Lens' s [r]      -> s -> [r]
concatOf :: Traversal' s [r] -> s -> [r]

concatMapOf :: Getting [r] s a -> (a -> [r]) -> s -> [r] #

Map a function over all the targets of a Fold of a container and concatenate the resulting lists.

>>> concatMapOf both (\x -> [x, x + 1]) (1,3)
[1,2,3,4]

concatMap ≡ concatMapOf folded

concatMapOf :: Getter s a     -> (a -> [r]) -> s -> [r]
concatMapOf :: Fold s a       -> (a -> [r]) -> s -> [r]
concatMapOf :: Lens' s a      -> (a -> [r]) -> s -> [r]
concatMapOf :: Iso' s a       -> (a -> [r]) -> s -> [r]
concatMapOf :: Traversal' s a -> (a -> [r]) -> s -> [r]

notElemOf :: Eq a => Getting All s a -> a -> s -> Bool #

Does the element not occur anywhere within a given Fold of the structure?

>>> notElemOf each 'd' ('a','b','c')
True

>>> notElemOf each 'a' ('a','b','c')
False

notElem ≡ notElemOf folded

notElemOf :: Eq a => Getter s a     -> a -> s -> Bool
notElemOf :: Eq a => Fold s a       -> a -> s -> Bool
notElemOf :: Eq a => Iso' s a       -> a -> s -> Bool
notElemOf :: Eq a => Lens' s a      -> a -> s -> Bool
notElemOf :: Eq a => Traversal' s a -> a -> s -> Bool
notElemOf :: Eq a => Prism' s a     -> a -> s -> Bool

elemOf :: Eq a => Getting Any s a -> a -> s -> Bool #

Does the element occur anywhere within a given Fold of the structure?

>>> elemOf both "hello" ("hello","world")
True

elem ≡ elemOf folded

elemOf :: Eq a => Getter s a     -> a -> s -> Bool
elemOf :: Eq a => Fold s a       -> a -> s -> Bool
elemOf :: Eq a => Lens' s a      -> a -> s -> Bool
elemOf :: Eq a => Iso' s a       -> a -> s -> Bool
elemOf :: Eq a => Traversal' s a -> a -> s -> Bool
elemOf :: Eq a => Prism' s a     -> a -> s -> Bool

msumOf :: MonadPlus m => Getting (Endo (m a)) s (m a) -> s -> m a #

The sum of a collection of actions, generalizing concatOf.

>>> msumOf both ("hello","world")
"helloworld"

>>> msumOf each (Nothing, Just "hello", Nothing)
Just "hello"

msum ≡ msumOf folded

msumOf :: MonadPlus m => Getter s (m a)     -> s -> m a
msumOf :: MonadPlus m => Fold s (m a)       -> s -> m a
msumOf :: MonadPlus m => Lens' s (m a)      -> s -> m a
msumOf :: MonadPlus m => Iso' s (m a)       -> s -> m a
msumOf :: MonadPlus m => Traversal' s (m a) -> s -> m a
msumOf :: MonadPlus m => Prism' s (m a)     -> s -> m a

asumOf :: Alternative f => Getting (Endo (f a)) s (f a) -> s -> f a #

The sum of a collection of actions, generalizing concatOf.

>>> asumOf both ("hello","world")
"helloworld"

>>> asumOf each (Nothing, Just "hello", Nothing)
Just "hello"

asum ≡ asumOf folded

asumOf :: Alternative f => Getter s (f a)     -> s -> f a
asumOf :: Alternative f => Fold s (f a)       -> s -> f a
asumOf :: Alternative f => Lens' s (f a)      -> s -> f a
asumOf :: Alternative f => Iso' s (f a)       -> s -> f a
asumOf :: Alternative f => Traversal' s (f a) -> s -> f a
asumOf :: Alternative f => Prism' s (f a)     -> s -> f a

sequenceOf_ :: Monad m => Getting (Sequenced a m) s (m a) -> s -> m () #

Evaluate each monadic action referenced by a Fold on the structure from left to right, and ignore the results.

>>> sequenceOf_ both (putStrLn "hello",putStrLn "world")
hello
world

sequence_ ≡ sequenceOf_ folded

sequenceOf_ :: Monad m => Getter s (m a)     -> s -> m ()
sequenceOf_ :: Monad m => Fold s (m a)       -> s -> m ()
sequenceOf_ :: Monad m => Lens' s (m a)      -> s -> m ()
sequenceOf_ :: Monad m => Iso' s (m a)       -> s -> m ()
sequenceOf_ :: Monad m => Traversal' s (m a) -> s -> m ()
sequenceOf_ :: Monad m => Prism' s (m a)     -> s -> m ()

forMOf_ :: Monad m => Getting (Sequenced r m) s a -> s -> (a -> m r) -> m () #

forMOf_ is mapMOf_ with two of its arguments flipped.

>>> forMOf_ both ("hello","world") putStrLn
hello
world

forM_ ≡ forMOf_ folded

forMOf_ :: Monad m => Getter s a     -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Fold s a       -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Lens' s a      -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Iso' s a       -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Traversal' s a -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Prism' s a     -> s -> (a -> m r) -> m ()

mapMOf_ :: Monad m => Getting (Sequenced r m) s a -> (a -> m r) -> s -> m () #

Map each target of a Fold on a structure to a monadic action, evaluate these actions from left to right, and ignore the results.

>>> mapMOf_ both putStrLn ("hello","world")
hello
world

mapM_ ≡ mapMOf_ folded

mapMOf_ :: Monad m => Getter s a     -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Fold s a       -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Lens' s a      -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Iso' s a       -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Traversal' s a -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Prism' s a     -> (a -> m r) -> s -> m ()

sequence1Of_ :: Functor f => Getting (TraversedF a f) s (f a) -> s -> f () #

See sequenceAOf_ and traverse1Of_.

sequence1Of_ :: Apply f => Fold1 s (f a) -> s -> f ()

Since: lens-4.16

for1Of_ :: Functor f => Getting (TraversedF r f) s a -> s -> (a -> f r) -> f () #

See forOf_ and traverse1Of_.

>>> for1Of_ both1 ("abc", "bcd") (\ks -> Map.fromList [ (k, ()) | k <- ks ])
fromList [('b',()),('c',())]

for1Of_ :: Apply f => Fold1 s a -> s -> (a -> f r) -> f ()

Since: lens-4.16

traverse1Of_ :: Functor f => Getting (TraversedF r f) s a -> (a -> f r) -> s -> f () #

Traverse over all of the targets of a Fold1, computing an Apply based answer.

As long as you have Applicative or Functor effect you are better using traverseOf_. The traverse1Of_ is useful only when you have genuine Apply effect.

>>> traverse1Of_ both1 (\ks -> Map.fromList [ (k, ()) | k <- ks ]) ("abc", "bcd")
fromList [('b',()),('c',())]

traverse1Of_ :: Apply f => Fold1 s a -> (a -> f r) -> s -> f ()

Since: lens-4.16

sequenceAOf_ :: Functor f => Getting (Traversed a f) s (f a) -> s -> f () #

Evaluate each action in observed by a Fold on a structure from left to right, ignoring the results.

sequenceA_ ≡ sequenceAOf_ folded

>>> sequenceAOf_ both (putStrLn "hello",putStrLn "world")
hello
world

sequenceAOf_ :: Functor f     => Getter s (f a)     -> s -> f ()
sequenceAOf_ :: Applicative f => Fold s (f a)       -> s -> f ()
sequenceAOf_ :: Functor f     => Lens' s (f a)      -> s -> f ()
sequenceAOf_ :: Functor f     => Iso' s (f a)       -> s -> f ()
sequenceAOf_ :: Applicative f => Traversal' s (f a) -> s -> f ()
sequenceAOf_ :: Applicative f => Prism' s (f a)     -> s -> f ()

forOf_ :: Functor f => Getting (Traversed r f) s a -> s -> (a -> f r) -> f () #

Traverse over all of the targets of a Fold (or Getter), computing an Applicative (or Functor)-based answer, but unlike forOf do not construct a new structure. forOf_ generalizes for_ to work over any Fold.

When passed a Getter, forOf_ can work over any Functor, but when passed a Fold, forOf_ requires an Applicative.

for_ ≡ forOf_ folded

>>> forOf_ both ("hello","world") putStrLn
hello
world

The rather specific signature of forOf_ allows it to be used as if the signature was any of:

iforOf_ l s ≡ forOf_ l s . Indexed

forOf_ :: Functor f     => Getter s a     -> s -> (a -> f r) -> f ()
forOf_ :: Applicative f => Fold s a       -> s -> (a -> f r) -> f ()
forOf_ :: Functor f     => Lens' s a      -> s -> (a -> f r) -> f ()
forOf_ :: Functor f     => Iso' s a       -> s -> (a -> f r) -> f ()
forOf_ :: Applicative f => Traversal' s a -> s -> (a -> f r) -> f ()
forOf_ :: Applicative f => Prism' s a     -> s -> (a -> f r) -> f ()

traverseOf_ :: Functor f => Getting (Traversed r f) s a -> (a -> f r) -> s -> f () #

Traverse over all of the targets of a Fold (or Getter), computing an Applicative (or Functor)-based answer, but unlike traverseOf do not construct a new structure. traverseOf_ generalizes traverse_ to work over any Fold.

When passed a Getter, traverseOf_ can work over any Functor, but when passed a Fold, traverseOf_ requires an Applicative.

>>> traverseOf_ both putStrLn ("hello","world")
hello
world

traverse_ ≡ traverseOf_ folded

traverseOf_ _2 :: Functor f => (c -> f r) -> (d, c) -> f ()
traverseOf_ _Left :: Applicative f => (a -> f b) -> Either a c -> f ()

itraverseOf_ l ≡ traverseOf_ l . Indexed

The rather specific signature of traverseOf_ allows it to be used as if the signature was any of:

traverseOf_ :: Functor f     => Getter s a     -> (a -> f r) -> s -> f ()
traverseOf_ :: Applicative f => Fold s a       -> (a -> f r) -> s -> f ()
traverseOf_ :: Functor f     => Lens' s a      -> (a -> f r) -> s -> f ()
traverseOf_ :: Functor f     => Iso' s a       -> (a -> f r) -> s -> f ()
traverseOf_ :: Applicative f => Traversal' s a -> (a -> f r) -> s -> f ()
traverseOf_ :: Applicative f => Prism' s a     -> (a -> f r) -> s -> f ()

sumOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a #

Calculate the Sum of every number targeted by a Fold.

>>> sumOf both (5,6)
11
>>> sumOf folded [1,2,3,4]
10
>>> sumOf (folded.both) [(1,2),(3,4)]
10
>>> import Data.Data.Lens
>>> sumOf biplate [(1::Int,[]),(2,[(3::Int,4::Int)])] :: Int
10

sum ≡ sumOf folded

This operation may be more strict than you would expect. If you want a lazier version use ala Sum . foldMapOf

sumOf _1 :: Num a => (a, b) -> a
sumOf (folded . _1) :: (Foldable f, Num a) => f (a, b) -> a

sumOf :: Num a => Getter s a     -> s -> a
sumOf :: Num a => Fold s a       -> s -> a
sumOf :: Num a => Lens' s a      -> s -> a
sumOf :: Num a => Iso' s a       -> s -> a
sumOf :: Num a => Traversal' s a -> s -> a
sumOf :: Num a => Prism' s a     -> s -> a

productOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a #

Calculate the Product of every number targeted by a Fold.

>>> productOf both (4,5)
20
>>> productOf folded [1,2,3,4,5]
120

product ≡ productOf folded

This operation may be more strict than you would expect. If you want a lazier version use ala Product . foldMapOf

productOf :: Num a => Getter s a     -> s -> a
productOf :: Num a => Fold s a       -> s -> a
productOf :: Num a => Lens' s a      -> s -> a
productOf :: Num a => Iso' s a       -> s -> a
productOf :: Num a => Traversal' s a -> s -> a
productOf :: Num a => Prism' s a     -> s -> a

noneOf :: Getting Any s a -> (a -> Bool) -> s -> Bool #

Returns True only if no targets of a Fold satisfy a predicate.

>>> noneOf each (is _Nothing) (Just 3, Just 4, Just 5)
True
>>> noneOf (folded.folded) (<10) [[13,99,20],[3,71,42]]
False

inoneOf l = noneOf l . Indexed

noneOf :: Getter s a     -> (a -> Bool) -> s -> Bool
noneOf :: Fold s a       -> (a -> Bool) -> s -> Bool
noneOf :: Lens' s a      -> (a -> Bool) -> s -> Bool
noneOf :: Iso' s a       -> (a -> Bool) -> s -> Bool
noneOf :: Traversal' s a -> (a -> Bool) -> s -> Bool
noneOf :: Prism' s a     -> (a -> Bool) -> s -> Bool

allOf :: Getting All s a -> (a -> Bool) -> s -> Bool #

Returns True if every target of a Fold satisfies a predicate.

>>> allOf both (>=3) (4,5)
True
>>> allOf folded (>=2) [1..10]
False

all ≡ allOf folded

iallOf l = allOf l . Indexed

allOf :: Getter s a     -> (a -> Bool) -> s -> Bool
allOf :: Fold s a       -> (a -> Bool) -> s -> Bool
allOf :: Lens' s a      -> (a -> Bool) -> s -> Bool
allOf :: Iso' s a       -> (a -> Bool) -> s -> Bool
allOf :: Traversal' s a -> (a -> Bool) -> s -> Bool
allOf :: Prism' s a     -> (a -> Bool) -> s -> Bool

anyOf :: Getting Any s a -> (a -> Bool) -> s -> Bool #

Returns True if any target of a Fold satisfies a predicate.

>>> anyOf both (=='x') ('x','y')
True
>>> import Data.Data.Lens
>>> anyOf biplate (== "world") (((),2::Int),"hello",("world",11::Int))
True

any ≡ anyOf folded

ianyOf l ≡ anyOf l . Indexed

anyOf :: Getter s a     -> (a -> Bool) -> s -> Bool
anyOf :: Fold s a       -> (a -> Bool) -> s -> Bool
anyOf :: Lens' s a      -> (a -> Bool) -> s -> Bool
anyOf :: Iso' s a       -> (a -> Bool) -> s -> Bool
anyOf :: Traversal' s a -> (a -> Bool) -> s -> Bool
anyOf :: Prism' s a     -> (a -> Bool) -> s -> Bool

orOf :: Getting Any s Bool -> s -> Bool #

Returns True if any target of a Fold is True.

>>> orOf both (True,False)
True
>>> orOf both (False,False)
False

or ≡ orOf folded

orOf :: Getter s Bool     -> s -> Bool
orOf :: Fold s Bool       -> s -> Bool
orOf :: Lens' s Bool      -> s -> Bool
orOf :: Iso' s Bool       -> s -> Bool
orOf :: Traversal' s Bool -> s -> Bool
orOf :: Prism' s Bool     -> s -> Bool

andOf :: Getting All s Bool -> s -> Bool #

Returns True if every target of a Fold is True.

>>> andOf both (True,False)
False
>>> andOf both (True,True)
True

and ≡ andOf folded

andOf :: Getter s Bool     -> s -> Bool
andOf :: Fold s Bool       -> s -> Bool
andOf :: Lens' s Bool      -> s -> Bool
andOf :: Iso' s Bool       -> s -> Bool
andOf :: Traversal' s Bool -> s -> Bool
andOf :: Prism' s Bool     -> s -> Bool

(^..) :: s -> Getting (Endo [a]) s a -> [a] infixl 8 #

A convenient infix (flipped) version of toListOf.

>>> [[1,2],[3]]^..id
[[[1,2],[3]]]
>>> [[1,2],[3]]^..traverse
[[1,2],[3]]
>>> [[1,2],[3]]^..traverse.traverse
[1,2,3]

>>> (1,2)^..both
[1,2]

toList xs ≡ xs ^.. folded
(^..) ≡ flip toListOf

(^..) :: s -> Getter s a     -> a :: s -> Fold s a       -> a :: s -> Lens' s a      -> a :: s -> Iso' s a       -> a :: s -> Traversal' s a -> a :: s -> Prism' s a     -> [a]

toNonEmptyOf :: Getting (NonEmptyDList a) s a -> s -> NonEmpty a #

Extract a NonEmpty of the targets of Fold1.

>>> toNonEmptyOf both1 ("hello", "world")
"hello" :| ["world"]

toNonEmptyOf :: Getter s a      -> s -> NonEmpty a
toNonEmptyOf :: Fold1 s a       -> s -> NonEmpty a
toNonEmptyOf :: Lens' s a       -> s -> NonEmpty a
toNonEmptyOf :: Iso' s a        -> s -> NonEmpty a
toNonEmptyOf :: Traversal1' s a -> s -> NonEmpty a
toNonEmptyOf :: Prism' s a      -> s -> NonEmpty a

toListOf :: Getting (Endo [a]) s a -> s -> [a] #

Extract a list of the targets of a Fold. See also (^..).

toList ≡ toListOf folded
(^..) ≡ flip toListOf

foldlOf :: Getting (Dual (Endo r)) s a -> (r -> a -> r) -> r -> s -> r #

Left-associative fold of the parts of a structure that are viewed through a Lens, Getter, Fold or Traversal.

foldl ≡ foldlOf folded

foldlOf :: Getter s a     -> (r -> a -> r) -> r -> s -> r
foldlOf :: Fold s a       -> (r -> a -> r) -> r -> s -> r
foldlOf :: Lens' s a      -> (r -> a -> r) -> r -> s -> r
foldlOf :: Iso' s a       -> (r -> a -> r) -> r -> s -> r
foldlOf :: Traversal' s a -> (r -> a -> r) -> r -> s -> r
foldlOf :: Prism' s a     -> (r -> a -> r) -> r -> s -> r

foldrOf :: Getting (Endo r) s a -> (a -> r -> r) -> r -> s -> r #

Right-associative fold of parts of a structure that are viewed through a Lens, Getter, Fold or Traversal.

foldr ≡ foldrOf folded

foldrOf :: Getter s a     -> (a -> r -> r) -> r -> s -> r
foldrOf :: Fold s a       -> (a -> r -> r) -> r -> s -> r
foldrOf :: Lens' s a      -> (a -> r -> r) -> r -> s -> r
foldrOf :: Iso' s a       -> (a -> r -> r) -> r -> s -> r
foldrOf :: Traversal' s a -> (a -> r -> r) -> r -> s -> r
foldrOf :: Prism' s a     -> (a -> r -> r) -> r -> s -> r

ifoldrOf l ≡ foldrOf l . Indexed

foldrOf :: Getting (Endo r) s a -> (a -> r -> r) -> r -> s -> r

foldOf :: Getting a s a -> s -> a #

Combine the elements of a structure viewed through a Lens, Getter, Fold or Traversal using a monoid.

>>> foldOf (folded.folded) [[Sum 1,Sum 4],[Sum 8, Sum 8],[Sum 21]]
Sum {getSum = 42}

fold = foldOf folded

foldOf ≡ view

foldOf ::             Getter s m     -> s -> m
foldOf :: Monoid m => Fold s m       -> s -> m
foldOf ::             Lens' s m      -> s -> m
foldOf ::             Iso' s m       -> s -> m
foldOf :: Monoid m => Traversal' s m -> s -> m
foldOf :: Monoid m => Prism' s m     -> s -> m

foldMapOf :: Getting r s a -> (a -> r) -> s -> r #

Map each part of a structure viewed through a Lens, Getter, Fold or Traversal to a monoid and combine the results.

>>> foldMapOf (folded . both . _Just) Sum [(Just 21, Just 21)]
Sum {getSum = 42}

foldMap = foldMapOf folded

foldMapOf ≡ views
ifoldMapOf l = foldMapOf l . Indexed

foldMapOf ::                Getter s a      -> (a -> r) -> s -> r
foldMapOf :: Monoid r    => Fold s a        -> (a -> r) -> s -> r
foldMapOf :: Semigroup r => Fold1 s a       -> (a -> r) -> s -> r
foldMapOf ::                Lens' s a       -> (a -> r) -> s -> r
foldMapOf ::                Iso' s a        -> (a -> r) -> s -> r
foldMapOf :: Monoid r    => Traversal' s a  -> (a -> r) -> s -> r
foldMapOf :: Semigroup r => Traversal1' s a -> (a -> r) -> s -> r
foldMapOf :: Monoid r    => Prism' s a      -> (a -> r) -> s -> r

foldMapOf :: Getting r s a -> (a -> r) -> s -> r

lined :: Applicative f => IndexedLensLike' Int f String String #

A Fold over the individual lines of a String.

lined :: Fold String String
lined :: Traversal' String String

lined :: IndexedFold Int String String
lined :: IndexedTraversal' Int String String

Note: This function type-checks as a Traversal but it doesn't satisfy the laws. It's only valid to use it when you don't insert any newline characters while traversing, and if your original String contains only isolated newline characters.

worded :: Applicative f => IndexedLensLike' Int f String String #

A Fold over the individual words of a String.

worded :: Fold String String
worded :: Traversal' String String

worded :: IndexedFold Int String String
worded :: IndexedTraversal' Int String String

Note: This function type-checks as a Traversal but it doesn't satisfy the laws. It's only valid to use it when you don't insert any whitespace characters while traversing, and if your original String contains only isolated space characters (and no other characters that count as space, such as non-breaking spaces).

droppingWhile :: (Conjoined p, Profunctor q, Applicative f) => (a -> Bool) -> Optical p q (Compose (State Bool) f) s t a a -> Optical p q f s t a a #

Obtain a Fold by dropping elements from another Fold, Lens, Iso, Getter or Traversal while a predicate holds.

dropWhile p ≡ toListOf (droppingWhile p folded)

>>> toListOf (droppingWhile (<=3) folded) [1..6]
[4,5,6]

>>> toListOf (droppingWhile (<=3) folded) [1,6,1]
[6,1]

droppingWhile :: (a -> Bool) -> Fold s a                         -> Fold s a
droppingWhile :: (a -> Bool) -> Getter s a                       -> Fold s a
droppingWhile :: (a -> Bool) -> Traversal' s a                   -> Fold s a                -- see notes
droppingWhile :: (a -> Bool) -> Lens' s a                        -> Fold s a                -- see notes
droppingWhile :: (a -> Bool) -> Prism' s a                       -> Fold s a                -- see notes
droppingWhile :: (a -> Bool) -> Iso' s a                         -> Fold s a                -- see notes

droppingWhile :: (a -> Bool) -> IndexPreservingTraversal' s a    -> IndexPreservingFold s a -- see notes
droppingWhile :: (a -> Bool) -> IndexPreservingLens' s a         -> IndexPreservingFold s a -- see notes
droppingWhile :: (a -> Bool) -> IndexPreservingGetter s a        -> IndexPreservingFold s a
droppingWhile :: (a -> Bool) -> IndexPreservingFold s a          -> IndexPreservingFold s a

droppingWhile :: (a -> Bool) -> IndexedTraversal' i s a          -> IndexedFold i s a       -- see notes
droppingWhile :: (a -> Bool) -> IndexedLens' i s a               -> IndexedFold i s a       -- see notes
droppingWhile :: (a -> Bool) -> IndexedGetter i s a              -> IndexedFold i s a
droppingWhile :: (a -> Bool) -> IndexedFold i s a                -> IndexedFold i s a

Note: Many uses of this combinator will yield something that meets the types, but not the laws of a valid Traversal or IndexedTraversal. The Traversal and IndexedTraversal laws are only satisfied if the new values you assign to the first target also does not pass the predicate! Otherwise subsequent traversals will visit fewer elements and Traversal fusion is not sound.

So for any traversal t and predicate p, droppingWhile p t may not be lawful, but (dropping 1 . droppingWhile p) t is. For example:

>>> let l  :: Traversal' [Int] Int; l  = droppingWhile (<= 1) traverse
>>> let l' :: Traversal' [Int] Int; l' = dropping 1 l

l is not a lawful setter because over l f . over l g ≢ over l (f . g):

>>> [1,2,3] & l .~ 0 & l .~ 4
[1,0,0]
>>> [1,2,3] & l .~ 4
[1,4,4]

l' on the other hand behaves lawfully:

>>> [1,2,3] & l' .~ 0 & l' .~ 4
[1,2,4]
>>> [1,2,3] & l' .~ 4
[1,2,4]

takingWhile :: (Conjoined p, Applicative f) => (a -> Bool) -> Over p (TakingWhile p f a a) s t a a -> Over p f s t a a #

Obtain a Fold by taking elements from another Fold, Lens, Iso, Getter or Traversal while a predicate holds.

takeWhile p ≡ toListOf (takingWhile p folded)

>>> timingOut $ toListOf (takingWhile (<=3) folded) [1..]
[1,2,3]

takingWhile :: (a -> Bool) -> Fold s a                         -> Fold s a
takingWhile :: (a -> Bool) -> Getter s a                       -> Fold s a
takingWhile :: (a -> Bool) -> Traversal' s a                   -> Fold s a -- * See note below
takingWhile :: (a -> Bool) -> Lens' s a                        -> Fold s a -- * See note below
takingWhile :: (a -> Bool) -> Prism' s a                       -> Fold s a -- * See note below
takingWhile :: (a -> Bool) -> Iso' s a                         -> Fold s a -- * See note below
takingWhile :: (a -> Bool) -> IndexedTraversal' i s a          -> IndexedFold i s a -- * See note below
takingWhile :: (a -> Bool) -> IndexedLens' i s a               -> IndexedFold i s a -- * See note below
takingWhile :: (a -> Bool) -> IndexedFold i s a                -> IndexedFold i s a
takingWhile :: (a -> Bool) -> IndexedGetter i s a              -> IndexedFold i s a

Note: When applied to a Traversal, takingWhile yields something that can be used as if it were a Traversal, but which is not a Traversal per the laws, unless you are careful to ensure that you do not invalidate the predicate when writing back through it.

filtered :: (Choice p, Applicative f) => (a -> Bool) -> Optic' p f a a #

Obtain an Fold that can be composed with to filter another Lens, Iso, Getter, Fold (or Traversal).

