Data.Comp.Param.Multi.HDifunctor

This module defines higher-order difunctors, a hybrid between higher-order functors (Johann, Ghani, POPL '08), and difunctors (Meijer, Hutton, FPCA '95). Higher-order difunctors are used to define signatures for compositional parametric generalised data types.

Documentation

class HDifunctor f where

This class represents higher-order difunctors.

Methods

hdimap :: (a :-> b) -> (c :-> d) -> f b c :-> f a d

Instances

HDifunctor f => HDifunctor ((:&:) f p)

(HDifunctor f, HDifunctor g) => HDifunctor ((:+:) f g)

class HFunctor h where

This class represents higher-order functors (Johann, Ghani, POPL '08) which are endofunctors on the category of endofunctors.

Methods

hfmap :: (:->) f g -> (:->) (h f) (h g)

A higher-order functor f also maps a natural transformation g :-> h to a natural transformation f g :-> f h

Instances

HDifunctor f => HFunctor (f a)

A higher-order difunctor gives rise to a higher-order functor when restricted to a particular contravariant argument.

Functor f => HFunctor (Compose f)

newtype I a :: * -> *

The identity Functor.

Constructors

I

Fields

unI :: a

Instances

Functor I

Foldable I

Traversable I

newtype K a i :: * -> * -> *

The parametrised constant functor.

Constructors

K

Fields

unK :: a

Instances

Functor (K a)

Foldable (K a)

Traversable (K a)

Eq a => PEq (K a)

Ord a => POrd (K a)

Eq a => Eq (K a i)

Ord a => Ord (K a i)

data E f :: (* -> *) -> * where

Constructors

E :: f i -> E f

Fields

unE :: f i

data A f :: (* -> *) -> *

Constructors

A

Fields

unA :: forall i. f i

type (:->) f g = forall i. f i -> g i infixr 0

This type represents natural transformations.

type NatM m f g = forall i. f i -> m (g i)