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 |

`Applicative`

functors for free

## Synopsis

- data Ap f a where
- 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.

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

to `Ap`

f`g`

.

runAp t == retractApp . hoistApp t

runAp_ :: Monoid m => (forall a. f a -> m) -> Ap f b -> m #

Perform a monoidal analysis over free applicative value.

Example:

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

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

Tear down a free `Applicative`

using iteration.

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

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 #