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Data.Bitraversable

Copyright (C) 2011-2016 Edward Kmett
License BSD-style (see the file LICENSE)
Maintainer [email protected]
Stability provisional
Portability portable
Safe Haskell Trustworthy
Language Haskell2010

Description

Since: 4.10.0.0

class (Bifunctor t, Bifoldable t) => Bitraversable t where Source

Bitraversable identifies bifunctorial data structures whose elements can be traversed in order, performing Applicative or Monad actions at each element, and collecting a result structure with the same shape.

As opposed to Traversable data structures, which have one variety of element on which an action can be performed, Bitraversable data structures have two such varieties of elements.

A definition of bitraverse must satisfy the following laws:

naturality
bitraverse (t . f) (t . g) ≡ t . bitraverse f g for every applicative transformation t
identity
bitraverse Identity IdentityIdentity
composition
Compose . fmap (bitraverse g1 g2) . bitraverse f1 f2 ≡ traverse (Compose . fmap g1 . f1) (Compose . fmap g2 . f2)

where an applicative transformation is a function

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

preserving the Applicative operations:

t (pure x) = pure x
t (f <*> x) = t f <*> t x

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

newtype Identity a = Identity { runIdentity :: a }

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

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

Some simple examples are Either and '(,)':

instance Bitraversable Either where
  bitraverse f _ (Left x) = Left <$> f x
  bitraverse _ g (Right y) = Right <$> g y

instance Bitraversable (,) where
  bitraverse f g (x, y) = (,) <$> f x <*> g y

Bitraversable relates to its superclasses in the following ways:

bimap f g ≡ runIdentity . bitraverse (Identity . f) (Identity . g)
bifoldMap f g = getConst . bitraverse (Const . f) (Const . g)

These are available as bimapDefault and bifoldMapDefault respectively.

Since: 4.10.0.0

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> t a b -> f (t c d) Source

Evaluates the relevant functions at each element in the structure, running the action, and builds a new structure with the same shape, using the results produced from sequencing the actions.

bitraverse f g ≡ bisequenceA . bimap f g

For a version that ignores the results, see bitraverse_.

Since: 4.10.0.0

Instances

Bitraversable Either

Since: 4.10.0.0

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Either a b -> f (Either c d) Source

Bitraversable (,)

Since: 4.10.0.0

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (a, b) -> f (c, d) Source

Bitraversable Arg

Since: 4.10.0.0

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d) Source

Bitraversable ((,,) x)

Since: 4.10.0.0

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (x, a, b) -> f (x, c, d) Source

Bitraversable (Const *)

Since: 4.10.0.0

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Const * a b -> f (Const * c d) Source

Bitraversable (K1 * i)

Since: 4.10.0.0

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> K1 * i a b -> f (K1 * i c d) Source

Bitraversable ((,,,) x y)

Since: 4.10.0.0

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (x, y, a, b) -> f (x, y, c, d) Source

Bitraversable ((,,,,) x y z)

Since: 4.10.0.0

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (x, y, z, a, b) -> f (x, y, z, c, d) Source

Bitraversable ((,,,,,) x y z w)

Since: 4.10.0.0

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (x, y, z, w, a, b) -> f (x, y, z, w, c, d) Source

Bitraversable ((,,,,,,) x y z w v)

Since: 4.10.0.0

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (x, y, z, w, v, a, b) -> f (x, y, z, w, v, c, d) Source

bisequenceA :: (Bitraversable t, Applicative f) => t (f a) (f b) -> f (t a b) Source

Alias for bisequence.

Since: 4.10.0.0

bisequence :: (Bitraversable t, Applicative f) => t (f a) (f b) -> f (t a b) Source

Sequences all the actions in a structure, building a new structure with the same shape using the results of the actions. For a version that ignores the results, see bisequence_.

bisequencebitraverse id id

Since: 4.10.0.0

bimapM :: (Bitraversable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f (t c d) Source

Alias for bitraverse.

Since: 4.10.0.0

bifor :: (Bitraversable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f (t c d) Source

bifor is bitraverse with the structure as the first argument. For a version that ignores the results, see bifor_.

Since: 4.10.0.0

biforM :: (Bitraversable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f (t c d) Source

Alias for bifor.

Since: 4.10.0.0

bimapAccumL :: Bitraversable t => (a -> b -> (a, c)) -> (a -> d -> (a, e)) -> a -> t b d -> (a, t c e) Source

The bimapAccumL function behaves like a combination of bimap and bifoldl; it traverses a structure from left to right, threading a state of type a and using the given actions to compute new elements for the structure.

Since: 4.10.0.0

bimapAccumR :: Bitraversable t => (a -> b -> (a, c)) -> (a -> d -> (a, e)) -> a -> t b d -> (a, t c e) Source

The bimapAccumR function behaves like a combination of bimap and bifoldl; it traverses a structure from right to left, threading a state of type a and using the given actions to compute new elements for the structure.

Since: 4.10.0.0

bimapDefault :: forall t a b c d. Bitraversable t => (a -> b) -> (c -> d) -> t a c -> t b d Source

A default definition of bimap in terms of the Bitraversable operations.

bimapDefault f g ≡
     runIdentity . bitraverse (Identity . f) (Identity . g)

Since: 4.10.0.0

bifoldMapDefault :: forall t m a b. (Bitraversable t, Monoid m) => (a -> m) -> (b -> m) -> t a b -> m Source

A default definition of bifoldMap in terms of the Bitraversable operations.

bifoldMapDefault f g ≡
    getConst . bitraverse (Const . f) (Const . g)

Since: 4.10.0.0

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.2.1/docs/html/libraries/base-4.10.0.0/Data-Bitraversable.html