Copyright | (C) 2008-2013 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 |

# Documentation

class Bifunctor p where Source

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

Bifunctor Either | |

Bifunctor (,) | |

Bifunctor Const | |

Bifunctor Arg | |

Bifunctor ((,,) x) | |

Bifunctor (Tagged *) | |

Functor f => Bifunctor (Clown f) | |

Bifunctor p => Bifunctor (Flip p) | |

Functor g => Bifunctor (Joker g) | |

Bifunctor p => Bifunctor (WrappedBifunctor p) | |

Bifunctor ((,,,) x y) | |

(Bifunctor f, Bifunctor g) => Bifunctor (Product f g) | |

(Functor f, Bifunctor p) => Bifunctor (Tannen f p) | |

Bifunctor ((,,,,) x y z) | |

(Bifunctor p, Functor f, Functor g) => Bifunctor (Biff p f g) |