Modulefree-5.2Haskell2010

Control.Applicative.Trans.Free

Applicative functor transformers for free

Contents

Free Applicative
Free Alternative

Synopsis

newtype ApT
data ApF
value liftApT
value liftApO
value runApT
value runApF
value runApT_
value hoistApT
value hoistApF
value transApT
value transApF
value joinApT
type Ap
value runAp
value runAp_
value retractAp
type Alt
value runAlt

Packagefree-5.2
Exports18
LanguageHaskell2010
LicenceBSD-3-Clause
SourceFree.hs

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.

newtypenewtype ApT (f :: Type -> Type) (g :: Type -> Type) a

Source#

The free Applicative transformer for a Functor f over Applicative g.

Constructors

ApT
- getApT :: g (ApF f g a)

Instances4Functor, Applicative, Alternative, Apply

Functor g => Functor (ApT f g)Defined in free-5.2 · Control.Applicative.Trans.Free
Applicative g => Applicative (ApT f g)Defined in free-5.2 · Control.Applicative.Trans.Free
Alternative g => Alternative (ApT f g)Defined in free-5.2 · Control.Applicative.Trans.Free
Applicative g => Apply (ApT f g)Defined in free-5.2 · Control.Applicative.Trans.Free

datadata ApF (f :: Type -> Type) (g :: Type -> Type) a where

Source#

The free Applicative for a Functor f.

Constructors

Pure :: a -> ApF f g a
Ap :: f a -> ApT f g (a -> b) -> ApF f g a

Instances3Functor, Applicative, Apply

Functor g => Functor (ApF f g)Defined in free-5.2 · Control.Applicative.Trans.Free
Applicative g => Applicative (ApF f g)Defined in free-5.2 · Control.Applicative.Trans.Free
Applicative g => Apply (ApF f g)Defined in free-5.2 · Control.Applicative.Trans.Free

valueliftApT :: Applicative g => f a -> ApT f g a

Source#

A version of lift that can be used with no constraint for f.

valueliftApO :: Functor g => g a -> ApT f g a

Source#

Lift an action of the "outer" Functor g a to ApT f g a.

valuerunApT

:: (Applicative h, Functor g)
=> forall a. f a -> h a
-> forall a. g (h a) -> h a
-> ApT f g b
-> h b

Source#

Given natural transformations f ~> h and g . h ~> h this gives a natural transformation ApT f g ~> h.

valuerunApF

:: (Applicative h, Functor g)
=> forall a. f a -> h a
-> forall a. g (h a) -> h a
-> ApF f g b
-> h b

Source#

Given natural transformations f ~> h and g . h ~> h this gives a natural transformation ApF f g ~> h.

valuerunApT_

:: (Functor g, Monoid m)
=> forall a. f a -> m
-> g m -> m
-> ApT f g b
-> m

Source#

Perform a monoidal analysis over ApT f g b value.

Examples:

height :: (Functor g, Foldable g) => ApT f g a -> Int
height = getSum . runApT_ (_ -> Sum 1) maximum

size :: (Functor g, Foldable g) => ApT f g a -> Int
size = getSum . runApT_ (_ -> Sum 1) fold

valuehoistApT :: Functor g => (forall a. f a -> f' a) -> ApT f g b -> ApT f' g b

Source#

Given a natural transformation from f to f' this gives a monoidal natural transformation from ApT f g to ApT f' g.

valuehoistApF :: Functor g => (forall a. f a -> f' a) -> ApF f g b -> ApF f' g b

Source#

Given a natural transformation from f to f' this gives a monoidal natural transformation from ApF f g to ApF f' g.

valuetransApT :: Functor g => (forall a. g a -> g' a) -> ApT f g b -> ApT f g' b

Source#

Given a natural transformation from g to g' this gives a monoidal natural transformation from ApT f g to ApT f g'.

valuetransApF :: Functor g => (forall a. g a -> g' a) -> ApF f g b -> ApF f g' b

Source#

Given a natural transformation from g to g' this gives a monoidal natural transformation from ApF f g to ApF f g'.

valuejoinApT :: Monad m => ApT f m a -> m (Ap f a)

Source#

Pull out and join m layers of ApT f m a.

Free Applicative

typetype Ap (f :: Type -> Type) = ApT f Identity

Source#

The free Applicative for a Functor f.

valuerunAp :: 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.

Property

prop> runAp t == retractApp . hoistApp t

valuerunAp_ :: Monoid m => (forall x. f x -> m) -> Ap f a -> m

Source#

Perform a monoidal analysis over free applicative value.

Example:

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

valueretractAp :: 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.

Property

prop> retractApp == runAp id

Free Alternative

typetype Alt (f :: Type -> Type) = ApT f []

Source#

The free Alternative for a Functor f.

valuerunAlt

:: (Alternative g, Foldable t)
=> forall x. f x -> g x
-> ApT f t a
-> g a

Source#

Given a natural transformation from f to g, this gives a canonical monoidal natural transformation from Alt f to g.