Control.Applicative.Free

Applicative functors for free

Documentation

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.

See Free Applicative Functors, by Paolo Capriotti and Ambrus Kaposi, for some applications.

data Ap f a where

The free Applicative for a Functor f.

Constructors

Pure :: a -> Ap f a

Ap :: f a -> Ap f (a -> b) -> Ap f b

Instances

Functor (Ap f)

Methods

fmap :: (a -> b) -> Ap f a -> Ap f b

(<$) :: a -> Ap f b -> Ap f a

Applicative (Ap f)

Methods

pure :: 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

Comonad f => Comonad (Ap f)

Methods

extract :: Ap f a -> a

duplicate :: Ap f a -> Ap f (Ap f a)

extend :: (Ap f a -> b) -> Ap f a -> Ap f b

Apply (Ap f)

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

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

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

Perform a monoidal analysis over free applicative value.

Example:

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

liftAp :: f a -> Ap f a

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

iterAp :: Functor g => (g a -> a) -> Ap g a -> a

Tear down a free Applicative using iteration.

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

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

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

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

retractApp == runAp id

Examples

Validation form