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 |

Language | Haskell98 |

- class Bifunctor p where
- class Bifunctor p => Biapply p where
- (<<$>>) :: (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

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

*Since: 4.8.0.0*

Bifunctor Either | |

Bifunctor (,) | |

Bifunctor Arg | |

Bifunctor (K1 i) | |

Bifunctor ((,,) x1) | |

Bifunctor (Const *) | |

Bifunctor (Tagged *) | |

Bifunctor (Constant *) | |

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 #

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

Biapply (,) Source # | |

Biapply Arg Source # | |

Semigroup x => Biapply ((,,) x) Source # | |

Biapply (Const *) Source # | |

Biapply (Tagged *) 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 # | |