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 | Safe |

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
- 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
- closedCorep :: Corepresentable p => p a b -> p (x -> a) (x -> b)
- data Prep p a where
- prepAdj :: (forall a. Prep p a -> g a) -> p :-> Star g
- unprepAdj :: (p :-> Star g) -> Prep p a -> g a
- prepUnit :: p :-> Star (Prep p)
- prepCounit :: Prep (Star f) a -> f a
- newtype Coprep p a = Coprep {
- runCoprep :: forall r. p a r -> r

- coprepAdj :: (forall a. f a -> Coprep p a) -> p :-> Costar f
- uncoprepAdj :: (p :-> Costar f) -> f a -> Coprep p a
- coprepUnit :: p :-> Costar (Coprep p)
- coprepCounit :: f a -> Coprep (Costar f) a

# Representable Profunctors

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

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') #

`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) #

Default definition for `first'`

given that p is `Representable`

.

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

Default definition for `second'`

given that p is `Representable`

.

# Corepresentable Profunctors

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

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 #

Laws:

`cotabulate`

`.`

`cosieve`

≡`id`

`cosieve`

`.`

`cotabulate`

≡`id`

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') #

`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 #

Default definition for `unfirst`

given that `p`

is `Corepresentable`

.

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

Default definition for `unsecond`

given that `p`

is `Corepresentable`

.

closedCorep :: Corepresentable p => p a b -> p (x -> a) (x -> b) #

Default definition for `closed`

given that `p`

is `Corepresentable`

# Prep -| Star

`Prep`

-|`Star`

:: [Hask, Hask] -> Prof

This gives rise to a monad in `Prof`

, `('Star'.'Prep')`

, and
a comonad in `[Hask,Hask]`

`('Prep'.'Star')`

(Monad (Rep p), Representable p) => Monad (Prep p) # | |

Profunctor p => Functor (Prep p) # | |

(Applicative (Rep p), Representable p) => Applicative (Prep p) # | |

prepCounit :: Prep (Star f) a -> f a #

# Coprep -| Costar

uncoprepAdj :: (p :-> Costar f) -> f a -> Coprep p a #

coprepUnit :: p :-> Costar (Coprep p) #

coprepCounit :: f a -> Coprep (Costar f) a #