Copyright | (C) 2011-2015 Edward Kmett, |
---|---|

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

Maintainer | Edward Kmett <ekmett@gmail.com> |

Stability | provisional |

Portability | Type-Families |

Safe Haskell | Trustworthy |

Language | Haskell2010 |

- class (Sieve p (Rep p), Strong p) => Representable p where
- tabulated :: (Representable p, Representable q) => Iso (d -> Rep p c) (d' -> Rep q c') (p d c) (q d' c')
- firstRep :: Representable p => p a b -> p (a, c) (b, c)
- secondRep :: Representable p => p a b -> p (c, a) (c, b)
- class (Cosieve p (Corep p), Costrong p) => Corepresentable p where
- type Corep p :: * -> *
- cotabulate :: (Corep p d -> c) -> p d c

- cotabulated :: (Corepresentable p, Corepresentable q) => Iso (Corep p d -> c) (Corep q d' -> c') (p d c) (q d' c')
- unfirstCorep :: Corepresentable p => p (a, d) (b, d) -> p a b
- unsecondCorep :: Corepresentable p => p (d, a) (d, b) -> p a b

# Representable Profunctors

class (Sieve p (Rep p), Strong p) => Representable p where Source

A `Profunctor`

`p`

is `Representable`

if there exists a `Functor`

`f`

such that
`p d c`

is isomorphic to `d -> f c`

.

Representable (->) | |

(Monad m, Functor m) => Representable (Kleisli m) | |

Representable (Forget r) | |

Functor f => Representable (Star f) | |

(Representable p, Representable q) => Representable (Procompose p q) | The composition of two |

tabulated :: (Representable p, Representable q) => Iso (d -> Rep p c) (d' -> Rep q c') (p d c) (q d' c') Source

`tabulate`

and `sieve`

form two halves of an isomorphism.

This can be used with the combinators from the `lens`

package.

`tabulated`

::`Representable`

p =>`Iso'`

(d ->`Rep`

p c) (p d c)

firstRep :: Representable p => p a b -> p (a, c) (b, c) Source

Default definition for `first'`

given that p is `Representable`

.

secondRep :: Representable p => p a b -> p (c, a) (c, b) Source

Default definition for `second'`

given that p is `Representable`

.

# Corepresentable Profunctors

class (Cosieve p (Corep p), Costrong p) => Corepresentable p where Source

A `Profunctor`

`p`

is `Corepresentable`

if there exists a `Functor`

`f`

such that
`p d c`

is isomorphic to `f d -> c`

.

cotabulate :: (Corep p d -> c) -> p d c Source

Corepresentable (->) | |

Functor w => Corepresentable (Cokleisli w) | |

Corepresentable (Tagged *) | |

Functor f => Corepresentable (Costar f) | |

(Corepresentable p, Corepresentable q) => Corepresentable (Procompose p q) |

cotabulated :: (Corepresentable p, Corepresentable q) => Iso (Corep p d -> c) (Corep q d' -> c') (p d c) (q d' c') Source

`cotabulate`

and `cosieve`

form two halves of an isomorphism.

This can be used with the combinators from the `lens`

package.

`cotabulated`

::`Corep`

f p =>`Iso'`

(f d -> c) (p d c)

unfirstCorep :: Corepresentable p => p (a, d) (b, d) -> p a b Source

Default definition for `unfirst`

given that p is `Corepresentable`

.

unsecondCorep :: Corepresentable p => p (d, a) (d, b) -> p a b Source

Default definition for `unsecond`

given that p is `Corepresentable`

.