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 => (f :~> g) -> g a

Instances

c ~=> Monad => Monad (HFree c a)

The free monad of a functor.

Defined in Data.Functor.HFree

Methods

(>>=) :: HFree c a a0 -> (a0 -> HFree c a b) -> HFree c a b

(>>) :: HFree c a a0 -> HFree c a b -> HFree c a b

return :: a0 -> HFree c a a0

c ~=> Functor => Functor (HFree c a)

Defined in Data.Functor.HFree

Methods

fmap :: (a0 -> b) -> HFree c a a0 -> HFree c a b

(<$) :: a0 -> HFree c a b -> HFree c a a0

c ~=> Applicative => Applicative (HFree c a)

Defined in Data.Functor.HFree

Methods

pure :: a0 -> HFree c a a0

(<*>) :: HFree c a (a0 -> b) -> HFree c a a0 -> HFree c a b

liftA2 :: (a0 -> b -> c0) -> HFree c a a0 -> HFree c a b -> HFree c a c0

(*>) :: HFree c a a0 -> HFree c a b -> HFree c a b

(<*) :: HFree c a a0 -> HFree c a b -> HFree c a a0

c ~=> Contravariant => Contravariant (HFree c a)

Defined in Data.Functor.HFree

Methods

contramap :: (a0 -> b) -> HFree c a b -> HFree c a a0

(>$) :: b -> HFree c a b -> HFree c a a0

c ~=> Alternative => Alternative (HFree c a)

Defined in Data.Functor.HFree

Methods

empty :: HFree c a a0

(<|>) :: HFree c a a0 -> HFree c a a0 -> HFree c a a0

some :: HFree c a a0 -> HFree c a [a0]

many :: HFree c a a0 -> HFree c a [a0]

c ~=> Divisible => Divisible (HFree c a)

Defined in Data.Functor.HFree

Methods

divide :: (a0 -> (b, c0)) -> HFree c a b -> HFree c a c0 -> HFree c a a0

conquer :: HFree c a a0

c ~=> Decidable => Decidable (HFree c a)

Defined in Data.Functor.HFree

Methods

lose :: (a0 -> Void) -> HFree c a a0

choose :: (a0 -> Either b c0) -> HFree c a b -> HFree c a c0 -> HFree c a a0

deriveHFreeInstance :: Name -> Q [Dec]

Derive the instance of HFree c f a for the class c,.

For example:

deriveHFreeInstance ''Functor

unit :: f :~> HFree c f

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

counit :: c f => HFree c f :~> f

counit = rightAdjunct id

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

leftAdjunct f = f . unit

transform :: (forall r. c r => (g :~> r) -> f :~> r) -> HFree c f :~> HFree c g

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

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

liftFree :: f a -> HFree c f a

lowerFree :: c f => HFree c f a -> f a

convert :: (c (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