Copyright	(C) 2012-2013 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	GADTs, Rank2Types
Safe Haskell	Safe-Inferred
Language	Haskell2010

Control.Applicative.Trans.Free

Contents

Free Applicative
Free Alternative

Description

Applicative functor transformers for free

Synopsis

Documentation

Compared to the free monad transformers, 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.

newtype ApT f g a Source

The free Applicative transformer for a Functor f over Applicative g.

Constructors

ApT
Fields getApT :: g (ApF f g a)

Instances

Alternative g => Alternative (ApT f g)
Functor g => Functor (ApT f g)
Applicative g => Applicative (ApT f g)
Applicative g => Apply (ApT f g)
Typeable ((* -> ) -> ( -> ) -> -> *) ApT

data ApF f g a where Source

The free Applicative for a Functor f.

Constructors

Pure :: a -> ApF f g a
Ap :: f a -> ApT f g (a -> b) -> ApF f g b

Instances

Functor g => Functor (ApF f g)
Applicative g => Applicative (ApF f g)
Applicative g => Apply (ApF f g)
Typeable ((* -> ) -> ( -> ) -> -> *) ApF

liftApT :: Applicative g => f a -> ApT f g a Source

A version of lift that can be used with no constraint for f.

liftApO :: Functor g => g a -> ApT f g a Source

Lift an action of the "outer" Functor g a to ApT f g a.

runApT :: (Applicative h, Functor g) => (forall a. f a -> h a) -> (forall a. g (h a) -> h a) -> ApT f g b -> h b Source

Given natural transformations f ~> h and g . h ~> h this gives a natural transformation ApT f g ~> h.

runApF :: (Applicative h, Functor g) => (forall a. f a -> h a) -> (forall a. g (h a) -> h a) -> ApF f g b -> h b Source

Given natural transformations f ~> h and g . h ~> h this gives a natural transformation ApF f g ~> h.

runApT_ :: (Functor g, Monoid m) => (forall a. f a -> m) -> (g m -> m) -> ApT f g b -> m Source

Perform a monoidal analysis over ApT f g b value.

Examples:

height :: (Functor g, Foldable g) => ApT f g a -> Int
height = getSum . runApT_ (_ -> Sum 1) maximum

size :: (Functor g, Foldable g) => ApT f g a -> Int
size = getSum . runApT_ (_ -> Sum 1) fold

hoistApT :: Functor g => (forall a. f a -> f' a) -> ApT f g b -> ApT f' g b Source

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

hoistApF :: Functor g => (forall a. f a -> f' a) -> ApF f g b -> ApF f' g b Source

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

transApT :: Functor g => (forall a. g a -> g' a) -> ApT f g b -> ApT f g' b Source

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

transApF :: Functor g => (forall a. g a -> g' a) -> ApF f g b -> ApF f g' b Source

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

Free Applicative

type Ap f = ApT f Identity Source

The free Applicative for a Functor f.

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 x. f x -> m) -> Ap f a -> m Source

Perform a monoidal analysis over free applicative value.

Example:

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

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

Free Alternative

type Alt f = ApT f [] Source

The free Alternative for a Functor f.

runAlt :: (Alternative g, Foldable t) => (forall x. f x -> g x) -> ApT f t a -> g a Source

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