Copyright | (C) 2008-2014 Edward Kmett, |
---|---|

License | BSD-style (see the file LICENSE) |

Maintainer | libraries@haskell.org |

Stability | provisional |

Portability | portable |

Safe Haskell | Safe |

Language | Haskell2010 |

*Since: 4.8.0.0*

- class Bifunctor p where

# Documentation

class Bifunctor p where Source #

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*

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

Bifunctor Either Source # | |

Bifunctor (,) Source # | |

Bifunctor Arg Source # | |

Bifunctor (K1 i) Source # | |

Bifunctor ((,,) x1) Source # | |

Bifunctor (Const *) Source # | |

Bifunctor ((,,,) x1 x2) Source # | |

Bifunctor ((,,,,) x1 x2 x3) Source # | |

Bifunctor ((,,,,,) x1 x2 x3 x4) Source # | |

Bifunctor ((,,,,,,) x1 x2 x3 x4 x5) Source # | |