Copyright | (C) 2011-2013 Edward Kmett |
---|---|

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

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

Stability | provisional |

Portability | portable |

Safe Haskell | Trustworthy |

Language | Haskell2010 |

For a good explanation of profunctors in Haskell see Dan Piponi's article:

http://blog.sigfpe.com/2011/07/profunctors-in-haskell.html

This module includes *unsafe* composition operators that are useful in
practice when it comes to generating optimal core in GHC.

If you import this module you are taking upon yourself the obligation
that you will only call the operators with `#`

in their names with functions
that are operationally identity such as `newtype`

constructors or the field
accessor of a `newtype`

.

# Profunctors

class Profunctor p where Source

Formally, the class `Profunctor`

represents a profunctor
from `Hask`

-> `Hask`

.

Intuitively it is a bifunctor where the first argument is contravariant and the second argument is covariant.

You can define a `Profunctor`

by either defining `dimap`

or by defining both
`lmap`

and `rmap`

.

If you supply `dimap`

, you should ensure that:

`dimap`

`id`

`id`

≡`id`

If you supply `lmap`

and `rmap`

, ensure:

`lmap`

`id`

≡`id`

`rmap`

`id`

≡`id`

If you supply both, you should also ensure:

`dimap`

f g ≡`lmap`

f`.`

`rmap`

g

These ensure by parametricity:

`dimap`

(f`.`

g) (h`.`

i) ≡`dimap`

g h`.`

`dimap`

f i`lmap`

(f`.`

g) ≡`lmap`

g`.`

`lmap`

f`rmap`

(f`.`

g) ≡`rmap`

f`.`

`rmap`

g

dimap :: (a -> b) -> (c -> d) -> p b c -> p a d Source

lmap :: (a -> b) -> p b c -> p a c Source

rmap :: (b -> c) -> p a b -> p a c Source

(#.) :: Coercible c b => (b -> c) -> p a b -> p a c infixr 9 Source

Strictly map the second argument argument covariantly with a function that is assumed operationally to be a cast, such as a newtype constructor.

*Note:* This operation is explicitly *unsafe*
since an implementation may choose to use
`unsafeCoerce`

to implement this combinator
and it has no way to validate that your function
meets the requirements.

If you implement this combinator with
`unsafeCoerce`

, then you are taking upon yourself
the obligation that you don't use GADT-like
tricks to distinguish values.

If you import Data.Profunctor.Unsafe you are taking upon yourself the obligation that you will only call this with a first argument that is operationally identity.

The semantics of this function with respect to bottoms should match the default definition:

(`#.`

) ≡ \f -> \p -> p `seq``rmap`

f p

(.#) :: Coercible b a => p b c -> (a -> b) -> p a c infixl 8 Source

Strictly map the first argument argument contravariantly with a function that is assumed operationally to be a cast, such as a newtype constructor.

*Note:* This operation is explicitly *unsafe*
since an implementation may choose to use
`unsafeCoerce`

to implement this combinator
and it has no way to validate that your function
meets the requirements.

If you implement this combinator with
`unsafeCoerce`

, then you are taking upon yourself
the obligation that you don't use GADT-like
tricks to distinguish values.

If you import Data.Profunctor.Unsafe you are taking upon yourself the obligation that you will only call this with a second argument that is operationally identity.

(`.#`

) ≡ \p -> p `seq` \f ->`lmap`

f p

Profunctor (->) | |

Monad m => Profunctor (Kleisli m) | |

Functor w => Profunctor (Cokleisli w) | |

Profunctor (Tagged *) | |

Profunctor (Forget r) | |

Arrow p => Profunctor (WrappedArrow p) | |

Functor f => Profunctor (Costar f) | |

Functor f => Profunctor (Star f) | |

Profunctor p => Profunctor (Environment p) | |

Profunctor p => Profunctor (Closure p) | |

Profunctor p => Profunctor (Codensity p) | |

Profunctor p => Profunctor (Copastro p) | |

Profunctor p => Profunctor (Cotambara p) | |

Profunctor p => Profunctor (Pastro p) | |

Profunctor p => Profunctor (Tambara p) | |

(Functor f, Profunctor p) => Profunctor (Cayley f p) | |

(Profunctor p, Profunctor q) => Profunctor (Rift p q) | |

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

(Profunctor p, Profunctor q) => Profunctor (Ran p q) |