Copyright | (C) 2011-2016 Edward Kmett |
---|---|

License | BSD-style (see the file LICENSE) |

Maintainer | libraries@haskell.org |

Stability | provisional |

Portability | portable |

Safe Haskell | Trustworthy |

Language | Haskell2010 |

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 Identity ≡ Identity`

*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

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

Bitraversable Either | Since: 4.10.0.0 |

Bitraversable (,) | Since: 4.10.0.0 |

Bitraversable Arg | Since: 4.10.0.0 |

Bitraversable ((,,) x) | Since: 4.10.0.0 |

Bitraversable (Const *) | Since: 4.10.0.0 |

Bitraversable (K1 * i) | Since: 4.10.0.0 |

Bitraversable ((,,,) x y) | Since: 4.10.0.0 |

Bitraversable ((,,,,) x y z) | Since: 4.10.0.0 |

Bitraversable ((,,,,,) x y z w) | Since: 4.10.0.0 |

Bitraversable ((,,,,,,) x y z w v) | Since: 4.10.0.0 |

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_`

.

`bisequence`

≡`bitraverse`

`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