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.Final

Contents

Examples

Description

Final encoding of free Applicative functors.

Synopsis

newtype Ap (f :: Type -> Type) a = Ap {
- _runAp :: forall (g :: Type -> Type). Applicative g => (forall x. f x -> g x) -> g 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
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.

newtype Ap (f :: Type -> Type) a Source #

The free Applicative for a Functor f.

Constructors

Ap
Fields _runAp :: forall (g :: Type -> Type). Applicative g => (forall x. f x -> g x) -> g a

Instances

Instances details

Applicative (Ap f) Source #
Instance details Defined in Control.Applicative.Free.Final 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.Final Methods fmap :: (a -> b) -> Ap f a -> Ap f b # (<$) :: a -> Ap f b -> Ap f a #
Apply (Ap f) Source #
Instance details Defined in Control.Applicative.Free.Final 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 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.

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