Note: This is not a legal Traversal, unless you are very careful not to invalidate the predicate on the target.

Note: This is also not a legal Prism, unless you are very careful not to inject a value that matches the predicate.

As a counter example, consider that given evens = filtered even the second Traversal law is violated:

over evens succ . over evens succ /= over evens (succ . succ)

So, in order for this to qualify as a legal Traversal you can only use it for actions that preserve the result of the predicate!

>>> [1..10]^..folded.filtered even
[2,4,6,8,10]

This will preserve an index if it is present.

iterated :: Apply f => (a -> a) -> LensLike' f a a #

x ^. iterated f returns an infinite Fold1 of repeated applications of f to x.

toListOf (iterated f) a ≡ iterate f a

iterated :: (a -> a) -> Fold1 a a

unfolded :: (b -> Maybe (a, b)) -> Fold b a #

Build a Fold that unfolds its values from a seed.

unfoldr ≡ toListOf . unfolded

>>> 10^..unfolded (\b -> if b == 0 then Nothing else Just (b, b-1))
[10,9,8,7,6,5,4,3,2,1]

cycled :: Apply f => LensLike f s t a b -> LensLike f s t a b #

Transform a non-empty Fold into a Fold1 that loops over its elements over and over.

>>> timingOut $ [1,2,3]^..taking 7 (cycled traverse)
[1,2,3,1,2,3,1]

cycled :: Fold1 s a -> Fold1 s a

replicated :: Int -> Fold a a #

A Fold that replicates its input n times.

replicate n ≡ toListOf (replicated n)

>>> 5^..replicated 20
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]

repeated :: Apply f => LensLike' f a a #

Form a Fold1 by repeating the input forever.

repeat ≡ toListOf repeated

>>> timingOut $ 5^..taking 20 repeated
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]

repeated :: Fold1 a a

folded64 :: Foldable f => IndexedFold Int64 (f a) a #

Obtain a Fold from any Foldable indexed by ordinal position.

folded :: Foldable f => IndexedFold Int (f a) a #

Obtain a Fold from any Foldable indexed by ordinal position.

>>> Just 3^..folded
[3]

>>> Nothing^..folded
[]

>>> [(1,2),(3,4)]^..folded.both
[1,2,3,4]

ifoldring :: (Indexable i p, Contravariant f, Applicative f) => ((i -> a -> f a -> f a) -> f a -> s -> f a) -> Over p f s t a b #

Obtain FoldWithIndex by lifting ifoldr like function.

foldring :: (Contravariant f, Applicative f) => ((a -> f a -> f a) -> f a -> s -> f a) -> LensLike f s t a b #

Obtain a Fold by lifting foldr like function.

>>> [1,2,3,4]^..foldring foldr
[1,2,3,4]

ifolding :: (Foldable f, Indexable i p, Contravariant g, Applicative g) => (s -> f (i, a)) -> Over p g s t a b #

folding :: Foldable f => (s -> f a) -> Fold s a #

Obtain a Fold by lifting an operation that returns a Foldable result.

This can be useful to lift operations from Data.List and elsewhere into a Fold.

>>> [1,2,3,4]^..folding tail
[2,3,4]

_Show :: (Read a, Show a) => Prism' String a #

This is an improper prism for text formatting based on Read and Show.

This Prism is "improper" in the sense that it normalizes the text formatting, but round tripping is idempotent given sane 'Read'/'Show' instances.

>>> _Show # 2
"2"

>>> "EQ" ^? _Show :: Maybe Ordering
Just EQ

_Show ≡ prism' show readMaybe

nearly :: a -> (a -> Bool) -> Prism' a () #

This Prism compares for approximate equality with a given value and a predicate for testing, an example where the value is the empty list and the predicate checks that a list is empty (same as _Empty with the AsEmpty list instance):

>>> nearly [] null # ()
[]
>>> [1,2,3,4] ^? nearly [] null
Nothing

nearly [] null :: Prism' [a] ()

To comply with the Prism laws the arguments you supply to nearly a p are somewhat constrained.

We assume p x holds iff x ≡ a. Under that assumption then this is a valid Prism.

This is useful when working with a type where you can test equality for only a subset of its values, and the prism selects such a value.

only :: Eq a => a -> Prism' a () #

This Prism compares for exact equality with a given value.

>>> only 4 # ()
4

>>> 5 ^? only 4
Nothing

_Void :: Prism s s a Void #

Void is a logically uninhabited data type.

This is a Prism that will always fail to match.

_Nothing :: Prism' (Maybe a) () #

This Prism provides the Traversal of a Nothing in a Maybe.

>>> Nothing ^? _Nothing
Just ()

>>> Just () ^? _Nothing
Nothing

But you can turn it around and use it to construct Nothing as well:

>>> _Nothing # ()
Nothing

_Just :: Prism (Maybe a) (Maybe b) a b #

This Prism provides a Traversal for tweaking the target of the value of Just in a Maybe.

>>> over _Just (+1) (Just 2)
Just 3

Unlike traverse this is a Prism, and so you can use it to inject as well:

>>> _Just # 5
Just 5

>>> 5^.re _Just
Just 5

Interestingly,

m ^? _Just ≡ m

>>> Just x ^? _Just
Just x

>>> Nothing ^? _Just
Nothing

_Right :: Prism (Either c a) (Either c b) a b #

This Prism provides a Traversal for tweaking the Right half of an Either:

>>> over _Right (+1) (Left 2)
Left 2

>>> over _Right (+1) (Right 2)
Right 3

>>> Right "hello" ^._Right
"hello"

>>> Left "hello" ^._Right :: [Double]
[]

It also can be turned around to obtain the embedding into the Right half of an Either:

>>> _Right # 5
Right 5

>>> 5^.re _Right
Right 5

_Left :: Prism (Either a c) (Either b c) a b #

This Prism provides a Traversal for tweaking the Left half of an Either:

>>> over _Left (+1) (Left 2)
Left 3

>>> over _Left (+1) (Right 2)
Right 2

>>> Right 42 ^._Left :: String
""

>>> Left "hello" ^._Left
"hello"

It also can be turned around to obtain the embedding into the Left half of an Either:

>>> _Left # 5
Left 5

>>> 5^.re _Left
Left 5

matching :: APrism s t a b -> s -> Either t a #

Retrieve the value targeted by a Prism or return the original value while allowing the type to change if it does not match.

>>> matching _Just (Just 12)
Right 12

>>> matching _Just (Nothing :: Maybe Int) :: Either (Maybe Bool) Int
Left Nothing

isn't :: APrism s t a b -> s -> Bool #

Check to see if this Prism doesn't match.

>>> isn't _Left (Right 12)
True

>>> isn't _Left (Left 12)
False

>>> isn't _Empty []
False

below :: Traversable f => APrism' s a -> Prism' (f s) (f a) #

lift a Prism through a Traversable functor, giving a Prism that matches only if all the elements of the container match the Prism.

>>> [Left 1, Right "foo", Left 4, Right "woot"]^..below _Right
[]

>>> [Right "hail hydra!", Right "foo", Right "blah", Right "woot"]^..below _Right
[["hail hydra!","foo","blah","woot"]]

aside :: APrism s t a b -> Prism (e, s) (e, t) (e, a) (e, b) #

Use a Prism to work over part of a structure.

without :: APrism s t a b -> APrism u v c d -> Prism (Either s u) (Either t v) (Either a c) (Either b d) #

Given a pair of prisms, project sums.

Viewing a Prism as a co-Lens, this combinator can be seen to be dual to alongside.

outside :: Representable p => APrism s t a b -> Lens (p t r) (p s r) (p b r) (p a r) #

Use a Prism as a kind of first-class pattern.

outside :: Prism s t a b -> Lens (t -> r) (s -> r) (b -> r) (a -> r)

prism' :: (b -> s) -> (s -> Maybe a) -> Prism s s a b #

This is usually used to build a Prism', when you have to use an operation like cast which already returns a Maybe.

prism :: (b -> t) -> (s -> Either t a) -> Prism s t a b #

Build a Prism.

Either t a is used instead of Maybe a to permit the types of s and t to differ.

clonePrism :: APrism s t a b -> Prism s t a b #

Clone a Prism so that you can reuse the same monomorphically typed Prism for different purposes.

See cloneLens and cloneTraversal for examples of why you might want to do this.

withPrism :: APrism s t a b -> ((b -> t) -> (s -> Either t a) -> r) -> r #

Convert APrism to the pair of functions that characterize it.

type APrism s t a b = Market a b a (Identity b) -> Market a b s (Identity t) #

If you see this in a signature for a function, the function is expecting a Prism.

type APrism' s a = APrism s s a a #

type APrism' = Simple APrism

reuses :: MonadState b m => AReview t b -> (t -> r) -> m r #

This can be used to turn an Iso or Prism around and use the current state through it the other way, applying a function.

reuses ≡ uses . re
reuses (unto f) g ≡ gets (g . f)

>>> evalState (reuses _Left isLeft) (5 :: Int)
True

reuses :: MonadState a m => Prism' s a -> (s -> r) -> m r
reuses :: MonadState a m => Iso' s a   -> (s -> r) -> m r

reuse :: MonadState b m => AReview t b -> m t #

This can be used to turn an Iso or Prism around and use a value (or the current environment) through it the other way.

reuse ≡ use . re
reuse . unto ≡ gets

>>> evalState (reuse _Left) 5
Left 5

>>> evalState (reuse (unto succ)) 5
6

reuse :: MonadState a m => Prism' s a -> m s
reuse :: MonadState a m => Iso' s a   -> m s

reviews :: MonadReader b m => AReview t b -> (t -> r) -> m r #

This can be used to turn an Iso or Prism around and view a value (or the current environment) through it the other way, applying a function.

reviews ≡ views . re
reviews (unto f) g ≡ g . f

>>> reviews _Left isRight "mustard"
False

>>> reviews (unto succ) (*2) 3
8

Usually this function is used in the (->) Monad with a Prism or Iso, in which case it may be useful to think of it as having one of these more restricted type signatures:

reviews :: Iso' s a   -> (s -> r) -> a -> r
reviews :: Prism' s a -> (s -> r) -> a -> r

However, when working with a Monad transformer stack, it is sometimes useful to be able to review the current environment, in which case it may be beneficial to think of it as having one of these slightly more liberal type signatures:

reviews :: MonadReader a m => Iso' s a   -> (s -> r) -> m r
reviews :: MonadReader a m => Prism' s a -> (s -> r) -> m r

(#) :: AReview t b -> b -> t infixr 8 #

An infix alias for review.

unto f # x ≡ f x
l # x ≡ x ^. re l

This is commonly used when using a Prism as a smart constructor.

>>> _Left # 4
Left 4

But it can be used for any Prism

>>> base 16 # 123
"7b"

(#) :: Iso'      s a -> a -> s
(#) :: Prism'    s a -> a -> s
(#) :: Review    s a -> a -> s
(#) :: Equality' s a -> a -> s

review :: MonadReader b m => AReview t b -> m t #

This can be used to turn an Iso or Prism around and view a value (or the current environment) through it the other way.

review ≡ view . re
review . unto ≡ id

>>> review _Left "mustard"
Left "mustard"

>>> review (unto succ) 5
6

Usually review is used in the (->) Monad with a Prism or Iso, in which case it may be useful to think of it as having one of these more restricted type signatures:

review :: Iso' s a   -> a -> s
review :: Prism' s a -> a -> s

However, when working with a Monad transformer stack, it is sometimes useful to be able to review the current environment, in which case it may be beneficial to think of it as having one of these slightly more liberal type signatures:

review :: MonadReader a m => Iso' s a   -> m s
review :: MonadReader a m => Prism' s a -> m s

re :: AReview t b -> Getter b t #

Turn a Prism or Iso around to build a Getter.

If you have an Iso, from is a more powerful version of this function that will return an Iso instead of a mere Getter.

>>> 5 ^.re _Left
Left 5

>>> 6 ^.re (_Left.unto succ)
Left 7

review  ≡ view  . re
reviews ≡ views . re
reuse   ≡ use   . re
reuses  ≡ uses  . re

re :: Prism s t a b -> Getter b t
re :: Iso s t a b   -> Getter b t

un :: (Profunctor p, Bifunctor p, Functor f) => Getting a s a -> Optic' p f a s #

Turn a Getter around to get a Review

un = unto . view
unto = un . to

>>> un (to length) # [1,2,3]
3

unto :: (Profunctor p, Bifunctor p, Functor f) => (b -> t) -> Optic p f s t a b #

An analogue of to for review.

unto :: (b -> t) -> Review' t b

unto = un . to

getting :: (Profunctor p, Profunctor q, Functor f, Contravariant f) => Optical p q f s t a b -> Optical' p q f s a #

Coerce a Getter-compatible Optical to an Optical'. This is useful when using a Traversal that is not simple as a Getter or a Fold.

getting :: Traversal s t a b          -> Fold s a
getting :: Lens s t a b               -> Getter s a
getting :: IndexedTraversal i s t a b -> IndexedFold i s a
getting :: IndexedLens i s t a b      -> IndexedGetter i s a

(^@.) :: s -> IndexedGetting i (i, a) s a -> (i, a) infixl 8 #

View the index and value of an IndexedGetter or IndexedLens.

This is the same operation as iview with the arguments flipped.

The fixity and semantics are such that subsequent field accesses can be performed with (.).

(^@.) :: s -> IndexedGetter i s a -> (i, a)
(^@.) :: s -> IndexedLens' i s a  -> (i, a)

The result probably doesn't have much meaning when applied to an IndexedFold.

iuses :: MonadState s m => IndexedGetting i r s a -> (i -> a -> r) -> m r #

Use a function of the index and value of an IndexedGetter into the current state.

When applied to an IndexedFold the result will be a monoidal summary instead of a single answer.

iuse :: MonadState s m => IndexedGetting i (i, a) s a -> m (i, a) #

Use the index and value of an IndexedGetter into the current state as a pair.

When applied to an IndexedFold the result will most likely be a nonsensical monoidal summary of the indices tupled with a monoidal summary of the values and probably not whatever it is you wanted.

iviews :: MonadReader s m => IndexedGetting i r s a -> (i -> a -> r) -> m r #

View a function of the index and value of an IndexedGetter into the current environment.

When applied to an IndexedFold the result will be a monoidal summary instead of a single answer.

iviews ≡ ifoldMapOf

iview :: MonadReader s m => IndexedGetting i (i, a) s a -> m (i, a) #

View the index and value of an IndexedGetter into the current environment as a pair.

When applied to an IndexedFold the result will most likely be a nonsensical monoidal summary of the indices tupled with a monoidal summary of the values and probably not whatever it is you wanted.

ilistenings :: MonadWriter w m => IndexedGetting i v w u -> (i -> u -> v) -> m a -> m (a, v) #

This is a generalized form of listen that only extracts the portion of the log that is focused on by a Getter. If given a Fold or a Traversal then a monoidal summary of the parts of the log that are visited will be returned.

ilistenings :: MonadWriter w m             => IndexedGetter w u     -> (i -> u -> v) -> m a -> m (a, v)
ilistenings :: MonadWriter w m             => IndexedLens' w u      -> (i -> u -> v) -> m a -> m (a, v)
ilistenings :: (MonadWriter w m, Monoid v) => IndexedFold w u       -> (i -> u -> v) -> m a -> m (a, v)
ilistenings :: (MonadWriter w m, Monoid v) => IndexedTraversal' w u -> (i -> u -> v) -> m a -> m (a, v)

listenings :: MonadWriter w m => Getting v w u -> (u -> v) -> m a -> m (a, v) #

This is a generalized form of listen that only extracts the portion of the log that is focused on by a Getter. If given a Fold or a Traversal then a monoidal summary of the parts of the log that are visited will be returned.

listenings :: MonadWriter w m             => Getter w u     -> (u -> v) -> m a -> m (a, v)
listenings :: MonadWriter w m             => Lens' w u      -> (u -> v) -> m a -> m (a, v)
listenings :: MonadWriter w m             => Iso' w u       -> (u -> v) -> m a -> m (a, v)
listenings :: (MonadWriter w m, Monoid v) => Fold w u       -> (u -> v) -> m a -> m (a, v)
listenings :: (MonadWriter w m, Monoid v) => Traversal' w u -> (u -> v) -> m a -> m (a, v)
listenings :: (MonadWriter w m, Monoid v) => Prism' w u     -> (u -> v) -> m a -> m (a, v)

ilistening :: MonadWriter w m => IndexedGetting i (i, u) w u -> m a -> m (a, (i, u)) #

This is a generalized form of listen that only extracts the portion of the log that is focused on by a Getter. If given a Fold or a Traversal then a monoidal summary of the parts of the log that are visited will be returned.

ilistening :: MonadWriter w m             => IndexedGetter i w u     -> m a -> m (a, (i, u))
ilistening :: MonadWriter w m             => IndexedLens' i w u      -> m a -> m (a, (i, u))
ilistening :: (MonadWriter w m, Monoid u) => IndexedFold i w u       -> m a -> m (a, (i, u))
ilistening :: (MonadWriter w m, Monoid u) => IndexedTraversal' i w u -> m a -> m (a, (i, u))

listening :: MonadWriter w m => Getting u w u -> m a -> m (a, u) #

This is a generalized form of listen that only extracts the portion of the log that is focused on by a Getter. If given a Fold or a Traversal then a monoidal summary of the parts of the log that are visited will be returned.

listening :: MonadWriter w m             => Getter w u     -> m a -> m (a, u)
listening :: MonadWriter w m             => Lens' w u      -> m a -> m (a, u)
listening :: MonadWriter w m             => Iso' w u       -> m a -> m (a, u)
listening :: (MonadWriter w m, Monoid u) => Fold w u       -> m a -> m (a, u)
listening :: (MonadWriter w m, Monoid u) => Traversal' w u -> m a -> m (a, u)
listening :: (MonadWriter w m, Monoid u) => Prism' w u     -> m a -> m (a, u)

uses :: MonadState s m => LensLike' (Const r :: Type -> Type) s a -> (a -> r) -> m r #

Use the target of a Lens, Iso or Getter in the current state, or use a summary of a Fold or Traversal that points to a monoidal value.

>>> evalState (uses _1 length) ("hello","world")
5

uses :: MonadState s m             => Getter s a     -> (a -> r) -> m r
uses :: (MonadState s m, Monoid r) => Fold s a       -> (a -> r) -> m r
uses :: MonadState s m             => Lens' s a      -> (a -> r) -> m r
uses :: MonadState s m             => Iso' s a       -> (a -> r) -> m r
uses :: (MonadState s m, Monoid r) => Traversal' s a -> (a -> r) -> m r

uses :: MonadState s m => Getting r s t a b -> (a -> r) -> m r

use :: MonadState s m => Getting a s a -> m a #

Use the target of a Lens, Iso, or Getter in the current state, or use a summary of a Fold or Traversal that points to a monoidal value.

>>> evalState (use _1) (a,b)
a

>>> evalState (use _1) ("hello","world")
"hello"

use :: MonadState s m             => Getter s a     -> m a
use :: (MonadState s m, Monoid r) => Fold s r       -> m r
use :: MonadState s m             => Iso' s a       -> m a
use :: MonadState s m             => Lens' s a      -> m a
use :: (MonadState s m, Monoid r) => Traversal' s r -> m r

(^.) :: s -> Getting a s a -> a infixl 8 #

View the value pointed to by a Getter or Lens or the result of folding over all the results of a Fold or Traversal that points at a monoidal values.

This is the same operation as view with the arguments flipped.

The fixity and semantics are such that subsequent field accesses can be performed with (.).

>>> (a,b)^._2
b

>>> ("hello","world")^._2
"world"

>>> import Data.Complex
>>> ((0, 1 :+ 2), 3)^._1._2.to magnitude
2.23606797749979

(^.) ::             s -> Getter s a     -> a
(^.) :: Monoid m => s -> Fold s m       -> m
(^.) ::             s -> Iso' s a       -> a
(^.) ::             s -> Lens' s a      -> a
(^.) :: Monoid m => s -> Traversal' s m -> m

views :: MonadReader s m => LensLike' (Const r :: Type -> Type) s a -> (a -> r) -> m r #

View a function of the value pointed to by a Getter or Lens or the result of folding over the result of mapping the targets of a Fold or Traversal.

views l f ≡ view (l . to f)

>>> views (to f) g a
g (f a)

>>> views _2 length (1,"hello")
5

As views is commonly used to access the target of a Getter or obtain a monoidal summary of the targets of a Fold, It may be useful to think of it as having one of these more restricted signatures:

views ::             Getter s a     -> (a -> r) -> s -> r
views :: Monoid m => Fold s a       -> (a -> m) -> s -> m
views ::             Iso' s a       -> (a -> r) -> s -> r
views ::             Lens' s a      -> (a -> r) -> s -> r
views :: Monoid m => Traversal' s a -> (a -> m) -> s -> m

In a more general setting, such as when working with a Monad transformer stack you can use:

views :: MonadReader s m             => Getter s a     -> (a -> r) -> m r
views :: (MonadReader s m, Monoid r) => Fold s a       -> (a -> r) -> m r
views :: MonadReader s m             => Iso' s a       -> (a -> r) -> m r
views :: MonadReader s m             => Lens' s a      -> (a -> r) -> m r
views :: (MonadReader s m, Monoid r) => Traversal' s a -> (a -> r) -> m r

views :: MonadReader s m => Getting r s a -> (a -> r) -> m r

view :: MonadReader s m => Getting a s a -> m a #

View the value pointed to by a Getter, Iso or Lens or the result of folding over all the results of a Fold or Traversal that points at a monoidal value.

view . to ≡ id

>>> view (to f) a
f a

>>> view _2 (1,"hello")
"hello"

>>> view (to succ) 5
6

>>> view (_2._1) ("hello",("world","!!!"))
"world"

As view is commonly used to access the target of a Getter or obtain a monoidal summary of the targets of a Fold, It may be useful to think of it as having one of these more restricted signatures:

view ::             Getter s a     -> s -> a
view :: Monoid m => Fold s m       -> s -> m
view ::             Iso' s a       -> s -> a
view ::             Lens' s a      -> s -> a
view :: Monoid m => Traversal' s m -> s -> m

In a more general setting, such as when working with a Monad transformer stack you can use:

view :: MonadReader s m             => Getter s a     -> m a
view :: (MonadReader s m, Monoid a) => Fold s a       -> m a
view :: MonadReader s m             => Iso' s a       -> m a
view :: MonadReader s m             => Lens' s a      -> m a
view :: (MonadReader s m, Monoid a) => Traversal' s a -> m a

ilike :: (Indexable i p, Contravariant f, Functor f) => i -> a -> Over' p f s a #

ilike :: i -> a -> IndexedGetter i s a

like :: (Profunctor p, Contravariant f, Functor f) => a -> Optic' p f s a #

Build an constant-valued (index-preserving) Getter from an arbitrary Haskell value.

like a . like b ≡ like b
a ^. like b ≡ b
a ^. like b ≡ a ^. to (const b)

This can be useful as a second case failing a Fold e.g. foo failing like 0

like :: a -> IndexPreservingGetter s a

ito :: (Indexable i p, Contravariant f) => (s -> (i, a)) -> Over' p f s a #

ito :: (s -> (i, a)) -> IndexedGetter i s a

to :: (Profunctor p, Contravariant f) => (s -> a) -> Optic' p f s a #

Build an (index-preserving) Getter from an arbitrary Haskell function.

to f . to g ≡ to (g . f)

a ^. to f ≡ f a

>>> a ^.to f
f a

>>> ("hello","world")^.to snd
"world"

>>> 5^.to succ
6

>>> (0, -5)^._2.to abs
5

to :: (s -> a) -> IndexPreservingGetter s a

type Getting r s a = (a -> Const r a) -> s -> Const r s #

When you see this in a type signature it indicates that you can pass the function a Lens, Getter, Traversal, Fold, Prism, Iso, or one of the indexed variants, and it will just "do the right thing".

Most Getter combinators are able to be used with both a Getter or a Fold in limited situations, to do so, they need to be monomorphic in what we are going to extract with Const. To be compatible with Lens, Traversal and Iso we also restricted choices of the irrelevant t and b parameters.

If a function accepts a Getting r s a, then when r is a Monoid, then you can pass a Fold (or Traversal), otherwise you can only pass this a Getter or Lens.

type IndexedGetting i m s a = Indexed i a (Const m a) -> s -> Const m s #

Used to consume an IndexedFold.

type Accessing (p :: Type -> Type -> Type) m s a = p a (Const m a) -> s -> Const m s #

This is a convenient alias used when consuming (indexed) getters and (indexed) folds in a highly general fashion.

