Data.Functor.Utils

Documentation

type family Applicatives lst :: Constraint where ...

Equations

Applicatives '[] = ()

Applicatives (f ': fs) = (Applicative f, Applicatives fs)

type family Functors lst :: Constraint where ...

Equations

Functors '[] = ()

Functors (f ': fs) = (Functor f, Functors fs)

fmap0 :: (a -> b) -> a -> b

fmap1 :: Functor f => (a -> b) -> f a -> f b

fmap2 :: Functors '[f1, f2] => (a -> b) -> f2 (f1 a) -> f2 (f1 b)

fmap3 :: Functors '[f1, f2, f3] => (a -> b) -> f3 (f2 (f1 a)) -> f3 (f2 (f1 b))

fmap4 :: Functors '[f1, f2, f3, f4] => (a -> b) -> f4 (f3 (f2 (f1 a))) -> f4 (f3 (f2 (f1 b)))

fmap5 :: Functors '[f1, f2, f3, f4, f5] => (a -> b) -> f5 (f4 (f3 (f2 (f1 a)))) -> f5 (f4 (f3 (f2 (f1 b))))

(.) :: Functor f1 => (a -> b) -> f1 a -> f1 b infixr 9

(.:) :: Functors '[f1, f2] => (a -> b) -> f2 (f1 a) -> f2 (f1 b) infixr 8

(.:.) :: Functors '[f1, f2, f3] => (a -> b) -> f3 (f2 (f1 a)) -> f3 (f2 (f1 b)) infixr 8

(.::) :: Functors '[f1, f2, f3, f4] => (a -> b) -> f4 (f3 (f2 (f1 a))) -> f4 (f3 (f2 (f1 b))) infixr 8

(.::.) :: Functors '[f1, f2, f3, f4, f5] => (a -> b) -> f5 (f4 (f3 (f2 (f1 a)))) -> f5 (f4 (f3 (f2 (f1 b)))) infixr 8

(∘) :: Functor f1 => (a -> b) -> f1 a -> f1 b infixr 9

(∘∘) :: Functors '[f1, f2] => (a -> b) -> f2 (f1 a) -> f2 (f1 b) infixr 8

(∘∘∘) :: Functors '[f1, f2, f3] => (a -> b) -> f3 (f2 (f1 a)) -> f3 (f2 (f1 b)) infixr 8

(∘∘∘∘) :: Functors '[f1, f2, f3, f4] => (a -> b) -> f4 (f3 (f2 (f1 a))) -> f4 (f3 (f2 (f1 b))) infixr 8

(∘∘∘∘∘) :: Functors '[f1, f2, f3, f4, f5] => (a -> b) -> f5 (f4 (f3 (f2 (f1 a)))) -> f5 (f4 (f3 (f2 (f1 b)))) infixr 8

(<<$>>) :: Functors '[f1, f2] => (a -> b) -> f2 (f1 a) -> f2 (f1 b) infixl 4

(<<<$>>>) :: Functors '[f1, f2, f3] => (a -> b) -> f3 (f2 (f1 a)) -> f3 (f2 (f1 b)) infixl 4

(<<<<$>>>>) :: Functors '[f1, f2, f3, f4] => (a -> b) -> f4 (f3 (f2 (f1 a))) -> f4 (f3 (f2 (f1 b))) infixl 4

(<<<<<$>>>>>) :: Functors '[f1, f2, f3, f4, f5] => (a -> b) -> f5 (f4 (f3 (f2 (f1 a)))) -> f5 (f4 (f3 (f2 (f1 b)))) infixl 4

(<<*>>) :: Applicatives '[f1, f2] => f2 (f1 (a -> b)) -> f2 (f1 a) -> f2 (f1 b) infixl 4

(<<<*>>>) :: Applicatives '[f1, f2, f3] => f3 (f2 (f1 (a -> b))) -> f3 (f2 (f1 a)) -> f3 (f2 (f1 b)) infixl 4

