Data.Functor.HCofree

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

Compared to Data.Functor.Cofree we're going up a level. These free functors go between categories of functors and the natural transformations between them.

Documentation

type (:~>) f g = forall b. f b -> g b

Natural transformations.

data HCofree c g a where

The higher order cofree functor for constraint c.

Constructors

HCofree :: (c f, Functor f) => (f :~> g) -> f a -> HCofree c g a

Instances

Functor (HCofree c g)

Foldable (HCofree Foldable g)

Foldable (HCofree Traversable g)

Traversable (HCofree Traversable g)

Comonad (HCofree Comonad g)

The cofree comonad of a functor.

counit :: HCofree c g :~> g

leftAdjunct :: (c f, Functor f) => (f :~> g) -> f :~> HCofree c g

unit :: (c g, Functor g) => g :~> HCofree c g

unit = leftAdjunct id

rightAdjunct :: (f :~> HCofree c g) -> f :~> g

rightAdjunct f = counit . f

hfmap :: (f :~> g) -> HCofree c f :~> HCofree c g

liftCofree :: (c f, Functor f) => f a -> HCofree c f a

lowerCofree :: HCofree c f a -> f a

convert :: (c (t f), Functor (t f), Comonad f, ComonadTrans t) => t f a -> HCofree c f a

coiter :: c Identity => (forall b. b -> f b) -> a -> HCofree c f a

unwrap :: HCofree Comonad g a -> g (HCofree Comonad g a)