| Copyright | (C) 2011-2014 Edward Kmett |
|---|---|
| License | BSD-style (see the file LICENSE) |
| Maintainer | Edward Kmett <ekmett@gmail.com> |
| Stability | provisional |
| Portability | portable |
| Safe Haskell | Safe-Inferred |
| Language | Haskell98 |
Data.Distributive
Description
- class Functor g => Distributive g where
- distribute :: Functor f => f (g a) -> g (f a)
- collect :: Functor f => (a -> g b) -> f a -> g (f b)
- distributeM :: Monad m => m (g a) -> g (m a)
- collectM :: Monad m => (a -> g b) -> m a -> g (m b)
- cotraverse :: (Functor f, Distributive g) => (f a -> b) -> f (g a) -> g b
- comapM :: (Monad m, Distributive g) => (m a -> b) -> m (g a) -> g b
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.
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.
Minimal complete definition
Nothing
Methods
distribute :: Functor f => f (g a) -> g (f a)
collect :: Functor f => (a -> g b) -> f a -> g (f b)
collectf =distribute.fmapf
distributeM :: Monad m => m (g a) -> g (m a)
The dual of sequence
distributeM=fmapunwrapMonad.distribute.WrapMonad
collectM :: Monad m => (a -> g b) -> m a -> g (m b)
collectM=distributeM.liftMf
Instances
| Distributive Identity | |
| Distributive ((->) e) | |
| Distributive (Proxy *) | |
| Distributive f => Distributive (Reverse f) | |
| Distributive f => Distributive (Backwards f) | |
| Distributive g => Distributive (IdentityT g) | |
| Distributive g => Distributive (ReaderT e g) | |
| Distributive (Tagged * t) | |
| (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
cotraversef =fmapf .distribute
comapM :: (Monad m, Distributive g) => (m a -> b) -> m (g a) -> g b
The dual of mapM
comapMf =fmapf .distributeM