(<<<<*>>>>) :: Applicatives '[f1, f2, f3, f4] => f4 (f3 (f2 (f1 (a -> b)))) -> f4 (f3 (f2 (f1 a))) -> f4 (f3 (f2 (f1 b))) infixl 4

(<<<<<*>>>>>) :: Applicatives '[f1, f2, f3, f4, f5] => f5 (f4 (f3 (f2 (f1 (a -> b))))) -> f5 (f4 (f3 (f2 (f1 a)))) -> f5 (f4 (f3 (f2 (f1 b)))) infixl 4

(|$) :: (a -> b) -> a -> (a, b) infixl 4

($|) :: (a -> b) -> a -> (b, a) infixl 4

(<|$>) :: Functor f => (a -> b) -> f a -> f (a, b) infixl 4

(<$|>) :: Functor f => (a -> b) -> f a -> f (b, a) infixl 4

composed :: Iso' (f (g a)) (Compose f g a)

nested :: (Functor f1, Functor f2) => (f2 (Compose f3 g1 a1) -> f1 (Compose f4 g2 a2)) -> f2 (f3 (g1 a1)) -> f1 (f4 (g2 a2))

following functions are usefull when operating on nested structures with lenses, for example | given function foo :: a -> m (n a) and a lens l :: Lens' x a, we can use | nested l foo to get signature of x -> m (n x)

newtype Compose (f :: k -> Type) (g :: k1 -> k) (a :: k1) :: forall k k1. (k -> Type) -> (k1 -> k) -> k1 -> Type infixr 9

Right-to-left composition of functors. The composition of applicative functors is always applicative, but the composition of monads is not always a monad.

Constructors

Compose infixr 9

Fields

• getCompose :: f (g a)

Instances

Functor f => Generic1 (Compose f g :: k -> Type)

Defined in Data.Functor.Compose

Associated Types

type Rep1 (Compose f g) :: k -> Type

Methods

from1 :: Compose f g a -> Rep1 (Compose f g) a

to1 :: Rep1 (Compose f g) a -> Compose f g a

Sieve (ReifiedIndexedFold i) (Compose [] ((,) i))

Defined in Control.Lens.Reified

Methods

sieve :: ReifiedIndexedFold i a b -> a -> Compose [] ((,) i) b

(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (i, j) (Compose f g)

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

(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (i, j) (Compose f g)

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

(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (i, j) (Compose f g)

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

(Functor f, Functor g) => Functor (Compose f g)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

fmap :: (a -> b) -> Compose f g a -> Compose f g b

(<$) :: a -> Compose f g b -> Compose f g a

(Applicative f, Applicative g) => Applicative (Compose f g)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

pure :: a -> Compose f g a

(<*>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b

liftA2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c

(*>) :: Compose f g a -> Compose f g b -> Compose f g b

(<*) :: Compose f g a -> Compose f g b -> Compose f g a

(Foldable f, Foldable g) => Foldable (Compose f g)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

fold :: Monoid m => Compose f g m -> m

foldMap :: Monoid m => (a -> m) -> Compose f g a -> m

foldr :: (a -> b -> b) -> b -> Compose f g a -> b

foldr' :: (a -> b -> b) -> b -> Compose f g a -> b

foldl :: (b -> a -> b) -> b -> Compose f g a -> b

foldl' :: (b -> a -> b) -> b -> Compose f g a -> b

foldr1 :: (a -> a -> a) -> Compose f g a -> a

foldl1 :: (a -> a -> a) -> Compose f g a -> a

toList :: Compose f g a -> [a]

null :: Compose f g a -> Bool

length :: Compose f g a -> Int

elem :: Eq a => a -> Compose f g a -> Bool

maximum :: Ord a => Compose f g a -> a

minimum :: Ord a => Compose f g a -> a

sum :: Num a => Compose f g a -> a

product :: Num a => Compose f g a -> a

(Traversable f, Traversable g) => Traversable (Compose f g)

Since: base-4.9.0.0

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)

(Functor f, Contravariant g) => Contravariant (Compose f g)

