Safe Haskell	Safe
Language	Haskell2010

Bitraversable

Contents

Bitraversable
- Default Bifunctor implementation
- Default Bifoldable implementation
Bitraversable1
- Default Bifoldable1 implementation

Synopsis

class (Bifunctor t, Bifoldable t) => Bitraversable (t :: * -> * -> *) where
bisequence :: (Bitraversable t, Applicative f) => t (f a) (f b) -> f (t a b)
bifor :: (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 :: Bitraversable t => (a -> b) -> (c -> d) -> t a c -> t b d
bifoldMapDefault :: (Bitraversable t, Monoid m) => (a -> m) -> (b -> m) -> t a b -> m
class (Bifoldable1 t, Bitraversable t) => Bitraversable1 (t :: * -> * -> *) where
bifoldMap1Default :: (Bitraversable1 t, Semigroup m) => (a -> m) -> (b -> m) -> t a b -> m

Bitraversable

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: 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: base-4.10.0.0

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.

bitraverse f g ≡ bisequenceA . bimap f 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
Instance details 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
Instance details 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
Instance details 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
Instance details Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (x, a, b) -> f (x, c, d) #
Bitraversable (Const :: * -> * -> *)	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) #
Traversable f => Bitraversable (FreeF f)
Instance details Defined in Control.Monad.Trans.Free Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> FreeF f a b -> f0 (FreeF f c d) #
Traversable f => Bitraversable (CofreeF f)
Instance details Defined in Control.Comonad.Trans.Cofree Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> CofreeF f a b -> f0 (CofreeF f c d) #
Bitraversable (Tagged :: * -> * -> *)
Instance details Defined in Data.Tagged Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Tagged a b -> f (Tagged c d) #
Bitraversable (K1 i :: * -> * -> *)	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) #
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) #
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) #
Bitraversable p => Bitraversable (WrappedBifunctor p)
Instance details Defined in Data.Bifunctor.Wrapped Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> WrappedBifunctor p a b -> f (WrappedBifunctor p c d) #
Traversable g => Bitraversable (Joker g :: * -> * -> *)
Instance details Defined in Data.Bifunctor.Joker Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Joker g a b -> f (Joker g c d) #
Bitraversable p => Bitraversable (Flip p)
Instance details Defined in Data.Bifunctor.Flip Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Flip p a b -> f (Flip p c d) #
Traversable f => Bitraversable (Clown f :: * -> * -> *)
Instance details Defined in Data.Bifunctor.Clown Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> Clown f a b -> f0 (Clown f c d) #
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) #
(Bitraversable p, Bitraversable q) => Bitraversable (Sum p q)
Instance details Defined in Data.Bifunctor.Sum Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Sum p q a b -> f (Sum p q c d) #
(Bitraversable f, Bitraversable g) => Bitraversable (Product f g)
Instance details Defined in Data.Bifunctor.Product Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> Product f g a b -> f0 (Product f g c d) #
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) #
(Traversable f, Bitraversable p) => Bitraversable (Tannen f p)
Instance details Defined in Data.Bifunctor.Tannen Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> Tannen f p a b -> f0 (Tannen f p c d) #
(Bitraversable p, Traversable f, Traversable g) => Bitraversable (Biff p f g)
Instance details Defined in Data.Bifunctor.Biff Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> Biff p f g a b -> f0 (Biff p f g c d) #

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 ≡ bitraverse id id

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

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

Default `Bifunctor` implementation

bimapDefault :: Bitraversable t => (a -> b) -> (c -> d) -> t a c -> t b d #

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

Default `Bifoldable` implementation

bifoldMapDefault :: (Bitraversable t, Monoid m) => (a -> m) -> (b -> m) -> t a b -> m #

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

Bitraversable1

class (Bifoldable1 t, Bitraversable t) => Bitraversable1 (t :: * -> * -> *) where #

