Data.Functor.HHFree

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

Compared to Data.Functor.HFree we have 2 two parameters.

Documentation

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

Natural transformations.

newtype HHFree c f a b

The higher order free functor over two type parameters for constraint c.

Constructors

HHFree

Fields

• runHHFree :: forall g. c g => (f :~~> g) -> g a b

Instances

ProfunctorFunctor (HHFree c)

Defined in Data.Functor.HHFree

Methods

promap :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Profunctor p => (p :-> q) -> HHFree c p :-> HHFree c q

ProfunctorMonad (HHFree c)

Defined in Data.Functor.HHFree

Methods

proreturn :: forall (p :: Type -> Type -> Type). Profunctor p => p :-> HHFree c p

projoin :: forall (p :: Type -> Type -> Type). Profunctor p => HHFree c (HHFree c p) :-> HHFree c p

BifunctorMonad (HHFree c :: (Type -> Type -> Type) -> Type -> Type -> Type)

Defined in Data.Functor.HHFree

Methods

bireturn :: forall (p :: k -> k1 -> Type). p :-> HHFree c p

bibind :: forall (p :: k -> k1 -> Type) (q :: k -> k1 -> Type). (p :-> HHFree c q) -> HHFree c p :-> HHFree c q

bijoin :: forall (p :: k -> k1 -> Type). HHFree c (HHFree c p) :-> HHFree c p

BifunctorFunctor (HHFree c :: (Type -> Type -> Type) -> Type -> Type -> Type)

Defined in Data.Functor.HHFree

Methods

bifmap :: forall (p :: k -> k1 -> Type) (q :: k -> k1 -> Type). (p :-> q) -> HHFree c p :-> HHFree c q

c ~=> (Category :: (Type -> Type -> Type) -> Constraint) => Category (HHFree c a :: Type -> Type -> Type)

Defined in Data.Functor.HHFree

Methods

id :: forall (a0 :: k). HHFree c a a0 a0

(.) :: forall (b :: k) (c0 :: k) (a0 :: k). HHFree c a b c0 -> HHFree c a a0 b -> HHFree c a a0 c0

c ~=> Bifunctor => Bifunctor (HHFree c a)

Defined in Data.Functor.HHFree

Methods

bimap :: (a0 -> b) -> (c0 -> d) -> HHFree c a a0 c0 -> HHFree c a b d

first :: (a0 -> b) -> HHFree c a a0 c0 -> HHFree c a b c0

second :: (b -> c0) -> HHFree c a a0 b -> HHFree c a a0 c0

c ~=> Arrow => Arrow (HHFree c a)

Defined in Data.Functor.HHFree

Methods

arr :: (b -> c0) -> HHFree c a b c0

first :: HHFree c a b c0 -> HHFree c a (b, d) (c0, d)

second :: HHFree c a b c0 -> HHFree c a (d, b) (d, c0)

(***) :: HHFree c a b c0 -> HHFree c a b' c' -> HHFree c a (b, b') (c0, c')

(&&&) :: HHFree c a b c0 -> HHFree c a b c' -> HHFree c a b (c0, c')

c ~=> ArrowZero => ArrowZero (HHFree c a)

Defined in Data.Functor.HHFree

Methods

zeroArrow :: HHFree c a b c0

c ~=> ArrowPlus => ArrowPlus (HHFree c a)

Defined in Data.Functor.HHFree

Methods

(<+>) :: HHFree c a b c0 -> HHFree c a b c0 -> HHFree c a b c0

c ~=> ArrowChoice => ArrowChoice (HHFree c a)

Defined in Data.Functor.HHFree

Methods

left :: HHFree c a b c0 -> HHFree c a (Either b d) (Either c0 d)

right :: HHFree c a b c0 -> HHFree c a (Either d b) (Either d c0)

(+++) :: HHFree c a b c0 -> HHFree c a b' c' -> HHFree c a (Either b b') (Either c0 c')

(|||) :: HHFree c a b d -> HHFree c a c0 d -> HHFree c a (Either b c0) d

(forall (x :: Type -> Type -> Type). c x => ArrowApply x) => ArrowApply (HHFree c f)

Defined in Data.Functor.HHFree

Methods

app :: HHFree c f (HHFree c f b c0, b) c0

c ~=> ArrowLoop => ArrowLoop (HHFree c a)

Defined in Data.Functor.HHFree

Methods

loop :: HHFree c a (b, d) (c0, d) -> HHFree c a b c0

c ~=> Biapplicative => Biapplicative (HHFree c a)

Defined in Data.Functor.HHFree

Methods

bipure :: a0 -> b -> HHFree c a a0 b

(<<*>>) :: HHFree c a (a0 -> b) (c0 -> d) -> HHFree c a a0 c0 -> HHFree c a b d

biliftA2 :: (a0 -> b -> c0) -> (d -> e -> f) -> HHFree c a a0 d -> HHFree c a b e -> HHFree c a c0 f

(*>>) :: HHFree c a a0 b -> HHFree c a c0 d -> HHFree c a c0 d

(<<*) :: HHFree c a a0 b -> HHFree c a c0 d -> HHFree c a a0 b

c ~=> Choice => Choice (HHFree c a)

Defined in Data.Functor.HHFree

Methods

left' :: HHFree c a a0 b -> HHFree c a (Either a0 c0) (Either b c0)

right' :: HHFree c a a0 b -> HHFree c a (Either c0 a0) (Either c0 b)

c ~=> Closed => Closed (HHFree c a)

Defined in Data.Functor.HHFree

Methods

closed :: HHFree c a a0 b -> HHFree c a (x -> a0) (x -> b)

c ~=> Strong => Strong (HHFree c a)

Defined in Data.Functor.HHFree

Methods

first' :: HHFree c a a0 b -> HHFree c a (a0, c0) (b, c0)

second' :: HHFree c a a0 b -> HHFree c a (c0, a0) (c0, b)

c ~=> Profunctor => Profunctor (HHFree c a)

Defined in Data.Functor.HHFree

Methods

dimap :: (a0 -> b) -> (c0 -> d) -> HHFree c a b c0 -> HHFree c a a0 d

lmap :: (a0 -> b) -> HHFree c a b c0 -> HHFree c a a0 c0

rmap :: (b -> c0) -> HHFree c a a0 b -> HHFree c a a0 c0

(#.) :: forall a0 b c0 q. Coercible c0 b => q b c0 -> HHFree c a a0 b -> HHFree c a a0 c0

(.#) :: forall a0 b c0 q. Coercible b a0 => HHFree c a b c0 -> q a0 b -> HHFree c a a0 c0

deriveHHFreeInstance :: Name -> Q [Dec]

Derive the instance of HHFree c f a b for the class c,.

For example:

deriveHHFreeInstance ''Category

unit :: f :~~> HHFree c f

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

counit :: c f => HHFree c f :~~> f

counit = rightAdjunct id

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

leftAdjunct f = f . unit

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

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

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