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Language	Haskell2010

Data.PolyKinded.Functor

Contents

Mappings of different variance

Description

Poly-kinded Functor type class. KFunctor generalizes functors, bifunctors, profunctors, ... by declaring a list of Variances for a type constructor.

Synopsis

class KFunctor (f :: k) (v :: Variances) (as :: LoT k) (bs :: LoT k) | f -> v where
- kfmap :: Mappings v as bs -> (f :@@: as) -> f :@@: bs
kmapo :: forall f v as bs. KFunctor f v as bs => Mappings v as bs -> (f :@@: as) -> f :@@: bs
data Variance
- = Co
- | Contra
- | Phantom
type Variances = [Variance]
type family Mapping (v :: Variance) a b where ...
data Mappings (v :: Variances) (x :: LoT k) (y :: LoT k) where
- M0 :: Mappings '[] LoT0 LoT0
- (:^:) :: Mapping v a b -> Mappings vs as bs -> Mappings (v ': vs) (a :&&: as) (b :&&: bs)

Documentation

class KFunctor (f :: k) (v :: Variances) (as :: LoT k) (bs :: LoT k) | f -> v where Source #

Declares that the type constructor f is a generalized functor whose variances for each type argument are given by v.

Methods

kfmap :: Mappings v as bs -> (f :@@: as) -> f :@@: bs Source #

The generalized version of fmap, bimap, dimap, and so on.

kmapo :: forall f v as bs. KFunctor f v as bs => Mappings v as bs -> (f :@@: as) -> f :@@: bs Source #

The generalized version of fmap, bimap, dimap, and so on. This version uses Split to obtain better type inference.

Mappings of different variance

data Variance Source #

Possible variances for each argument of a type constructor.

Constructors

Co	The functor is covariant in this position.
Contra	The functor is contravariant in this position.
Phantom	This position is not used in any constructor.

type Variances = [Variance] Source #

type family Mapping (v :: Variance) a b where ... Source #

If a KFunctor needs to map an f ... a ... to an f ... b ..., a Mapping v a b specifies which function needs to be provided for that position depending on its variance v.

Equations

Mapping Co a b = a -> b
Mapping Contra a b = b -> a
Mapping Phantom a b = ()

data Mappings (v :: Variances) (x :: LoT k) (y :: LoT k) where Source #

List of mappings for the list of variances v.

Constructors

M0 :: Mappings '[] LoT0 LoT0
(:^:) :: Mapping v a b -> Mappings vs as bs -> Mappings (v ': vs) (a :&&: as) (b :&&: bs) infixr 5