Control.Applicative.Free.Fast

Description

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

Synopsis

The Sequence of Effects

data ASeq f 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, u)

reduceASeq :: 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.

hoistASeq :: (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.

traverseASeq :: 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.

rebaseASeq :: 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

newtype Ap f a Source #

The faster free Applicative.

Constructors

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

Instances

Instances details
 Functor (Ap f) Source # Instance detailsDefined in Control.Applicative.Free.Fast Methodsfmap :: (a -> b) -> Ap f a -> Ap f b #(<\$) :: a -> Ap f b -> Ap f a # Source # Instance detailsDefined in Control.Applicative.Free.Fast Methodspure :: a -> Ap f a #(<*>) :: Ap f (a -> b) -> Ap f a -> Ap f b #liftA2 :: (a -> b -> c) -> Ap f a -> Ap f b -> Ap f c #(*>) :: Ap f a -> Ap f b -> Ap f b #(<*) :: Ap f a -> Ap f b -> Ap f a # Apply (Ap f) Source # Instance detailsDefined in Control.Applicative.Free.Fast Methods(<.>) :: Ap f (a -> b) -> Ap f a -> Ap f b #(.>) :: Ap f a -> Ap f b -> Ap f b #(<.) :: Ap f a -> Ap f b -> Ap f a #liftF2 :: (a -> b -> c) -> Ap f a -> Ap f b -> Ap f c #

liftAp :: f a -> Ap f a Source #

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

retractAp :: 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.

retractApp == runAp id

runAp :: 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.

runAp t == retractApp . hoistApp t

runAp_ :: 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)


hoistAp :: (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.