Data.Distributive

Documentation

class Functor g => Distributive g where

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.

Methods

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

The dual of sequenceA

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

distribute = collect id

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

collect f = distribute . fmap f

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

The dual of sequence

distributeM = fmap unwrapMonad . distribute . WrapMonad

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

collectM = distributeM . liftM f

Instances

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 b

The dual of traverse

cotraverse f = fmap f . distribute

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

The dual of mapM

comapM f = fmap f . distributeM