Portability	GADTs, Rank2Types
Stability	provisional
Maintainer	Edward Kmett <ekmett@gmail.com>
Safe Haskell	None

Control.Applicative.Free

Contents

Examples

Description

Applicative functors for free

Synopsis

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 whereSource

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)
Typeable1 f => Typeable1 (Ap f)
Applicative (Ap f)
Apply (Ap f)

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

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 -> mSource

Perform a monoidal analysis over free applicative value.

Example:

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

liftAp :: f a -> Ap f aSource

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

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

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 aSource

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