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


-- | Haskell 98 comonads
--   
--   Haskell 98 comonads
@package comonad
@version 0.6.2


module Control.Comonad

-- | $definition
class Functor w => Comonad w
extract :: Comonad w => w a -> a
duplicate :: Comonad w => w a -> w (w a)
extend :: Comonad w => (w a -> b) -> w a -> w b

-- | <a>extend</a> with the arguments swapped. Dual to <a>&gt;&gt;=</a> for
--   a <a>Monad</a>.
(=>>) :: Comonad w => w a -> (w a -> b) -> w b

-- | <a>extend</a> in operator form
(<<=) :: Comonad w => (w a -> b) -> w a -> w b

-- | A suitable default definition for <a>fmap</a> for a <a>Comonad</a>.
--   Promotes a function to a comonad.
--   
--   <pre>
--   fmap f    = extend (f . extract)
--   </pre>
liftW :: Comonad w => (a -> b) -> w a -> w b

-- | Comonadic fixed point
wfix :: Comonad w => w (w a -> a) -> a

-- | The <a>Cokleisli</a> <a>Arrow</a>s of a given <a>Comonad</a>
newtype Cokleisli w a b
Cokleisli :: (w a -> b) -> Cokleisli w a b
runCokleisli :: Cokleisli w a b -> w a -> b

-- | Left-to-right Cokleisli composition
(=>=) :: Comonad w => (w a -> b) -> (w b -> c) -> w a -> c

-- | Right-to-left Cokleisli composition
(=<=) :: Comonad w => (w b -> c) -> (w a -> b) -> w a -> c
instance Monad (Cokleisli w a)
instance Applicative (Cokleisli w a)
instance Functor (Cokleisli w a)
instance Comonad w => ArrowChoice (Cokleisli w)
instance Comonad w => ArrowApply (Cokleisli w)
instance Comonad w => Arrow (Cokleisli w)
instance Comonad w => Category (Cokleisli w)
instance Typeable1 w => Typeable2 (Cokleisli w)
instance Comonad w => Comonad (IdentityT w)
instance Comonad Identity
instance Monoid m => Comonad ((->) m)
instance Comonad ((,) e)


module Data.Distributive

-- | This is the categorical dual of <tt>Traversable</tt>
--   
--   Minimal definition: <tt>mapW</tt> or <a>distribute</a>
--   
--   <pre>
--   mapW = fmap f . duplicate
--   distribute = mapW id
--   </pre>
--   
--   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
cotraverse :: (Distributive g, Comonad w) => (w a -> b) -> w (g a) -> g b
distribute :: (Distributive g, Comonad w) => w (g a) -> g (w a)

-- | Every <a>Distributive</a> is a <a>Functor</a>. This is a valid default
--   definition.
fmapDefault :: Distributive g => (a -> b) -> g a -> g b
instance Distributive g => Distributive (IdentityT g)
instance Distributive ((->) e)
instance Distributive Identity