distributive-0.5.0.2: Distributive functors -- Dual to Traversable

Data.Distributive

Description

Synopsis

# Documentation

class Functor g => Distributive g where Source

This is the categorical dual of Traversable.

Due to the lack of non-trivial comonoids in Haskell, we can restrict ourselves to requiring a Functor rather than some Coapplicative class. Categorically every Distributive functor is actually a right adjoint, and so it must be Representable endofunctor and preserve all limits. This is a fancy way of saying it isomorphic to (->) x for some x.

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.

Methods

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

The dual of sequenceA

>>> distribute [(+1),(+2)] 1
[2,3]

distribute = collect id

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

Instances

The dual of traverse
cotraverse f = fmap f . distribute
The dual of mapM
comapM f = fmap f . distributeM