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

(Eq1 f, Eq1 g) => Eq1 (Compose f g)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

liftEq :: (a -> b -> Bool) -> Compose f g a -> Compose f g b -> Bool

(Ord1 f, Ord1 g) => Ord1 (Compose f g)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

liftCompare :: (a -> b -> Ordering) -> Compose f g a -> Compose f g b -> Ordering

(Read1 f, Read1 g) => Read1 (Compose f g)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Compose f g a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Compose f g a]

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Compose f g a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Compose f g a]

(Show1 f, Show1 g) => Show1 (Compose f g)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Compose f g a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Compose f g a] -> ShowS

(Alternative f, Applicative g) => Alternative (Compose f g)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

empty :: Compose f g a

(<|>) :: Compose f g a -> Compose f g a -> Compose f g a

some :: Compose f g a -> Compose f g [a]

many :: Compose f g a -> Compose f g [a]

(Settable f, Settable g) => Settable (Compose f g)

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)

(Traversable1 f, Traversable1 g) => Traversable1 (Compose f g)

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)

(Eq1 f, Eq1 g, Eq a) => Eq (Compose f g a)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

(==) :: Compose f g a -> Compose f g a -> Bool

(/=) :: Compose f g a -> Compose f g a -> Bool

(Typeable a, Typeable f, Typeable g, Typeable k1, Typeable k2, Data (f (g a))) => Data (Compose f g a)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g0. g0 -> c g0) -> Compose f g a -> c (Compose f g a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Compose f g a)

toConstr :: Compose f g a -> Constr

dataTypeOf :: Compose f g a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Compose f g a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Compose f g a))

gmapT :: (forall b. Data b => b -> b) -> Compose f g a -> Compose f g a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r

gmapQ :: (forall d. Data d => d -> u) -> Compose f g a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Compose f g a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a)

(Ord1 f, Ord1 g, Ord a) => Ord (Compose f g a)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

compare :: Compose f g a -> Compose f g a -> Ordering

(<) :: Compose f g a -> Compose f g a -> Bool

(<=) :: Compose f g a -> Compose f g a -> Bool

(>) :: Compose f g a -> Compose f g a -> Bool

(>=) :: Compose f g a -> Compose f g a -> Bool

max :: Compose f g a -> Compose f g a -> Compose f g a

min :: Compose f g a -> Compose f g a -> Compose f g a

(Read1 f, Read1 g, Read a) => Read (Compose f g a)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

readsPrec :: Int -> ReadS (Compose f g a)

readList :: ReadS [Compose f g a]

readPrec :: ReadPrec (Compose f g a)

readListPrec :: ReadPrec [Compose f g a]

(Show1 f, Show1 g, Show a) => Show (Compose f g a)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

showsPrec :: Int -> Compose f g a -> ShowS

show :: Compose f g a -> String

showList :: [Compose f g a] -> ShowS

Generic (Compose f g a)

Defined in Data.Functor.Compose

Associated Types

type Rep (Compose f g a) :: Type -> Type

Methods

from :: Compose f g a -> Rep (Compose f g a) x

to :: Rep (Compose f g a) x -> Compose f g a

Wrapped (Compose f g a)

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))

t ~ Compose f' g' a' => Rewrapped (Compose f g a) t

Defined in Control.Lens.Wrapped

type Rep1 (Compose f g :: k -> Type)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

type Rep1 (Compose f g :: k -> Type) = D1 (MetaData "Compose" "Data.Functor.Compose" "base" True) (C1 (MetaCons "Compose" PrefixI True) (S1 (MetaSel (Just "getCompose") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (f :.: Rec1 g)))

type Rep (Compose f g a)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

type Rep (Compose f g a) = D1 (MetaData "Compose" "Data.Functor.Compose" "base" True) (C1 (MetaCons "Compose" PrefixI True) (S1 (MetaSel (Just "getCompose") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f (g a)))))

type Unwrapped (Compose f g a)

Defined in Control.Lens.Wrapped

type Unwrapped (Compose f g a) = f (g a)