semigroupoids-5.0.1: Semigroupoids: Category sans id

Copyright (C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE) Edward Kmett provisional portable Safe Haskell98

Data.Bifunctor.Apply

Contents

Description

Synopsis

• class Bifunctor p where
• bimap :: (a -> b) -> (c -> d) -> p a c -> p b d
• first :: (a -> b) -> p a c -> p b c
• second :: (b -> c) -> p a b -> p a c
• class Bifunctor p => Biapply p where
• (<<.>>) :: p (a -> b) (c -> d) -> p a c -> p b d
• (.>>) :: p a b -> p c d -> p c d
• (<<.) :: p a b -> p c d -> p a b
• (<<\$>>) :: (a -> b) -> a -> b
• (<<..>>) :: Biapply p => p a c -> p (a -> b) (c -> d) -> p b d
• bilift2 :: Biapply w => (a -> b -> c) -> (d -> e -> f) -> w a d -> w b e -> w c f
• bilift3 :: Biapply w => (a -> b -> c -> d) -> (e -> f -> g -> h) -> w a e -> w b f -> w c g -> w d h

Biappliable bifunctors

class Bifunctor p where

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 idid

If you supply first and second, ensure:

first idid
second idid

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

Since: 4.8.0.0

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.

secondbimap id

Instances

 Bifunctor ((,,) x1) Bifunctor ((,,,) x1 x2) Bifunctor ((,,,,) x1 x2 x3) Bifunctor p => Bifunctor (WrappedBifunctor * * p) Functor g => Bifunctor (Joker * * g) Bifunctor p => Bifunctor (Flip * * p) Functor f => Bifunctor (Clown * * f) Bifunctor ((,,,,,) x1 x2 x3 x4) (Bifunctor f, Bifunctor g) => Bifunctor (Product * * f g) Bifunctor ((,,,,,,) x1 x2 x3 x4 x5) (Functor f, Bifunctor p) => Bifunctor (Tannen * * * f p) (Bifunctor p, Functor f, Functor g) => Bifunctor (Biff * * * * p f g)

class Bifunctor p => Biapply p where Source

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

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

(<<\$>>) :: (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