Portability | portable |
---|---|

Stability | provisional |

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

Safe Haskell | Safe-Inferred |

- class Functor g => Distributive g where
- distribute :: Functor f => f (g a) -> g (f a)
- collect :: Functor f => (a -> g b) -> f a -> g (f b)
- distributeM :: Monad m => m (g a) -> g (m a)
- collectM :: Monad m => (a -> g b) -> m a -> g (m b)

- cotraverse :: (Functor f, Distributive g) => (f a -> b) -> f (g a) -> g b
- comapM :: (Monad m, Distributive g) => (m a -> b) -> m (g a) -> g b

# Documentation

class Functor g => Distributive g whereSource

This is the categorical dual of `Traversable`

. However, there appears
to be little benefit to allow the distribution via an arbitrary comonad
so we restrict ourselves to `Functor`

.

Minimal complete definition: `distribute`

or `collect`

To be distributable a container will need to have a way to consistently zip a potentially infinite number of copies of itself. This effectively means that the holes in all values of that type, must have the same cardinality, fixed sized vectors, infinite streams, functions, etc. and no extra information to try to merge together.

distribute :: Functor f => f (g a) -> g (f a)Source

collect :: Functor f => (a -> g b) -> f a -> g (f b)Source

`collect`

f =`distribute`

.`fmap`

f

distributeM :: Monad m => m (g a) -> g (m a)Source

The dual of `sequence`

`distributeM`

=`fmap`

`unwrapMonad`

.`distribute`

.`WrapMonad`

collectM :: Monad m => (a -> g b) -> m a -> g (m b)Source

`collectM`

=`distributeM`

.`liftM`

f

Distributive Identity | |

Distributive ((->) e) | |

Distributive f => Distributive (Backwards f) | |

Distributive g => Distributive (IdentityT g) | |

Distributive f => Distributive (Reverse f) | |

Distributive g => Distributive (ReaderT e g) | |

(Distributive f, Distributive g) => Distributive (Compose f g) | |

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

cotraverse :: (Functor f, Distributive g) => (f a -> b) -> f (g a) -> g bSource

The dual of `traverse`

`cotraverse`

f =`fmap`

f .`distribute`

comapM :: (Monad m, Distributive g) => (m a -> b) -> m (g a) -> g bSource

The dual of `mapM`

`comapM`

f =`fmap`

f .`distributeM`