Copyright	(c) 2011 Patrick Bahr
License	BSD3
Maintainer	Patrick Bahr <paba@diku.dk>
Stability	experimental
Portability	non-portable (GHC Extensions)
Safe Haskell	Safe
Language	Haskell98

Data.Comp.Multi.HFunctor

Description

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

Synopsis

class HFunctor h where
- hfmap :: (f :-> g) -> h f :-> h g
type (:->) f g = forall i. f i -> g i
type (:=>) f a = forall i. f i -> a
type NatM m f g = forall i. f i -> m (g i)
newtype I a = I {
- unI :: a
}
newtype K a i = K {
- unK :: a
}
data A f = A {
- unA :: forall i. f i
}
data E f = forall i. E {
- unE :: f i
}
runE :: (f :=> b) -> E f -> b
rewriteE :: (forall l. f l -> f l) -> E f -> E f
rewriteEM :: Functor m => (forall l. f l -> m (f l)) -> E f -> m (E f)
data (f :.: (g :: (* -> *) -> * -> *)) (e :: * -> *) t = Comp (f (g e) t)
newtype HMonad m f i = HMonad {
- unHMonad :: m (f i)
}

Documentation

class HFunctor h where Source #

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 Source #

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

Instances

Instances details

All HFunctor fs => HFunctor (Sum fs) Source #
Instance details Defined in Data.Comp.Multi.Ops Methods hfmap :: forall (f :: Type -> Type) (g :: Type -> Type). (f :-> g) -> Sum fs f :-> Sum fs g Source #
HFunctor f => HFunctor (Cxt h f) Source #
Instance details Defined in Data.Comp.Multi.Term Methods hfmap :: forall (f0 :: Type -> Type) (g :: Type -> Type). (f0 :-> g) -> Cxt h f f0 :-> Cxt h f g Source #
Functor f => HFunctor (Compose f :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Data.Comp.Multi.HFunctor Methods hfmap :: forall (f0 :: Type -> Type) (g :: Type -> Type). (f0 :-> g) -> Compose f f0 :-> Compose f g Source #
HFunctor f => HFunctor (f :&: a) Source #
Instance details Defined in Data.Comp.Multi.Ops Methods hfmap :: forall (f0 :: Type -> Type) (g :: Type -> Type). (f0 :-> g) -> (f :&: a) f0 :-> (f :&: a) g Source #

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

This type represents natural transformations.

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

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) Source #

newtype I a Source #

The identity Functor.

Constructors

I
Fields unI :: a

Instances

Instances details

Functor I Source #
Instance details Defined in Data.Comp.Multi.HFunctor Methods fmap :: (a -> b) -> I a -> I b # (<$) :: a -> I b -> I a #
Foldable I Source #
Instance details Defined in Data.Comp.Multi.HFunctor Methods fold :: Monoid m => I m -> m # foldMap :: Monoid m => (a -> m) -> I a -> 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 Source #
Instance details 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 Source #

The parametrised constant functor.

Constructors

K
Fields unK :: a

Instances

Instances details

Functor (K a) Source #
Instance details 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) Source #
Instance details Defined in Data.Comp.Multi.HFunctor Methods fold :: Monoid m => K a m -> m # foldMap :: Monoid m => (a0 -> m) -> K a a0 -> 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) Source #
Instance details 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) #
Eq a => KEq (K a) Source #
Instance details Defined in Data.Comp.Multi.Equality Methods keq :: K a i -> K a j -> Bool Source #
Ord a => KOrd (K a) Source #
Instance details Defined in Data.Comp.Multi.Ordering Methods kcompare :: K a i -> K a j -> Ordering Source #
KShow (K ()) Source #
Instance details Defined in Data.Comp.Multi.Show Methods kshow :: K () i -> K String i Source #
KShow (K String) Source #
Instance details Defined in Data.Comp.Multi.Show Methods kshow :: K String i -> K String i Source #
Eq a => Eq (K a i) Source #
Instance details 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) Source #
Instance details 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 #
Generic (f (HFix f) l) => Generic (HFix f l) Source #
Instance details Defined in Data.Comp.Multi.Derive.Generic Associated Types type Rep (HFix f l) :: Type -> Type # Methods from :: HFix f l -> Rep (HFix f l) x # to :: Rep (HFix f l) x -> HFix f l #
type Rep (HFix f l) Source #
Instance details Defined in Data.Comp.Multi.Derive.Generic type Rep (HFix f l) = Rep (f (HFix f) l)

data A f Source #

Constructors

A
Fields unA :: forall i. f i

data E f Source #

Constructors

forall i. E
Fields unE :: f i

Instances

Instances details

KEq a => Eq (E a) Source #
Instance details Defined in Data.Comp.Multi.Equality Methods (==) :: E a -> E a -> Bool # (/=) :: E a -> E a -> Bool #
KOrd f => Ord (E f) Source #
Instance details 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 Source #

rewriteE :: (forall l. f l -> f l) -> E f -> E f Source #

rewriteEM :: Functor m => (forall l. f l -> m (f l)) -> E f -> m (E f) Source #

data (f :.: (g :: (* -> *) -> * -> *)) (e :: * -> *) t infixl 5 Source #

This data type denotes the composition of two functor families.

Constructors

Comp (f (g e) t)

newtype HMonad m f i Source #

Constructors

HMonad
Fields unHMonad :: m (f i)