Minimal complete definition

bitraverse1 | bisequence1

Methods

bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> t a c -> f (t b d) #

bisequence1 :: Apply f => t (f a) (f b) -> f (t a b) #

Instances

Bitraversable1 Either
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Either a c -> f (Either b d) # bisequence1 :: Apply f => Either (f a) (f b) -> f (Either a b) #
Bitraversable1 (,)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> (a, c) -> f (b, d) # bisequence1 :: Apply f => (f a, f b) -> f (a, b) #
Bitraversable1 Arg
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Arg a c -> f (Arg b d) # bisequence1 :: Apply f => Arg (f a) (f b) -> f (Arg a b) #
Bitraversable1 ((,,) x)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> (x, a, c) -> f (x, b, d) # bisequence1 :: Apply f => (x, f a, f b) -> f (x, a, b) #
Bitraversable1 (Const :: * -> * -> *)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Const a c -> f (Const b d) # bisequence1 :: Apply f => Const (f a) (f b) -> f (Const a b) #
Bitraversable1 (Tagged :: * -> * -> *)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Tagged a c -> f (Tagged b d) # bisequence1 :: Apply f => Tagged (f a) (f b) -> f (Tagged a b) #
Bitraversable1 ((,,,) x y)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> (x, y, a, c) -> f (x, y, b, d) # bisequence1 :: Apply f => (x, y, f a, f b) -> f (x, y, a, b) #
Bitraversable1 ((,,,,) x y z)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> (x, y, z, a, c) -> f (x, y, z, b, d) # bisequence1 :: Apply f => (x, y, z, f a, f b) -> f (x, y, z, a, b) #
Bitraversable1 p => Bitraversable1 (WrappedBifunctor p)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> WrappedBifunctor p a c -> f (WrappedBifunctor p b d) # bisequence1 :: Apply f => WrappedBifunctor p (f a) (f b) -> f (WrappedBifunctor p a b) #
Traversable1 g => Bitraversable1 (Joker g :: * -> * -> *)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Joker g a c -> f (Joker g b d) # bisequence1 :: Apply f => Joker g (f a) (f b) -> f (Joker g a b) #
Bitraversable1 p => Bitraversable1 (Flip p)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Flip p a c -> f (Flip p b d) # bisequence1 :: Apply f => Flip p (f a) (f b) -> f (Flip p a b) #
Traversable1 f => Bitraversable1 (Clown f :: * -> * -> *)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f0 => (a -> f0 b) -> (c -> f0 d) -> Clown f a c -> f0 (Clown f b d) # bisequence1 :: Apply f0 => Clown f (f0 a) (f0 b) -> f0 (Clown f a b) #
(Bitraversable1 f, Bitraversable1 g) => Bitraversable1 (Product f g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f0 => (a -> f0 b) -> (c -> f0 d) -> Product f g a c -> f0 (Product f g b d) # bisequence1 :: Apply f0 => Product f g (f0 a) (f0 b) -> f0 (Product f g a b) #
(Traversable1 f, Bitraversable1 p) => Bitraversable1 (Tannen f p)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f0 => (a -> f0 b) -> (c -> f0 d) -> Tannen f p a c -> f0 (Tannen f p b d) # bisequence1 :: Apply f0 => Tannen f p (f0 a) (f0 b) -> f0 (Tannen f p a b) #
(Bitraversable1 p, Traversable1 f, Traversable1 g) => Bitraversable1 (Biff p f g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f0 => (a -> f0 b) -> (c -> f0 d) -> Biff p f g a c -> f0 (Biff p f g b d) # bisequence1 :: Apply f0 => Biff p f g (f0 a) (f0 b) -> f0 (Biff p f g a b) #

Default `Bifoldable1` implementation

bifoldMap1Default :: (Bitraversable1 t, Semigroup m) => (a -> m) -> (b -> m) -> t a b -> m #

Bitraversable

Default Bifunctor implementation

Default Bifoldable implementation

Bitraversable1

Default Bifoldable1 implementation

Default `Bifunctor` implementation

Default `Bifoldable` implementation

Default `Bifoldable1` implementation