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

Data.Comp.Param.Multi.HDifunctor

Contents

Orphan instances

Description

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.

Synopsis

class HDifunctor f where
class HFunctor (h :: (* -> *) -> * -> *) where
newtype I a = I {
- unI :: a
}
newtype K a i = K {
- unK :: a
}
data E (f :: * -> *) where
- E :: E f
data A (f :: * -> *) = A {
- unA :: forall i. f i
}
type (:->) (f :: * -> *) (g :: * -> *) = forall i. f i -> g i
type NatM (m :: * -> *) (f :: * -> *) (g :: * -> *) = forall i. f i -> m (g i)

Documentation

class HDifunctor f where Source #

This class represents higher-order difunctors.

Minimal complete definition

hdimap

Methods

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

Instances

HDifunctor f => HDifunctor (f :&: p) Source #
Instance details Defined in Data.Comp.Param.Multi.Ops Methods hdimap :: (a :-> b) -> (c :-> d) -> (f :&: p) b c :-> (f :&: p) a d Source #
(HDifunctor f, HDifunctor g) => HDifunctor (f :+: g) Source #
Instance details Defined in Data.Comp.Param.Multi.Ops Methods hdimap :: (a :-> b) -> (c :-> d) -> (f :+: g) b c :-> (f :+: g) a d Source #

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

HDifunctor f => HFunctor (f a) #	A higher-order difunctor gives rise to a higher-order functor when restricted to a particular contravariant argument.
Instance details Defined in Data.Comp.Param.Multi.HDifunctor Methods hfmap :: (f0 :-> g) -> f a f0 :-> f a g #
Functor f => HFunctor (Compose f :: (* -> ) -> -> *)
Instance details Defined in Data.Comp.Multi.HFunctor Methods hfmap :: (f0 :-> g) -> Compose f f0 :-> Compose f g #

newtype I a #

The identity Functor.

Constructors

I
Fields unI :: a

Instances

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

The parametrised constant functor.

Constructors

K
Fields unK :: a

Instances

Functor (K a)
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)
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 # 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)
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 => PEq (K a) Source #
Instance details Defined in Data.Comp.Param.Multi.Equality Methods peq :: K a i -> K a j -> FreshM Bool Source #
Ord a => POrd (K a) Source #
Instance details Defined in Data.Comp.Param.Multi.Ordering Methods pcompare :: K a i -> K a j -> FreshM Ordering Source #
Eq a => Eq (K a i)
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)
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 #

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

Constructors

E :: E f

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) #

Orphan instances

HDifunctor f => HFunctor (f a) Source #	A higher-order difunctor gives rise to a higher-order functor when restricted to a particular contravariant argument.
Instance details Methods hfmap :: (f0 :-> g) -> f a f0 :-> f a g #