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


-- | Haskell 98 comonads
--   
--   Haskell 98 comonads
@package comonad
@version 1.0


module Data.Functor.Extend
class Functor w => Extend w
duplicate :: Extend w => w a -> w (w a)
extend :: Extend 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>.
(=>>) :: Extend w => w a -> (w a -> b) -> w b

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

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

-- | Right-to-left Cokleisli composition
(=<=) :: Extend w => (w b -> c) -> (w a -> b) -> w a -> c
instance Extend w => Extend (IdentityT w)
instance Extend Identity
instance Semigroup m => Extend ((->) m)
instance Extend ((,) e)
instance Extend (Either a)
instance Extend Maybe
instance Extend []


module Control.Comonad
class Functor w => Extend w
duplicate :: Extend w => w a -> w (w a)
extend :: Extend w => (w a -> b) -> w a -> w b

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

-- | Right-to-left Cokleisli composition
(=<=) :: Extend w => (w b -> c) -> (w a -> b) -> w a -> c

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

-- | $definition
class Extend w => Comonad w
extract :: Comonad w => w a -> a

-- | 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
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 (Semigroup m, Monoid m) => Comonad ((->) m)
instance Comonad ((,) e)