Data.Biapplicative

Biapplicative bifunctors

class Bifunctor p => Biapplicative p where

Minimal complete definition

bipure, ((<<*>>) | biliftA2)

Methods

bipure :: a -> b -> p a b

(<<*>>) :: p (a -> b) (c -> d) -> p a c -> p b d infixl 4

biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> p a d -> p b e -> p c f

Lift binary functions

(*>>) :: p a b -> p c d -> p c d infixl 4

a *>> b ≡ bimap (const id) (const id) <<$>> a <<*>> b

(<<*) :: p a b -> p c d -> p a b infixl 4

a <<* b ≡ bimap const const <<$>> a <<*>> b

Instances

Biapplicative (,)

Defined in Data.Biapplicative

Methods

bipure :: a -> b -> (a, b)

(<<*>>) :: (a -> b, c -> d) -> (a, c) -> (b, d)

biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> (a, d) -> (b, e) -> (c, f)

(*>>) :: (a, b) -> (c, d) -> (c, d)

(<<*) :: (a, b) -> (c, d) -> (a, b)

Biapplicative Arg

Defined in Data.Biapplicative

Methods

bipure :: a -> b -> Arg a b

(<<*>>) :: Arg (a -> b) (c -> d) -> Arg a c -> Arg b d

biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Arg a d -> Arg b e -> Arg c f

(*>>) :: Arg a b -> Arg c d -> Arg c d

(<<*) :: Arg a b -> Arg c d -> Arg a b

Monoid x => Biapplicative ((,,) x)

Defined in Data.Biapplicative

Methods

bipure :: a -> b -> (x, a, b)

(<<*>>) :: (x, a -> b, c -> d) -> (x, a, c) -> (x, b, d)

biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> (x, a, d) -> (x, b, e) -> (x, c, f)

(*>>) :: (x, a, b) -> (x, c, d) -> (x, c, d)

(<<*) :: (x, a, b) -> (x, c, d) -> (x, a, b)

Biapplicative (Const :: * -> * -> *)

Defined in Data.Biapplicative

Methods

bipure :: a -> b -> Const a b

(<<*>>) :: Const (a -> b) (c -> d) -> Const a c -> Const b d

biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Const a d -> Const b e -> Const c f

(*>>) :: Const a b -> Const c d -> Const c d

(<<*) :: Const a b -> Const c d -> Const a b

Biapplicative (Tagged :: * -> * -> *)

Defined in Data.Biapplicative

Methods

bipure :: a -> b -> Tagged a b

(<<*>>) :: Tagged (a -> b) (c -> d) -> Tagged a c -> Tagged b d

biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Tagged a d -> Tagged b e -> Tagged c f

(*>>) :: Tagged a b -> Tagged c d -> Tagged c d

(<<*) :: Tagged a b -> Tagged c d -> Tagged a b

(Monoid x, Monoid y) => Biapplicative ((,,,) x y)

Defined in Data.Biapplicative

Methods

bipure :: a -> b -> (x, y, a, b)

(<<*>>) :: (x, y, a -> b, c -> d) -> (x, y, a, c) -> (x, y, b, d)

biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> (x, y, a, d) -> (x, y, b, e) -> (x, y, c, f)

(*>>) :: (x, y, a, b) -> (x, y, c, d) -> (x, y, c, d)

(<<*) :: (x, y, a, b) -> (x, y, c, d) -> (x, y, a, b)

(Monoid x, Monoid y, Monoid z) => Biapplicative ((,,,,) x y z)

Defined in Data.Biapplicative

Methods

bipure :: a -> b -> (x, y, z, a, b)

(<<*>>) :: (x, y, z, a -> b, c -> d) -> (x, y, z, a, c) -> (x, y, z, b, d)

biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> (x, y, z, a, d) -> (x, y, z, b, e) -> (x, y, z, c, f)

