Copyright	(C) 2011-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell98

Data.Biapplicative

Contents

Biapplicative bifunctors

Description

Synopsis

Biapplicative bifunctors

class Bifunctor p => Biapplicative p where Source #

Minimal complete definition

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

Methods

bipure :: a -> b -> p a b Source #

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

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

Lift binary functions

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

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

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

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

Instances

Biapplicative (,) Source #
Methods bipure :: a -> b -> (a, b) Source # (<<>>) :: (a -> b, c -> d) -> (a, c) -> (b, d) Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> (a, d) -> (b, e) -> (c, f) Source # (>>) :: (a, b) -> (c, d) -> (c, d) Source # (<<*) :: (a, b) -> (c, d) -> (a, b) Source #
Biapplicative Arg Source #
Methods bipure :: a -> b -> Arg a b Source # (<<>>) :: Arg (a -> b) (c -> d) -> Arg a c -> Arg b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Arg a d -> Arg b e -> Arg c f Source # (>>) :: Arg a b -> Arg c d -> Arg c d Source # (<<*) :: Arg a b -> Arg c d -> Arg a b Source #
Monoid x => Biapplicative ((,,) x) Source #
Methods bipure :: a -> b -> (x, a, b) Source # (<<>>) :: (x, a -> b, c -> d) -> (x, a, c) -> (x, b, d) Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> (x, a, d) -> (x, b, e) -> (x, c, f) Source # (>>) :: (x, a, b) -> (x, c, d) -> (x, c, d) Source # (<<*) :: (x, a, b) -> (x, c, d) -> (x, a, b) Source #
Biapplicative (Const *) Source #
Methods bipure :: a -> b -> Const * a b Source # (<<>>) :: Const (a -> b) (c -> d) -> Const * a c -> Const * b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Const * a d -> Const * b e -> Const * c f Source # (>>) :: Const a b -> Const * c d -> Const * c d Source # (<<) :: Const a b -> Const * c d -> Const * a b Source #
Biapplicative (Tagged *) Source #
Methods bipure :: a -> b -> Tagged * a b Source # (<<>>) :: Tagged (a -> b) (c -> d) -> Tagged * a c -> Tagged * b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Tagged * a d -> Tagged * b e -> Tagged * c f Source # (>>) :: Tagged a b -> Tagged * c d -> Tagged * c d Source # (<<) :: Tagged a b -> Tagged * c d -> Tagged * a b Source #
(Monoid x, Monoid y) => Biapplicative ((,,,) x y) Source #
Methods bipure :: a -> b -> (x, y, a, b) Source # (<<>>) :: (x, y, a -> b, c -> d) -> (x, y, a, c) -> (x, y, b, d) Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> (x, y, a, d) -> (x, y, b, e) -> (x, y, c, f) Source # (>>) :: (x, y, a, b) -> (x, y, c, d) -> (x, y, c, d) Source # (<<*) :: (x, y, a, b) -> (x, y, c, d) -> (x, y, a, b) Source #
(Monoid x, Monoid y, Monoid z) => Biapplicative ((,,,,) x y z) Source #
Methods bipure :: a -> b -> (x, y, z, a, b) Source # (<<>>) :: (x, y, z, a -> b, c -> d) -> (x, y, z, a, c) -> (x, y, z, b, d) Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> (x, y, z, a, d) -> (x, y, z, b, e) -> (x, y, z, c, f) Source # (>>) :: (x, y, z, a, b) -> (x, y, z, c, d) -> (x, y, z, c, d) Source # (<<*) :: (x, y, z, a, b) -> (x, y, z, c, d) -> (x, y, z, a, b) Source #
Applicative f => Biapplicative (Clown * * f) Source #
Methods bipure :: a -> b -> Clown * * f a b Source # (<<>>) :: Clown * f (a -> b) (c -> d) -> Clown * * f a c -> Clown * * f b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Clown * * f a d -> Clown * * f b e -> Clown * * f c f Source # (>>) :: Clown * f a b -> Clown * * f c d -> Clown * * f c d Source # (<<) :: Clown * f a b -> Clown * * f c d -> Clown * * f a b Source #
Biapplicative p => Biapplicative (Flip * * p) Source #
Methods bipure :: a -> b -> Flip * * p a b Source # (<<>>) :: Flip * p (a -> b) (c -> d) -> Flip * * p a c -> Flip * * p b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Flip * * p a d -> Flip * * p b e -> Flip * * p c f Source # (>>) :: Flip * p a b -> Flip * * p c d -> Flip * * p c d Source # (<<) :: Flip * p a b -> Flip * * p c d -> Flip * * p a b Source #
