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	Safe-Inferred
Language	Haskell98

Data.Bifunctor.Apply

Contents

Description

Synopsis

Biappliable bifunctors

class Bifunctor p where

Minimal definition either bimap or first and second

Formally, the class Bifunctor represents a bifunctor from Hask -> Hask.

Intuitively it is a bifunctor where both the first and second arguments are covariant.

You can define a Bifunctor by either defining bimap or by defining both first and second.

If you supply bimap, you should ensure that:

bimap id id ≡ id

If you supply first and second, ensure:

first id ≡ id
second id ≡ id

If you supply both, you should also ensure:

bimap f g ≡ first f . second g

These ensure by parametricity:

bimap  (f . g) (h . i) ≡ bimap f h . bimap g i
first  (f . g) ≡ first  f . first  g
second (f . g) ≡ second f . second g

Minimal complete definition

Methods

bimap :: (a -> b) -> (c -> d) -> p a c -> p b d

Map over both arguments at the same time.

bimap f g ≡ first f . second g

first :: (a -> b) -> p a c -> p b c

Map covariantly over the first argument.

first f ≡ bimap f id

second :: (b -> c) -> p a b -> p a c

Map covariantly over the second argument.

second ≡ bimap id

Instances

Bifunctor Either
Bifunctor (,)
Bifunctor Const
Bifunctor Arg
Bifunctor ((,,) x)
Bifunctor p => Bifunctor (WrappedBifunctor p)
Functor g => Bifunctor (Joker g)
Bifunctor p => Bifunctor (Flip p)
Functor f => Bifunctor (Clown f)
Bifunctor (Tagged *)
Bifunctor ((,,,) x y)
(Functor f, Bifunctor p) => Bifunctor (Tannen f p)
(Bifunctor f, Bifunctor g) => Bifunctor (Product f g)
Bifunctor ((,,,,) x y z)
(Bifunctor p, Functor f, Functor g) => Bifunctor (Biff p f g)
Bifunctor ((,,,,,) x y z w)
Bifunctor ((,,,,,,) x y z w v)

Minimal complete definition

Methods

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

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

a .> b ≡ const id <$> a <.> b

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

a <. b ≡ const <$> a <.> b

Instances

Biapply (,)
Biapply Const
Biapply Arg
Semigroup x => Biapply ((,,) x)
Biapply p => Biapply (WrappedBifunctor p)
Apply g => Biapply (Joker g)
Biapply p => Biapply (Flip p)
Apply f => Biapply (Clown f)
Biapply (Tagged *)
(Semigroup x, Semigroup y) => Biapply ((,,,) x y)
(Apply f, Biapply p) => Biapply (Tannen f p)
(Biapply p, Biapply q) => Biapply (Product p q)
(Semigroup x, Semigroup y, Semigroup z) => Biapply ((,,,,) x y z)
(Biapply p, Apply f, Apply g) => Biapply (Biff p f g)

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

(<<..>>) :: Biapply p => p a c -> p (a -> b) (c -> d) -> p b d infixl 4 Source

bilift2 :: Biapply w => (a -> b -> c) -> (d -> e -> f) -> w a d -> w b e -> w c f Source

Lift binary functions

bilift3 :: Biapply 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