License	BSD-style (see the file LICENSE)
Maintainer	sjoerd@w3future.com
Stability	experimental
Portability	non-portable
Safe Haskell	Safe
Language	Haskell2010

Data.Functor.HHFree

Description

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.

Synopsis

Documentation

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

Natural transformations.

newtype HHFree c f a b Source #

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) Source #
Methods promap :: Profunctor p => (p :-> q) -> HHFree c p :-> HHFree c q #
ProfunctorMonad (HHFree c) Source #
Methods proreturn :: Profunctor p => p :-> HHFree c p # projoin :: Profunctor p => HHFree c (HHFree c p) :-> HHFree c p #
BifunctorMonad * * (HHFree c) Source #
Methods bireturn :: p a b -> t p a b # bibind :: (HHFree c :-> k1) p (t q) -> (HHFree c :-> k1) (t p) (t q) # bijoin :: t (t p) a b -> t p a b #
BifunctorFunctor * * * * (HHFree c) Source #
Methods bifmap :: (HHFree c :-> k1) p q -> (k2 :-> k3) (t p) (t q) #
SuperClass1 (* -> * -> ) (Category ) c => Category * (HHFree c f) Source #
Methods id :: cat a a # (.) :: cat b c -> cat a b -> cat a c #
SuperClass1 (* -> * -> *) Bifunctor c => Bifunctor (HHFree c f) Source #
Methods bimap :: (a -> b) -> (c -> d) -> HHFree c f a c -> HHFree c f b d # first :: (a -> b) -> HHFree c f a c -> HHFree c f b c # second :: (b -> c) -> HHFree c f a b -> HHFree c f a c #
SuperClass1 (* -> * -> *) Arrow c => Arrow (HHFree c f) Source #
Methods arr :: (b -> c) -> HHFree c f b c # first :: HHFree c f b c -> HHFree c f (b, d) (c, d) # second :: HHFree c f b c -> HHFree c f (d, b) (d, c) # (***) :: HHFree c f b c -> HHFree c f b' c' -> HHFree c f (b, b') (c, c') # (&&&) :: HHFree c f b c -> HHFree c f b c' -> HHFree c f b (c, c') #
SuperClass1 (* -> * -> *) ArrowZero c => ArrowZero (HHFree c f) Source #
Methods zeroArrow :: HHFree c f b c #
SuperClass1 (* -> * -> *) ArrowPlus c => ArrowPlus (HHFree c f) Source #
Methods (<+>) :: HHFree c f b c -> HHFree c f b c -> HHFree c f b c #
SuperClass1 (* -> * -> *) ArrowChoice c => ArrowChoice (HHFree c f) Source #
Methods left :: HHFree c f b c -> HHFree c f (Either b d) (Either c d) # right :: HHFree c f b c -> HHFree c f (Either d b) (Either d c) # (+++) :: HHFree c f b c -> HHFree c f b' c' -> HHFree c f (Either b b') (Either c c') # (\|\|\|) :: HHFree c f b d -> HHFree c f c d -> HHFree c f (Either b c) d #
SuperClass1 (* -> * -> *) ArrowApply c => ArrowApply (HHFree c f) Source #
Methods app :: HHFree c f (HHFree c f b c, b) c #
SuperClass1 (* -> * -> *) ArrowLoop c => ArrowLoop (HHFree c f) Source #
Methods loop :: HHFree c f (b, d) (c, d) -> HHFree c f b c #
SuperClass1 (* -> * -> *) Biapplicative c => Biapplicative (HHFree c f) Source #
Methods bipure :: a -> b -> HHFree c f a b # (<<>>) :: HHFree c f (a -> b) (c -> d) -> HHFree c f a c -> HHFree c f b d # (>>) :: HHFree c f a b -> HHFree c f c d -> HHFree c f c d # (<<*) :: HHFree c f a b -> HHFree c f c d -> HHFree c f a b #
SuperClass1 (* -> * -> *) Choice c => Choice (HHFree c f) Source #
Methods left' :: HHFree c f a b -> HHFree c f (Either a c) (Either b c) # right' :: HHFree c f a b -> HHFree c f (Either c a) (Either c b) #
SuperClass1 (* -> * -> *) Closed c => Closed (HHFree c f) Source #
Methods closed :: HHFree c f a b -> HHFree c f (x -> a) (x -> b) #
SuperClass1 (* -> * -> *) Strong c => Strong (HHFree c f) Source #
Methods first' :: HHFree c f a b -> HHFree c f (a, c) (b, c) # second' :: HHFree c f a b -> HHFree c f (c, a) (c, b) #
SuperClass1 (* -> * -> *) Profunctor c => Profunctor (HHFree c f) Source #
Methods dimap :: (a -> b) -> (c -> d) -> HHFree c f b c -> HHFree c f a d # lmap :: (a -> b) -> HHFree c f b c -> HHFree c f a c # rmap :: (b -> c) -> HHFree c f a b -> HHFree c f a c # (#.) :: Coercible * c b => (b -> c) -> HHFree c f a b -> HHFree c f a c # (.#) :: Coercible * b a => HHFree c f b c -> (a -> b) -> HHFree c f a c #

unit :: f :~~> HHFree c f Source #

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

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

counit = rightAdjunct id

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

leftAdjunct f = f . unit

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

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

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