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`

functor transformers for free

## Synopsis

- newtype ApT f g a = ApT {}
- data ApF f g a where
- 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.

The free `Applicative`

transformer for a `Functor`

`f`

over
`Applicative`

`g`

.

## Instances

Functor g => Functor (ApT f g) # | |

Applicative g => Applicative (ApT f g) # | |

Alternative g => Alternative (ApT f g) # | |

Applicative g => Apply (ApT f g) # | |

The free `Applicative`

for a `Functor`

`f`

.

## Instances

Functor g => Functor (ApF f g) # | |

Applicative g => Applicative (ApF f g) # | |

Applicative g => Apply (ApF f g) # | |

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

A version of `lift`

that can be used with no constraint for `f`

.

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`

.

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'`

.

# Free Applicative

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 `ApF`

f`g`

.

runAp t == retractApp . hoistApp t

retractAp :: Applicative f => Ap f a -> f a #

# Free Alternative

The free `Alternative`

for a `Functor`

`f`

.