_19' :: Field19 s t a b => Lens s t a b #

Strict version of _19

_18' :: Field18 s t a b => Lens s t a b #

Strict version of _18

_17' :: Field17 s t a b => Lens s t a b #

Strict version of _17

_16' :: Field16 s t a b => Lens s t a b #

Strict version of _16

_15' :: Field15 s t a b => Lens s t a b #

Strict version of _15

_14' :: Field14 s t a b => Lens s t a b #

Strict version of _14

_13' :: Field13 s t a b => Lens s t a b #

Strict version of _13

_12' :: Field12 s t a b => Lens s t a b #

Strict version of _12

_11' :: Field11 s t a b => Lens s t a b #

Strict version of _11

_10' :: Field10 s t a b => Lens s t a b #

Strict version of _10

_9' :: Field9 s t a b => Lens s t a b #

Strict version of _9

_8' :: Field8 s t a b => Lens s t a b #

Strict version of _8

_7' :: Field7 s t a b => Lens s t a b #

Strict version of _7

_6' :: Field6 s t a b => Lens s t a b #

Strict version of _6

_5' :: Field5 s t a b => Lens s t a b #

Strict version of _5

_4' :: Field4 s t a b => Lens s t a b #

Strict version of _4

_3' :: Field3 s t a b => Lens s t a b #

Strict version of _3

_2' :: Field2 s t a b => Lens s t a b #

Strict version of _2

_1' :: Field1 s t a b => Lens s t a b #

Strict version of _1

class Field1 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to 1st field of a tuple.

Minimal complete definition

Nothing

Methods

_1 :: Lens s t a b #

Access the 1st field of a tuple (and possibly change its type).

>>> (1,2)^._1
1

>>> _1 .~ "hello" $ (1,2)
("hello",2)

>>> (1,2) & _1 .~ "hello"
("hello",2)

>>> _1 putStrLn ("hello","world")
hello
((),"world")

This can also be used on larger tuples as well:

>>> (1,2,3,4,5) & _1 +~ 41
(42,2,3,4,5)

_1 :: Lens (a,b) (a',b) a a'
_1 :: Lens (a,b,c) (a',b,c) a a'
_1 :: Lens (a,b,c,d) (a',b,c,d) a a'
...
_1 :: Lens (a,b,c,d,e,f,g,h,i) (a',b,c,d,e,f,g,h,i) a a'

Instances

Field1 (Identity a) (Identity b) a b
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (Identity a) (Identity b) a b #
Field1 (a, b) (a', b) a a'	`_1` k ~(a,b) = (\a' -> (a',b)) `<$>` k a
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b) (a', b) a a' #
Field1 (a, b, c) (a', b, c) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c) (a', b, c) a a' #
Field1 (a, b, c, d) (a', b, c, d) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d) (a', b, c, d) a a' #
Field1 ((f :: g) p) ((f' :: g) p) (f p) (f' p)
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens ((f :: g) p) ((f' :: g) p) (f p) (f' p) #
Field1 (Product f g a) (Product f' g a) (f a) (f' a)
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (Product f g a) (Product f' g a) (f a) (f' a) #
Field1 (a, b, c, d, e) (a', b, c, d, e) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e) (a', b, c, d, e) a a' #
Field1 (a, b, c, d, e, f) (a', b, c, d, e, f) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f) (a', b, c, d, e, f) a a' #
Field1 (a, b, c, d, e, f, g) (a', b, c, d, e, f, g) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g) (a', b, c, d, e, f, g) a a' #
Field1 (a, b, c, d, e, f, g, h) (a', b, c, d, e, f, g, h) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h) (a', b, c, d, e, f, g, h) a a' #
Field1 (a, b, c, d, e, f, g, h, i) (a', b, c, d, e, f, g, h, i) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i) (a', b, c, d, e, f, g, h, i) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j) (a', b, c, d, e, f, g, h, i, j) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j) (a', b, c, d, e, f, g, h, i, j) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j, kk) (a', b, c, d, e, f, g, h, i, j, kk) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a', b, c, d, e, f, g, h, i, j, kk) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l) (a', b, c, d, e, f, g, h, i, j, kk, l) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a', b, c, d, e, f, g, h, i, j, kk, l) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a', b, c, d, e, f, g, h, i, j, kk, l, m) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a', b, c, d, e, f, g, h, i, j, kk, l, m) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) a a' #

class Field2 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 2nd field of a tuple.

Minimal complete definition

Nothing

Methods

_2 :: Lens s t a b #

Access the 2nd field of a tuple.

>>> _2 .~ "hello" $ (1,(),3,4)
(1,"hello",3,4)

>>> (1,2,3,4) & _2 *~ 3
(1,6,3,4)

>>> _2 print (1,2)
2
(1,())

anyOf _2 :: (s -> Bool) -> (a, s) -> Bool
traverse . _2 :: (Applicative f, Traversable t) => (a -> f b) -> t (s, a) -> f (t (s, b))
foldMapOf (traverse . _2) :: (Traversable t, Monoid m) => (s -> m) -> t (b, s) -> m

Instances

Field2 (a, b) (a, b') b b'	`_2` k ~(a,b) = (\b' -> (a,b')) `<$>` k b
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b) (a, b') b b' #
Field2 (a, b, c) (a, b', c) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c) (a, b', c) b b' #
Field2 (a, b, c, d) (a, b', c, d) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d) (a, b', c, d) b b' #
Field2 ((f :: g) p) ((f :: g') p) (g p) (g' p)
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens ((f :: g) p) ((f :: g') p) (g p) (g' p) #
Field2 (Product f g a) (Product f g' a) (g a) (g' a)
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (Product f g a) (Product f g' a) (g a) (g' a) #
Field2 (a, b, c, d, e) (a, b', c, d, e) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e) (a, b', c, d, e) b b' #
Field2 (a, b, c, d, e, f) (a, b', c, d, e, f) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f) (a, b', c, d, e, f) b b' #
Field2 (a, b, c, d, e, f, g) (a, b', c, d, e, f, g) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g) (a, b', c, d, e, f, g) b b' #
Field2 (a, b, c, d, e, f, g, h) (a, b', c, d, e, f, g, h) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h) (a, b', c, d, e, f, g, h) b b' #
Field2 (a, b, c, d, e, f, g, h, i) (a, b', c, d, e, f, g, h, i) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i) (a, b', c, d, e, f, g, h, i) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j) (a, b', c, d, e, f, g, h, i, j) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b', c, d, e, f, g, h, i, j) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j, kk) (a, b', c, d, e, f, g, h, i, j, kk) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b', c, d, e, f, g, h, i, j, kk) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b', c, d, e, f, g, h, i, j, kk, l) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b', c, d, e, f, g, h, i, j, kk, l) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b', c, d, e, f, g, h, i, j, kk, l, m) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b', c, d, e, f, g, h, i, j, kk, l, m) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) b b' #

class Field3 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 3rd field of a tuple.

Minimal complete definition

Nothing

Methods

_3 :: Lens s t a b #

Access the 3rd field of a tuple.

Instances

Field3 (a, b, c) (a, b, c') c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c) (a, b, c') c c' #
Field3 (a, b, c, d) (a, b, c', d) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d) (a, b, c', d) c c' #
Field3 (a, b, c, d, e) (a, b, c', d, e) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e) (a, b, c', d, e) c c' #
Field3 (a, b, c, d, e, f) (a, b, c', d, e, f) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f) (a, b, c', d, e, f) c c' #
Field3 (a, b, c, d, e, f, g) (a, b, c', d, e, f, g) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g) (a, b, c', d, e, f, g) c c' #
Field3 (a, b, c, d, e, f, g, h) (a, b, c', d, e, f, g, h) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h) (a, b, c', d, e, f, g, h) c c' #
Field3 (a, b, c, d, e, f, g, h, i) (a, b, c', d, e, f, g, h, i) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c', d, e, f, g, h, i) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j) (a, b, c', d, e, f, g, h, i, j) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c', d, e, f, g, h, i, j) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c', d, e, f, g, h, i, j, kk) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c', d, e, f, g, h, i, j, kk) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c', d, e, f, g, h, i, j, kk, l) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c', d, e, f, g, h, i, j, kk, l) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c', d, e, f, g, h, i, j, kk, l, m) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c', d, e, f, g, h, i, j, kk, l, m) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p, q) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p, q) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) c c' #

class Field4 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provide access to the 4th field of a tuple.

Minimal complete definition

Nothing

Methods

_4 :: Lens s t a b #

Access the 4th field of a tuple.

Instances

Field4 (a, b, c, d) (a, b, c, d') d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d) (a, b, c, d') d d' #
Field4 (a, b, c, d, e) (a, b, c, d', e) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e) (a, b, c, d', e) d d' #
Field4 (a, b, c, d, e, f) (a, b, c, d', e, f) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f) (a, b, c, d', e, f) d d' #
Field4 (a, b, c, d, e, f, g) (a, b, c, d', e, f, g) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g) (a, b, c, d', e, f, g) d d' #
Field4 (a, b, c, d, e, f, g, h) (a, b, c, d', e, f, g, h) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h) (a, b, c, d', e, f, g, h) d d' #
Field4 (a, b, c, d, e, f, g, h, i) (a, b, c, d', e, f, g, h, i) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c, d', e, f, g, h, i) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d', e, f, g, h, i, j) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d', e, f, g, h, i, j) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d', e, f, g, h, i, j, kk) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d', e, f, g, h, i, j, kk) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d', e, f, g, h, i, j, kk, l) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d', e, f, g, h, i, j, kk, l) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d', e, f, g, h, i, j, kk, l, m) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d', e, f, g, h, i, j, kk, l, m) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p, q) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p, q) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p, q, r) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p, q, r) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) d d' #

class Field5 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 5th field of a tuple.

Minimal complete definition

Nothing

Methods

_5 :: Lens s t a b #

Access the 5th field of a tuple.

Instances

Field5 (a, b, c, d, e) (a, b, c, d, e') e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e) (a, b, c, d, e') e e' #
Field5 (a, b, c, d, e, f) (a, b, c, d, e', f) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f) (a, b, c, d, e', f) e e' #
Field5 (a, b, c, d, e, f, g) (a, b, c, d, e', f, g) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g) (a, b, c, d, e', f, g) e e' #
Field5 (a, b, c, d, e, f, g, h) (a, b, c, d, e', f, g, h) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h) (a, b, c, d, e', f, g, h) e e' #
Field5 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e', f, g, h, i) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c, d, e', f, g, h, i) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e', f, g, h, i, j) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e', f, g, h, i, j) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e', f, g, h, i, j, kk) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e', f, g, h, i, j, kk) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e', f, g, h, i, j, kk, l) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e', f, g, h, i, j, kk, l) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e', f, g, h, i, j, kk, l, m) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e', f, g, h, i, j, kk, l, m) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p, q) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p, q) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p, q, r) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p, q, r) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p, q, r, s) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p, q, r, s) e e' #

class Field6 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 6th element of a tuple.

Minimal complete definition

Nothing

Methods

_6 :: Lens s t a b #

Access the 6th field of a tuple.

Instances

Field6 (a, b, c, d, e, f) (a, b, c, d, e, f') f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f) (a, b, c, d, e, f') f f' #
Field6 (a, b, c, d, e, f, g) (a, b, c, d, e, f', g) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g) (a, b, c, d, e, f', g) f f' #
Field6 (a, b, c, d, e, f, g, h) (a, b, c, d, e, f', g, h) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h) (a, b, c, d, e, f', g, h) f f' #
Field6 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f', g, h, i) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f', g, h, i) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f', g, h, i, j) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f', g, h, i, j) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f', g, h, i, j, kk) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f', g, h, i, j, kk) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f', g, h, i, j, kk, l) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f', g, h, i, j, kk, l) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f', g, h, i, j, kk, l, m) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f', g, h, i, j, kk, l, m) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p, q) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p, q) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p, q, r) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p, q, r) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p, q, r, s) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p, q, r, s) f f' #

class Field7 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provide access to the 7th field of a tuple.

Minimal complete definition

Nothing

Methods

_7 :: Lens s t a b #

Access the 7th field of a tuple.

Instances

Field7 (a, b, c, d, e, f, g) (a, b, c, d, e, f, g') g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g) (a, b, c, d, e, f, g') g g' #
Field7 (a, b, c, d, e, f, g, h) (a, b, c, d, e, f, g', h) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h) (a, b, c, d, e, f, g', h) g g' #
Field7 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g', h, i) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g', h, i) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g', h, i, j) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g', h, i, j) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g', h, i, j, kk) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g', h, i, j, kk) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g', h, i, j, kk, l) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g', h, i, j, kk, l) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g', h, i, j, kk, l, m) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g', h, i, j, kk, l, m) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p, q) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p, q) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p, q, r) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p, q, r) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p, q, r, s) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p, q, r, s) g g' #

class Field8 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provide access to the 8th field of a tuple.

Minimal complete definition

Nothing

Methods

_8 :: Lens s t a b #

Access the 8th field of a tuple.

Instances

Field8 (a, b, c, d, e, f, g, h) (a, b, c, d, e, f, g, h') h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h) (a, b, c, d, e, f, g, h') h h' #
Field8 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g, h', i) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g, h', i) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h', i, j) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h', i, j) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h', i, j, kk) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h', i, j, kk) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h', i, j, kk, l) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h', i, j, kk, l) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h', i, j, kk, l, m) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h', i, j, kk, l, m) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p, q) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p, q) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p, q, r) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p, q, r) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p, q, r, s) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p, q, r, s) h h' #

class Field9 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 9th field of a tuple.

Minimal complete definition

Nothing

Methods

_9 :: Lens s t a b #

Access the 9th field of a tuple.

Instances

Field9 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g, h, i') i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g, h, i') i i' #
Field9 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h, i', j) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h, i', j) i i' #
Field9 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h, i', j, kk) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h, i', j, kk) i i' #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i', j, kk, l) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i', j, kk, l) i i' #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i', j, kk, l, m) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i', j, kk, l, m) i i' #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n) i i' #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o) i i' #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p) i i' #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p, q) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p, q) i i' #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p, q, r) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p, q, r) i i' #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p, q, r, s) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p, q, r, s) i i' #

class Field10 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 10th field of a tuple.

Minimal complete definition

Nothing

Methods

_10 :: Lens s t a b #

Access the 10th field of a tuple.

Instances

Field10 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h, i, j') j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h, i, j') j j' #
Field10 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h, i, j', kk) j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h, i, j', kk) j j' #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i, j', kk, l) j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i, j', kk, l) j j' #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j', kk, l, m) j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j', kk, l, m) j j' #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n) j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n) j j' #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o) j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o) j j' #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p) j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p) j j' #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p, q) j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p, q) j j' #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p, q, r) j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p, q, r) j j' #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p, q, r, s) j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p, q, r, s) j j' #

class Field11 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 11th field of a tuple.

Minimal complete definition

Nothing

Methods

_11 :: Lens s t a b #

Access the 11th field of a tuple.

Instances

Field11 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h, i, j, kk') kk kk'
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h, i, j, kk') kk kk' #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i, j, kk', l) kk kk'
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i, j, kk', l) kk kk' #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j, kk', l, m) kk kk'
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j, kk', l, m) kk kk' #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n) kk kk'
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n) kk kk' #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o) kk kk'
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o) kk kk' #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p) kk kk'
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p) kk kk' #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p, q) kk kk'
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p, q) kk kk' #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p, q, r) kk kk'
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p, q, r) kk kk' #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p, q, r, s) kk kk'
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p, q, r, s) kk kk' #

class Field12 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 12th field of a tuple.

Minimal complete definition

Nothing

Methods

_12 :: Lens s t a b #

Access the 12th field of a tuple.

Instances

Field12 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i, j, kk, l') l l'
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i, j, kk, l') l l' #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j, kk, l', m) l l'
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j, kk, l', m) l l' #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n) l l'
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n) l l' #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o) l l'
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o) l l' #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p) l l'
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p) l l' #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p, q) l l'
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p, q) l l' #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p, q, r) l l'
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p, q, r) l l' #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p, q, r, s) l l'
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p, q, r, s) l l' #

class Field13 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 13th field of a tuple.

Minimal complete definition

Nothing

Methods

_13 :: Lens s t a b #

Access the 13th field of a tuple.

Instances

Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j, kk, l, m') m m'
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j, kk, l, m') m m' #
Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n) m m'
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n) m m' #
Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o) m m'
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o) m m' #
Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p) m m'
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p) m m' #
Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p, q) m m'
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p, q) m m' #
Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p, q, r) m m'
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p, q, r) m m' #
Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p, q, r, s) m m'
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p, q, r, s) m m' #

class Field14 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 14th field of a tuple.

Minimal complete definition

Nothing

Methods

_14 :: Lens s t a b #

Access the 14th field of a tuple.

Instances

Field14 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n') n n'
Instance details Defined in Control.Lens.Tuple Methods _14 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n') n n' #
Field14 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o) n n'
Instance details Defined in Control.Lens.Tuple Methods _14 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o) n n' #
Field14 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p) n n'
Instance details Defined in Control.Lens.Tuple Methods _14 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p) n n' #
Field14 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p, q) n n'
Instance details Defined in Control.Lens.Tuple Methods _14 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p, q) n n' #
Field14 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p, q, r) n n'
Instance details Defined in Control.Lens.Tuple Methods _14 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p, q, r) n n' #
Field14 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p, q, r, s) n n'
Instance details Defined in Control.Lens.Tuple Methods _14 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p, q, r, s) n n' #

class Field15 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 15th field of a tuple.

Minimal complete definition

Nothing

Methods

_15 :: Lens s t a b #

Access the 15th field of a tuple.

Instances

Field15 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o') o o'
Instance details Defined in Control.Lens.Tuple Methods _15 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o') o o' #
Field15 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p) o o'
Instance details Defined in Control.Lens.Tuple Methods _15 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p) o o' #
Field15 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p, q) o o'
Instance details Defined in Control.Lens.Tuple Methods _15 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p, q) o o' #
Field15 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p, q, r) o o'
Instance details Defined in Control.Lens.Tuple Methods _15 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p, q, r) o o' #
Field15 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p, q, r, s) o o'
Instance details Defined in Control.Lens.Tuple Methods _15 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p, q, r, s) o o' #

class Field16 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 16th field of a tuple.

Minimal complete definition

Nothing

Methods

_16 :: Lens s t a b #

Access the 16th field of a tuple.

Instances

Field16 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p') p p'
Instance details Defined in Control.Lens.Tuple Methods _16 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p') p p' #
Field16 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p', q) p p'
Instance details Defined in Control.Lens.Tuple Methods _16 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p', q) p p' #
Field16 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p', q, r) p p'
Instance details Defined in Control.Lens.Tuple Methods _16 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p', q, r) p p' #
Field16 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p', q, r, s) p p'
Instance details Defined in Control.Lens.Tuple Methods _16 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p', q, r, s) p p' #

class Field17 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 17th field of a tuple.

Minimal complete definition

Nothing

Methods

_17 :: Lens s t a b #

Access the 17th field of a tuple.

Instances

Field17 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q') q q'
Instance details Defined in Control.Lens.Tuple Methods _17 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q') q q' #
Field17 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q', r) q q'
Instance details Defined in Control.Lens.Tuple Methods _17 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q', r) q q' #
Field17 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q', r, s) q q'
Instance details Defined in Control.Lens.Tuple Methods _17 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q', r, s) q q' #

class Field18 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 18th field of a tuple.

Minimal complete definition

Nothing

Methods

_18 :: Lens s t a b #

Access the 18th field of a tuple.

Instances

Field18 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r') r r'
Instance details Defined in Control.Lens.Tuple Methods _18 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r') r r' #
Field18 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r', s) r r'
Instance details Defined in Control.Lens.Tuple Methods _18 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r', s) r r' #

class Field19 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 19th field of a tuple.

Minimal complete definition

Nothing

Methods

_19 :: Lens s t a b #

Access the 19th field of a tuple.

Instances

Field19 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s') s s'
Instance details Defined in Control.Lens.Tuple Methods _19 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s') s s' #

fusing :: Functor f => LensLike (Yoneda f) s t a b -> LensLike f s t a b #

Fuse a composition of lenses using Yoneda to provide fmap fusion.

In general, given a pair of lenses foo and bar

fusing (foo.bar) = foo.bar

however, foo and bar are either going to fmap internally or they are trivial.

fusing exploits the Yoneda lemma to merge these separate uses into a single fmap.

This is particularly effective when the choice of functor f is unknown at compile time or when the Lens foo.bar in the above description is recursive or complex enough to prevent inlining.

fusing :: Lens s t a b -> Lens s t a b

united :: Lens' a () #

We can always retrieve a () from any type.

>>> "hello"^.united
()

>>> "hello" & united .~ ()
"hello"

devoid :: Over p f Void Void a b #

There is a field for every type in the Void. Very zen.

>>> [] & mapped.devoid +~ 1
[]

>>> Nothing & mapped.devoid %~ abs
Nothing

devoid :: Lens' Void a

(<#=) :: MonadState s m => ALens s s a b -> b -> m b infix 4 #

A version of (<.=) that works on ALens.

(<#~) :: ALens s t a b -> b -> s -> (b, t) infixr 4 #

A version of (<.~) that works on ALens.

>>> ("hello","there") & _2 <#~ "world"
("world",("hello","world"))

(#%%=) :: MonadState s m => ALens s s a b -> (a -> (r, b)) -> m r infix 4 #

A version of (%%=) that works on ALens.

(<#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m b infix 4 #

A version of (<%=) that works on ALens.

(<#%~) :: ALens s t a b -> (a -> b) -> s -> (b, t) infixr 4 #

A version of (<%~) that works on ALens.

>>> ("hello","world") & _2 <#%~ length
(5,("hello",5))

(#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m () infix 4 #

A version of (%=) that works on ALens.

(#=) :: MonadState s m => ALens s s a b -> b -> m () infix 4 #

A version of (.=) that works on ALens.

(#%%~) :: Functor f => ALens s t a b -> (a -> f b) -> s -> f t infixr 4 #

A version of (%%~) that works on ALens.

>>> ("hello","world") & _2 #%%~ \x -> (length x, x ++ "!")
(5,("hello","world!"))

(#%~) :: ALens s t a b -> (a -> b) -> s -> t infixr 4 #

A version of (%~) that works on ALens.

>>> ("hello","world") & _2 #%~ length
("hello",5)

(#~) :: ALens s t a b -> b -> s -> t infixr 4 #

A version of (.~) that works on ALens.

>>> ("hello","there") & _2 #~ "world"
("hello","world")

storing :: ALens s t a b -> b -> s -> t #

A version of set that works on ALens.

>>> storing _2 "world" ("hello","there")
("hello","world")

(^#) :: s -> ALens s t a b -> a infixl 8 #

A version of (^.) that works on ALens.

>>> ("hello","world")^#_2
"world"

(<<%@=) :: MonadState s m => Over (Indexed i) ((,) a) s s a b -> (i -> a -> b) -> m a infix 4 #

Adjust the target of an IndexedLens returning the old value, or adjust all of the targets of an IndexedTraversal within the current state, and return a monoidal summary of the old values.

(<<%@=) :: MonadState s m                 => IndexedLens i s s a b      -> (i -> a -> b) -> m a
(<<%@=) :: (MonadState s m, Monoid b) => IndexedTraversal i s s a b -> (i -> a -> b) -> m a

(<%@=) :: MonadState s m => Over (Indexed i) ((,) b) s s a b -> (i -> a -> b) -> m b infix 4 #

Adjust the target of an IndexedLens returning the intermediate result, or adjust all of the targets of an IndexedTraversal within the current state, and return a monoidal summary of the intermediate results.

(<%@=) :: MonadState s m                 => IndexedLens i s s a b      -> (i -> a -> b) -> m b
(<%@=) :: (MonadState s m, Monoid b) => IndexedTraversal i s s a b -> (i -> a -> b) -> m b

(%%@=) :: MonadState s m => Over (Indexed i) ((,) r) s s a b -> (i -> a -> (r, b)) -> m r infix 4 #

Adjust the target of an IndexedLens returning a supplementary result, or adjust all of the targets of an IndexedTraversal within the current state, and return a monoidal summary of the supplementary results.

l %%@= f ≡ state (l %%@~ f)

(%%@=) :: MonadState s m                 => IndexedLens i s s a b      -> (i -> a -> (r, b)) -> s -> m r
(%%@=) :: (MonadState s m, Monoid r) => IndexedTraversal i s s a b -> (i -> a -> (r, b)) -> s -> m r

(%%@~) :: Over (Indexed i) f s t a b -> (i -> a -> f b) -> s -> f t infixr 4 #

Adjust the target of an IndexedLens returning a supplementary result, or adjust all of the targets of an IndexedTraversal and return a monoidal summary of the supplementary results and the answer.

(%%@~) ≡ withIndex

(%%@~) :: Functor f => IndexedLens i s t a b      -> (i -> a -> f b) -> s -> f t
(%%@~) :: Applicative f => IndexedTraversal i s t a b -> (i -> a -> f b) -> s -> f t

In particular, it is often useful to think of this function as having one of these even more restricted type signatures:

(%%@~) ::             IndexedLens i s t a b      -> (i -> a -> (r, b)) -> s -> (r, t)
(%%@~) :: Monoid r => IndexedTraversal i s t a b -> (i -> a -> (r, b)) -> s -> (r, t)

(<<%@~) :: Over (Indexed i) ((,) a) s t a b -> (i -> a -> b) -> s -> (a, t) infixr 4 #

Adjust the target of an IndexedLens returning the old value, or adjust all of the targets of an IndexedTraversal and return a monoidal summary of the old values along with the answer.

(<<%@~) ::             IndexedLens i s t a b      -> (i -> a -> b) -> s -> (a, t)
(<<%@~) :: Monoid a => IndexedTraversal i s t a b -> (i -> a -> b) -> s -> (a, t)

(<%@~) :: Over (Indexed i) ((,) b) s t a b -> (i -> a -> b) -> s -> (b, t) infixr 4 #

Adjust the target of an IndexedLens returning the intermediate result, or adjust all of the targets of an IndexedTraversal and return a monoidal summary along with the answer.

l <%~ f ≡ l <%@~ const f

When you do not need access to the index then (<%~) is more liberal in what it can accept.

