Data.Functor.Cofree

A cofree functor is right adjoint to a forgetful functor. In this package the forgetful functor forgets class constraints.

Documentation

data Cofree c b where

The cofree functor for constraint c.

Constructors

Cofree :: c a => (a -> b) -> a -> Cofree c b

Instances

(ForallF c Identity, ForallF c (Cofree c), ForallF c (Compose (Cofree c) (Cofree c))) => Monad (Cofree c)

Functor (Cofree c)

(ForallF c Identity, ForallF c (Cofree c), ForallF c (Compose (Cofree c) (Cofree c))) => Applicative (Cofree c)

ForallF c (Cofree c) => Comonad (Cofree c)

counit :: Cofree c b -> b

leftAdjunct :: c a => (a -> b) -> a -> Cofree c b

leftAdjunctF :: ForallF c f => (f a -> b) -> f a -> Cofree c b

unit :: c b => b -> Cofree c b

unit = leftAdjunct id

rightAdjunct :: (a -> Cofree c b) -> a -> b

rightAdjunct f = counit . f

convert :: (c (w a), Comonad w) => w a -> Cofree c a

Products

type Product c m n = Cofree c (m, n)

product :: c a => (a -> m) -> (a -> n) -> a -> Product c m n

outL :: Product c m n -> m

outR :: Product c m n -> n

type TerminalObject c = Cofree c ()

terminal :: c a => a -> TerminalObject c