-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Haskell 98 Distributive functors -- Dual to Traversable
--   
--   Haskell 98 Distributive functors -- Dual to Traversable
@package distributive
@version 0.3


module Data.Distributive

-- | This is the categorical dual of <tt>Traversable</tt>. However, there
--   appears to be little benefit to allow the distribution via an
--   arbitrary comonad so we restrict ourselves to <a>Functor</a>.
--   
--   Minimal complete definition: <a>distribute</a> or <a>collect</a>
--   
--   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.
class Functor g => Distributive g where distribute = collect id collect f = distribute . fmap f distributeM = fmap unwrapMonad . distribute . WrapMonad collectM f = distributeM . liftM f
distribute :: (Distributive g, Functor f) => f (g a) -> g (f a)
collect :: (Distributive g, Functor f) => (a -> g b) -> f a -> g (f b)
distributeM :: (Distributive g, Monad m) => m (g a) -> g (m a)
collectM :: (Distributive g, Monad m) => (a -> g b) -> m a -> g (m b)

-- | The dual of <a>traverse</a>
--   
--   <pre>
--   <a>cotraverse</a> f = <a>fmap</a> f . <a>distribute</a>
--   </pre>
cotraverse :: (Functor f, Distributive g) => (f a -> b) -> f (g a) -> g b

-- | The dual of <a>mapM</a>
--   
--   <pre>
--   <a>comapM</a> f = <a>fmap</a> f . <a>distributeM</a>
--   </pre>
comapM :: (Monad m, Distributive g) => (m a -> b) -> m (g a) -> g b
instance Distributive f => Distributive (Reverse f)
instance Distributive f => Distributive (Backwards f)
instance (Distributive f, Distributive g) => Distributive (Product f g)
instance (Distributive f, Distributive g) => Distributive (Compose f g)
instance Distributive g => Distributive (IdentityT g)
instance Distributive g => Distributive (ReaderT e g)
instance Distributive ((->) e)
instance Distributive Identity