distributive-0.4: 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`.

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

 Distributive Identity Distributive ((->) e) Distributive (Proxy *) Distributive f => Distributive (Reverse f) Distributive f => Distributive (Backwards f) Distributive g => Distributive (IdentityT g) Distributive (Tagged * t) 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``