Modulefree-5.2Haskell2010

Control.Applicative.Free.Fast

A faster free applicative. Based on Dave Menendez's work.

Contents

The Sequence of Effects
The Faster Free Applicative

Synopsis

data ASeq
value reduceASeq
value hoistASeq
value traverseASeq
value rebaseASeq
newtype Ap
value liftAp
value retractAp
value runAp
value runAp_
value hoistAp

Packagefree-5.2
Exports11
LanguageHaskell2010
LicenceBSD-3-Clause
SourceFast.hs

The Sequence of Effects

datadata ASeq (f :: Type -> Type) a where

Source#

The free applicative is composed of a sequence of effects, and a pure function to apply that sequence to. The fast free applicative separates these from each other, so that the sequence may be built up independently, and so that fmap can run in constant time by having immediate access to the pure function.

Constructors

ANil :: ASeq f ()
ACons :: f a -> ASeq f u -> ASeq f a

valuereduceASeq :: Applicative f => ASeq f u -> f u

Source#

Interprets the sequence of effects using the semantics for pure and <*> given by the Applicative instance for f.

valuehoistASeq :: (forall x. f x -> g x) -> ASeq f a -> ASeq g a

Source#

Given a natural transformation from f to g this gives a natural transformation from ASeq f to ASeq g.

valuetraverseASeq

:: Applicative h
=> forall x. f x -> h (g x)
-> ASeq f a
-> h (ASeq g a)

Source#

Traverse a sequence with resepect to its interpretation type f.

valuerebaseASeq

:: ASeq f u
-> forall x. (x -> y) -> ASeq f x -> z
-> v -> u -> y
-> ASeq f v
-> z

Source#

It may not be obvious, but this essentially acts like ++, traversing the first sequence and creating a new one by appending the second sequence. The difference is that this also has to modify the return functions and that the return type depends on the input types.

See the source of hoistAp as an example usage.

The Faster Free Applicative

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

Source#

The faster free Applicative.

Constructors

Ap
- unAp :: forall u y z. (forall x. (x -> y) -> ASeq f x -> z) -> (u -> a -> y) -> ASeq f u -> z

Instances3Functor, Applicative, Apply

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

valueliftAp :: f a -> Ap f a

Source#

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

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

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)

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

Source#

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