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

(forall (x :: Type -> Type). c x => Monad x) => Monad (HFree c f)

The free monad of a functor.

Defined in Data.Functor.HFree

Methods

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

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

return :: a -> HFree c f a

fail :: String -> HFree c f a

(forall (x :: Type -> Type). c x => Functor x) => Functor (HFree c f)

Defined in Data.Functor.HFree

Methods

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

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

(forall (x :: Type -> Type). c x => Applicative x) => Applicative (HFree c f)

Defined in Data.Functor.HFree

Methods

pure :: a -> HFree c f a

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

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

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

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

(forall (x :: Type -> Type). c x => Contravariant x) => Contravariant (HFree c f)

Defined in Data.Functor.HFree

Methods

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

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

(forall (x :: Type -> Type). c x => Alternative x) => Alternative (HFree c f)

Defined in Data.Functor.HFree

Methods

empty :: HFree c f a

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

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

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

(forall (x :: Type -> Type). c x => Divisible x) => Divisible (HFree c f)

Defined in Data.Functor.HFree

Methods

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

conquer :: HFree c f a

(forall (x :: Type -> Type). c x => Decidable x) => Decidable (HFree c f)

Defined in Data.Functor.HFree

Methods

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

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

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