(*>>) :: (x, y, z, a, b) -> (x, y, z, c, d) -> (x, y, z, c, d)

(<<*) :: (x, y, z, a, b) -> (x, y, z, c, d) -> (x, y, z, a, b)

Applicative f => Biapplicative (Clown f :: * -> * -> *)

Defined in Data.Bifunctor.Clown

Methods

bipure :: a -> b -> Clown f a b

(<<*>>) :: Clown f (a -> b) (c -> d) -> Clown f a c -> Clown f b d

biliftA2 :: (a -> b -> c) -> (d -> e -> f0) -> Clown f a d -> Clown f b e -> Clown f c f0

(*>>) :: Clown f a b -> Clown f c d -> Clown f c d

(<<*) :: Clown f a b -> Clown f c d -> Clown f a b

Biapplicative p => Biapplicative (Flip p)

Defined in Data.Bifunctor.Flip

Methods

bipure :: a -> b -> Flip p a b

(<<*>>) :: Flip p (a -> b) (c -> d) -> Flip p a c -> Flip p b d

biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Flip p a d -> Flip p b e -> Flip p c f

(*>>) :: Flip p a b -> Flip p c d -> Flip p c d

(<<*) :: Flip p a b -> Flip p c d -> Flip p a b

Applicative g => Biapplicative (Joker g :: * -> * -> *)

Defined in Data.Bifunctor.Joker

Methods

bipure :: a -> b -> Joker g a b

(<<*>>) :: Joker g (a -> b) (c -> d) -> Joker g a c -> Joker g b d

biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Joker g a d -> Joker g b e -> Joker g c f

(*>>) :: Joker g a b -> Joker g c d -> Joker g c d

(<<*) :: Joker g a b -> Joker g c d -> Joker g a b

Biapplicative p => Biapplicative (WrappedBifunctor p)

Defined in Data.Bifunctor.Wrapped

Methods

bipure :: a -> b -> WrappedBifunctor p a b

(<<*>>) :: WrappedBifunctor p (a -> b) (c -> d) -> WrappedBifunctor p a c -> WrappedBifunctor p b d

biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> WrappedBifunctor p a d -> WrappedBifunctor p b e -> WrappedBifunctor p c f

(*>>) :: WrappedBifunctor p a b -> WrappedBifunctor p c d -> WrappedBifunctor p c d

(<<*) :: WrappedBifunctor p a b -> WrappedBifunctor p c d -> WrappedBifunctor p a b

(Monoid x, Monoid y, Monoid z, Monoid w) => Biapplicative ((,,,,,) x y z w)

Defined in Data.Biapplicative

Methods

bipure :: a -> b -> (x, y, z, w, a, b)

(<<*>>) :: (x, y, z, w, a -> b, c -> d) -> (x, y, z, w, a, c) -> (x, y, z, w, b, d)

biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> (x, y, z, w, a, d) -> (x, y, z, w, b, e) -> (x, y, z, w, c, f)

(*>>) :: (x, y, z, w, a, b) -> (x, y, z, w, c, d) -> (x, y, z, w, c, d)

(<<*) :: (x, y, z, w, a, b) -> (x, y, z, w, c, d) -> (x, y, z, w, a, b)

(Biapplicative f, Biapplicative g) => Biapplicative (Product f g)

Defined in Data.Bifunctor.Product

Methods

bipure :: a -> b -> Product f g a b

(<<*>>) :: Product f g (a -> b) (c -> d) -> Product f g a c -> Product f g b d

biliftA2 :: (a -> b -> c) -> (d -> e -> f0) -> Product f g a d -> Product f g b e -> Product f g c f0

(*>>) :: Product f g a b -> Product f g c d -> Product f g c d

(<<*) :: Product f g a b -> Product f g c d -> Product f g a b

(Monoid x, Monoid y, Monoid z, Monoid w, Monoid v) => Biapplicative ((,,,,,,) x y z w v)

