Portability | GADTs, Rank2Types |
---|---|

Stability | provisional |

Maintainer | Edward Kmett <ekmett@gmail.com> |

Safe Haskell | None |

`Applicative`

functors for free

# 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 aSource

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 -> mSource

Perform a monoidal analysis over free applicative value.

Example:

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

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

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 aSource