If you do not need the intermediate result, you can use (%@~) or even (%~).

(<%@~) ::             IndexedLens i s t a b      -> (i -> a -> b) -> s -> (b, t)
(<%@~) :: Monoid b => IndexedTraversal i s t a b -> (i -> a -> b) -> s -> (b, t)

overA :: Arrow ar => LensLike (Context a b) s t a b -> ar a b -> ar s t #

over for Arrows.

Unlike over, overA can't accept a simple Setter, but requires a full lens, or close enough.

>>> overA _1 ((+1) *** (+2)) ((1,2),6)
((2,4),6)

overA :: Arrow ar => Lens s t a b -> ar a b -> ar s t

(<<>=) :: (MonadState s m, Monoid r) => LensLike' ((,) r) s r -> r -> m r infix 4 #

mappend a monoidal value onto the end of the target of a Lens into your Monad's state and return the result.

When you do not need the result of the operation, (<>=) is more flexible.

(<<>~) :: Monoid m => LensLike ((,) m) s t m m -> m -> s -> (m, t) infixr 4 #

mappend a monoidal value onto the end of the target of a Lens and return the result.

When you do not need the result of the operation, (<>~) is more flexible.

(<<~) :: MonadState s m => ALens s s a b -> m b -> m b infixr 2 #

Run a monadic action, and set the target of Lens to its result.

(<<~) :: MonadState s m => Iso s s a b   -> m b -> m b
(<<~) :: MonadState s m => Lens s s a b  -> m b -> m b

NB: This is limited to taking an actual Lens than admitting a Traversal because there are potential loss of state issues otherwise.

(<<<>=) :: (MonadState s m, Monoid r) => LensLike' ((,) r) s r -> r -> m r infix 4 #

Modify the target of a Lens into your Monad's state by mappending a value and return the old value that was replaced.

When you do not need the result of the operation, (<>=) is more flexible.

(<<<>=) :: (MonadState s m, Monoid r) => Lens' s r -> r -> m r
(<<<>=) :: (MonadState s m, Monoid r) => Iso' s r -> r -> m r

(<<&&=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool infix 4 #

Modify the target of a Lens into your Monad's state by taking its logical && with a value and return the old value that was replaced.

When you do not need the result of the operation, (&&=) is more flexible.

(<<&&=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
(<<&&=) :: MonadState s m => Iso' s Bool -> Bool -> m Bool

(<<||=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool infix 4 #

Modify the target of a Lens into your Monad's state by taking its logical || with a value and return the old value that was replaced.

When you do not need the result of the operation, (||=) is more flexible.

(<<||=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
(<<||=) :: MonadState s m => Iso' s Bool -> Bool -> m Bool

(<<**=) :: (MonadState s m, Floating a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Modify the target of a Lens into your Monad's state by raising it by an arbitrary power and return the old value that was replaced.

When you do not need the result of the operation, (**=) is more flexible.

(<<**=) :: (MonadState s m, Floating a) => Lens' s a -> a -> m a
(<<**=) :: (MonadState s m, Floating a) => Iso' s a -> a -> m a

(<<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> m a infix 4 #

Modify the target of a Lens into your Monad's state by raising it by an integral power and return the old value that was replaced.

When you do not need the result of the operation, (^^=) is more flexible.

(<<^^=) :: (MonadState s m, Fractional a, Integral e) => Lens' s a -> e -> m a
(<<^^=) :: (MonadState s m, Fractional a, Integral e) => Iso' s a -> e -> m a

(<<^=) :: (MonadState s m, Num a, Integral e) => LensLike' ((,) a) s a -> e -> m a infix 4 #

Modify the target of a Lens into your Monad's state by raising it by a non-negative power and return the old value that was replaced.

When you do not need the result of the operation, (^=) is more flexible.

(<<^=) :: (MonadState s m, Num a, Integral e) => Lens' s a -> e -> m a
(<<^=) :: (MonadState s m, Num a, Integral e) => Iso' s a -> a -> m a

(<<//=) :: (MonadState s m, Fractional a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Modify the target of a Lens into your Monads state by dividing by a value and return the old value that was replaced.

When you do not need the result of the operation, (//=) is more flexible.

(<<//=) :: (MonadState s m, Fractional a) => Lens' s a -> a -> m a
(<<//=) :: (MonadState s m, Fractional a) => Iso' s a -> a -> m a

(<<*=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Modify the target of a Lens into your Monad's state by multipling a value and return the old value that was replaced.

When you do not need the result of the operation, (*=) is more flexible.

(<<*=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
(<<*=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a

(<<-=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Modify the target of a Lens into your Monad's state by subtracting a value and return the old value that was replaced.

When you do not need the result of the operation, (-=) is more flexible.

(<<-=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
(<<-=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a

(<<+=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Modify the target of a Lens into your Monad's state by adding a value and return the old value that was replaced.

When you do not need the result of the operation, (+=) is more flexible.

(<<+=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
(<<+=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a

(<<?=) :: MonadState s m => LensLike ((,) a) s s a (Maybe b) -> b -> m a infix 4 #

Replace the target of a Lens into your Monad's state with Just a user supplied value and return the old value that was replaced.

When applied to a Traversal, this will return a monoidal summary of all of the old values present.

When you do not need the result of the operation, (?=) is more flexible.

(<<?=) :: MonadState s m             => Lens s t a (Maybe b)      -> b -> m a
(<<?=) :: MonadState s m             => Iso s t a (Maybe b)       -> b -> m a
(<<?=) :: (MonadState s m, Monoid a) => Traversal s t a (Maybe b) -> b -> m a

(<<.=) :: MonadState s m => LensLike ((,) a) s s a b -> b -> m a infix 4 #

Replace the target of a Lens into your Monad's state with a user supplied value and return the old value that was replaced.

When applied to a Traversal, this will return a monoidal summary of all of the old values present.

When you do not need the result of the operation, (.=) is more flexible.

(<<.=) :: MonadState s m             => Lens' s a      -> a -> m a
(<<.=) :: MonadState s m             => Iso' s a       -> a -> m a
(<<.=) :: (MonadState s m, Monoid a) => Traversal' s a -> a -> m a

(<<%=) :: (Strong p, MonadState s m) => Over p ((,) a) s s a b -> p a b -> m a infix 4 #

Modify the target of a Lens into your Monad's state by a user supplied function and return the old value that was replaced.

When applied to a Traversal, this will return a monoidal summary of all of the old values present.

When you do not need the result of the operation, (%=) is more flexible.

(<<%=) :: MonadState s m             => Lens' s a      -> (a -> a) -> m a
(<<%=) :: MonadState s m             => Iso' s a       -> (a -> a) -> m a
(<<%=) :: (MonadState s m, Monoid a) => Traversal' s a -> (a -> a) -> m a

(<<%=) :: MonadState s m => LensLike ((,)a) s s a b -> (a -> b) -> m a

(<&&=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool infix 4 #

Logically && a Boolean valued Lens into your Monad's state and return the result.

When you do not need the result of the operation, (&&=) is more flexible.

(<&&=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
(<&&=) :: MonadState s m => Iso' s Bool  -> Bool -> m Bool

(<||=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool infix 4 #

Logically || a Boolean valued Lens into your Monad's state and return the result.

When you do not need the result of the operation, (||=) is more flexible.

(<||=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
(<||=) :: MonadState s m => Iso' s Bool  -> Bool -> m Bool

(<**=) :: (MonadState s m, Floating a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Raise the target of a floating-point valued Lens into your Monad's state to an arbitrary power and return the result.

When you do not need the result of the operation, (**=) is more flexible.

(<**=) :: (MonadState s m, Floating a) => Lens' s a -> a -> m a
(<**=) :: (MonadState s m, Floating a) => Iso' s a -> a -> m a

(<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> m a infix 4 #

Raise the target of a fractionally valued Lens into your Monad's state to an Integral power and return the result.

When you do not need the result of the operation, (^^=) is more flexible.

(<^^=) :: (MonadState s m, Fractional b, Integral e) => Lens' s a -> e -> m a
(<^^=) :: (MonadState s m, Fractional b, Integral e) => Iso' s a  -> e -> m a

(<^=) :: (MonadState s m, Num a, Integral e) => LensLike' ((,) a) s a -> e -> m a infix 4 #

Raise the target of a numerically valued Lens into your Monad's state to a non-negative Integral power and return the result.

When you do not need the result of the operation, (^=) is more flexible.

(<^=) :: (MonadState s m, Num a, Integral e) => Lens' s a -> e -> m a
(<^=) :: (MonadState s m, Num a, Integral e) => Iso' s a -> e -> m a

(<//=) :: (MonadState s m, Fractional a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Divide the target of a fractionally valued Lens into your Monad's state and return the result.

When you do not need the result of the division, (//=) is more flexible.

(<//=) :: (MonadState s m, Fractional a) => Lens' s a -> a -> m a
(<//=) :: (MonadState s m, Fractional a) => Iso' s a -> a -> m a

(<*=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Multiply the target of a numerically valued Lens into your Monad's state and return the result.

When you do not need the result of the multiplication, (*=) is more flexible.

(<*=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
(<*=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a

(<-=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Subtract from the target of a numerically valued Lens into your Monad's state and return the result.

When you do not need the result of the subtraction, (-=) is more flexible.

(<-=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
(<-=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a

(<+=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Add to the target of a numerically valued Lens into your Monad's state and return the result.

When you do not need the result of the addition, (+=) is more flexible.

(<+=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
(<+=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a

(<%=) :: MonadState s m => LensLike ((,) b) s s a b -> (a -> b) -> m b infix 4 #

Modify the target of a Lens into your Monad's state by a user supplied function and return the result.

When applied to a Traversal, it this will return a monoidal summary of all of the intermediate results.

When you do not need the result of the operation, (%=) is more flexible.

(<%=) :: MonadState s m             => Lens' s a      -> (a -> a) -> m a
(<%=) :: MonadState s m             => Iso' s a       -> (a -> a) -> m a
(<%=) :: (MonadState s m, Monoid a) => Traversal' s a -> (a -> a) -> m a

(<<<>~) :: Monoid r => LensLike' ((,) r) s r -> r -> s -> (r, s) infixr 4 #

Modify the target of a monoidally valued Lens by mappending a new value and return the old value.

When you do not need the old value, (<>~) is more flexible.

>>> (Sum a,b) & _1 <<<>~ Sum c
(Sum {getSum = a},(Sum {getSum = a + c},b))

>>> _2 <<<>~ ", 007" $ ("James", "Bond")
("Bond",("James","Bond, 007"))

(<<<>~) :: Monoid r => Lens' s r -> r -> s -> (r, s)
(<<<>~) :: Monoid r => Iso' s r -> r -> s -> (r, s)

(<<&&~) :: LensLike' ((,) Bool) s Bool -> Bool -> s -> (Bool, s) infixr 4 #

Logically && the target of a Bool-valued Lens and return the old value.

When you do not need the old value, (&&~) is more flexible.

>>> (False,6) & _1 <<&&~ True
(False,(False,6))

>>> ("hello",True) & _2 <<&&~ False
(True,("hello",False))

(<<&&~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
(<<&&~) :: Iso' s Bool -> Bool -> s -> (Bool, s)

(<<||~) :: LensLike' ((,) Bool) s Bool -> Bool -> s -> (Bool, s) infixr 4 #

Logically || the target of a Bool-valued Lens and return the old value.

When you do not need the old value, (||~) is more flexible.

>>> (False,6) & _1 <<||~ True
(False,(True,6))

>>> ("hello",True) & _2 <<||~ False
(True,("hello",True))

(<<||~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
(<<||~) :: Iso' s Bool -> Bool -> s -> (Bool, s)

(<<**~) :: Floating a => LensLike' ((,) a) s a -> a -> s -> (a, s) infixr 4 #

Raise the target of a floating-point valued Lens to an arbitrary power and return the old value.

When you do not need the old value, (**~) is more flexible.

>>> (a,b) & _1 <<**~ c
(a,(a**c,b))

>>> (a,b) & _2 <<**~ c
(b,(a,b**c))

(<<**~) :: Floating a => Lens' s a -> a -> s -> (a, s)
(<<**~) :: Floating a => Iso' s a -> a -> s -> (a, s)

(<<^^~) :: (Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> s -> (a, s) infixr 4 #

Raise the target of a fractionally valued Lens to an integral power and return the old value.

When you do not need the old value, (^^~) is more flexible.

(<<^^~) :: (Fractional a, Integral e) => Lens' s a -> e -> s -> (a, s)
(<<^^~) :: (Fractional a, Integral e) => Iso' s a -> e -> S -> (a, s)

(<<^~) :: (Num a, Integral e) => LensLike' ((,) a) s a -> e -> s -> (a, s) infixr 4 #

Raise the target of a numerically valued Lens to a non-negative power and return the old value.

When you do not need the old value, (^~) is more flexible.

(<<^~) :: (Num a, Integral e) => Lens' s a -> e -> s -> (a, s)
(<<^~) :: (Num a, Integral e) => Iso' s a -> e -> s -> (a, s)

(<<//~) :: Fractional a => LensLike' ((,) a) s a -> a -> s -> (a, s) infixr 4 #

Divide the target of a numerically valued Lens and return the old value.

When you do not need the old value, (//~) is more flexible.

>>> (a,b) & _1 <<//~ c
(a,(a / c,b))

>>> ("Hawaii",10) & _2 <<//~ 2
(10.0,("Hawaii",5.0))

(<<//~) :: Fractional a => Lens' s a -> a -> s -> (a, s)
(<<//~) :: Fractional a => Iso' s a -> a -> s -> (a, s)

(<<*~) :: Num a => LensLike' ((,) a) s a -> a -> s -> (a, s) infixr 4 #

Multiply the target of a numerically valued Lens and return the old value.

When you do not need the old value, (-~) is more flexible.

>>> (a,b) & _1 <<*~ c
(a,(a * c,b))

>>> (a,b) & _2 <<*~ c
(b,(a,b * c))

(<<*~) :: Num a => Lens' s a -> a -> s -> (a, s)
(<<*~) :: Num a => Iso' s a -> a -> s -> (a, s)

(<<-~) :: Num a => LensLike' ((,) a) s a -> a -> s -> (a, s) infixr 4 #

Decrement the target of a numerically valued Lens and return the old value.

When you do not need the old value, (-~) is more flexible.

>>> (a,b) & _1 <<-~ c
(a,(a - c,b))

>>> (a,b) & _2 <<-~ c
(b,(a,b - c))

(<<-~) :: Num a => Lens' s a -> a -> s -> (a, s)
(<<-~) :: Num a => Iso' s a -> a -> s -> (a, s)

(<<+~) :: Num a => LensLike' ((,) a) s a -> a -> s -> (a, s) infixr 4 #

Increment the target of a numerically valued Lens and return the old value.

When you do not need the old value, (+~) is more flexible.

>>> (a,b) & _1 <<+~ c
(a,(a + c,b))

>>> (a,b) & _2 <<+~ c
(b,(a,b + c))

(<<+~) :: Num a => Lens' s a -> a -> s -> (a, s)
(<<+~) :: Num a => Iso' s a -> a -> s -> (a, s)

(<<?~) :: LensLike ((,) a) s t a (Maybe b) -> b -> s -> (a, t) infixr 4 #

Replace the target of a Lens with a Just value, but return the old value.

If you do not need the old value (?~) is more flexible.

>>> import Data.Map as Map
>>> _2.at "hello" <<?~ "world" $ (42,Map.fromList [("goodnight","gracie")])
(Nothing,(42,fromList [("goodnight","gracie"),("hello","world")]))

(<<?~) :: Iso s t a (Maybe b)       -> b -> s -> (a, t)
(<<?~) :: Lens s t a (Maybe b)      -> b -> s -> (a, t)
(<<?~) :: Traversal s t a (Maybe b) -> b -> s -> (a, t)

(<<.~) :: LensLike ((,) a) s t a b -> b -> s -> (a, t) infixr 4 #

Replace the target of a Lens, but return the old value.

When you do not need the old value, (.~) is more flexible.

(<<.~) ::             Lens s t a b      -> b -> s -> (a, t)
(<<.~) ::             Iso s t a b       -> b -> s -> (a, t)
(<<.~) :: Monoid a => Traversal s t a b -> b -> s -> (a, t)

(<<%~) :: LensLike ((,) a) s t a b -> (a -> b) -> s -> (a, t) infixr 4 #

Modify the target of a Lens, but return the old value.

When you do not need the old value, (%~) is more flexible.

(<<%~) ::             Lens s t a b      -> (a -> b) -> s -> (a, t)
(<<%~) ::             Iso s t a b       -> (a -> b) -> s -> (a, t)
(<<%~) :: Monoid a => Traversal s t a b -> (a -> b) -> s -> (a, t)

(<&&~) :: LensLike ((,) Bool) s t Bool Bool -> Bool -> s -> (Bool, t) infixr 4 #

Logically && a Boolean valued Lens and return the result.

When you do not need the result of the operation, (&&~) is more flexible.

(<&&~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
(<&&~) :: Iso' s Bool  -> Bool -> s -> (Bool, s)

(<||~) :: LensLike ((,) Bool) s t Bool Bool -> Bool -> s -> (Bool, t) infixr 4 #

Logically || a Boolean valued Lens and return the result.

When you do not need the result of the operation, (||~) is more flexible.

(<||~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
(<||~) :: Iso' s Bool  -> Bool -> s -> (Bool, s)

(<**~) :: Floating a => LensLike ((,) a) s t a a -> a -> s -> (a, t) infixr 4 #

Raise the target of a floating-point valued Lens to an arbitrary power and return the result.

When you do not need the result of the operation, (**~) is more flexible.

(<**~) :: Floating a => Lens' s a -> a -> s -> (a, s)
(<**~) :: Floating a => Iso' s a  -> a -> s -> (a, s)

(<^^~) :: (Fractional a, Integral e) => LensLike ((,) a) s t a a -> e -> s -> (a, t) infixr 4 #

Raise the target of a fractionally valued Lens to an Integral power and return the result.

When you do not need the result of the operation, (^^~) is more flexible.

(<^^~) :: (Fractional a, Integral e) => Lens' s a -> e -> s -> (a, s)
(<^^~) :: (Fractional a, Integral e) => Iso' s a -> e -> s -> (a, s)

(<^~) :: (Num a, Integral e) => LensLike ((,) a) s t a a -> e -> s -> (a, t) infixr 4 #

Raise the target of a numerically valued Lens to a non-negative Integral power and return the result.

When you do not need the result of the operation, (^~) is more flexible.

(<^~) :: (Num a, Integral e) => Lens' s a -> e -> s -> (a, s)
(<^~) :: (Num a, Integral e) => Iso' s a -> e -> s -> (a, s)

(<//~) :: Fractional a => LensLike ((,) a) s t a a -> a -> s -> (a, t) infixr 4 #

Divide the target of a fractionally valued Lens and return the result.

When you do not need the result of the division, (//~) is more flexible.

(<//~) :: Fractional a => Lens' s a -> a -> s -> (a, s)
(<//~) :: Fractional a => Iso'  s a -> a -> s -> (a, s)

(<*~) :: Num a => LensLike ((,) a) s t a a -> a -> s -> (a, t) infixr 4 #

Multiply the target of a numerically valued Lens and return the result.

When you do not need the result of the multiplication, (*~) is more flexible.

(<*~) :: Num a => Lens' s a -> a -> s -> (a, s)
(<*~) :: Num a => Iso'  s a -> a -> s -> (a, s)

(<-~) :: Num a => LensLike ((,) a) s t a a -> a -> s -> (a, t) infixr 4 #

Decrement the target of a numerically valued Lens and return the result.

When you do not need the result of the subtraction, (-~) is more flexible.

(<-~) :: Num a => Lens' s a -> a -> s -> (a, s)
(<-~) :: Num a => Iso' s a  -> a -> s -> (a, s)

(<+~) :: Num a => LensLike ((,) a) s t a a -> a -> s -> (a, t) infixr 4 #

Increment the target of a numerically valued Lens and return the result.

When you do not need the result of the addition, (+~) is more flexible.

(<+~) :: Num a => Lens' s a -> a -> s -> (a, s)
(<+~) :: Num a => Iso' s a  -> a -> s -> (a, s)

(<%~) :: LensLike ((,) b) s t a b -> (a -> b) -> s -> (b, t) infixr 4 #

Modify the target of a Lens and return the result.

When you do not need the result of the operation, (%~) is more flexible.

(<%~) ::             Lens s t a b      -> (a -> b) -> s -> (b, t)
(<%~) ::             Iso s t a b       -> (a -> b) -> s -> (b, t)
(<%~) :: Monoid b => Traversal s t a b -> (a -> b) -> s -> (b, t)

cloneIndexedLens :: AnIndexedLens i s t a b -> IndexedLens i s t a b #

Clone an IndexedLens as an IndexedLens with the same index.

cloneIndexPreservingLens :: ALens s t a b -> IndexPreservingLens s t a b #

Clone a Lens as an IndexedPreservingLens that just passes through whatever index is on any IndexedLens, IndexedFold, IndexedGetter or IndexedTraversal it is composed with.

cloneLens :: ALens s t a b -> Lens s t a b #

Cloning a Lens is one way to make sure you aren't given something weaker, such as a Traversal and can be used as a way to pass around lenses that have to be monomorphic in f.

Note: This only accepts a proper Lens.

>>> let example l x = set (cloneLens l) (x^.cloneLens l + 1) x in example _2 ("hello",1,"you")
("hello",2,"you")

locus :: IndexedComonadStore p => Lens (p a c s) (p b c s) a b #

This Lens lets you view the current pos of any indexed store comonad and seek to a new position. This reduces the API for working these instances to a single Lens.

ipos w ≡ w ^. locus
iseek s w ≡ w & locus .~ s
iseeks f w ≡ w & locus %~ f

locus :: Lens' (Context' a s) a
locus :: Conjoined p => Lens' (Pretext' p a s) a
locus :: Conjoined p => Lens' (PretextT' p g a s) a

alongside :: LensLike (AlongsideLeft f b') s t a b -> LensLike (AlongsideRight f t) s' t' a' b' -> LensLike f (s, s') (t, t') (a, a') (b, b') #

alongside makes a Lens from two other lenses or a Getter from two other getters by executing them on their respective halves of a product.

>>> (Left a, Right b)^.alongside chosen chosen
(a,b)

>>> (Left a, Right b) & alongside chosen chosen .~ (c,d)
(Left c,Right d)

alongside :: Lens   s t a b -> Lens   s' t' a' b' -> Lens   (s,s') (t,t') (a,a') (b,b')
alongside :: Getter s   a   -> Getter s'    a'    -> Getter (s,s')        (a,a')

chosen :: IndexPreservingLens (Either a a) (Either b b) a b #

This is a Lens that updates either side of an Either, where both sides have the same type.

chosen ≡ choosing id id

>>> Left a^.chosen
a

>>> Right a^.chosen
a

>>> Right "hello"^.chosen
"hello"

>>> Right a & chosen *~ b
Right (a * b)

chosen :: Lens (Either a a) (Either b b) a b
chosen f (Left a)  = Left <$> f a
chosen f (Right a) = Right <$> f a

choosing :: Functor f => LensLike f s t a b -> LensLike f s' t' a b -> LensLike f (Either s s') (Either t t') a b #

Merge two lenses, getters, setters, folds or traversals.

chosen ≡ choosing id id

choosing :: Getter s a     -> Getter s' a     -> Getter (Either s s') a
choosing :: Fold s a       -> Fold s' a       -> Fold (Either s s') a
choosing :: Lens' s a      -> Lens' s' a      -> Lens' (Either s s') a
choosing :: Traversal' s a -> Traversal' s' a -> Traversal' (Either s s') a
choosing :: Setter' s a    -> Setter' s' a    -> Setter' (Either s s') a

inside :: Corepresentable p => ALens s t a b -> Lens (p e s) (p e t) (p e a) (p e b) #

Lift a Lens so it can run under a function (or other corepresentable profunctor).

inside :: Lens s t a b -> Lens (e -> s) (e -> t) (e -> a) (e -> b)

>>> (\x -> (x-1,x+1)) ^. inside _1 $ 5
4

>>> runState (modify (1:) >> modify (2:)) ^. (inside _2) $ []
[2,1]

(??) :: Functor f => f (a -> b) -> a -> f b infixl 1 #

This is convenient to flip argument order of composite functions defined as:

fab ?? a = fmap ($ a) fab

For the Functor instance f = ((->) r) you can reason about this function as if the definition was (??) ≡ flip:

>>> (h ?? x) a
h a x

>>> execState ?? [] $ modify (1:)
[1]

>>> over _2 ?? ("hello","world") $ length
("hello",5)

>>> over ?? length ?? ("hello","world") $ _2
("hello",5)

(%%=) :: MonadState s m => Over p ((,) r) s s a b -> p a (r, b) -> m r infix 4 #

Modify the target of a Lens in the current state returning some extra information of type r or modify all targets of a Traversal in the current state, extracting extra information of type r and return a monoidal summary of the changes.

>>> runState (_1 %%= \x -> (f x, g x)) (a,b)
(f a,(g a,b))

(%%=) ≡ (state .)

It may be useful to think of (%%=), instead, as having either of the following more restricted type signatures:

(%%=) :: MonadState s m             => Iso s s a b       -> (a -> (r, b)) -> m r
(%%=) :: MonadState s m             => Lens s s a b      -> (a -> (r, b)) -> m r
(%%=) :: (MonadState s m, Monoid r) => Traversal s s a b -> (a -> (r, b)) -> m r

(%%~) :: LensLike f s t a b -> (a -> f b) -> s -> f t infixr 4 #

(%%~) can be used in one of two scenarios:

When applied to a Lens, it can edit the target of the Lens in a structure, extracting a functorial result.

