distributive-0.3.1: Haskell 98 Distributive functors -- Dual to Traversable

Portability portable provisional Edward Kmett Safe-Inferred

Data.Distributive

Description

Synopsis

# 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.

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

 Distributive Identity Distributive ((->) e) Distributive f => Distributive (Reverse f) Distributive f => Distributive (Backwards f) Distributive g => Distributive (IdentityT g) 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``