Modulefree-5.2Haskell2010

Control.Applicative.Free

Applicative functors for free

1 type
6 values

Packagefree-5.2
Exports7
LanguageHaskell2010
LicenceBSD-3-Clause
SourceFree.hs

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.

datadata Ap (f :: Type -> Type) a where

The free Applicative for a Functor f.

Constructors

Pure :: a -> Ap f a
Ap :: f a1 -> Ap f (a1 -> a) -> Ap f a

Instances10Functor, Applicative, Foldable, Foldable1, Eq1, Ord1, …

Functor (Ap f)Defined in free-5.2 · Control.Applicative.Free
Applicative (Ap f)Defined in free-5.2 · Control.Applicative.Free
Foldable f => Foldable (Ap f)Defined in free-5.2 · Control.Applicative.Free
```
foldMap f == foldMap f . runAp toList
```
Foldable1 f => Foldable1 (Ap f)Defined in free-5.2 · Control.Applicative.Free
```
foldMap f == foldMap f . runAp toNonEmpty
```
Eq1 f => Eq1 (Ap f)Defined in free-5.2 · Control.Applicative.Free
Ord1 f => Ord1 (Ap f)Defined in free-5.2 · Control.Applicative.Free
Comonad f => Comonad (Ap f)Defined in free-5.2 · Control.Applicative.Free
Apply (Ap f)Defined in free-5.2 · Control.Applicative.Free
(Eq1 f, Eq a) => Eq (Ap f a)Defined in free-5.2 · Control.Applicative.Free
(Ord1 f, Ord a) => Ord (Ap f a)Defined in free-5.2 · Control.Applicative.Free

valuerunAp :: 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 Ap f to g.

Property

prop> runAp t == retractApp . hoistApp t

valuerunAp_ :: 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)

valueliftAp :: f a -> Ap f a

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

valueiterAp :: Functor g => (g a -> a) -> Ap g a -> a

Tear down a free Applicative using iteration.

valuehoistAp :: (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.

valueretractAp :: Applicative f => Ap f a -> f a

Interprets the free applicative functor over f using the semantics for pure and <*> given by the Applicative instance for f.

Property

prop> retractApp == runAp id

Examples

0 declarations

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