Control.Lens.Traversal

A Traversal s t a b is a generalization of traverse from Traversable. It allows you to traverse over a structure and change out its contents with monadic or Applicative side-effects. Starting from

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

we monomorphize the contents and result to obtain

type Traversal s t a b = forall f. Applicative f => (a -> f b) -> s -> f t

A Traversal can be used as a Fold. Any Traversal can be used for Getting like a Fold, because given a Monoid m, we have an Applicative for (Const m). Everything you know how to do with a Traversable container, you can with a Traversal, and here we provide combinators that generalize the usual Traversable operations.

Traversals

type Traversal s t a b = forall f. 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 ATraversal s t a b = LensLike (Bazaar (->) 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 (->) 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

Traversing and Lensing

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

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

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

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

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

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

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)]

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)

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

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

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

Parts and Holes

Common Traversals

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

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

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

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 Complex

Since: base-4.9.0.0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 SmallArray

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

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 Vector

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 (Either a)

Since: base-4.7.0.0

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

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

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

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)

Ix i => Traversable (Array i)

Since: base-2.1

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

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

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 (Map k)

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)

Traversable f => Traversable (Cofree f)

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 f => Traversable (Free f)

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)

Traversable f => Traversable (ListT f)

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 (MaybeT f)

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)

Traversable p => Traversable (Ap p)

Defined in Util

Methods

traverse :: Applicative f => (a -> f b) -> Ap p a -> f (Ap p b)

sequenceA :: Applicative f => Ap p (f a) -> f (Ap p a)

mapM :: Monad m => (a -> m b) -> Ap p a -> m (Ap p b)

sequence :: Monad m => Ap p (m a) -> m (Ap p a)

Traversable (Level i)

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 (Rec1 f)

Since: base-4.9.0.0

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

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

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

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

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

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

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

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

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

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)

Traversable f => Traversable (IdentityT f)

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 (ErrorT e f)

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 (ExceptT e f)

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 (WriterT w f)

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)

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 (Tagged s)

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.

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)

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 f => Traversable (Backwards f)

Derived instance.

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 (AlongsideRight f a)

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 (AlongsideLeft f b)

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 (K1 i c :: Type -> Type)

Since: base-4.9.0.0

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

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

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 (Product f g)

Since: base-4.9.0.0

Defined in Data.Functor.Product

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Product f g a -> f0 (Product f g b)

sequenceA :: Applicative f0 => Product f g (f0 a) -> f0 (Product f g a)

mapM :: Monad m => (a -> m b) -> Product f g a -> m (Product f g b)

sequence :: Monad m => Product f g (m a) -> m (Product f g a)

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

Since: base-4.9.0.0

Defined in Data.Functor.Sum

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Sum f g a -> f0 (Sum f g b)

sequenceA :: Applicative f0 => Sum f g (f0 a) -> f0 (Sum f g a)

mapM :: Monad m => (a -> m b) -> Sum f g a -> m (Sum f g b)

sequence :: Monad m => Sum f g (m a) -> m (Sum f g a)

Traversable (Magma i t b)

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

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

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

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)

(Traversable f, Traversable (s a)) => Traversable (Tannen f s a)

Defined in Data.Bifunctor.Tannen

Methods

traverse :: Applicative f0 => (a0 -> f0 b) -> Tannen f s a a0 -> f0 (Tannen f s a b)

sequenceA :: Applicative f0 => Tannen f s a (f0 a0) -> f0 (Tannen f s a a0)

mapM :: Monad m => (a0 -> m b) -> Tannen f s a a0 -> m (Tannen f s a b)

sequence :: Monad m => Tannen f s a (m a0) -> m (Tannen f s a a0)

(Traversable (s (f a)), Traversable g) => Traversable (Biff s f g a)

Defined in Data.Bifunctor.Biff

Methods

traverse :: Applicative f0 => (a0 -> f0 b) -> Biff s f g a a0 -> f0 (Biff s f g a b)

sequenceA :: Applicative f0 => Biff s f g a (f0 a0) -> f0 (Biff s f g a a0)

mapM :: Monad m => (a0 -> m b) -> Biff s f g a a0 -> m (Biff s f g a b)

sequence :: Monad m => Biff s f g a (m a0) -> m (Biff s f g a a0)

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

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. Use each to traverse the elements of arbitrary homogeneous tuples.

>>> (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

Implementation Details

newtype Bazaar p 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. Applicative f => p a (f b) -> f t

Instances

Profunctor p => Bizarre p (Bazaar p)

Defined in Control.Lens.Internal.Bazaar

Methods

bazaar :: Applicative f => p a (f b) -> Bazaar p a b t -> f t

IndexedFunctor (Bazaar p)

Defined in Control.Lens.Internal.Bazaar

Methods

ifmap :: (s -> t) -> Bazaar p a b s -> Bazaar p a b t

Functor (Bazaar p a b)

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)

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

type Bazaar' p 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 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. Applicative f => p a (f b) -> f t

Instances

Profunctor p => Bizarre1 p (Bazaar1 p)

Defined in Control.Lens.Internal.Bazaar

Methods

bazaar1 :: Applicative f => p a (f b) -> Bazaar1 p a b t -> f t

IndexedFunctor (Bazaar1 p)

Defined in Control.Lens.Internal.Bazaar

Methods

ifmap :: (s -> t) -> Bazaar1 p a b s -> Bazaar1 p a b t

Functor (Bazaar1 p a b)

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

type Bazaar1' p 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