Modulefree-5.2Haskell2010

Control.Applicative.Free.Final

Final encoding of free Applicative functors.

Contents

Examples

Synopsis

newtype Ap
value runAp
value runAp_
value liftAp
value hoistAp
value retractAp

Packagefree-5.2
Exports6
LanguageHaskell2010
LicenceBSD-3-Clause
SourceFinal.hs

Compared to the free monad, they are less expressive. However, they are also more flexible to inspect and interpret, as the number of ways in which the values can be nested is more limited.

newtypenewtype Ap (f :: Type -> Type) a

Source#

The free Applicative for a Functor f.

Constructors

Ap
- _runAp :: forall (g :: Type -> Type). Applicative g => (forall x. f x -> g x) -> g a

Instances3Functor, Applicative, Apply

Functor (Ap f)Defined in free-5.2 · Control.Applicative.Free.Final
Applicative (Ap f)Defined in free-5.2 · Control.Applicative.Free.Final
Apply (Ap f)Defined in free-5.2 · Control.Applicative.Free.Final

valuerunAp :: Applicative g => (forall x. f x -> g x) -> Ap f a -> g a

Source#

Given a natural transformation from f to g, this gives a canonical monoidal natural transformation from Ap f to g.

Property

prop> runAp t == retractApp . hoistApp t

valuerunAp_ :: Monoid m => (forall a. f a -> m) -> Ap f b -> m

Source#

Perform a monoidal analysis over free applicative value.

Example:

count :: Ap f a -> Int
count = getSum . runAp_ (\_ -> Sum 1)

valueliftAp :: f a -> Ap f a

Source#

A version of lift that can be used with just a Functor for f.

valuehoistAp :: (forall a. f a -> g a) -> Ap f b -> Ap g b

Source#

Given a natural transformation from f to g this gives a monoidal natural transformation from Ap f to Ap g.

valueretractAp :: Applicative f => Ap f a -> f a

Source#

Interprets the free applicative functor over f using the semantics for pure and <*> given by the Applicative instance for f.

Property

prop> retractApp == runAp id

Examples

Validation form