Control.Selective.Free

This is a library for selective applicative functors, or just selective functors for short, an abstraction between applicative functors and monads, introduced in this paper: https://www.staff.ncl.ac.uk/andrey.mokhov/selective-functors.pdf.

This module defines free selective functors using the ideas from the Sjoerd Visscher's package 'free-functors': https://hackage.haskell.org/package/free-functors-1.0.1/docs/Data-Functor-HFree.html.

Free selective functors

newtype Select f a

Free selective functors.

Constructors

Select (forall g. Selective g => (forall x. f x -> g x) -> g a)

Instances

Applicative (Select f)

Defined in Control.Selective.Free

Methods

pure :: a -> Select f a

(<*>) :: Select f (a -> b) -> Select f a -> Select f b

liftA2 :: (a -> b -> c) -> Select f a -> Select f b -> Select f c

(*>) :: Select f a -> Select f b -> Select f b

(<*) :: Select f a -> Select f b -> Select f a

Functor (Select f)

Defined in Control.Selective.Free

Methods

fmap :: (a -> b) -> Select f a -> Select f b

(<$) :: a -> Select f b -> Select f a

Selective (Select f)

Defined in Control.Selective.Free

Methods

select :: Select f (Either a b) -> Select f (a -> b) -> Select f b

liftSelect :: f a -> Select f a

Lift a functor into a free selective computation.

Static analysis

getPure :: Select f a -> Maybe a

Extract the resulting value if there are no necessary effects.

getEffects :: Functor f => Select f a -> [f ()]

Collect all possible effects in the order they appear in a free selective computation.

getNecessaryEffects :: Functor f => Select f a -> [f ()]

Extract all necessary effects in the order they appear in a free selective computation.

runSelect :: Selective g => (forall x. f x -> g x) -> Select f a -> g a

Given a natural transformation from f to g, this gives a canonical natural transformation from Select f to g. Note that here we rely on the fact that g is a lawful selective functor.

foldSelect :: Monoid m => (forall x. f x -> m) -> Select f a -> m

Concatenate all effects of a free selective computation.