Defined in Data.Biapplicative

Methods

bipure :: a -> b -> (x, y, z, w, v, a, b)

(<<*>>) :: (x, y, z, w, v, a -> b, c -> d) -> (x, y, z, w, v, a, c) -> (x, y, z, w, v, b, d)

biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> (x, y, z, w, v, a, d) -> (x, y, z, w, v, b, e) -> (x, y, z, w, v, c, f)

(*>>) :: (x, y, z, w, v, a, b) -> (x, y, z, w, v, c, d) -> (x, y, z, w, v, c, d)

(<<*) :: (x, y, z, w, v, a, b) -> (x, y, z, w, v, c, d) -> (x, y, z, w, v, a, b)

(Applicative f, Biapplicative p) => Biapplicative (Tannen f p)

Defined in Data.Bifunctor.Tannen

Methods

bipure :: a -> b -> Tannen f p a b

(<<*>>) :: Tannen f p (a -> b) (c -> d) -> Tannen f p a c -> Tannen f p b d

biliftA2 :: (a -> b -> c) -> (d -> e -> f0) -> Tannen f p a d -> Tannen f p b e -> Tannen f p c f0

(*>>) :: Tannen f p a b -> Tannen f p c d -> Tannen f p c d

(<<*) :: Tannen f p a b -> Tannen f p c d -> Tannen f p a b

(Biapplicative p, Applicative f, Applicative g) => Biapplicative (Biff p f g)

Defined in Data.Bifunctor.Biff

Methods

bipure :: a -> b -> Biff p f g a b

(<<*>>) :: Biff p f g (a -> b) (c -> d) -> Biff p f g a c -> Biff p f g b d

biliftA2 :: (a -> b -> c) -> (d -> e -> f0) -> Biff p f g a d -> Biff p f g b e -> Biff p f g c f0

(*>>) :: Biff p f g a b -> Biff p f g c d -> Biff p f g c d

(<<*) :: Biff p f g a b -> Biff p f g c d -> Biff p f g a b

(<<$>>) :: (a -> b) -> a -> b infixl 4

(<<**>>) :: Biapplicative p => p a c -> p (a -> b) (c -> d) -> p b d infixl 4

biliftA3 :: Biapplicative w => (a -> b -> c -> d) -> (e -> f -> g -> h) -> w a e -> w b f -> w c g -> w d h

Lift ternary functions

traverseBia :: (Traversable t, Biapplicative p) => (a -> p b c) -> t a -> p (t b) (t c)

Traverse a Traversable container in a Biapplicative.

traverseBia satisfies the following properties:

Pairing

traverseBia (,) t = (t, t)

Composition

traverseBia (Biff . bimap g h . f) = Biff . bimap (traverse g) (traverse h) . traverseBia f

traverseBia (Tannen . fmap f . g) = Tannen . fmap (traverseBia f) . traverse g

Naturality

 t . traverseBia f = traverseBia (t . f)

for every biapplicative transformation t.

A biapplicative transformation from a Biapplicative P to a Biapplicative Q is a function

t :: P a b -> Q a b

preserving the Biapplicative operations. That is,

• t (bipure x y) = bipure x y

• t (x <<*>> y) = t x <<*>> t y

Performance note

traverseBia is fairly efficient, and uses compiler rewrite rules to be even more efficient for a few important types like []. However, if performance is critical, you might consider writing a container-specific implementation.

sequenceBia :: (Traversable t, Biapplicative p) => t (p b c) -> p (t b) (t c)

Perform all the Biappicative actions in a Traversable container and produce a container with all the results.

sequenceBia = traverseBia id

traverseBiaWith :: forall p a b c s t. Biapplicative p => (forall f x. Applicative f => (a -> f x) -> s -> f (t x)) -> (a -> p b c) -> s -> p (t b) (t c)

A version of traverseBia that doesn't care how the traversal is done.

traverseBia = traverseBiaWith traverse

module Data.Bifunctor