Data.Comp.Multi.HFunctor

This module defines higher-order functors (Johann, Ghani, POPL '08), i.e. endofunctors on the category of endofunctors.

Documentation

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

HFunctor f => HFunctor (Cxt h f)

HFunctor f => HFunctor ((:&:) * f a)

(HFunctor f, HFunctor g) => HFunctor ((:+:) * f g)

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

This type represents natural transformations.

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

This type represents co-cones from f to a. f :=> a is isomorphic to f :-> K a

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

newtype I a

The identity Functor.

Constructors

I

Fields

unI :: a

Instances

Functor I

newtype K a i

The parametrised constant functor.

Constructors

K

Fields

unK :: a

Instances

Functor (K a)

KShow (K String)

KShow (K ())

Eq a => KEq (K a)

Ord a => KOrd (K a)

Eq a => Eq (K a i)

Ord a => Ord (K a i)

data A f

Constructors

A

Fields

unA :: forall i. f i

data E f

Constructors

forall i . E

Fields

unE :: f i

Instances

KEq a => Eq (E a)

KOrd f => Ord (E f)

runE :: (f :=> b) -> E f -> b

data (f :.: g) e t infixl 5

This data type denotes the composition of two functor families.

Constructors

Comp f (g e) t