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
Language	Haskell2010

Control.Applicative.Trans.Free

Contents

Free Applicative
Free Alternative

Description

Applicative functor transformers for free

Synopsis

newtype ApT f g a = ApT {
- getApT :: g (ApF f g a)
}
data ApF f g a where
- Pure :: a -> ApF f g a
- Ap :: f a -> ApT f g (a -> b) -> ApF f g b
liftApT :: Applicative g => f a -> ApT f g a
liftApO :: Functor g => g a -> 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
runApF :: (Applicative h, Functor g) => (forall a. f a -> h a) -> (forall a. g (h a) -> h a) -> ApF f g b -> h b
runApT_ :: (Functor g, Monoid m) => (forall a. f a -> m) -> (g m -> m) -> ApT f g b -> m
hoistApT :: Functor g => (forall a. f a -> f' a) -> ApT f g b -> ApT f' g b
hoistApF :: Functor g => (forall a. f a -> f' a) -> ApF f g b -> ApF f' g b
transApT :: Functor g => (forall a. g a -> g' a) -> ApT f g b -> ApT f g' b
transApF :: Functor g => (forall a. g a -> g' a) -> ApF f g b -> ApF f g' b
joinApT :: Monad m => ApT f m a -> m (Ap f a)
type Ap f = ApT f Identity
runAp :: Applicative g => (forall x. f x -> g x) -> Ap f a -> g a
runAp_ :: Monoid m => (forall x. f x -> m) -> Ap f a -> m
retractAp :: Applicative f => Ap f a -> f a
type Alt f = ApT f []
runAlt :: (Alternative g, Foldable t) => (forall x. f x -> g x) -> ApT f t a -> g a

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 #

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

Constructors

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

Instances

Instances details

Functor g => Functor (ApT f g) #
Instance details Defined in Control.Applicative.Trans.Free Methods fmap :: (a -> b) -> ApT f g a -> ApT f g b # (<$) :: a -> ApT f g b -> ApT f g a #
Applicative g => Applicative (ApT f g) #
Instance details Defined in Control.Applicative.Trans.Free Methods pure :: a -> ApT f g a # (<>) :: ApT f g (a -> b) -> ApT f g a -> ApT f g b # liftA2 :: (a -> b -> c) -> ApT f g a -> ApT f g b -> ApT f g c # (>) :: ApT f g a -> ApT f g b -> ApT f g b # (<*) :: ApT f g a -> ApT f g b -> ApT f g a #
Alternative g => Alternative (ApT f g) #
Instance details Defined in Control.Applicative.Trans.Free Methods empty :: ApT f g a # (<\|>) :: ApT f g a -> ApT f g a -> ApT f g a # some :: ApT f g a -> ApT f g [a] # many :: ApT f g a -> ApT f g [a] #
Applicative g => Apply (ApT f g) #
Instance details Defined in Control.Applicative.Trans.Free Methods (<.>) :: ApT f g (a -> b) -> ApT f g a -> ApT f g b # (.>) :: ApT f g a -> ApT f g b -> ApT f g b # (<.) :: ApT f g a -> ApT f g b -> ApT f g a # liftF2 :: (a -> b -> c) -> ApT f g a -> ApT f g b -> ApT f g c #

data ApF f g a where #

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

Instances details

Functor g => Functor (ApF f g) #
Instance details Defined in Control.Applicative.Trans.Free Methods fmap :: (a -> b) -> ApF f g a -> ApF f g b # (<$) :: a -> ApF f g b -> ApF f g a #
Applicative g => Applicative (ApF f g) #
Instance details Defined in Control.Applicative.Trans.Free Methods pure :: a -> ApF f g a # (<>) :: ApF f g (a -> b) -> ApF f g a -> ApF f g b # liftA2 :: (a -> b -> c) -> ApF f g a -> ApF f g b -> ApF f g c # (>) :: ApF f g a -> ApF f g b -> ApF f g b # (<*) :: ApF f g a -> ApF f g b -> ApF f g a #
Applicative g => Apply (ApF f g) #
Instance details Defined in Control.Applicative.Trans.Free Methods (<.>) :: ApF f g (a -> b) -> ApF f g a -> ApF f g b # (.>) :: ApF f g a -> ApF f g b -> ApF f g b # (<.) :: ApF f g a -> ApF f g b -> ApF f g a # liftF2 :: (a -> b -> c) -> ApF f g a -> ApF f g b -> ApF f g c #

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

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

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

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 #

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 #

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 #

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 #

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 #

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 #

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 #

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

joinApT :: Monad m => ApT f m a -> m (Ap f a) #

Pull out and join m layers of ApT f m a.

Free Applicative

type Ap f = ApT f Identity #

The free Applicative for a Functor f.

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

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 #

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 [] #

The free Alternative for a Functor f.

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

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