License	BSD-style (see the file LICENSE)
Maintainer	sjoerd@w3future.com
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Data.Functor.HHCofree

Description

A cofree functor is right adjoint to a forgetful functor. In this package the forgetful functor forgets class constraints.

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

Synopsis

type (:~~>) f g = forall c d. f c d -> g c d
data HHCofree c g a b where
- HHCofree :: c f => (f :~~> g) -> f a b -> HHCofree c g a b
deriveHHCofreeInstance :: Name -> Q [Dec]
counit :: HHCofree c g :~~> g
leftAdjunct :: c f => (f :~~> g) -> f :~~> HHCofree c g
unit :: c g => g :~~> HHCofree c g
rightAdjunct :: (f :~~> HHCofree c g) -> f :~~> g
transform :: (forall r. c r => (r :~~> f) -> r :~~> g) -> HHCofree c f :~~> HHCofree c g
hfmap :: (f :~~> g) -> HHCofree c f :~~> HHCofree c g
hextend :: (HHCofree c f :~~> g) -> HHCofree c f :~~> HHCofree c g

Documentation

type (:~~>) f g = forall c d. f c d -> g c d Source #

Natural transformations.

data HHCofree c g a b where Source #

The higher order cofree functor for constraint c.

Constructors

HHCofree :: c f => (f :~~> g) -> f a b -> HHCofree c g a b

Instances

Instances details

ProfunctorComonad (HHCofree c) Source #
Instance details Defined in Data.Functor.HHCofree Methods proextract :: forall (p :: Type -> Type -> Type). Profunctor p => HHCofree c p :-> p produplicate :: forall (p :: Type -> Type -> Type). Profunctor p => HHCofree c p :-> HHCofree c (HHCofree c p)
BifunctorComonad (HHCofree c :: (Type -> Type -> Type) -> Type -> Type -> Type) Source #
Instance details Defined in Data.Functor.HHCofree Methods biextract :: forall (p :: k -> k1 -> Type). HHCofree c p :-> p biextend :: forall (p :: k -> k1 -> Type) (q :: k -> k1 -> Type). (HHCofree c p :-> q) -> HHCofree c p :-> HHCofree c q biduplicate :: forall (p :: k -> k1 -> Type). HHCofree c p :-> HHCofree c (HHCofree c p)
ProfunctorFunctor (HHCofree c :: (Type -> Type -> Type) -> Type -> Type -> Type) Source #
Instance details Defined in Data.Functor.HHCofree Methods promap :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Profunctor p => (p :-> q) -> HHCofree c p :-> HHCofree c q
BifunctorFunctor (HHCofree c :: (Type -> Type -> Type) -> Type -> Type -> Type) Source #
Instance details Defined in Data.Functor.HHCofree Methods bifmap :: forall (p :: k -> k1 -> Type) (q :: k -> k1 -> Type). (p :-> q) -> HHCofree c p :-> HHCofree c q
(c ~=> Bifunctor, c (HHCofree c a)) => Bifunctor (HHCofree c a) Source #
Instance details Defined in Data.Functor.HHCofree Methods bimap :: (a0 -> b) -> (c0 -> d) -> HHCofree c a a0 c0 -> HHCofree c a b d # first :: (a0 -> b) -> HHCofree c a a0 c0 -> HHCofree c a b c0 # second :: (b -> c0) -> HHCofree c a a0 b -> HHCofree c a a0 c0 #
(c ~=> Choice, c (HHCofree c a)) => Choice (HHCofree c a) Source #
Instance details Defined in Data.Functor.HHCofree Methods left' :: HHCofree c a a0 b -> HHCofree c a (Either a0 c0) (Either b c0) right' :: HHCofree c a a0 b -> HHCofree c a (Either c0 a0) (Either c0 b)
(c ~=> Closed, c (HHCofree c a)) => Closed (HHCofree c a) Source #
Instance details Defined in Data.Functor.HHCofree Methods closed :: HHCofree c a a0 b -> HHCofree c a (x -> a0) (x -> b)
(c ~=> Strong, c (HHCofree c a)) => Strong (HHCofree c a) Source #
Instance details Defined in Data.Functor.HHCofree Methods first' :: HHCofree c a a0 b -> HHCofree c a (a0, c0) (b, c0) second' :: HHCofree c a a0 b -> HHCofree c a (c0, a0) (c0, b)
(c ~=> Profunctor, c (HHCofree c a)) => Profunctor (HHCofree c a) Source #
Instance details Defined in Data.Functor.HHCofree Methods dimap :: (a0 -> b) -> (c0 -> d) -> HHCofree c a b c0 -> HHCofree c a a0 d lmap :: (a0 -> b) -> HHCofree c a b c0 -> HHCofree c a a0 c0 rmap :: (b -> c0) -> HHCofree c a a0 b -> HHCofree c a a0 c0 (#.) :: forall a0 b c0 q. Coercible c0 b => q b c0 -> HHCofree c a a0 b -> HHCofree c a a0 c0 (.#) :: forall a0 b c0 q. Coercible b a0 => HHCofree c a b c0 -> q a0 b -> HHCofree c a a0 c0

deriveHHCofreeInstance :: Name -> Q [Dec] Source #

Derive the instance of HHCofree c a for the class c.

For example:

deriveHHCofreeInstance ''Profunctor

counit :: HHCofree c g :~~> g Source #

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

unit :: c g => g :~~> HHCofree c g Source #

unit = leftAdjunct id

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

rightAdjunct f = counit . f

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

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

hextend :: (HHCofree c f :~~> g) -> HHCofree c f :~~> HHCofree c g Source #