When applied to a Traversal, it can edit the targets of the traversals, extracting an applicative summary of its actions.

>>> [66,97,116,109,97,110] & each %%~ \a -> ("na", chr a)
("nananananana","Batman")

For all that the definition of this combinator is just:

(%%~) ≡ id

It may be beneficial to think about it as if it had these even more restricted types, however:

(%%~) :: Functor f =>     Iso s t a b       -> (a -> f b) -> s -> f t
(%%~) :: Functor f =>     Lens s t a b      -> (a -> f b) -> s -> f t
(%%~) :: Applicative f => Traversal s t a b -> (a -> f b) -> s -> f t

When applied to a Traversal, it can edit the targets of the traversals, extracting a supplemental monoidal summary of its actions, by choosing f = ((,) m)

(%%~) ::             Iso s t a b       -> (a -> (r, b)) -> s -> (r, t)
(%%~) ::             Lens s t a b      -> (a -> (r, b)) -> s -> (r, t)
(%%~) :: Monoid m => Traversal s t a b -> (a -> (m, b)) -> s -> (m, t)

(&~) :: s -> State s a -> s infixl 1 #

This can be used to chain lens operations using op= syntax rather than op~ syntax for simple non-type-changing cases.

>>> (10,20) & _1 .~ 30 & _2 .~ 40
(30,40)

>>> (10,20) &~ do _1 .= 30; _2 .= 40
(30,40)

This does not support type-changing assignment, e.g.

>>> (10,20) & _1 .~ "hello"
("hello",20)

ilens :: (s -> (i, a)) -> (s -> b -> t) -> IndexedLens i s t a b #

Build an IndexedLens from a Getter and a Setter.

iplens :: (s -> a) -> (s -> b -> t) -> IndexPreservingLens s t a b #

Build an index-preserving Lens from a Getter and a Setter.

lens :: (s -> a) -> (s -> b -> t) -> Lens s t a b #

Build a Lens from a getter and a setter.

lens :: Functor f => (s -> a) -> (s -> b -> t) -> (a -> f b) -> s -> f t

>>> s ^. lens getter setter
getter s

>>> s & lens getter setter .~ b
setter s b

>>> s & lens getter setter %~ f
setter s (f (getter s))

lens :: (s -> a) -> (s -> a -> s) -> Lens' s a

type ALens s t a b = LensLike (Pretext ((->) :: Type -> Type -> Type) a b) s t a b #

When you see this as an argument to a function, it expects a Lens.

This type can also be used when you need to store a Lens in a container, since it is rank-1. You can turn them back into a Lens with cloneLens, or use it directly with combinators like storing and (^#).

type ALens' s a = ALens s s a a #

type ALens' = Simple ALens

type AnIndexedLens i s t a b = Optical (Indexed i) ((->) :: Type -> Type -> Type) (Pretext (Indexed i) a b) s t a b #

When you see this as an argument to a function, it expects an IndexedLens

type AnIndexedLens' i s a = AnIndexedLens i s s a a #

type AnIndexedLens' = Simple (AnIndexedLens i)

imapOf :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t #

Map with index. (Deprecated alias for iover).

When you do not need access to the index, then mapOf is more liberal in what it can accept.

mapOf l ≡ imapOf l . const

imapOf :: IndexedSetter i s t a b    -> (i -> a -> b) -> s -> t
imapOf :: IndexedLens i s t a b      -> (i -> a -> b) -> s -> t
imapOf :: IndexedTraversal i s t a b -> (i -> a -> b) -> s -> t

mapOf :: ASetter s t a b -> (a -> b) -> s -> t #

mapOf is a deprecated alias for over.

assignA :: Arrow p => ASetter s t a b -> p s b -> p s t #

Run an arrow command and use the output to set all the targets of a Lens, Setter or Traversal to the result.

assignA can be used very similarly to (<~), except that the type of the object being modified can change; for example:

runKleisli action ((), (), ()) where
  action =      assignA _1 (Kleisli (const getVal1))
           >>> assignA _2 (Kleisli (const getVal2))
           >>> assignA _3 (Kleisli (const getVal3))
  getVal1 :: Either String Int
  getVal1 = ...
  getVal2 :: Either String Bool
  getVal2 = ...
  getVal3 :: Either String Char
  getVal3 = ...

has the type Either String (Int, Bool, Char)

assignA :: Arrow p => Iso s t a b       -> p s b -> p s t
assignA :: Arrow p => Lens s t a b      -> p s b -> p s t
assignA :: Arrow p => Traversal s t a b -> p s b -> p s t
assignA :: Arrow p => Setter s t a b    -> p s b -> p s t

(.@=) :: MonadState s m => AnIndexedSetter i s s a b -> (i -> b) -> m () infix 4 #

Replace every target in the current state of an IndexedSetter, IndexedLens or IndexedTraversal with access to the index.

When you do not need access to the index then (.=) is more liberal in what it can accept.

l .= b ≡ l .@= const b

(.@=) :: MonadState s m => IndexedSetter i s s a b    -> (i -> b) -> m ()
(.@=) :: MonadState s m => IndexedLens i s s a b      -> (i -> b) -> m ()
(.@=) :: MonadState s m => IndexedTraversal i s t a b -> (i -> b) -> m ()

imodifying :: MonadState s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m () #

This is an alias for (%@=).

(%@=) :: MonadState s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m () infix 4 #

Adjust every target in the current state of an IndexedSetter, IndexedLens or IndexedTraversal with access to the index.

When you do not need access to the index then (%=) is more liberal in what it can accept.

l %= f ≡ l %@= const f

(%@=) :: MonadState s m => IndexedSetter i s s a b    -> (i -> a -> b) -> m ()
(%@=) :: MonadState s m => IndexedLens i s s a b      -> (i -> a -> b) -> m ()
(%@=) :: MonadState s m => IndexedTraversal i s t a b -> (i -> a -> b) -> m ()

(.@~) :: AnIndexedSetter i s t a b -> (i -> b) -> s -> t infixr 4 #

Replace every target of an IndexedSetter, IndexedLens or IndexedTraversal with access to the index.

(.@~) ≡ iset

When you do not need access to the index then (.~) is more liberal in what it can accept.

l .~ b ≡ l .@~ const b

(.@~) :: IndexedSetter i s t a b    -> (i -> b) -> s -> t
(.@~) :: IndexedLens i s t a b      -> (i -> b) -> s -> t
(.@~) :: IndexedTraversal i s t a b -> (i -> b) -> s -> t

(%@~) :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t infixr 4 #

Adjust every target of an IndexedSetter, IndexedLens or IndexedTraversal with access to the index.

(%@~) ≡ iover

When you do not need access to the index then (%~) is more liberal in what it can accept.

l %~ f ≡ l %@~ const f

(%@~) :: IndexedSetter i s t a b    -> (i -> a -> b) -> s -> t
(%@~) :: IndexedLens i s t a b      -> (i -> a -> b) -> s -> t
(%@~) :: IndexedTraversal i s t a b -> (i -> a -> b) -> s -> t

isets :: ((i -> a -> b) -> s -> t) -> IndexedSetter i s t a b #

Build an IndexedSetter from an imap-like function.

Your supplied function f is required to satisfy:

f id ≡ id
f g . f h ≡ f (g . h)

Equational reasoning:

isets . iover ≡ id
iover . isets ≡ id

Another way to view isets is that it takes a "semantic editor combinator" which has been modified to carry an index and transforms it into a IndexedSetter.

iset :: AnIndexedSetter i s t a b -> (i -> b) -> s -> t #

Set with index. Equivalent to iover with the current value ignored.

When you do not need access to the index, then set is more liberal in what it can accept.

set l ≡ iset l . const

iset :: IndexedSetter i s t a b    -> (i -> b) -> s -> t
iset :: IndexedLens i s t a b      -> (i -> b) -> s -> t
iset :: IndexedTraversal i s t a b -> (i -> b) -> s -> t

iover :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t #

Map with index. This is an alias for imapOf.

When you do not need access to the index, then over is more liberal in what it can accept.

over l ≡ iover l . const
iover l ≡ over l . Indexed

iover :: IndexedSetter i s t a b    -> (i -> a -> b) -> s -> t
iover :: IndexedLens i s t a b      -> (i -> a -> b) -> s -> t
iover :: IndexedTraversal i s t a b -> (i -> a -> b) -> s -> t

icensoring :: MonadWriter w m => IndexedSetter i w w u v -> (i -> u -> v) -> m a -> m a #

This is a generalization of censor that alows you to censor just a portion of the resulting MonadWriter, with access to the index of an IndexedSetter.

censoring :: MonadWriter w m => Setter w w u v -> (u -> v) -> m a -> m a #

This is a generalization of censor that alows you to censor just a portion of the resulting MonadWriter.

ipassing :: MonadWriter w m => IndexedSetter i w w u v -> m (a, i -> u -> v) -> m a #

This is a generalization of pass that alows you to modify just a portion of the resulting MonadWriter with access to the index of an IndexedSetter.

passing :: MonadWriter w m => Setter w w u v -> m (a, u -> v) -> m a #

This is a generalization of pass that alows you to modify just a portion of the resulting MonadWriter.

scribe :: (MonadWriter t m, Monoid s) => ASetter s t a b -> b -> m () #

Write to a fragment of a larger Writer format.

(<>=) :: (MonadState s m, Monoid a) => ASetter' s a -> a -> m () infix 4 #

Modify the target(s) of a Lens', Iso, Setter or Traversal by mappending a value.

>>> execState (do _1 <>= Sum c; _2 <>= Product d) (Sum a,Product b)
(Sum {getSum = a + c},Product {getProduct = b * d})

>>> execState (both <>= "!!!") ("hello","world")
("hello!!!","world!!!")

(<>=) :: (MonadState s m, Monoid a) => Setter' s a -> a -> m ()
(<>=) :: (MonadState s m, Monoid a) => Iso' s a -> a -> m ()
(<>=) :: (MonadState s m, Monoid a) => Lens' s a -> a -> m ()
(<>=) :: (MonadState s m, Monoid a) => Traversal' s a -> a -> m ()

(<>~) :: Monoid a => ASetter s t a a -> a -> s -> t infixr 4 #

Modify the target of a monoidally valued by mappending another value.

>>> (Sum a,b) & _1 <>~ Sum c
(Sum {getSum = a + c},b)

>>> (Sum a,Sum b) & both <>~ Sum c
(Sum {getSum = a + c},Sum {getSum = b + c})

>>> both <>~ "!!!" $ ("hello","world")
("hello!!!","world!!!")

(<>~) :: Monoid a => Setter s t a a    -> a -> s -> t
(<>~) :: Monoid a => Iso s t a a       -> a -> s -> t
(<>~) :: Monoid a => Lens s t a a      -> a -> s -> t
(<>~) :: Monoid a => Traversal s t a a -> a -> s -> t

(<?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m b infix 4 #

Set Just a value with pass-through

This is useful for chaining assignment without round-tripping through your Monad stack.

do x <- at "foo" <?= ninety_nine_bottles_of_beer_on_the_wall

If you do not need a copy of the intermediate result, then using l ?= d will avoid unused binding warnings.

(<?=) :: MonadState s m => Setter s s a (Maybe b)    -> b -> m b
(<?=) :: MonadState s m => Iso s s a (Maybe b)       -> b -> m b
(<?=) :: MonadState s m => Lens s s a (Maybe b)      -> b -> m b
(<?=) :: MonadState s m => Traversal s s a (Maybe b) -> b -> m b

(<.=) :: MonadState s m => ASetter s s a b -> b -> m b infix 4 #

Set with pass-through

This is useful for chaining assignment without round-tripping through your Monad stack.

do x <- _2 <.= ninety_nine_bottles_of_beer_on_the_wall

If you do not need a copy of the intermediate result, then using l .= d will avoid unused binding warnings.

(<.=) :: MonadState s m => Setter s s a b    -> b -> m b
(<.=) :: MonadState s m => Iso s s a b       -> b -> m b
(<.=) :: MonadState s m => Lens s s a b      -> b -> m b
(<.=) :: MonadState s m => Traversal s s a b -> b -> m b

(<~) :: MonadState s m => ASetter s s a b -> m b -> m () infixr 2 #

Run a monadic action, and set all of the targets of a Lens, Setter or Traversal to its result.

(<~) :: MonadState s m => Iso s s a b       -> m b -> m ()
(<~) :: MonadState s m => Lens s s a b      -> m b -> m ()
(<~) :: MonadState s m => Traversal s s a b -> m b -> m ()
(<~) :: MonadState s m => Setter s s a b    -> m b -> m ()

As a reasonable mnemonic, this lets you store the result of a monadic action in a Lens rather than in a local variable.

do foo <- bar
   ...

will store the result in a variable, while

do foo <~ bar
   ...

will store the result in a Lens, Setter, or Traversal.

(||=) :: MonadState s m => ASetter' s Bool -> Bool -> m () infix 4 #

Modify the target(s) of a Lens', 'Iso, Setter or Traversal by taking their logical || with a value.

>>> execState (do _1 ||= True; _2 ||= False; _3 ||= True; _4 ||= False) (True,True,False,False)
(True,True,True,False)

(||=) :: MonadState s m => Setter' s Bool    -> Bool -> m ()
(||=) :: MonadState s m => Iso' s Bool       -> Bool -> m ()
(||=) :: MonadState s m => Lens' s Bool      -> Bool -> m ()
(||=) :: MonadState s m => Traversal' s Bool -> Bool -> m ()

(&&=) :: MonadState s m => ASetter' s Bool -> Bool -> m () infix 4 #

Modify the target(s) of a Lens', Iso, Setter or Traversal by taking their logical && with a value.

>>> execState (do _1 &&= True; _2 &&= False; _3 &&= True; _4 &&= False) (True,True,False,False)
(True,False,False,False)

(&&=) :: MonadState s m => Setter' s Bool    -> Bool -> m ()
(&&=) :: MonadState s m => Iso' s Bool       -> Bool -> m ()
(&&=) :: MonadState s m => Lens' s Bool      -> Bool -> m ()
(&&=) :: MonadState s m => Traversal' s Bool -> Bool -> m ()

(**=) :: (MonadState s m, Floating a) => ASetter' s a -> a -> m () infix 4 #

Raise the target(s) of a numerically valued Lens, Setter or Traversal to an arbitrary power

>>> execState (do _1 **= c; _2 **= d) (a,b)
(a**c,b**d)

(**=) ::  (MonadState s m, Floating a) => Setter' s a    -> a -> m ()
(**=) ::  (MonadState s m, Floating a) => Iso' s a       -> a -> m ()
(**=) ::  (MonadState s m, Floating a) => Lens' s a      -> a -> m ()
(**=) ::  (MonadState s m, Floating a) => Traversal' s a -> a -> m ()

(^^=) :: (MonadState s m, Fractional a, Integral e) => ASetter' s a -> e -> m () infix 4 #

Raise the target(s) of a numerically valued Lens, Setter or Traversal to an integral power.

(^^=) ::  (MonadState s m, Fractional a, Integral e) => Setter' s a    -> e -> m ()
(^^=) ::  (MonadState s m, Fractional a, Integral e) => Iso' s a       -> e -> m ()
(^^=) ::  (MonadState s m, Fractional a, Integral e) => Lens' s a      -> e -> m ()
(^^=) ::  (MonadState s m, Fractional a, Integral e) => Traversal' s a -> e -> m ()

(^=) :: (MonadState s m, Num a, Integral e) => ASetter' s a -> e -> m () infix 4 #

Raise the target(s) of a numerically valued Lens, Setter or Traversal to a non-negative integral power.

(^=) ::  (MonadState s m, Num a, Integral e) => Setter' s a    -> e -> m ()
(^=) ::  (MonadState s m, Num a, Integral e) => Iso' s a       -> e -> m ()
(^=) ::  (MonadState s m, Num a, Integral e) => Lens' s a      -> e -> m ()
(^=) ::  (MonadState s m, Num a, Integral e) => Traversal' s a -> e -> m ()

(//=) :: (MonadState s m, Fractional a) => ASetter' s a -> a -> m () infix 4 #

Modify the target(s) of a Lens', Iso, Setter or Traversal by dividing by a value.

>>> execState (do _1 //= c; _2 //= d) (a,b)
(a / c,b / d)

(//=) :: (MonadState s m, Fractional a) => Setter' s a    -> a -> m ()
(//=) :: (MonadState s m, Fractional a) => Iso' s a       -> a -> m ()
(//=) :: (MonadState s m, Fractional a) => Lens' s a      -> a -> m ()
(//=) :: (MonadState s m, Fractional a) => Traversal' s a -> a -> m ()

(*=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m () infix 4 #

Modify the target(s) of a Lens', Iso, Setter or Traversal by multiplying by value.

>>> execState (do _1 *= c; _2 *= d) (a,b)
(a * c,b * d)

(*=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
(*=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
(*=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
(*=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()

(-=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m () infix 4 #

Modify the target(s) of a Lens', Iso, Setter or Traversal by subtracting a value.

>>> execState (do _1 -= c; _2 -= d) (a,b)
(a - c,b - d)

(-=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
(-=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
(-=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
(-=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()

(+=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m () infix 4 #

Modify the target(s) of a Lens', Iso, Setter or Traversal by adding a value.

Example:

fresh :: MonadState Int m => m Int
fresh = do
  id += 1
  use id

>>> execState (do _1 += c; _2 += d) (a,b)
(a + c,b + d)

>>> execState (do _1.at 1.non 0 += 10) (Map.fromList [(2,100)],"hello")
(fromList [(1,10),(2,100)],"hello")

(+=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
(+=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
(+=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
(+=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()

(?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m () infix 4 #

Replace the target of a Lens or all of the targets of a Setter or Traversal in our monadic state with Just a new value, irrespective of the old.

>>> execState (do at 1 ?= a; at 2 ?= b) Map.empty
fromList [(1,a),(2,b)]

>>> execState (do _1 ?= b; _2 ?= c) (Just a, Nothing)
(Just b,Just c)

(?=) :: MonadState s m => Iso' s (Maybe a)       -> a -> m ()
(?=) :: MonadState s m => Lens' s (Maybe a)      -> a -> m ()
(?=) :: MonadState s m => Traversal' s (Maybe a) -> a -> m ()
(?=) :: MonadState s m => Setter' s (Maybe a)    -> a -> m ()

modifying :: MonadState s m => ASetter s s a b -> (a -> b) -> m () #

This is an alias for (%=).

(%=) :: MonadState s m => ASetter s s a b -> (a -> b) -> m () infix 4 #

Map over the target of a Lens or all of the targets of a Setter or Traversal in our monadic state.

>>> execState (do _1 %= f;_2 %= g) (a,b)
(f a,g b)

>>> execState (do both %= f) (a,b)
(f a,f b)

(%=) :: MonadState s m => Iso' s a       -> (a -> a) -> m ()
(%=) :: MonadState s m => Lens' s a      -> (a -> a) -> m ()
(%=) :: MonadState s m => Traversal' s a -> (a -> a) -> m ()
(%=) :: MonadState s m => Setter' s a    -> (a -> a) -> m ()

(%=) :: MonadState s m => ASetter s s a b -> (a -> b) -> m ()

(.=) :: MonadState s m => ASetter s s a b -> b -> m () infix 4 #

Replace the target of a Lens or all of the targets of a Setter or Traversal in our monadic state with a new value, irrespective of the old.

This is an infix version of assign.

>>> execState (do _1 .= c; _2 .= d) (a,b)
(c,d)

>>> execState (both .= c) (a,b)
(c,c)

(.=) :: MonadState s m => Iso' s a       -> a -> m ()
(.=) :: MonadState s m => Lens' s a      -> a -> m ()
(.=) :: MonadState s m => Traversal' s a -> a -> m ()
(.=) :: MonadState s m => Setter' s a    -> a -> m ()

It puts the state in the monad or it gets the hose again.

assign :: MonadState s m => ASetter s s a b -> b -> m () #

Replace the target of a Lens or all of the targets of a Setter or Traversal in our monadic state with a new value, irrespective of the old.

This is an alias for (.=).

>>> execState (do assign _1 c; assign _2 d) (a,b)
(c,d)

>>> execState (both .= c) (a,b)
(c,c)

assign :: MonadState s m => Iso' s a       -> a -> m ()
assign :: MonadState s m => Lens' s a      -> a -> m ()
assign :: MonadState s m => Traversal' s a -> a -> m ()
assign :: MonadState s m => Setter' s a    -> a -> m ()

(&&~) :: ASetter s t Bool Bool -> Bool -> s -> t infixr 4 #

Logically && the target(s) of a Bool-valued Lens or Setter.

>>> both &&~ True $ (False, True)
(False,True)

>>> both &&~ False $ (False, True)
(False,False)

(&&~) :: Setter' s Bool    -> Bool -> s -> s
(&&~) :: Iso' s Bool       -> Bool -> s -> s
(&&~) :: Lens' s Bool      -> Bool -> s -> s
(&&~) :: Traversal' s Bool -> Bool -> s -> s

(||~) :: ASetter s t Bool Bool -> Bool -> s -> t infixr 4 #

Logically || the target(s) of a Bool-valued Lens or Setter.

>>> both ||~ True $ (False,True)
(True,True)

>>> both ||~ False $ (False,True)
(False,True)

(||~) :: Setter' s Bool    -> Bool -> s -> s
(||~) :: Iso' s Bool       -> Bool -> s -> s
(||~) :: Lens' s Bool      -> Bool -> s -> s
(||~) :: Traversal' s Bool -> Bool -> s -> s

(**~) :: Floating a => ASetter s t a a -> a -> s -> t infixr 4 #

Raise the target(s) of a floating-point valued Lens, Setter or Traversal to an arbitrary power.

>>> (a,b) & _1 **~ c
(a**c,b)

>>> (a,b) & both **~ c
(a**c,b**c)

>>> _2 **~ 10 $ (3,2)
(3,1024.0)

(**~) :: Floating a => Setter' s a    -> a -> s -> s
(**~) :: Floating a => Iso' s a       -> a -> s -> s
(**~) :: Floating a => Lens' s a      -> a -> s -> s
(**~) :: Floating a => Traversal' s a -> a -> s -> s

(^^~) :: (Fractional a, Integral e) => ASetter s t a a -> e -> s -> t infixr 4 #

Raise the target(s) of a fractionally valued Lens, Setter or Traversal to an integral power.

>>> (1,2) & _2 ^^~ (-1)
(1,0.5)

(^^~) :: (Fractional a, Integral e) => Setter' s a    -> e -> s -> s
(^^~) :: (Fractional a, Integral e) => Iso' s a       -> e -> s -> s
(^^~) :: (Fractional a, Integral e) => Lens' s a      -> e -> s -> s
(^^~) :: (Fractional a, Integral e) => Traversal' s a -> e -> s -> s

(^~) :: (Num a, Integral e) => ASetter s t a a -> e -> s -> t infixr 4 #

Raise the target(s) of a numerically valued Lens, Setter or Traversal to a non-negative integral power.

>>> (1,3) & _2 ^~ 2
(1,9)

(^~) :: (Num a, Integral e) => Setter' s a    -> e -> s -> s
(^~) :: (Num a, Integral e) => Iso' s a       -> e -> s -> s
(^~) :: (Num a, Integral e) => Lens' s a      -> e -> s -> s
(^~) :: (Num a, Integral e) => Traversal' s a -> e -> s -> s

(//~) :: Fractional a => ASetter s t a a -> a -> s -> t infixr 4 #

Divide the target(s) of a numerically valued Lens, Iso, Setter or Traversal.

>>> (a,b) & _1 //~ c
(a / c,b)

>>> (a,b) & both //~ c
(a / c,b / c)

>>> ("Hawaii",10) & _2 //~ 2
("Hawaii",5.0)

(//~) :: Fractional a => Setter' s a    -> a -> s -> s
(//~) :: Fractional a => Iso' s a       -> a -> s -> s
(//~) :: Fractional a => Lens' s a      -> a -> s -> s
(//~) :: Fractional a => Traversal' s a -> a -> s -> s

(-~) :: Num a => ASetter s t a a -> a -> s -> t infixr 4 #

Decrement the target(s) of a numerically valued Lens, Iso, Setter or Traversal.

>>> (a,b) & _1 -~ c
(a - c,b)

>>> (a,b) & both -~ c
(a - c,b - c)

>>> _1 -~ 2 $ (1,2)
(-1,2)

>>> mapped.mapped -~ 1 $ [[4,5],[6,7]]
[[3,4],[5,6]]

(-~) :: Num a => Setter' s a    -> a -> s -> s
(-~) :: Num a => Iso' s a       -> a -> s -> s
(-~) :: Num a => Lens' s a      -> a -> s -> s
(-~) :: Num a => Traversal' s a -> a -> s -> s

(*~) :: Num a => ASetter s t a a -> a -> s -> t infixr 4 #

Multiply the target(s) of a numerically valued Lens, Iso, Setter or Traversal.

>>> (a,b) & _1 *~ c
(a * c,b)

>>> (a,b) & both *~ c
(a * c,b * c)

>>> (1,2) & _2 *~ 4
(1,8)

>>> Just 24 & mapped *~ 2
Just 48

(*~) :: Num a => Setter' s a    -> a -> s -> s
(*~) :: Num a => Iso' s a       -> a -> s -> s
(*~) :: Num a => Lens' s a      -> a -> s -> s
(*~) :: Num a => Traversal' s a -> a -> s -> s

(+~) :: Num a => ASetter s t a a -> a -> s -> t infixr 4 #

Increment the target(s) of a numerically valued Lens, Setter or Traversal.