Applicative g => Biapplicative (Joker * * g) Source #
Methods bipure :: a -> b -> Joker * * g a b Source # (<<>>) :: Joker * g (a -> b) (c -> d) -> Joker * * g a c -> Joker * * g b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Joker * * g a d -> Joker * * g b e -> Joker * * g c f Source # (>>) :: Joker * g a b -> Joker * * g c d -> Joker * * g c d Source # (<<) :: Joker * g a b -> Joker * * g c d -> Joker * * g a b Source #
Biapplicative p => Biapplicative (WrappedBifunctor * * p) Source #
Methods bipure :: a -> b -> WrappedBifunctor * * p a b Source # (<<>>) :: WrappedBifunctor * p (a -> b) (c -> d) -> WrappedBifunctor * * p a c -> WrappedBifunctor * * p b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> WrappedBifunctor * * p a d -> WrappedBifunctor * * p b e -> WrappedBifunctor * * p c f Source # (>>) :: WrappedBifunctor * p a b -> WrappedBifunctor * * p c d -> WrappedBifunctor * * p c d Source # (<<) :: WrappedBifunctor * p a b -> WrappedBifunctor * * p c d -> WrappedBifunctor * * p a b Source #
(Monoid x, Monoid y, Monoid z, Monoid w) => Biapplicative ((,,,,,) x y z w) Source #
Methods bipure :: a -> b -> (x, y, z, w, a, b) Source # (<<>>) :: (x, y, z, w, a -> b, c -> d) -> (x, y, z, w, a, c) -> (x, y, z, w, b, d) Source # 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) Source # (>>) :: (x, y, z, w, a, b) -> (x, y, z, w, c, d) -> (x, y, z, w, c, d) Source # (<<*) :: (x, y, z, w, a, b) -> (x, y, z, w, c, d) -> (x, y, z, w, a, b) Source #
(Biapplicative f, Biapplicative g) => Biapplicative (Product * * f g) Source #
Methods bipure :: a -> b -> Product * * f g a b Source # (<<>>) :: Product * f g (a -> b) (c -> d) -> Product * * f g a c -> Product * * f g b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Product * * f g a d -> Product * * f g b e -> Product * * f g c f Source # (>>) :: Product * f g a b -> Product * * f g c d -> Product * * f g c d Source # (<<) :: Product * f g a b -> Product * * f g c d -> Product * * f g a b Source #
(Monoid x, Monoid y, Monoid z, Monoid w, Monoid v) => Biapplicative ((,,,,,,) x y z w v) Source #
Methods bipure :: a -> b -> (x, y, z, w, v, a, b) Source # (<<>>) :: (x, y, z, w, v, a -> b, c -> d) -> (x, y, z, w, v, a, c) -> (x, y, z, w, v, b, d) Source # 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) Source # (>>) :: (x, y, z, w, v, a, b) -> (x, y, z, w, v, c, d) -> (x, y, z, w, v, c, d) Source # (<<*) :: (x, y, z, w, v, a, b) -> (x, y, z, w, v, c, d) -> (x, y, z, w, v, a, b) Source #
(Applicative f, Biapplicative p) => Biapplicative (Tannen * * * f p) Source #
Methods bipure :: a -> b -> Tannen * * * f p a b Source # (<<>>) :: Tannen * * f p (a -> b) (c -> d) -> Tannen * * * f p a c -> Tannen * * * f p b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Tannen * * * f p a d -> Tannen * * * f p b e -> Tannen * * * f p c f Source # (>>) :: Tannen * * f p a b -> Tannen * * * f p c d -> Tannen * * * f p c d Source # (<<) :: Tannen * * f p a b -> Tannen * * * f p c d -> Tannen * * * f p a b Source #
(Biapplicative p, Applicative f, Applicative g) => Biapplicative (Biff * * * * p f g) Source #
Methods bipure :: a -> b -> Biff * * * * p f g a b Source # (<<>>) :: Biff * * * p f g (a -> b) (c -> d) -> Biff * * * * p f g a c -> Biff * * * * p f g b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Biff * * * * p f g a d -> Biff * * * * p f g b e -> Biff * * * * p f g c f Source # (>>) :: Biff * * * p f g a b -> Biff * * * * p f g c d -> Biff * * * * p f g c d Source # (<<) :: Biff * * * p f g a b -> Biff * * * * p f g c d -> Biff * * * * p f g a b Source #

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

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

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

Lift ternary functions

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

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) Source #

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) Source #

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

traverseBia = traverseBiaWith traverse

module Data.Bifunctor