/Haskell 8

# Data.Bitraversable

Copyright (C) 2011-2016 Edward Kmett BSD-style (see the file LICENSE) [email protected] provisional portable Trustworthy Haskell2010

#### Description

Since: base-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 ≡ bitraverse (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 from Data.Functor.Identity and Data.Functor.Compose.

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: base-4.10.0.0

Nothing

#### 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: base-4.10.0.0

##### Instances
Instances details
Bitraversable Either

Since: base-4.10.0.0

Instance details

Defined in Data.Bitraversable

#### Methods

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

Bitraversable (,)

Since: base-4.10.0.0

Instance details

Defined in Data.Bitraversable

#### Methods

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

Bitraversable Arg

Since: base-4.10.0.0

Instance details

Defined in Data.Semigroup

#### Methods

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

Bitraversable ((,,) x)

Since: base-4.10.0.0

Instance details

Defined in Data.Bitraversable

#### Methods

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

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) Source

Bitraversable (K1 i :: 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) -> K1 i a b -> f (K1 i c d) Source

Bitraversable ((,,,) x y)

Since: base-4.10.0.0

Instance details

Defined in Data.Bitraversable

#### 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: base-4.10.0.0

Instance details

Defined in Data.Bitraversable

#### 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: base-4.10.0.0

Instance details

Defined in Data.Bitraversable

#### 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: base-4.10.0.0

Instance details

Defined in Data.Bitraversable

#### 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: base-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: base-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: base-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: base-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: base-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: base-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: base-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: base-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: base-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/8.8.3/docs/html/libraries/base-4.13.0.0/Data-Bitraversable.html