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.

Minimal complete definition

hfmap

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)

Defined in Data.Comp.Multi.Term

Methods

hfmap :: (f0 :-> g) -> Cxt h f f0 :-> Cxt h f g

Functor f => HFunctor (Compose f :: (* -> *) -> * -> *)

Defined in Data.Comp.Multi.HFunctor

Methods

hfmap :: (f0 :-> g) -> Compose f f0 :-> Compose f g

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

Defined in Data.Comp.Multi.Ops

Methods

hfmap :: (f0 :-> g) -> (f :&: a) f0 :-> (f :&: a) g

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

Defined in Data.Comp.Multi.Ops

Methods

hfmap :: (f0 :-> g0) -> (f :+: g) f0 :-> (f :+: g) g0

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

Defined in Data.Comp.Multi.HFunctor

Methods

fmap :: (a -> b) -> I a -> I b

(<$) :: a -> I b -> I a

Foldable I

Defined in Data.Comp.Multi.HFunctor

Methods

fold :: Monoid m => I m -> m

foldMap :: Monoid m => (a -> m) -> I a -> m

foldr :: (a -> b -> b) -> b -> I a -> b

foldr' :: (a -> b -> b) -> b -> I a -> b

foldl :: (b -> a -> b) -> b -> I a -> b

foldl' :: (b -> a -> b) -> b -> I a -> b

foldr1 :: (a -> a -> a) -> I a -> a

foldl1 :: (a -> a -> a) -> I a -> a

toList :: I a -> [a]

null :: I a -> Bool

length :: I a -> Int

elem :: Eq a => a -> I a -> Bool

maximum :: Ord a => I a -> a

minimum :: Ord a => I a -> a

sum :: Num a => I a -> a

product :: Num a => I a -> a

Traversable I

Defined in Data.Comp.Multi.HFunctor

Methods

traverse :: Applicative f => (a -> f b) -> I a -> f (I b)

sequenceA :: Applicative f => I (f a) -> f (I a)

mapM :: Monad m => (a -> m b) -> I a -> m (I b)

sequence :: Monad m => I (m a) -> m (I a)

newtype K a i

The parametrised constant functor.

Constructors

K

Fields

• unK :: a

Instances

Functor (K a)

Defined in Data.Comp.Multi.HFunctor

Methods

fmap :: (a0 -> b) -> K a a0 -> K a b

(<$) :: a0 -> K a b -> K a a0

Foldable (K a)

Defined in Data.Comp.Multi.HFunctor

Methods

fold :: Monoid m => K a m -> m

foldMap :: Monoid m => (a0 -> m) -> K a a0 -> m

foldr :: (a0 -> b -> b) -> b -> K a a0 -> b

foldr' :: (a0 -> b -> b) -> b -> K a a0 -> b

foldl :: (b -> a0 -> b) -> b -> K a a0 -> b

foldl' :: (b -> a0 -> b) -> b -> K a a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> K a a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> K a a0 -> a0

toList :: K a a0 -> [a0]

null :: K a a0 -> Bool

length :: K a a0 -> Int

elem :: Eq a0 => a0 -> K a a0 -> Bool

maximum :: Ord a0 => K a a0 -> a0

minimum :: Ord a0 => K a a0 -> a0

sum :: Num a0 => K a a0 -> a0

product :: Num a0 => K a a0 -> a0

Traversable (K a)

Defined in Data.Comp.Multi.HFunctor

Methods

traverse :: Applicative f => (a0 -> f b) -> K a a0 -> f (K a b)

sequenceA :: Applicative f => K a (f a0) -> f (K a a0)

mapM :: Monad m => (a0 -> m b) -> K a a0 -> m (K a b)

sequence :: Monad m => K a (m a0) -> m (K a a0)

KShow (K ())

Defined in Data.Comp.Multi.Show

Methods

kshow :: K () i -> K String i

KShow (K String)

Defined in Data.Comp.Multi.Show

Methods

kshow :: K String i -> K String i

Eq a => KEq (K a)

Defined in Data.Comp.Multi.Equality

Methods

keq :: K a i -> K a j -> Bool

Ord a => KOrd (K a)

Defined in Data.Comp.Multi.Ordering

Methods

kcompare :: K a i -> K a j -> Ordering

Eq a => Eq (K a i)

Defined in Data.Comp.Multi.HFunctor

Methods

(==) :: K a i -> K a i -> Bool

(/=) :: K a i -> K a i -> Bool

Ord a => Ord (K a i)

Defined in Data.Comp.Multi.HFunctor

Methods

compare :: K a i -> K a i -> Ordering

(<) :: K a i -> K a i -> Bool

(<=) :: K a i -> K a i -> Bool

(>) :: K a i -> K a i -> Bool

(>=) :: K a i -> K a i -> Bool

max :: K a i -> K a i -> K a i

min :: K a i -> K a i -> K a i

data A f

Constructors

A

Fields

• unA :: forall i. f i

data E f

Constructors

E

Fields

• unE :: f i

Instances

KEq a => Eq (E a)

Defined in Data.Comp.Multi.Equality

Methods

(==) :: E a -> E a -> Bool

(/=) :: E a -> E a -> Bool

KOrd f => Ord (E f)

Defined in Data.Comp.Multi.Ordering

Methods

compare :: E f -> E f -> Ordering

(<) :: E f -> E f -> Bool

(<=) :: E f -> E f -> Bool

(>) :: E f -> E f -> Bool

(>=) :: E f -> E f -> Bool

max :: E f -> E f -> E f

min :: E f -> E f -> 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)