Copyright	(C) 2011-2016 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	portable
Safe Haskell	Safe
Language	Haskell98

Data.Distributive

Description

Synopsis

Documentation

class Functor g => Distributive g where

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.

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.

Minimal complete definition

distribute | collect

Methods

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

The dual of sequenceA

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

distribute = collect id
distribute . distribute = id

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

collect f = distribute . fmap f
fmap f = runIdentity . collect (Identity . f)
fmap distribute . collect f = getCompose . collect (Compose . 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 U1
Distributive Par1
Distributive Identity
Distributive Complex
Distributive Dual
Distributive Sum
Distributive Product
Distributive Min
Distributive Max
Distributive First
Distributive Last
Distributive ((->) e)
Distributive f => Distributive (Rec1 f)
Distributive (Proxy *)
Distributive f => Distributive (Reverse f)
Distributive f => Distributive (Backwards f)
Distributive g => Distributive (IdentityT g)
(Distributive a, Distributive b) => Distributive ((:*:) a b)
(Distributive a, Distributive b) => Distributive ((:.:) a b)
Distributive (Tagged * t)
(Distributive f, Distributive g) => Distributive (Product f g)
(Distributive f, Distributive g) => Distributive (Compose f g)
Distributive g => Distributive (ReaderT e g)
Distributive f => Distributive (M1 i c f)

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

The dual of traverse

cotraverse f = fmap f . distribute

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

The dual of mapM

comapM f = fmap f . distributeM

fmapCollect :: Distributive f => (a -> b) -> f a -> f b

fmapCollect is a viable default definition for fmap given a Distributive instance defined in terms of collect.