>>> (a,b) & _1 +~ c
(a + c,b)

>>> (a,b) & both +~ c
(a + c,b + c)

>>> (1,2) & _2 +~ 1
(1,3)

>>> [(a,b),(c,d)] & traverse.both +~ e
[(a + e,b + e),(c + e,d + e)]

(+~) :: Num a => Setter' s a    -> a -> s -> s
(+~) :: Num a => Iso' s a       -> a -> s -> s
(+~) :: Num a => Lens' s a      -> a -> s -> s
(+~) :: Num a => Traversal' s a -> a -> s -> s

(<?~) :: ASetter s t a (Maybe b) -> b -> s -> (b, t) infixr 4 #

Set to Just a value with pass-through.

This is mostly present for consistency, but may be useful for for chaining assignments.

If you do not need a copy of the intermediate result, then using l ?~ d directly is a good idea.

>>> import Data.Map as Map
>>> _2.at "hello" <?~ "world" $ (42,Map.fromList [("goodnight","gracie")])
("world",(42,fromList [("goodnight","gracie"),("hello","world")]))

(<?~) :: Setter s t a (Maybe b)    -> b -> s -> (b, t)
(<?~) :: Iso s t a (Maybe b)       -> b -> s -> (b, t)
(<?~) :: Lens s t a (Maybe b)      -> b -> s -> (b, t)
(<?~) :: Traversal s t a (Maybe b) -> b -> s -> (b, t)

(<.~) :: ASetter s t a b -> b -> s -> (b, t) infixr 4 #

Set with pass-through.

This is mostly present for consistency, but may be useful for chaining assignments.

If you do not need a copy of the intermediate result, then using l .~ t directly is a good idea.

>>> (a,b) & _1 <.~ c
(c,(c,b))

>>> ("good","morning","vietnam") & _3 <.~ "world"
("world",("good","morning","world"))

>>> (42,Map.fromList [("goodnight","gracie")]) & _2.at "hello" <.~ Just "world"
(Just "world",(42,fromList [("goodnight","gracie"),("hello","world")]))

(<.~) :: Setter s t a b    -> b -> s -> (b, t)
(<.~) :: Iso s t a b       -> b -> s -> (b, t)
(<.~) :: Lens s t a b      -> b -> s -> (b, t)
(<.~) :: Traversal s t a b -> b -> s -> (b, t)

(?~) :: ASetter s t a (Maybe b) -> b -> s -> t infixr 4 #

Set the target of a Lens, Traversal or Setter to Just a value.

l ?~ t ≡ set l (Just t)

>>> Nothing & id ?~ a
Just a

>>> Map.empty & at 3 ?~ x
fromList [(3,x)]

(?~) :: Setter s t a (Maybe b)    -> b -> s -> t
(?~) :: Iso s t a (Maybe b)       -> b -> s -> t
(?~) :: Lens s t a (Maybe b)      -> b -> s -> t
(?~) :: Traversal s t a (Maybe b) -> b -> s -> t

(.~) :: ASetter s t a b -> b -> s -> t infixr 4 #

Replace the target of a Lens or all of the targets of a Setter or Traversal with a constant value.

This is an infix version of set, provided for consistency with (.=).

f <$ a ≡ mapped .~ f $ a

>>> (a,b,c,d) & _4 .~ e
(a,b,c,e)

>>> (42,"world") & _1 .~ "hello"
("hello","world")

>>> (a,b) & both .~ c
(c,c)

(.~) :: Setter s t a b    -> b -> s -> t
(.~) :: Iso s t a b       -> b -> s -> t
(.~) :: Lens s t a b      -> b -> s -> t
(.~) :: Traversal s t a b -> b -> s -> t

(%~) :: ASetter s t a b -> (a -> b) -> s -> t infixr 4 #

Modifies the target of a Lens or all of the targets of a Setter or Traversal with a user supplied function.

This is an infix version of over.

fmap f ≡ mapped %~ f
fmapDefault f ≡ traverse %~ f

>>> (a,b,c) & _3 %~ f
(a,b,f c)

>>> (a,b) & both %~ f
(f a,f b)

>>> _2 %~ length $ (1,"hello")
(1,5)

>>> traverse %~ f $ [a,b,c]
[f a,f b,f c]

>>> traverse %~ even $ [1,2,3]
[False,True,False]

>>> traverse.traverse %~ length $ [["hello","world"],["!!!"]]
[[5,5],[3]]

(%~) :: Setter s t a b    -> (a -> b) -> s -> t
(%~) :: Iso s t a b       -> (a -> b) -> s -> t
(%~) :: Lens s t a b      -> (a -> b) -> s -> t
(%~) :: Traversal s t a b -> (a -> b) -> s -> t

set' :: ASetter' s a -> a -> s -> s #

Replace the target of a Lens or all of the targets of a Setter' or Traversal with a constant value, without changing its type.

This is a type restricted version of set, which retains the type of the original.

>>> set' mapped x [a,b,c,d]
[x,x,x,x]

>>> set' _2 "hello" (1,"world")
(1,"hello")

>>> set' mapped 0 [1,2,3,4]
[0,0,0,0]

Note: Attempting to adjust set' a Fold or Getter will fail at compile time with an relatively nice error message.

set' :: Setter' s a    -> a -> s -> s
set' :: Iso' s a       -> a -> s -> s
set' :: Lens' s a      -> a -> s -> s
set' :: Traversal' s a -> a -> s -> s

set :: ASetter s t a b -> b -> s -> t #

Replace the target of a Lens or all of the targets of a Setter or Traversal with a constant value.

(<$) ≡ set mapped

>>> set _2 "hello" (1,())
(1,"hello")

>>> set mapped () [1,2,3,4]
[(),(),(),()]

Note: Attempting to set a Fold or Getter will fail at compile time with an relatively nice error message.

set :: Setter s t a b    -> b -> s -> t
set :: Iso s t a b       -> b -> s -> t
set :: Lens s t a b      -> b -> s -> t
set :: Traversal s t a b -> b -> s -> t

over :: ASetter s t a b -> (a -> b) -> s -> t #

Modify the target of a Lens or all the targets of a Setter or Traversal with a function.

fmap ≡ over mapped
fmapDefault ≡ over traverse
sets . over ≡ id
over . sets ≡ id

Given any valid Setter l, you can also rely on the law:

over l f . over l g = over l (f . g)

e.g.

>>> over mapped f (over mapped g [a,b,c]) == over mapped (f . g) [a,b,c]
True

Another way to view over is to say that it transforms a Setter into a "semantic editor combinator".

>>> over mapped f (Just a)
Just (f a)

>>> over mapped (*10) [1,2,3]
[10,20,30]

>>> over _1 f (a,b)
(f a,b)

>>> over _1 show (10,20)
("10",20)

over :: Setter s t a b -> (a -> b) -> s -> t
over :: ASetter s t a b -> (a -> b) -> s -> t

cloneIndexedSetter :: AnIndexedSetter i s t a b -> IndexedSetter i s t a b #

Clone an IndexedSetter.

cloneIndexPreservingSetter :: ASetter s t a b -> IndexPreservingSetter s t a b #

Build an IndexPreservingSetter from any Setter.

cloneSetter :: ASetter s t a b -> Setter s t a b #

Restore ASetter to a full Setter.

sets :: (Profunctor p, Profunctor q, Settable f) => (p a b -> q s t) -> Optical p q f s t a b #

Build a Setter, IndexedSetter or IndexPreservingSetter depending on your choice of Profunctor.

sets :: ((a -> b) -> s -> t) -> Setter s t a b

setting :: ((a -> b) -> s -> t) -> IndexPreservingSetter s t a b #

Build an index-preserving Setter from a map-like function.

Your supplied function f is required to satisfy:

f id ≡ id
f g . f h ≡ f (g . h)

Equational reasoning:

setting . over ≡ id
over . setting ≡ id

Another way to view sets is that it takes a "semantic editor combinator" and transforms it into a Setter.

setting :: ((a -> b) -> s -> t) -> Setter s t a b

argument :: Profunctor p => Setter (p b r) (p a r) a b #

This Setter can be used to map over the input of a Profunctor.

The most common Profunctor to use this with is (->).

>>> (argument %~ f) g x
g (f x)

>>> (argument %~ show) length [1,2,3]
7

>>> (argument %~ f) h x y
h (f x) y

Map over the argument of the result of a function -- i.e., its second argument:

>>> (mapped.argument %~ f) h x y
h x (f y)

argument :: Setter (b -> r) (a -> r) a b

contramapped :: Contravariant f => Setter (f b) (f a) a b #

This Setter can be used to map over all of the inputs to a Contravariant.

contramap ≡ over contramapped

>>> getPredicate (over contramapped (*2) (Predicate even)) 5
True

>>> getOp (over contramapped (*5) (Op show)) 100
"500"

>>> Prelude.map ($ 1) $ over (mapped . _Unwrapping' Op . contramapped) (*12) [(*2),(+1),(^3)]
[24,13,1728]

lifted :: Monad m => Setter (m a) (m b) a b #

This setter can be used to modify all of the values in a Monad.

You sometimes have to use this rather than mapped -- due to temporary insanity Functor was not a superclass of Monad until GHC 7.10.

liftM ≡ over lifted

>>> over lifted f [a,b,c]
[f a,f b,f c]

>>> set lifted b (Just a)
Just b

If you want an IndexPreservingSetter use setting liftM.

mapped :: Functor f => Setter (f a) (f b) a b #

This Setter can be used to map over all of the values in a Functor.

fmap ≡ over mapped
fmapDefault ≡ over traverse
(<$) ≡ set mapped

>>> over mapped f [a,b,c]
[f a,f b,f c]

>>> over mapped (+1) [1,2,3]
[2,3,4]

>>> set mapped x [a,b,c]
[x,x,x]

>>> [[a,b],[c]] & mapped.mapped +~ x
[[a + x,b + x],[c + x]]

>>> over (mapped._2) length [("hello","world"),("leaders","!!!")]
[("hello",5),("leaders",3)]

mapped :: Functor f => Setter (f a) (f b) a b

If you want an IndexPreservingSetter use setting fmap.

type ASetter s t a b = (a -> Identity b) -> s -> Identity t #

Running a Setter instantiates it to a concrete type.

When consuming a setter directly to perform a mapping, you can use this type, but most user code will not need to use this type.

type ASetter' s a = ASetter s s a a #

This is a useful alias for use when consuming a Setter'.

Most user code will never have to use this type.

type ASetter' = Simple ASetter

type AnIndexedSetter i s t a b = Indexed i a (Identity b) -> s -> Identity t #

Running an IndexedSetter instantiates it to a concrete type.

When consuming a setter directly to perform a mapping, you can use this type, but most user code will not need to use this type.

type AnIndexedSetter' i s a = AnIndexedSetter i s s a a #

type AnIndexedSetter' i = Simple (AnIndexedSetter i)

type Setting (p :: Type -> Type -> Type) s t a b = p a (Identity b) -> s -> Identity t #

This is a convenient alias when defining highly polymorphic code that takes both ASetter and AnIndexedSetter as appropriate. If a function takes this it is expecting one of those two things based on context.

type Setting' (p :: Type -> Type -> Type) s a = Setting p s s a a #

This is a convenient alias when defining highly polymorphic code that takes both ASetter' and AnIndexedSetter' as appropriate. If a function takes this it is expecting one of those two things based on context.

type Lens s t a b = forall (f :: Type -> Type). Functor f => (a -> f b) -> s -> f t #

A Lens is actually a lens family as described in http://comonad.com/reader/2012/mirrored-lenses/.

With great power comes great responsibility and a Lens is subject to the three common sense Lens laws:

1) You get back what you put in:

view l (set l v s)  ≡ v

2) Putting back what you got doesn't change anything:

set l (view l s) s  ≡ s

3) Setting twice is the same as setting once:

set l v' (set l v s) ≡ set l v' s

These laws are strong enough that the 4 type parameters of a Lens cannot vary fully independently. For more on how they interact, read the "Why is it a Lens Family?" section of http://comonad.com/reader/2012/mirrored-lenses/.

There are some emergent properties of these laws:

1) set l s must be injective for every s This is a consequence of law #1

2) set l must be surjective, because of law #2, which indicates that it is possible to obtain any v from some s such that set s v = s

3) Given just the first two laws you can prove a weaker form of law #3 where the values v that you are setting match:

set l v (set l v s) ≡ set l v s

Every Lens can be used directly as a Setter or Traversal.

You can also use a Lens for Getting as if it were a Fold or Getter.

Since every Lens is a valid Traversal, the Traversal laws are required of any Lens you create:

l pure ≡ pure
fmap (l f) . l g ≡ getCompose . l (Compose . fmap f . g)

type Lens s t a b = forall f. Functor f => LensLike f s t a b

type Lens' s a = Lens s s a a #

type Lens' = Simple Lens

type IndexedLens i s t a b = forall (f :: Type -> Type) (p :: Type -> Type -> Type). (Indexable i p, Functor f) => p a (f b) -> s -> f t #

Every IndexedLens is a valid Lens and a valid IndexedTraversal.

type IndexedLens' i s a = IndexedLens i s s a a #

type IndexedLens' i = Simple (IndexedLens i)

type IndexPreservingLens s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Functor f) => p a (f b) -> p s (f t) #

An IndexPreservingLens leaves any index it is composed with alone.

type IndexPreservingLens' s a = IndexPreservingLens s s a a #

type IndexPreservingLens' = Simple IndexPreservingLens

type Traversal s t a b = forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t #

A Traversal can be used directly as a Setter or a Fold (but not as a Lens) and provides the ability to both read and update multiple fields, subject to some relatively weak Traversal laws.

These have also been known as multilenses, but they have the signature and spirit of

traverse :: Traversable f => Traversal (f a) (f b) a b

and the more evocative name suggests their application.

Most of the time the Traversal you will want to use is just traverse, but you can also pass any Lens or Iso as a Traversal, and composition of a Traversal (or Lens or Iso) with a Traversal (or Lens or Iso) using (.) forms a valid Traversal.

The laws for a Traversal t follow from the laws for Traversable as stated in "The Essence of the Iterator Pattern".

t pure ≡ pure
fmap (t f) . t g ≡ getCompose . t (Compose . fmap f . g)

One consequence of this requirement is that a Traversal needs to leave the same number of elements as a candidate for subsequent Traversal that it started with. Another testament to the strength of these laws is that the caveat expressed in section 5.5 of the "Essence of the Iterator Pattern" about exotic Traversable instances that traverse the same entry multiple times was actually already ruled out by the second law in that same paper!

type Traversal' s a = Traversal s s a a #

type Traversal' = Simple Traversal

type Traversal1 s t a b = forall (f :: Type -> Type). Apply f => (a -> f b) -> s -> f t #

type Traversal1' s a = Traversal1 s s a a #

type IndexedTraversal i s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Applicative f) => p a (f b) -> s -> f t #

Every IndexedTraversal is a valid Traversal or IndexedFold.

The Indexed constraint is used to allow an IndexedTraversal to be used directly as a Traversal.

The Traversal laws are still required to hold.

In addition, the index i should satisfy the requirement that it stays unchanged even when modifying the value a, otherwise traversals like indices break the Traversal laws.

type IndexedTraversal' i s a = IndexedTraversal i s s a a #

type IndexedTraversal' i = Simple (IndexedTraversal i)

type IndexedTraversal1 i s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Apply f) => p a (f b) -> s -> f t #

type IndexedTraversal1' i s a = IndexedTraversal1 i s s a a #

type IndexPreservingTraversal s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Applicative f) => p a (f b) -> p s (f t) #

An IndexPreservingLens leaves any index it is composed with alone.

type IndexPreservingTraversal' s a = IndexPreservingTraversal s s a a #

type IndexPreservingTraversal' = Simple IndexPreservingTraversal

type IndexPreservingTraversal1 s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Apply f) => p a (f b) -> p s (f t) #

type IndexPreservingTraversal1' s a = IndexPreservingTraversal1 s s a a #

type Setter s t a b = forall (f :: Type -> Type). Settable f => (a -> f b) -> s -> f t #

The only LensLike law that can apply to a Setter l is that

set l y (set l x a) ≡ set l y a

You can't view a Setter in general, so the other two laws are irrelevant.

However, two Functor laws apply to a Setter:

over l id ≡ id
over l f . over l g ≡ over l (f . g)

These can be stated more directly:

l pure ≡ pure
l f . untainted . l g ≡ l (f . untainted . g)

You can compose a Setter with a Lens or a Traversal using (.) from the Prelude and the result is always only a Setter and nothing more.

>>> over traverse f [a,b,c,d]
[f a,f b,f c,f d]

>>> over _1 f (a,b)
(f a,b)

>>> over (traverse._1) f [(a,b),(c,d)]
[(f a,b),(f c,d)]

>>> over both f (a,b)
(f a,f b)

>>> over (traverse.both) f [(a,b),(c,d)]
[(f a,f b),(f c,f d)]

type Setter' s a = Setter s s a a #

A Setter' is just a Setter that doesn't change the types.

These are particularly common when talking about monomorphic containers. e.g.

sets Data.Text.map :: Setter' Text Char

type Setter' = Simple Setter

type IndexedSetter i s t a b = forall (f :: Type -> Type) (p :: Type -> Type -> Type). (Indexable i p, Settable f) => p a (f b) -> s -> f t #

Every IndexedSetter is a valid Setter.

The Setter laws are still required to hold.

type IndexedSetter' i s a = IndexedSetter i s s a a #

type IndexedSetter' i = Simple (IndexedSetter i)

type IndexPreservingSetter s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Settable f) => p a (f b) -> p s (f t) #

An IndexPreservingSetter can be composed with a IndexedSetter, IndexedTraversal or IndexedLens and leaves the index intact, yielding an IndexedSetter.

type IndexPreservingSetter' s a = IndexPreservingSetter s s a a #

type IndexedPreservingSetter' i = Simple IndexedPreservingSetter

type Iso s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Profunctor p, Functor f) => p a (f b) -> p s (f t) #

Isomorphism families can be composed with another Lens using (.) and id.

Since every Iso is both a valid Lens and a valid Prism, the laws for those types imply the following laws for an Iso f:

f . from f ≡ id
from f . f ≡ id

Note: Composition with an Iso is index- and measure- preserving.

type Iso' s a = Iso s s a a #

type Iso' = Simple Iso

type Review t b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Choice p, Bifunctor p, Settable f) => Optic' p f t b #

This is a limited form of a Prism that can only be used for re operations.

Like with a Getter, there are no laws to state for a Review.

You can generate a Review by using unto. You can also use any Prism or Iso directly as a Review.

type AReview t b = Optic' (Tagged :: Type -> Type -> Type) Identity t b #

If you see this in a signature for a function, the function is expecting a Review (in practice, this usually means a Prism).

type Prism s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Choice p, Applicative f) => p a (f b) -> p s (f t) #

A Prism l is a Traversal that can also be turned around with re to obtain a Getter in the opposite direction.

There are two laws that a Prism should satisfy:

First, if I re or review a value with a Prism and then preview or use (^?), I will get it back:

preview l (review l b) ≡ Just b

Second, if you can extract a value a using a Prism l from a value s, then the value s is completely described by l and a:

If preview l s ≡ Just a then review l a ≡ s

These two laws imply that the Traversal laws hold for every Prism and that we traverse at most 1 element:

lengthOf l x <= 1

It may help to think of this as a Iso that can be partial in one direction.

Every Prism is a valid Traversal.

Every Iso is a valid Prism.

For example, you might have a Prism' Integer Natural allows you to always go from a Natural to an Integer, and provide you with tools to check if an Integer is a Natural and/or to edit one if it is.

nat :: Prism' Integer Natural
nat = prism toInteger $ \ i ->
   if i < 0
   then Left i
   else Right (fromInteger i)

Now we can ask if an Integer is a Natural.

>>> 5^?nat
Just 5

>>> (-5)^?nat
Nothing

We can update the ones that are:

>>> (-3,4) & both.nat *~ 2
(-3,8)

And we can then convert from a Natural to an Integer.

>>> 5 ^. re nat -- :: Natural
5

Similarly we can use a Prism to traverse the Left half of an Either:

>>> Left "hello" & _Left %~ length
Left 5

or to construct an Either:

>>> 5^.re _Left
Left 5

such that if you query it with the Prism, you will get your original input back.

>>> 5^.re _Left ^? _Left
Just 5

Another interesting way to think of a Prism is as the categorical dual of a Lens -- a co-Lens, so to speak. This is what permits the construction of outside.

Note: Composition with a Prism is index-preserving.

type Prism' s a = Prism s s a a #

A Simple Prism.

type Equality (s :: k1) (t :: k2) (a :: k1) (b :: k2) = forall k3 (p :: k1 -> k3 -> Type) (f :: k2 -> k3). p a (f b) -> p s (f t) #

A witness that (a ~ s, b ~ t).

Note: Composition with an Equality is index-preserving.

type Equality' (s :: k2) (a :: k2) = Equality s s a a #

A Simple Equality.

type As (a :: k2) = Equality' a a #

Composable asTypeOf. Useful for constraining excess polymorphism, foo . (id :: As Int) . bar.

type Getter s a = forall (f :: Type -> Type). (Contravariant f, Functor f) => (a -> f a) -> s -> f s #

A Getter describes how to retrieve a single value in a way that can be composed with other LensLike constructions.

Unlike a Lens a Getter is read-only. Since a Getter cannot be used to write back there are no Lens laws that can be applied to it. In fact, it is isomorphic to an arbitrary function from (s -> a).

Moreover, a Getter can be used directly as a Fold, since it just ignores the Applicative.

type IndexedGetter i s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Contravariant f, Functor f) => p a (f a) -> s -> f s #

Every IndexedGetter is a valid IndexedFold and can be used for Getting like a Getter.

type IndexPreservingGetter s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Contravariant f, Functor f) => p a (f a) -> p s (f s) #

An IndexPreservingGetter can be used as a Getter, but when composed with an IndexedTraversal, IndexedFold, or IndexedLens yields an IndexedFold, IndexedFold or IndexedGetter respectively.

type Fold s a = forall (f :: Type -> Type). (Contravariant f, Applicative f) => (a -> f a) -> s -> f s #

A Fold describes how to retrieve multiple values in a way that can be composed with other LensLike constructions.

A Fold s a provides a structure with operations very similar to those of the Foldable typeclass, see foldMapOf and the other Fold combinators.

By convention, if there exists a foo method that expects a Foldable (f a), then there should be a fooOf method that takes a Fold s a and a value of type s.

A Getter is a legal Fold that just ignores the supplied Monoid.

Unlike a Traversal a Fold is read-only. Since a Fold cannot be used to write back there are no Lens laws that apply.

type IndexedFold i s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Contravariant f, Applicative f) => p a (f a) -> s -> f s #

Every IndexedFold is a valid Fold and can be used for Getting.

type IndexPreservingFold s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Contravariant f, Applicative f) => p a (f a) -> p s (f s) #

An IndexPreservingFold can be used as a Fold, but when composed with an IndexedTraversal, IndexedFold, or IndexedLens yields an IndexedFold respectively.

type Fold1 s a = forall (f :: Type -> Type). (Contravariant f, Apply f) => (a -> f a) -> s -> f s #

A relevant Fold (aka Fold1) has one or more targets.

type IndexedFold1 i s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Contravariant f, Apply f) => p a (f a) -> s -> f s #

type IndexPreservingFold1 s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Contravariant f, Apply f) => p a (f a) -> p s (f s) #

type Simple (f :: k -> k -> k1 -> k1 -> k2) (s :: k) (a :: k1) = f s s a a #

A Simple Lens, Simple Traversal, ... can be used instead of a Lens,Traversal, ... whenever the type variables don't change upon setting a value.

_imagPart :: Simple Lens (Complex a) a
traversed :: Simple (IndexedTraversal Int) [a] a

Note: To use this alias in your own code with LensLike f or Setter, you may have to turn on LiberalTypeSynonyms.

This is commonly abbreviated as a "prime" marker, e.g. Lens' = Simple Lens.

type Optic (p :: k1 -> k -> Type) (f :: k2 -> k) (s :: k1) (t :: k2) (a :: k1) (b :: k2) = p a (f b) -> p s (f t) #

A valid Optic l should satisfy the laws:

l pure ≡ pure
l (Procompose f g) = Procompose (l f) (l g)

This gives rise to the laws for Equality, Iso, Prism, Lens, Traversal, Traversal1, Setter, Fold, Fold1, and Getter as well along with their index-preserving variants.

type LensLike f s t a b = Optic (->) f s t a b

type Optic' (p :: k1 -> k -> Type) (f :: k1 -> k) (s :: k1) (a :: k1) = Optic p f s s a a #

type Optic' p f s a = Simple (Optic p f) s a

type Optical (p :: k2 -> k -> Type) (q :: k1 -> k -> Type) (f :: k3 -> k) (s :: k1) (t :: k3) (a :: k2) (b :: k3) = p a (f b) -> q s (f t) #

type LensLike f s t a b = Optical (->) (->) f s t a b

type Over p f s t a b = Optical p (->) f s t a b

type Optic p f s t a b = Optical p p f s t a b

type Optical' (p :: k1 -> k -> Type) (q :: k1 -> k -> Type) (f :: k1 -> k) (s :: k1) (a :: k1) = Optical p q f s s a a #

type Optical' p q f s a = Simple (Optical p q f) s a

type LensLike (f :: k -> Type) s (t :: k) a (b :: k) = (a -> f b) -> s -> f t #

Many combinators that accept a Lens can also accept a Traversal in limited situations.

They do so by specializing the type of Functor that they require of the caller.

