Data.Functor.HFree

A free functor is left adjoint to a forgetful functor. In this package the forgetful functor forgets class constraints.

Compared to Data.Functor.Free 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.

newtype HFree c f a

The higher order free functor for constraint c.

Constructors

HFree

Fields

runHFree :: forall g. (c g, Functor g) => (f :~> g) -> g a

Instances

Alternative (HFree Alternative f)

Monad (HFree Monad f)

The free monad of a functor.

Functor (HFree c f)

Applicative (HFree Alternative f)

Applicative (HFree Monad f)

Applicative (HFree Applicative f)

unit :: f :~> HFree c f

rightAdjunct :: (c g, Functor g) => (f :~> g) -> HFree c f :~> g

counit :: (c f, Functor f) => HFree c f :~> f

counit = rightAdjunct id

leftAdjunct :: (HFree c f :~> g) -> f :~> g

leftAdjunct f = f . unit

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

liftFree :: f a -> HFree c f a

lowerFree :: (c f, Functor f) => HFree c f a -> f a

convert :: (c (t f), Functor (t f), Monad f, MonadTrans t) => HFree c f a -> t f a

iter :: c Identity => (forall b. f b -> b) -> HFree c f a -> a

wrap :: f (HFree Monad f a) -> HFree Monad f a