| 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 |
Data.Bitraversable
Description
Since: base-4.10.0.0
Synopsis
- class (Bifunctor t, Bifoldable t) => Bitraversable t where
- bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> t a b -> f (t c d)
- bisequenceA :: (Bitraversable t, Applicative f) => t (f a) (f b) -> f (t a b)
- bisequence :: (Bitraversable t, Applicative f) => t (f a) (f b) -> f (t a b)
- bimapM :: (Bitraversable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f (t c d)
- bifor :: (Bitraversable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f (t c d)
- biforM :: (Bitraversable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f (t c d)
- bimapAccumL :: Bitraversable t => (a -> b -> (a, c)) -> (a -> d -> (a, e)) -> a -> t b d -> (a, t c e)
- bimapAccumR :: Bitraversable t => (a -> b -> (a, c)) -> (a -> d -> (a, e)) -> a -> t b d -> (a, t c e)
- bimapDefault :: forall t a b c d. Bitraversable t => (a -> b) -> (c -> d) -> t a c -> t b d
- bifoldMapDefault :: forall t m a b. (Bitraversable t, Monoid m) => (a -> m) -> (b -> m) -> t a b -> m
Documentation
class (Bifunctor t, Bifoldable t) => Bitraversable t where #
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
for every applicative transformationbitraverse(t . f) (t . g) ≡ t .bitraversef gt- identity
bitraverseIdentityIdentity≡Identity- composition
Compose.fmap(bitraverseg1 g2) .bitraversef1 f2 ≡traverse(Compose.fmapg1 . f1) (Compose.fmapg2 . f2)
where an applicative transformation is a function
t :: (Applicativef,Applicativeg) => f a -> g a
preserving the Applicative operations:
t (purex) =purex 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:
bimapf g ≡runIdentity.bitraverse(Identity. f) (Identity. g)bifoldMapf g =getConst.bitraverse(Const. f) (Const. g)
These are available as bimapDefault and bifoldMapDefault respectively.
Since: base-4.10.0.0
Minimal complete definition
Nothing
Methods
bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> t a b -> f (t c d) #
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.
bitraversef g ≡bisequenceA.bimapf g
For a version that ignores the results, see bitraverse_.
Since: base-4.10.0.0
Instances
| Bitraversable Either # | Since: base-4.10.0.0 |
Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Either a b -> f (Either c d) # | |
| Bitraversable (,) # | Since: base-4.10.0.0 |
Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (a, b) -> f (c, d) # | |
| Bitraversable Arg # | Since: base-4.10.0.0 |
Defined in Data.Semigroup Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d) # | |
| Bitraversable ((,,) x) # | Since: base-4.10.0.0 |
Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (x, a, b) -> f (x, c, d) # | |
| Bitraversable (Const :: Type -> Type -> Type) # | Since: base-4.10.0.0 |
Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Const a b -> f (Const c d) # | |
| Bitraversable (K1 i :: Type -> Type -> Type) # | Since: base-4.10.0.0 |
Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> K1 i a b -> f (K1 i c d) # | |
| Bitraversable ((,,,) x y) # | Since: base-4.10.0.0 |
Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (x, y, a, b) -> f (x, y, c, d) # | |
| Bitraversable ((,,,,) x y z) # | Since: base-4.10.0.0 |
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) # | |
| Bitraversable ((,,,,,) x y z w) # | Since: base-4.10.0.0 |
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) # | |
| Bitraversable ((,,,,,,) x y z w v) # | Since: base-4.10.0.0 |
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) # | |
bisequenceA :: (Bitraversable t, Applicative f) => t (f a) (f b) -> f (t a b) #
Alias for bisequence.
Since: base-4.10.0.0
bisequence :: (Bitraversable t, Applicative f) => t (f a) (f b) -> f (t a b) #
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≡bitraverseidid
Since: base-4.10.0.0
bimapM :: (Bitraversable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f (t c d) #
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) #
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) #
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) #
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) #
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 #
A default definition of bimap in terms of the Bitraversable
operations.
bimapDefaultf 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 #
A default definition of bifoldMap in terms of the Bitraversable
operations.
bifoldMapDefaultf g ≡getConst.bitraverse(Const. f) (Const. g)
Since: base-4.10.0.0