If a function accepts a LensLike f s t a b for some Functor f, then they may be passed a Lens.

Further, if f is an Applicative, they may also be passed a Traversal.

type LensLike' (f :: Type -> Type) s a = LensLike f s s a a #

type LensLike' f = Simple (LensLike f)

type IndexedLensLike i (f :: k -> Type) s (t :: k) a (b :: k) = forall (p :: Type -> Type -> Type). Indexable i p => p a (f b) -> s -> f t #

Convenient alias for constructing indexed lenses and their ilk.

type IndexedLensLike' i (f :: Type -> Type) s a = IndexedLensLike i f s s a a #

Convenient alias for constructing simple indexed lenses and their ilk.

type Over (p :: k -> Type -> Type) (f :: k1 -> Type) s (t :: k1) (a :: k) (b :: k1) = p a (f b) -> s -> f t #

This is a convenient alias for use when you need to consume either indexed or non-indexed lens-likes based on context.

type Over' (p :: Type -> Type -> Type) (f :: Type -> Type) s a = Over p f s s a a #

This is a convenient alias for use when you need to consume either indexed or non-indexed lens-likes based on context.

type Over' p f = Simple (Over p f)

class (Applicative f, Distributive f, Traversable f) => Settable (f :: Type -> Type) #

Anything Settable must be isomorphic to the Identity Functor.

Minimal complete definition

untainted

Instances

Settable Identity	So you can pass our `Setter` into combinators from other lens libraries.
Instance details Defined in Control.Lens.Internal.Setter Methods untainted :: Identity a -> a # untaintedDot :: Profunctor p => p a (Identity b) -> p a b # taintedDot :: Profunctor p => p a b -> p a (Identity b) #
Settable f => Settable (Backwards f)	`backwards`
Instance details Defined in Control.Lens.Internal.Setter Methods untainted :: Backwards f a -> a # untaintedDot :: Profunctor p => p a (Backwards f b) -> p a b # taintedDot :: Profunctor p => p a b -> p a (Backwards f b) #
(Settable f, Settable g) => Settable (Compose f g)
Instance details Defined in Control.Lens.Internal.Setter Methods untainted :: Compose f g a -> a # untaintedDot :: Profunctor p => p a (Compose f g b) -> p a b # taintedDot :: Profunctor p => p a b -> p a (Compose f g b) #

retagged :: (Profunctor p, Bifunctor p) => p a b -> p s b #

This is a profunctor used internally to implement Review

It plays a role similar to that of Accessor or Const do for Control.Lens.Getter

class (Profunctor p, Bifunctor p) => Reviewable (p :: Type -> Type -> Type) #

This class is provided mostly for backwards compatibility with lens 3.8, but it can also shorten type signatures.

Instances

(Profunctor p, Bifunctor p) => Reviewable p
Instance details Defined in Control.Lens.Internal.Review

data Magma i t b a #

This provides a way to peek at the internal structure of a Traversal or IndexedTraversal

Instances

FunctorWithIndex i (Magma i t b)
Instance details Defined in Control.Lens.Indexed Methods imap :: (i -> a -> b0) -> Magma i t b a -> Magma i t b b0 # imapped :: IndexedSetter i (Magma i t b a) (Magma i t b b0) a b0 #
FoldableWithIndex i (Magma i t b)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (i -> a -> m) -> Magma i t b a -> m # ifolded :: IndexedFold i (Magma i t b a) a # ifoldr :: (i -> a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # ifoldl :: (i -> b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 # ifoldr' :: (i -> a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # ifoldl' :: (i -> b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 #
TraversableWithIndex i (Magma i t b)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (i -> a -> f b0) -> Magma i t b a -> f (Magma i t b b0) # itraversed :: IndexedTraversal i (Magma i t b a) (Magma i t b b0) a b0 #
Functor (Magma i t b)
Instance details Defined in Control.Lens.Internal.Magma Methods fmap :: (a -> b0) -> Magma i t b a -> Magma i t b b0 # (<$) :: a -> Magma i t b b0 -> Magma i t b a #
Foldable (Magma i t b)
Instance details Defined in Control.Lens.Internal.Magma Methods fold :: Monoid m => Magma i t b m -> m # foldMap :: Monoid m => (a -> m) -> Magma i t b a -> m # foldr :: (a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # foldr' :: (a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # foldl :: (b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 # foldl' :: (b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 # foldr1 :: (a -> a -> a) -> Magma i t b a -> a # foldl1 :: (a -> a -> a) -> Magma i t b a -> a # toList :: Magma i t b a -> [a] # null :: Magma i t b a -> Bool # length :: Magma i t b a -> Int # elem :: Eq a => a -> Magma i t b a -> Bool # maximum :: Ord a => Magma i t b a -> a # minimum :: Ord a => Magma i t b a -> a # sum :: Num a => Magma i t b a -> a # product :: Num a => Magma i t b a -> a #
Traversable (Magma i t b)
Instance details Defined in Control.Lens.Internal.Magma Methods traverse :: Applicative f => (a -> f b0) -> Magma i t b a -> f (Magma i t b b0) # sequenceA :: Applicative f => Magma i t b (f a) -> f (Magma i t b a) # mapM :: Monad m => (a -> m b0) -> Magma i t b a -> m (Magma i t b b0) # sequence :: Monad m => Magma i t b (m a) -> m (Magma i t b a) #
(Show i, Show a) => Show (Magma i t b a)
Instance details Defined in Control.Lens.Internal.Magma Methods showsPrec :: Int -> Magma i t b a -> ShowS # show :: Magma i t b a -> String # showList :: [Magma i t b a] -> ShowS #

data Level i a #

This data type represents a path-compressed copy of one level of a source data structure. We can safely use path-compression because we know the depth of the tree.

Path compression is performed by viewing a Level as a PATRICIA trie of the paths into the structure to leaves at a given depth, similar in many ways to a IntMap, but unlike a regular PATRICIA trie we do not need to store the mask bits merely the depth of the fork.

One invariant of this structure is that underneath a Two node you will not find any Zero nodes, so Zero can only occur at the root.

Instances

FunctorWithIndex i (Level i)
Instance details Defined in Control.Lens.Indexed Methods imap :: (i -> a -> b) -> Level i a -> Level i b # imapped :: IndexedSetter i (Level i a) (Level i b) a b #
FoldableWithIndex i (Level i)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (i -> a -> m) -> Level i a -> m # ifolded :: IndexedFold i (Level i a) a # ifoldr :: (i -> a -> b -> b) -> b -> Level i a -> b # ifoldl :: (i -> b -> a -> b) -> b -> Level i a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> Level i a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> Level i a -> b #
TraversableWithIndex i (Level i)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (i -> a -> f b) -> Level i a -> f (Level i b) # itraversed :: IndexedTraversal i (Level i a) (Level i b) a b #
Functor (Level i)
Instance details Defined in Control.Lens.Internal.Level Methods fmap :: (a -> b) -> Level i a -> Level i b # (<$) :: a -> Level i b -> Level i a #
Foldable (Level i)
Instance details Defined in Control.Lens.Internal.Level Methods fold :: Monoid m => Level i m -> m # foldMap :: Monoid m => (a -> m) -> Level i a -> m # foldr :: (a -> b -> b) -> b -> Level i a -> b # foldr' :: (a -> b -> b) -> b -> Level i a -> b # foldl :: (b -> a -> b) -> b -> Level i a -> b # foldl' :: (b -> a -> b) -> b -> Level i a -> b # foldr1 :: (a -> a -> a) -> Level i a -> a # foldl1 :: (a -> a -> a) -> Level i a -> a # toList :: Level i a -> [a] # null :: Level i a -> Bool # length :: Level i a -> Int # elem :: Eq a => a -> Level i a -> Bool # maximum :: Ord a => Level i a -> a # minimum :: Ord a => Level i a -> a # sum :: Num a => Level i a -> a # product :: Num a => Level i a -> a #
Traversable (Level i)
Instance details Defined in Control.Lens.Internal.Level Methods traverse :: Applicative f => (a -> f b) -> Level i a -> f (Level i b) # sequenceA :: Applicative f => Level i (f a) -> f (Level i a) # mapM :: Monad m => (a -> m b) -> Level i a -> m (Level i b) # sequence :: Monad m => Level i (m a) -> m (Level i a) #
(Eq i, Eq a) => Eq (Level i a)
Instance details Defined in Control.Lens.Internal.Level Methods (==) :: Level i a -> Level i a -> Bool # (/=) :: Level i a -> Level i a -> Bool #
(Ord i, Ord a) => Ord (Level i a)
Instance details Defined in Control.Lens.Internal.Level Methods compare :: Level i a -> Level i a -> Ordering # (<) :: Level i a -> Level i a -> Bool # (<=) :: Level i a -> Level i a -> Bool # (>) :: Level i a -> Level i a -> Bool # (>=) :: Level i a -> Level i a -> Bool # max :: Level i a -> Level i a -> Level i a # min :: Level i a -> Level i a -> Level i a #
(Read i, Read a) => Read (Level i a)
Instance details Defined in Control.Lens.Internal.Level Methods readsPrec :: Int -> ReadS (Level i a) # readList :: ReadS [Level i a] # readPrec :: ReadPrec (Level i a) # readListPrec :: ReadPrec [Level i a] #
(Show i, Show a) => Show (Level i a)
Instance details Defined in Control.Lens.Internal.Level Methods showsPrec :: Int -> Level i a -> ShowS # show :: Level i a -> String # showList :: [Level i a] -> ShowS #

class Reversing t where #

This class provides a generalized notion of list reversal extended to other containers.

Methods

reversing :: t -> t #

Instances

Reversing ByteString
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: ByteString -> ByteString #
Reversing ByteString
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: ByteString -> ByteString #
Reversing Text
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Text -> Text #
Reversing Text
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Text -> Text #
Reversing [a]
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: [a] -> [a] #
Reversing (NonEmpty a)
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: NonEmpty a -> NonEmpty a #
Reversing (Seq a)
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Seq a -> Seq a #
Prim a => Reversing (Vector a)
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Vector a -> Vector a #
Storable a => Reversing (Vector a)
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Vector a -> Vector a #
Unbox a => Reversing (Vector a)
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Vector a -> Vector a #
Reversing (Vector a)
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Vector a -> Vector a #

newtype Bazaar (p :: Type -> Type -> Type) a b t #

This is used to characterize a Traversal.

a.k.a. indexed Cartesian store comonad, indexed Kleene store comonad, or an indexed FunList.

http://twanvl.nl/blog/haskell/non-regular1

A Bazaar is like a Traversal that has already been applied to some structure.

Where a Context a b t holds an a and a function from b to t, a Bazaar a b t holds N as and a function from N bs to t, (where N might be infinite).

Mnemonically, a Bazaar holds many stores and you can easily add more.

This is a final encoding of Bazaar.

Constructors

Bazaar
Fields runBazaar :: forall (f :: Type -> Type). Applicative f => p a (f b) -> f t

Instances

Profunctor p => Bizarre p (Bazaar p)
Instance details Defined in Control.Lens.Internal.Bazaar Methods bazaar :: Applicative f => p a (f b) -> Bazaar p a b t -> f t #
Corepresentable p => Sellable p (Bazaar p)
Instance details Defined in Control.Lens.Internal.Bazaar Methods sell :: p a (Bazaar p a b b) #
IndexedFunctor (Bazaar p)
Instance details Defined in Control.Lens.Internal.Bazaar Methods ifmap :: (s -> t) -> Bazaar p a b s -> Bazaar p a b t #
Conjoined p => IndexedComonad (Bazaar p)
Instance details Defined in Control.Lens.Internal.Bazaar Methods iextract :: Bazaar p a a t -> t # iduplicate :: Bazaar p a c t -> Bazaar p a b (Bazaar p b c t) # iextend :: (Bazaar p b c t -> r) -> Bazaar p a c t -> Bazaar p a b r #
Functor (Bazaar p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods fmap :: (a0 -> b0) -> Bazaar p a b a0 -> Bazaar p a b b0 # (<$) :: a0 -> Bazaar p a b b0 -> Bazaar p a b a0 #
Applicative (Bazaar p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods pure :: a0 -> Bazaar p a b a0 # (<>) :: Bazaar p a b (a0 -> b0) -> Bazaar p a b a0 -> Bazaar p a b b0 # liftA2 :: (a0 -> b0 -> c) -> Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b c # (>) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b b0 # (<*) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b a0 #
(a ~ b, Conjoined p) => Comonad (Bazaar p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods extract :: Bazaar p a b a0 -> a0 # duplicate :: Bazaar p a b a0 -> Bazaar p a b (Bazaar p a b a0) # extend :: (Bazaar p a b a0 -> b0) -> Bazaar p a b a0 -> Bazaar p a b b0 #
(a ~ b, Conjoined p) => ComonadApply (Bazaar p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods (<@>) :: Bazaar p a b (a0 -> b0) -> Bazaar p a b a0 -> Bazaar p a b b0 # (@>) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b b0 # (<@) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b a0 #
Apply (Bazaar p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods (<.>) :: Bazaar p a b (a0 -> b0) -> Bazaar p a b a0 -> Bazaar p a b b0 # (.>) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b b0 # (<.) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b a0 # liftF2 :: (a0 -> b0 -> c) -> Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b c #

type Bazaar' (p :: Type -> Type -> Type) a = Bazaar p a a #

This alias is helpful when it comes to reducing repetition in type signatures.

type Bazaar' p a t = Bazaar p a a t

newtype Bazaar1 (p :: Type -> Type -> Type) a b t #

This is used to characterize a Traversal.

a.k.a. indexed Cartesian store comonad, indexed Kleene store comonad, or an indexed FunList.

http://twanvl.nl/blog/haskell/non-regular1

A Bazaar1 is like a Traversal that has already been applied to some structure.

Where a Context a b t holds an a and a function from b to t, a Bazaar1 a b t holds N as and a function from N bs to t, (where N might be infinite).

Mnemonically, a Bazaar1 holds many stores and you can easily add more.

This is a final encoding of Bazaar1.

Constructors

Bazaar1
Fields runBazaar1 :: forall (f :: Type -> Type). Apply f => p a (f b) -> f t

Instances

Profunctor p => Bizarre1 p (Bazaar1 p)
Instance details Defined in Control.Lens.Internal.Bazaar Methods bazaar1 :: Apply f => p a (f b) -> Bazaar1 p a b t -> f t #
Corepresentable p => Sellable p (Bazaar1 p)
Instance details Defined in Control.Lens.Internal.Bazaar Methods sell :: p a (Bazaar1 p a b b) #
IndexedFunctor (Bazaar1 p)
Instance details Defined in Control.Lens.Internal.Bazaar Methods ifmap :: (s -> t) -> Bazaar1 p a b s -> Bazaar1 p a b t #
Conjoined p => IndexedComonad (Bazaar1 p)
Instance details Defined in Control.Lens.Internal.Bazaar Methods iextract :: Bazaar1 p a a t -> t # iduplicate :: Bazaar1 p a c t -> Bazaar1 p a b (Bazaar1 p b c t) # iextend :: (Bazaar1 p b c t -> r) -> Bazaar1 p a c t -> Bazaar1 p a b r #
Functor (Bazaar1 p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods fmap :: (a0 -> b0) -> Bazaar1 p a b a0 -> Bazaar1 p a b b0 # (<$) :: a0 -> Bazaar1 p a b b0 -> Bazaar1 p a b a0 #
(a ~ b, Conjoined p) => Comonad (Bazaar1 p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods extract :: Bazaar1 p a b a0 -> a0 # duplicate :: Bazaar1 p a b a0 -> Bazaar1 p a b (Bazaar1 p a b a0) # extend :: (Bazaar1 p a b a0 -> b0) -> Bazaar1 p a b a0 -> Bazaar1 p a b b0 #
(a ~ b, Conjoined p) => ComonadApply (Bazaar1 p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods (<@>) :: Bazaar1 p a b (a0 -> b0) -> Bazaar1 p a b a0 -> Bazaar1 p a b b0 # (@>) :: Bazaar1 p a b a0 -> Bazaar1 p a b b0 -> Bazaar1 p a b b0 # (<@) :: Bazaar1 p a b a0 -> Bazaar1 p a b b0 -> Bazaar1 p a b a0 #
Apply (Bazaar1 p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods (<.>) :: Bazaar1 p a b (a0 -> b0) -> Bazaar1 p a b a0 -> Bazaar1 p a b b0 # (.>) :: Bazaar1 p a b a0 -> Bazaar1 p a b b0 -> Bazaar1 p a b b0 # (<.) :: Bazaar1 p a b a0 -> Bazaar1 p a b b0 -> Bazaar1 p a b a0 # liftF2 :: (a0 -> b0 -> c) -> Bazaar1 p a b a0 -> Bazaar1 p a b b0 -> Bazaar1 p a b c #

type Bazaar1' (p :: Type -> Type -> Type) a = Bazaar1 p a a #

This alias is helpful when it comes to reducing repetition in type signatures.

type Bazaar1' p a t = Bazaar1 p a a t

data Context a b t #

The indexed store can be used to characterize a Lens and is used by cloneLens.

Context a b t is isomorphic to newtype Context a b t = Context { runContext :: forall f. Functor f => (a -> f b) -> f t }, and to exists s. (s, Lens s t a b).

A Context is like a Lens that has already been applied to a some structure.

Constructors

Context (b -> t) a

Instances

IndexedFunctor Context
Instance details Defined in Control.Lens.Internal.Context Methods ifmap :: (s -> t) -> Context a b s -> Context a b t #
IndexedComonad Context
Instance details Defined in Control.Lens.Internal.Context Methods iextract :: Context a a t -> t # iduplicate :: Context a c t -> Context a b (Context b c t) # iextend :: (Context b c t -> r) -> Context a c t -> Context a b r #
IndexedComonadStore Context
Instance details Defined in Control.Lens.Internal.Context Methods ipos :: Context a c t -> a # ipeek :: c -> Context a c t -> t # ipeeks :: (a -> c) -> Context a c t -> t # iseek :: b -> Context a c t -> Context b c t # iseeks :: (a -> b) -> Context a c t -> Context b c t # iexperiment :: Functor f => (b -> f c) -> Context b c t -> f t # context :: Context a b t -> Context a b t #
a ~ b => ComonadStore a (Context a b)
Instance details Defined in Control.Lens.Internal.Context Methods pos :: Context a b a0 -> a # peek :: a -> Context a b a0 -> a0 # peeks :: (a -> a) -> Context a b a0 -> a0 # seek :: a -> Context a b a0 -> Context a b a0 # seeks :: (a -> a) -> Context a b a0 -> Context a b a0 # experiment :: Functor f => (a -> f a) -> Context a b a0 -> f a0 #
Functor (Context a b)
Instance details Defined in Control.Lens.Internal.Context Methods fmap :: (a0 -> b0) -> Context a b a0 -> Context a b b0 # (<$) :: a0 -> Context a b b0 -> Context a b a0 #
a ~ b => Comonad (Context a b)
Instance details Defined in Control.Lens.Internal.Context Methods extract :: Context a b a0 -> a0 # duplicate :: Context a b a0 -> Context a b (Context a b a0) # extend :: (Context a b a0 -> b0) -> Context a b a0 -> Context a b b0 #
Sellable ((->) :: Type -> Type -> Type) Context
Instance details Defined in Control.Lens.Internal.Context Methods sell :: a -> Context a b b #

type Context' a = Context a a #

type Context' a s = Context a a s

asIndex :: (Indexable i p, Contravariant f, Functor f) => p i (f i) -> Indexed i s (f s) #

When composed with an IndexedFold or IndexedTraversal this yields an (Indexed) Fold of the indices.

withIndex :: (Indexable i p, Functor f) => p (i, s) (f (j, t)) -> Indexed i s (f t) #

Fold a container with indices returning both the indices and the values.

The result is only valid to compose in a Traversal, if you don't edit the index as edits to the index have no effect.

>>> [10, 20, 30] ^.. ifolded . withIndex
[(0,10),(1,20),(2,30)]

>>> [10, 20, 30] ^.. ifolded . withIndex . alongside negated (re _Show)
[(0,"10"),(-1,"20"),(-2,"30")]

indexing64 :: Indexable Int64 p => ((a -> Indexing64 f b) -> s -> Indexing64 f t) -> p a (f b) -> s -> f t #

Transform a Traversal into an IndexedTraversal or a Fold into an IndexedFold, etc.

This combinator is like indexing except that it handles large traversals and folds gracefully.

indexing64 :: Traversal s t a b -> IndexedTraversal Int64 s t a b
indexing64 :: Prism s t a b     -> IndexedTraversal Int64 s t a b
indexing64 :: Lens s t a b      -> IndexedLens Int64 s t a b
indexing64 :: Iso s t a b       -> IndexedLens Int64 s t a b
indexing64 :: Fold s a          -> IndexedFold Int64 s a
indexing64 :: Getter s a        -> IndexedGetter Int64 s a

indexing64 :: Indexable Int64 p => LensLike (Indexing64 f) s t a b -> Over p f s t a b

indexing :: Indexable Int p => ((a -> Indexing f b) -> s -> Indexing f t) -> p a (f b) -> s -> f t #

Transform a Traversal into an IndexedTraversal or a Fold into an IndexedFold, etc.

indexing :: Traversal s t a b -> IndexedTraversal Int s t a b
indexing :: Prism s t a b     -> IndexedTraversal Int s t a b
indexing :: Lens s t a b      -> IndexedLens Int  s t a b
indexing :: Iso s t a b       -> IndexedLens Int s t a b
indexing :: Fold s a          -> IndexedFold Int s a
indexing :: Getter s a        -> IndexedGetter Int s a

indexing :: Indexable Int p => LensLike (Indexing f) s t a b -> Over p f s t a b

class (Choice p, Corepresentable p, Comonad (Corep p), Traversable (Corep p), Strong p, Representable p, Monad (Rep p), MonadFix (Rep p), Distributive (Rep p), Costrong p, ArrowLoop p, ArrowApply p, ArrowChoice p, Closed p) => Conjoined (p :: Type -> Type -> Type) where #

This is a Profunctor that is both Corepresentable by f and Representable by g such that f is left adjoint to g. From this you can derive a lot of structure due to the preservation of limits and colimits.

Minimal complete definition

Nothing

Methods

distrib :: Functor f => p a b -> p (f a) (f b) #

Conjoined is strong enough to let us distribute every Conjoined Profunctor over every Haskell Functor. This is effectively a generalization of fmap.

conjoined :: ((p ~ ((->) :: Type -> Type -> Type)) -> q (a -> b) r) -> q (p a b) r -> q (p a b) r #

This permits us to make a decision at an outermost point about whether or not we use an index.

Ideally any use of this function should be done in such a way so that you compute the same answer, but this cannot be enforced at the type level.

Instances

Conjoined ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods distrib :: Functor f => ReifiedGetter a b -> ReifiedGetter (f a) (f b) # conjoined :: ((ReifiedGetter ~ (->)) -> q (a -> b) r) -> q (ReifiedGetter a b) r -> q (ReifiedGetter a b) r #
Conjoined (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods distrib :: Functor f => Indexed i a b -> Indexed i (f a) (f b) # conjoined :: ((Indexed i ~ (->)) -> q (a -> b) r) -> q (Indexed i a b) r -> q (Indexed i a b) r #
Conjoined ((->) :: Type -> Type -> Type)
Instance details Defined in Control.Lens.Internal.Indexed Methods distrib :: Functor f => (a -> b) -> f a -> f b # conjoined :: (((->) ~ (->)) -> q (a -> b) r) -> q (a -> b) r -> q (a -> b) r #

class Conjoined p => Indexable i (p :: Type -> Type -> Type) where #

This class permits overloading of function application for things that also admit a notion of a key or index.

Methods

indexed :: p a b -> i -> a -> b #

Build a function from an indexed function.

