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

Data.Functor.HFree

Description

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.

Synopsis

type (:~>) f g = forall b. f b -> g b
newtype HFree c f a = HFree {
- runHFree :: forall g. c g => (f :~> g) -> g a
}
deriveHFreeInstance :: Name -> Q [Dec]
unit :: f :~> HFree c f
rightAdjunct :: c g => (f :~> g) -> HFree c f :~> g
counit :: c f => HFree c f :~> f
leftAdjunct :: (HFree c f :~> g) -> f :~> g
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

Documentation

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

Natural transformations.

newtype HFree c f a Source #

The higher order free functor for constraint c.

Constructors

HFree
Fields runHFree :: forall g. c g => (f :~> g) -> g a

Instances

Instances details

(c ~=> Monad, c (HFree c f)) => Monad (HFree c f) Source #	The free monad of a functor.
Instance details 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 #
(c ~=> Functor, c (HFree c a)) => Functor (HFree c a) Source #
Instance details Defined in Data.Functor.HFree Methods fmap :: (a0 -> b) -> HFree c a a0 -> HFree c a b # (<$) :: a0 -> HFree c a b -> HFree c a a0 #
(c ~=> Applicative, c (HFree c a)) => Applicative (HFree c a) Source #
Instance details Defined in Data.Functor.HFree Methods pure :: a0 -> HFree c a a0 # (<>) :: HFree c a (a0 -> b) -> HFree c a a0 -> HFree c a b # liftA2 :: (a0 -> b -> c0) -> HFree c a a0 -> HFree c a b -> HFree c a c0 # (>) :: HFree c a a0 -> HFree c a b -> HFree c a b # (<*) :: HFree c a a0 -> HFree c a b -> HFree c a a0 #
(c ~=> Contravariant, c (HFree c a)) => Contravariant (HFree c a) Source #
Instance details Defined in Data.Functor.HFree Methods contramap :: (a' -> a0) -> HFree c a a0 -> HFree c a a' # (>$) :: b -> HFree c a b -> HFree c a a0 #
(c ~=> Alternative, c (HFree c a)) => Alternative (HFree c a) Source #
Instance details 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 ~=> Decidable, c (HFree c a)) => Decidable (HFree c a) Source #
Instance details 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
(c ~=> Divisible, c (HFree c a)) => Divisible (HFree c a) Source #
Instance details 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

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

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

For example:

deriveHFreeInstance ''Functor

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

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

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

counit = rightAdjunct id

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

leftAdjunct f = f . unit

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

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

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

liftFree :: f a -> HFree c f a Source #

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

convert :: (c (t f), Monad f, MonadTrans t) => HFree c f a -> t f a Source #

iter :: c Identity => (forall b. f b -> b) -> HFree c f a -> a Source #

wrap :: f (HFree Monad f a) -> HFree Monad f a Source #