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.Free

Contents

Examples

Description

Applicative functors for free

Synopsis

data Ap (f :: Type -> Type) a where
- Pure :: forall a (f :: Type -> Type). a -> Ap f a
- Ap :: forall (f :: Type -> Type) a1 a. f a1 -> Ap f (a1 -> a) -> Ap f a
runAp :: Applicative g => (forall x. f x -> g x) -> Ap f a -> g a
runAp_ :: Monoid m => (forall a. f a -> m) -> Ap f b -> m
liftAp :: f a -> Ap f a
iterAp :: Functor g => (g a -> a) -> Ap g a -> a
hoistAp :: (forall a. f a -> g a) -> Ap f b -> Ap g b
retractAp :: Applicative f => Ap f a -> f a

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 :: Type -> Type) a where Source #

The free Applicative for a Functor f.

Constructors

Pure :: forall a (f :: Type -> Type). a -> Ap f a
Ap :: forall (f :: Type -> Type) a1 a. f a1 -> Ap f (a1 -> a) -> Ap f a

Instances

Instances details

Foldable f => Foldable (Ap f) Source #	foldMap f == foldMap f . `runAp` `toList`
Instance details Defined in Control.Applicative.Free Methods fold :: Monoid m => Ap f m -> m # foldMap :: Monoid m => (a -> m) -> Ap f a -> m # foldMap' :: Monoid m => (a -> m) -> Ap f a -> m # foldr :: (a -> b -> b) -> b -> Ap f a -> b # foldr' :: (a -> b -> b) -> b -> Ap f a -> b # foldl :: (b -> a -> b) -> b -> Ap f a -> b # foldl' :: (b -> a -> b) -> b -> Ap f a -> b # foldr1 :: (a -> a -> a) -> Ap f a -> a # foldl1 :: (a -> a -> a) -> Ap f a -> a # toList :: Ap f a -> [a] # null :: Ap f a -> Bool # length :: Ap f a -> Int # elem :: Eq a => a -> Ap f a -> Bool # maximum :: Ord a => Ap f a -> a # minimum :: Ord a => Ap f a -> a # sum :: Num a => Ap f a -> a # product :: Num a => Ap f a -> a #
Foldable1 f => Foldable1 (Ap f) Source #	foldMap f == foldMap f . `runAp` `toNonEmpty`
Instance details Defined in Control.Applicative.Free Methods fold1 :: Semigroup m => Ap f m -> m # foldMap1 :: Semigroup m => (a -> m) -> Ap f a -> m # foldMap1' :: Semigroup m => (a -> m) -> Ap f a -> m # toNonEmpty :: Ap f a -> NonEmpty a # maximum :: Ord a => Ap f a -> a # minimum :: Ord a => Ap f a -> a # head :: Ap f a -> a # last :: Ap f a -> a # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Ap f a -> b # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Ap f a -> b # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Ap f a -> b # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Ap f a -> b #
Eq1 f => Eq1 (Ap f) Source #
Instance details Defined in Control.Applicative.Free Methods liftEq :: (a -> b -> Bool) -> Ap f a -> Ap f b -> Bool #
Ord1 f => Ord1 (Ap f) Source #
Instance details Defined in Control.Applicative.Free Methods liftCompare :: (a -> b -> Ordering) -> Ap f a -> Ap f b -> Ordering #
Applicative (Ap f) Source #
Instance details Defined in Control.Applicative.Free 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 #
Functor (Ap f) Source #
Instance details Defined in Control.Applicative.Free Methods fmap :: (a -> b) -> Ap f a -> Ap f b # (<$) :: a -> Ap f b -> Ap f a #
Comonad f => Comonad (Ap f) Source #
Instance details Defined in Control.Applicative.Free 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) Source #
Instance details Defined in Control.Applicative.Free 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 #
(Eq1 f, Eq a) => Eq (Ap f a) Source #
Instance details Defined in Control.Applicative.Free Methods (==) :: Ap f a -> Ap f a -> Bool # (/=) :: Ap f a -> Ap f a -> Bool #
(Ord1 f, Ord a) => Ord (Ap f a) Source #
Instance details Defined in Control.Applicative.Free Methods compare :: Ap f a -> Ap f a -> Ordering # (<) :: Ap f a -> Ap f a -> Bool # (<=) :: Ap f a -> Ap f a -> Bool # (>) :: Ap f a -> Ap f a -> Bool # (>=) :: Ap f a -> Ap f a -> Bool # max :: Ap f a -> Ap f a -> Ap f a # min :: Ap f a -> Ap f a -> Ap f a #

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)

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

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

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

Tear down a free Applicative using iteration.

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

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 Source #

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