Instances

i ~ j => Indexable i (Indexed j)
Instance details Defined in Control.Lens.Internal.Indexed Methods indexed :: Indexed j a b -> i -> a -> b #
Indexable i ((->) :: Type -> Type -> Type)
Instance details Defined in Control.Lens.Internal.Indexed Methods indexed :: (a -> b) -> i -> a -> b #

newtype Indexed i a b #

A function with access to a index. This constructor may be useful when you need to store an Indexable in a container to avoid ImpredicativeTypes.

index :: Indexed i a b -> i -> a -> b

Constructors

Indexed
Fields runIndexed :: i -> a -> b

Instances

i ~ j => Indexable i (Indexed j)
Instance details Defined in Control.Lens.Internal.Indexed Methods indexed :: Indexed j a b -> i -> a -> b #
Arrow (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods arr :: (b -> c) -> Indexed i b c # first :: Indexed i b c -> Indexed i (b, d) (c, d) # second :: Indexed i b c -> Indexed i (d, b) (d, c) # (***) :: Indexed i b c -> Indexed i b' c' -> Indexed i (b, b') (c, c') # (&&&) :: Indexed i b c -> Indexed i b c' -> Indexed i b (c, c') #
ArrowChoice (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods left :: Indexed i b c -> Indexed i (Either b d) (Either c d) # right :: Indexed i b c -> Indexed i (Either d b) (Either d c) # (+++) :: Indexed i b c -> Indexed i b' c' -> Indexed i (Either b b') (Either c c') # (\|\|\|) :: Indexed i b d -> Indexed i c d -> Indexed i (Either b c) d #
ArrowApply (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods app :: Indexed i (Indexed i b c, b) c #
ArrowLoop (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods loop :: Indexed i (b, d) (c, d) -> Indexed i b c #
Profunctor (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods dimap :: (a -> b) -> (c -> d) -> Indexed i b c -> Indexed i a d # lmap :: (a -> b) -> Indexed i b c -> Indexed i a c # rmap :: (b -> c) -> Indexed i a b -> Indexed i a c # (#.) :: Coercible c b => q b c -> Indexed i a b -> Indexed i a c # (.#) :: Coercible b a => Indexed i b c -> q a b -> Indexed i a c #
Representable (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Associated Types type Rep (Indexed i) :: Type -> Type # Methods tabulate :: (d -> Rep (Indexed i) c) -> Indexed i d c #
Corepresentable (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Associated Types type Corep (Indexed i) :: Type -> Type # Methods cotabulate :: (Corep (Indexed i) d -> c) -> Indexed i d c #
Conjoined (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods distrib :: Functor f => Indexed i a b -> Indexed i (f a) (f b) # conjoined :: ((Indexed i ~ (->)) -> q (a -> b) r) -> q (Indexed i a b) r -> q (Indexed i a b) r #
Choice (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods left' :: Indexed i a b -> Indexed i (Either a c) (Either b c) # right' :: Indexed i a b -> Indexed i (Either c a) (Either c b) #
Closed (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods closed :: Indexed i a b -> Indexed i (x -> a) (x -> b) #
Strong (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods first' :: Indexed i a b -> Indexed i (a, c) (b, c) # second' :: Indexed i a b -> Indexed i (c, a) (c, b) #
Costrong (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods unfirst :: Indexed i (a, d) (b, d) -> Indexed i a b # unsecond :: Indexed i (d, a) (d, b) -> Indexed i a b #
Bizarre (Indexed Int) Mafic
Instance details Defined in Control.Lens.Internal.Magma Methods bazaar :: Applicative f => Indexed Int a (f b) -> Mafic a b t -> f t #
Category (Indexed i :: Type -> Type -> Type)
Instance details Defined in Control.Lens.Internal.Indexed Methods id :: Indexed i a a # (.) :: Indexed i b c -> Indexed i a b -> Indexed i a c #
Bizarre (Indexed i) (Molten i)
Instance details Defined in Control.Lens.Internal.Magma Methods bazaar :: Applicative f => Indexed i a (f b) -> Molten i a b t -> f t #
Sellable (Indexed i) (Molten i)
Instance details Defined in Control.Lens.Internal.Magma Methods sell :: Indexed i a (Molten i a b b) #
Cosieve (Indexed i) ((,) i)
Instance details Defined in Control.Lens.Internal.Indexed Methods cosieve :: Indexed i a b -> (i, a) -> b #
Sieve (Indexed i) ((->) i :: Type -> Type)
Instance details Defined in Control.Lens.Internal.Indexed Methods sieve :: Indexed i a b -> a -> i -> b #
Monad (Indexed i a)
Instance details Defined in Control.Lens.Internal.Indexed Methods (>>=) :: Indexed i a a0 -> (a0 -> Indexed i a b) -> Indexed i a b # (>>) :: Indexed i a a0 -> Indexed i a b -> Indexed i a b # return :: a0 -> Indexed i a a0 # fail :: String -> Indexed i a a0 #
Functor (Indexed i a)
Instance details Defined in Control.Lens.Internal.Indexed Methods fmap :: (a0 -> b) -> Indexed i a a0 -> Indexed i a b # (<$) :: a0 -> Indexed i a b -> Indexed i a a0 #
MonadFix (Indexed i a)
Instance details Defined in Control.Lens.Internal.Indexed Methods mfix :: (a0 -> Indexed i a a0) -> Indexed i a a0 #
Applicative (Indexed i a)
Instance details Defined in Control.Lens.Internal.Indexed Methods pure :: a0 -> Indexed i a a0 # (<>) :: Indexed i a (a0 -> b) -> Indexed i a a0 -> Indexed i a b # liftA2 :: (a0 -> b -> c) -> Indexed i a a0 -> Indexed i a b -> Indexed i a c # (>) :: Indexed i a a0 -> Indexed i a b -> Indexed i a b # (<*) :: Indexed i a a0 -> Indexed i a b -> Indexed i a a0 #
Apply (Indexed i a)
Instance details Defined in Control.Lens.Internal.Indexed Methods (<.>) :: Indexed i a (a0 -> b) -> Indexed i a a0 -> Indexed i a b # (.>) :: Indexed i a a0 -> Indexed i a b -> Indexed i a b # (<.) :: Indexed i a a0 -> Indexed i a b -> Indexed i a a0 # liftF2 :: (a0 -> b -> c) -> Indexed i a a0 -> Indexed i a b -> Indexed i a c #
Bind (Indexed i a)
Instance details Defined in Control.Lens.Internal.Indexed Methods (>>-) :: Indexed i a a0 -> (a0 -> Indexed i a b) -> Indexed i a b # join :: Indexed i a (Indexed i a a0) -> Indexed i a a0 #
type Rep (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed type Rep (Indexed i) = ((->) i :: Type -> Type)
type Corep (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed type Corep (Indexed i) = (,) i

data Traversed a (f :: Type -> Type) #

Used internally by traverseOf_ and the like.

The argument a of the result should not be used!

Instances

Applicative f => Semigroup (Traversed a f)
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: Traversed a f -> Traversed a f -> Traversed a f # sconcat :: NonEmpty (Traversed a f) -> Traversed a f # stimes :: Integral b => b -> Traversed a f -> Traversed a f #
Applicative f => Monoid (Traversed a f)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Traversed a f # mappend :: Traversed a f -> Traversed a f -> Traversed a f # mconcat :: [Traversed a f] -> Traversed a f #

data Sequenced a (m :: Type -> Type) #

Used internally by mapM_ and the like.

The argument a of the result should not be used!

See 4.16 Changelog entry for the explanation of "why not Apply f =>"?

Instances

Monad m => Semigroup (Sequenced a m)
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: Sequenced a m -> Sequenced a m -> Sequenced a m # sconcat :: NonEmpty (Sequenced a m) -> Sequenced a m # stimes :: Integral b => b -> Sequenced a m -> Sequenced a m #
Monad m => Monoid (Sequenced a m)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Sequenced a m # mappend :: Sequenced a m -> Sequenced a m -> Sequenced a m # mconcat :: [Sequenced a m] -> Sequenced a m #

data Leftmost a #

Used for preview.

Instances

Semigroup (Leftmost a)
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: Leftmost a -> Leftmost a -> Leftmost a # sconcat :: NonEmpty (Leftmost a) -> Leftmost a # stimes :: Integral b => b -> Leftmost a -> Leftmost a #
Monoid (Leftmost a)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Leftmost a # mappend :: Leftmost a -> Leftmost a -> Leftmost a # mconcat :: [Leftmost a] -> Leftmost a #

data Rightmost a #

Used for lastOf.

Instances

Semigroup (Rightmost a)
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: Rightmost a -> Rightmost a -> Rightmost a # sconcat :: NonEmpty (Rightmost a) -> Rightmost a # stimes :: Integral b => b -> Rightmost a -> Rightmost a #
Monoid (Rightmost a)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Rightmost a # mappend :: Rightmost a -> Rightmost a -> Rightmost a # mconcat :: [Rightmost a] -> Rightmost a #

class (Foldable1 t, Traversable t) => Traversable1 (t :: Type -> Type) where #

Minimal complete definition

traverse1 | sequence1

Methods

traverse1 :: Apply f => (a -> f b) -> t a -> f (t b) #

Instances

Traversable1 Par1
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Par1 a -> f (Par1 b) # sequence1 :: Apply f => Par1 (f b) -> f (Par1 b) #
Traversable1 Complex
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Complex a -> f (Complex b) # sequence1 :: Apply f => Complex (f b) -> f (Complex b) #
Traversable1 Min
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Min a -> f (Min b) # sequence1 :: Apply f => Min (f b) -> f (Min b) #
Traversable1 Max
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Max a -> f (Max b) # sequence1 :: Apply f => Max (f b) -> f (Max b) #
Traversable1 First
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> First a -> f (First b) # sequence1 :: Apply f => First (f b) -> f (First b) #
Traversable1 Last
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Last a -> f (Last b) # sequence1 :: Apply f => Last (f b) -> f (Last b) #
Traversable1 Identity
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Identity a -> f (Identity b) # sequence1 :: Apply f => Identity (f b) -> f (Identity b) #
Traversable1 Dual
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Dual a -> f (Dual b) # sequence1 :: Apply f => Dual (f b) -> f (Dual b) #
Traversable1 Sum
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Sum a -> f (Sum b) # sequence1 :: Apply f => Sum (f b) -> f (Sum b) #
Traversable1 Product
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Product a -> f (Product b) # sequence1 :: Apply f => Product (f b) -> f (Product b) #
Traversable1 NonEmpty
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) # sequence1 :: Apply f => NonEmpty (f b) -> f (NonEmpty b) #
Traversable1 Tree
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Tree a -> f (Tree b) # sequence1 :: Apply f => Tree (f b) -> f (Tree b) #
Traversable1 (V1 :: Type -> Type)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> V1 a -> f (V1 b) # sequence1 :: Apply f => V1 (f b) -> f (V1 b) #
Traversable1 ((,) a)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a0 -> f b) -> (a, a0) -> f (a, b) # sequence1 :: Apply f => (a, f b) -> f (a, b) #
Traversable1 f => Traversable1 (Cofree f)
Instance details Defined in Control.Comonad.Cofree Methods traverse1 :: Apply f0 => (a -> f0 b) -> Cofree f a -> f0 (Cofree f b) # sequence1 :: Apply f0 => Cofree f (f0 b) -> f0 (Cofree f b) #
Traversable1 f => Traversable1 (Free f)
Instance details Defined in Control.Monad.Free Methods traverse1 :: Apply f0 => (a -> f0 b) -> Free f a -> f0 (Free f b) # sequence1 :: Apply f0 => Free f (f0 b) -> f0 (Free f b) #
(Monad m, Traversable1 m) => Traversable1 (IterT m)
Instance details Defined in Control.Monad.Trans.Iter Methods traverse1 :: Apply f => (a -> f b) -> IterT m a -> f (IterT m b) # sequence1 :: Apply f => IterT m (f b) -> f (IterT m b) #
Traversable1 f => Traversable1 (Yoneda f)
Instance details Defined in Data.Functor.Yoneda Methods traverse1 :: Apply f0 => (a -> f0 b) -> Yoneda f a -> f0 (Yoneda f b) # sequence1 :: Apply f0 => Yoneda f (f0 b) -> f0 (Yoneda f b) #
Traversable1 f => Traversable1 (Lift f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Lift f a -> f0 (Lift f b) # sequence1 :: Apply f0 => Lift f (f0 b) -> f0 (Lift f b) #
Traversable1 f => Traversable1 (Rec1 f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Rec1 f a -> f0 (Rec1 f b) # sequence1 :: Apply f0 => Rec1 f (f0 b) -> f0 (Rec1 f b) #
Traversable1 f => Traversable1 (Alt f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Alt f a -> f0 (Alt f b) # sequence1 :: Apply f0 => Alt f (f0 b) -> f0 (Alt f b) #
Bitraversable1 p => Traversable1 (Join p)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Join p a -> f (Join p b) # sequence1 :: Apply f => Join p (f b) -> f (Join p b) #
Traversable1 f => Traversable1 (IdentityT f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> IdentityT f a -> f0 (IdentityT f b) # sequence1 :: Apply f0 => IdentityT f (f0 b) -> f0 (IdentityT f b) #
Traversable1 f => Traversable1 (Backwards f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Backwards f a -> f0 (Backwards f b) # sequence1 :: Apply f0 => Backwards f (f0 b) -> f0 (Backwards f b) #
Traversable1 f => Traversable1 (AlongsideLeft f b)
Instance details Defined in Control.Lens.Internal.Getter Methods traverse1 :: Apply f0 => (a -> f0 b0) -> AlongsideLeft f b a -> f0 (AlongsideLeft f b b0) # sequence1 :: Apply f0 => AlongsideLeft f b (f0 b0) -> f0 (AlongsideLeft f b b0) #
Traversable1 f => Traversable1 (AlongsideRight f a)
Instance details Defined in Control.Lens.Internal.Getter Methods traverse1 :: Apply f0 => (a0 -> f0 b) -> AlongsideRight f a a0 -> f0 (AlongsideRight f a b) # sequence1 :: Apply f0 => AlongsideRight f a (f0 b) -> f0 (AlongsideRight f a b) #
Traversable1 (Tagged a)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a0 -> f b) -> Tagged a a0 -> f (Tagged a b) # sequence1 :: Apply f => Tagged a (f b) -> f (Tagged a b) #
Traversable1 f => Traversable1 (Reverse f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Reverse f a -> f0 (Reverse f b) # sequence1 :: Apply f0 => Reverse f (f0 b) -> f0 (Reverse f b) #
(Traversable1 f, Traversable1 g) => Traversable1 (f :+: g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) # sequence1 :: Apply f0 => (f :+: g) (f0 b) -> f0 ((f :+: g) b) #
(Traversable1 f, Traversable1 g) => Traversable1 (f :*: g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> (f :: g) a -> f0 ((f :: g) b) # sequence1 :: Apply f0 => (f :: g) (f0 b) -> f0 ((f :: g) b) #
(Traversable1 f, Traversable1 g) => Traversable1 (Product f g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Product f g a -> f0 (Product f g b) # sequence1 :: Apply f0 => Product f g (f0 b) -> f0 (Product f g b) #
(Traversable1 f, Traversable1 g) => Traversable1 (Sum f g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Sum f g a -> f0 (Sum f g b) # sequence1 :: Apply f0 => Sum f g (f0 b) -> f0 (Sum f g b) #
Traversable1 f => Traversable1 (M1 i c f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> M1 i c f a -> f0 (M1 i c f b) # sequence1 :: Apply f0 => M1 i c f (f0 b) -> f0 (M1 i c f b) #
(Traversable1 f, Traversable1 g) => Traversable1 (f :.: g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) # sequence1 :: Apply f0 => (f :.: g) (f0 b) -> f0 ((f :.: g) b) #
(Traversable1 f, Traversable1 g) => Traversable1 (Compose f g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Compose f g a -> f0 (Compose f g b) # sequence1 :: Apply f0 => Compose f g (f0 b) -> f0 (Compose f g b) #
Traversable1 g => Traversable1 (Joker g a)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a0 -> f b) -> Joker g a a0 -> f (Joker g a b) # sequence1 :: Apply f => Joker g a (f b) -> f (Joker g a b) #

foldBy :: Foldable t => (a -> a -> a) -> a -> t a -> a #

Fold a value using its Foldable instance using explicitly provided Monoid operations. This is like fold where the Monoid instance can be manually specified.

foldBy mappend mempty ≡ fold

>>> foldBy (++) [] ["hello","world"]
"helloworld"

foldMapBy :: Foldable t => (r -> r -> r) -> r -> (a -> r) -> t a -> r #

Fold a value using its Foldable instance using explicitly provided Monoid operations. This is like foldMap where the Monoid instance can be manually specified.

foldMapBy mappend mempty ≡ foldMap

>>> foldMapBy (+) 0 length ["hello","world"]
10

traverseBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (a -> f b) -> t a -> f (t b) #

Traverse a container using its Traversable instance using explicitly provided Applicative operations. This is like traverse where the Applicative instance can be manually specified.

sequenceBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> t (f a) -> f (t a) #

Sequence a container using its Traversable instance using explicitly provided Applicative operations. This is like sequence where the Applicative instance can be manually specified.

class Profunctor p => Choice (p :: Type -> Type -> Type) where #

The generalization of Costar of Functor that is strong with respect to Either.

Note: This is also a notion of strength, except with regards to another monoidal structure that we can choose to equip Hask with: the cocartesian coproduct.

Minimal complete definition

left' | right'

Methods

left' :: p a b -> p (Either a c) (Either b c) #

Laws:

left' ≡ dimap swapE swapE . right' where
  swapE :: Either a b -> Either b a
  swapE = either Right Left
rmap Left ≡ lmap Left . left'
lmap (right f) . left' ≡ rmap (right f) . left'
left' . left' ≡ dimap assocE unassocE . left' where
  assocE :: Either (Either a b) c -> Either a (Either b c)
  assocE (Left (Left a)) = Left a
  assocE (Left (Right b)) = Right (Left b)
  assocE (Right c) = Right (Right c)
  unassocE :: Either a (Either b c) -> Either (Either a b) c
  unassocE (Left a) = Left (Left a)
  unassocE (Right (Left b) = Left (Right b)
  unassocE (Right (Right c)) = Right c)

right' :: p a b -> p (Either c a) (Either c b) #

Laws:

right' ≡ dimap swapE swapE . left' where
  swapE :: Either a b -> Either b a
  swapE = either Right Left
rmap Right ≡ lmap Right . right'
lmap (left f) . right' ≡ rmap (left f) . right'
right' . right' ≡ dimap unassocE assocE . right' where
  assocE :: Either (Either a b) c -> Either a (Either b c)
  assocE (Left (Left a)) = Left a
  assocE (Left (Right b)) = Right (Left b)
  assocE (Right c) = Right (Right c)
  unassocE :: Either a (Either b c) -> Either (Either a b) c
  unassocE (Left a) = Left (Left a)
  unassocE (Right (Left b) = Left (Right b)
  unassocE (Right (Right c)) = Right c)

Instances

Choice ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods left' :: ReifiedGetter a b -> ReifiedGetter (Either a c) (Either b c) # right' :: ReifiedGetter a b -> ReifiedGetter (Either c a) (Either c b) #
Choice ReifiedFold
Instance details Defined in Control.Lens.Reified Methods left' :: ReifiedFold a b -> ReifiedFold (Either a c) (Either b c) # right' :: ReifiedFold a b -> ReifiedFold (Either c a) (Either c b) #
Monad m => Choice (Kleisli m)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Kleisli m a b -> Kleisli m (Either a c) (Either b c) # right' :: Kleisli m a b -> Kleisli m (Either c a) (Either c b) #
Choice (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods left' :: Indexed i a b -> Indexed i (Either a c) (Either b c) # right' :: Indexed i a b -> Indexed i (Either c a) (Either c b) #
Profunctor p => Choice (TambaraSum p)
Instance details Defined in Data.Profunctor.Choice Methods left' :: TambaraSum p a b -> TambaraSum p (Either a c) (Either b c) # right' :: TambaraSum p a b -> TambaraSum p (Either c a) (Either c b) #
Choice (PastroSum p)
Instance details Defined in Data.Profunctor.Choice Methods left' :: PastroSum p a b -> PastroSum p (Either a c) (Either b c) # right' :: PastroSum p a b -> PastroSum p (Either c a) (Either c b) #
Choice p => Choice (Tambara p)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Tambara p a b -> Tambara p (Either a c) (Either b c) # right' :: Tambara p a b -> Tambara p (Either c a) (Either c b) #
Applicative f => Choice (Star f)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Star f a b -> Star f (Either a c) (Either b c) # right' :: Star f a b -> Star f (Either c a) (Either c b) #
Traversable w => Choice (Costar w)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Costar w a b -> Costar w (Either a c) (Either b c) # right' :: Costar w a b -> Costar w (Either c a) (Either c b) #
ArrowChoice p => Choice (WrappedArrow p)
Instance details Defined in Data.Profunctor.Choice Methods left' :: WrappedArrow p a b -> WrappedArrow p (Either a c) (Either b c) # right' :: WrappedArrow p a b -> WrappedArrow p (Either c a) (Either c b) #
Monoid r => Choice (Forget r)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Forget r a b -> Forget r (Either a c) (Either b c) # right' :: Forget r a b -> Forget r (Either c a) (Either c b) #
Choice (Tagged :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Tagged a b -> Tagged (Either a c) (Either b c) # right' :: Tagged a b -> Tagged (Either c a) (Either c b) #
Choice ((->) :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Choice Methods left' :: (a -> b) -> Either a c -> Either b c # right' :: (a -> b) -> Either c a -> Either c b #
Comonad w => Choice (Cokleisli w)	`extract` approximates `costrength`
Instance details Defined in Data.Profunctor.Choice Methods left' :: Cokleisli w a b -> Cokleisli w (Either a c) (Either b c) # right' :: Cokleisli w a b -> Cokleisli w (Either c a) (Either c b) #
Choice (Market a b)
Instance details Defined in Control.Lens.Internal.Prism Methods left' :: Market a b a0 b0 -> Market a b (Either a0 c) (Either b0 c) # right' :: Market a b a0 b0 -> Market a b (Either c a0) (Either c b0) #
(Functor f, Choice p) => Choice (Cayley f p)
Instance details Defined in Data.Profunctor.Cayley Methods left' :: Cayley f p a b -> Cayley f p (Either a c) (Either b c) # right' :: Cayley f p a b -> Cayley f p (Either c a) (Either c b) #
(Choice p, Choice q) => Choice (Procompose p q)
Instance details Defined in Data.Profunctor.Composition Methods left' :: Procompose p q a b -> Procompose p q (Either a c) (Either b c) # right' :: Procompose p q a b -> Procompose p q (Either c a) (Either c b) #
Functor f => Choice (Joker f :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Joker f a b -> Joker f (Either a c) (Either b c) # right' :: Joker f a b -> Joker f (Either c a) (Either c b) #
(Choice p, Choice q) => Choice (Product p q)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Product p q a b -> Product p q (Either a c) (Either b c) # right' :: Product p q a b -> Product p q (Either c a) (Either c b) #
(Functor f, Choice p) => Choice (Tannen f p)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Tannen f p a b -> Tannen f p (Either a c) (Either b c) # right' :: Tannen f p a b -> Tannen f p (Either c a) (Either c b) #

type NestedIxedCtx a = (NestedCtx a, Ixed a, Ixed (IxValue a)) Source #

type NestedAtCtx a = (NestedCtx a, At a, At (IxValue a)) Source #

type NestedCtx a = (Index a ~ Index (IxValue a), IxValue a ~ IxValue (IxValue a)) Source #

nestedAt :: (NestedAtCtx a, Mempty (IxValue a)) => NonEmpty (Index a) -> Lens' a (Maybe (IxValue a)) Source #

nestedDefAt :: NestedAtCtx a => IxValue a -> NonEmpty (Index a) -> Lens' a (Maybe (IxValue a)) Source #

nestedAt' :: (NestedAtCtx a, Mempty (IxValue a)) => NonEmpty (Index a) -> Lens' a (IxValue a) Source #

nestedIx :: NestedIxedCtx a => NonEmpty (Index a) -> Traversal' a (IxValue a) Source #

emptyMap :: Prism' (Map k a) () Source #

subMapAt :: (Functor f, Ord p) => p -> (Maybe a -> f (Maybe a)) -> Maybe (Map p a) -> f (Maybe (Map p a)) Source #

at' :: (Functor f, Ord p) => p -> (Maybe a -> f (Maybe a)) -> Maybe (Map p a) -> f (Maybe (Map p a)) Source #

unsafeLensedMapAt :: (Ord k, Default v) => k -> Lens' v a -> Lens' (Map k v) (Maybe a) Source #

Warning! This function does not hold lens laws: deleting and re-adding a key destroys everything appart of a, so `set l (Just x) (set l Nothing s) /= set l (Just x) s`

makeLenses' :: Name -> DecsQ Source #

makeLenses :: Name -> DecsQ Source #

makeClassy' :: Name -> DecsQ Source #

makeClassy :: Name -> DecsQ Source #

wrapped' :: (Wrapped s, Profunctor p, Functor f) => p (Unwrapped s) (f (Unwrapped s)) -> p s (f s) Source #

unwrapped' :: (Wrapped s, Profunctor p, Functor f) => p s (f s) -> p (Unwrapped s) (f (Unwrapped s)) Source #

wrapping' :: (Wrapped s, Profunctor p, Functor f) => (Unwrapped s -> s) -> p (Unwrapped s) (f (Unwrapped s)) -> p s (f s) Source #

unwrapping' :: (Wrapped s, Profunctor p, Functor f) => (Unwrapped s -> s) -> p s (f s) -> p (Unwrapped s) (f (Unwrapped s)) Source #

unwrap' :: (MonadReader s m, Wrapped s) => m (Unwrapped s) Source #

wrap' :: (MonadReader (Unwrapped s) m, Wrapped s) => m s Source #

wrapped :: (Rewrapped s t, Rewrapped t s, Profunctor p, Functor f) => p (Unwrapped s) (f (Unwrapped t)) -> p s (f t) Source #

unwrapped :: (Rewrapped s t, Rewrapped t s, Profunctor p, Functor f) => p t (f s) -> p (Unwrapped t) (f (Unwrapped s)) Source #

wrapping :: (Rewrapped s t, Rewrapped t s, Profunctor p, Functor f) => (Unwrapped s -> s) -> p (Unwrapped s) (f (Unwrapped t)) -> p s (f t) Source #

unwrapping :: (Rewrapped s t, Rewrapped t s, Profunctor p, Functor f) => (Unwrapped s -> s) -> p t (f s) -> p (Unwrapped t) (f (Unwrapped s)) Source #

_unwrap :: (MonadReader s m, Rewrapped s s) => m (Unwrapped s) Source #

_wrap :: (MonadReader (Unwrapped t) m, Rewrapped t t) => m t Source #

rewrap :: (Rewrapped s t, Rewrapped t s, Unwrapped t ~# Unwrapped s) => s -> t Source #

wrappedM' :: (Functor f, Wrapped b, Wrapped s) => (Unwrapped s -> f (Unwrapped b)) -> s -> f b Source #

wrap :: forall a. Coercible (Unwrapped a) a => Unwrapped a -> a Source #

unwrap :: forall a. Coercible a (Unwrapped a) => a -> Unwrapped a Source #