Control.Comonad

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Comonads

class Functor w => Comonad w where

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Methods

extract :: w a -> a

 extract . fmap f = f . extract

duplicate :: w a -> w (w a)

 duplicate = extend id
 fmap (fmap f) . duplicate = duplicate . fmap f

extend :: (w a -> b) -> w a -> w b

 extend f  = fmap f . duplicate

Instances

Comonad Identity

Monoid m => Comonad ((->) m)

Comonad ((,) e)

Comonad w => Comonad (IdentityT w)

(=>>) :: Comonad w => w a -> (w a -> b) -> w b

extend with the arguments swapped. Dual to >>= for a Monad.

(<<=) :: Comonad w => (w a -> b) -> w a -> w b

extend in operator form

liftW :: Comonad w => (a -> b) -> w a -> w b

A suitable default definition for fmap for a Comonad. Promotes a function to a comonad.

 fmap f    = extend (f . extract)

wfix :: Comonad w => w (w a -> a) -> a

Comonadic fixed point

Cokleisli Arrows

newtype Cokleisli w a b

The Cokleisli Arrows of a given Comonad

Constructors

Cokleisli

Fields

runCokleisli :: w a -> b

Instances

Typeable1 w => Typeable2 (Cokleisli w)

Comonad w => Arrow (Cokleisli w)

Comonad w => ArrowChoice (Cokleisli w)

Comonad w => ArrowApply (Cokleisli w)

Comonad w => Category (Cokleisli w)

Monad (Cokleisli w a)

Functor (Cokleisli w a)

Applicative (Cokleisli w a)

Cokleisli composition

(=>=) :: Comonad w => (w a -> b) -> (w b -> c) -> w a -> c

Left-to-right Cokleisli composition

(=<=) :: Comonad w => (w b -> c) -> (w a -> b) -> w a -> c

Right-to-left Cokleisli composition