{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE DeriveTraversable #-}
{-# LANGUAGE DeriveFoldable #-}
{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE ExistentialQuantification #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE IncoherentInstances #-}
module Data.Comp.Multi.HFunctor
(
HFunctor (..),
(:->),
(:=>),
NatM,
I (..),
K (..),
A (..),
E (..),
runE,
(:.:)(..)
) where
import Data.Functor.Compose
import Data.Kind
newtype I a = I {forall a. I a -> a
unI :: a} deriving (forall a b. a -> I b -> I a
forall a b. (a -> b) -> I a -> I b
forall (f :: * -> *).
(forall a b. (a -> b) -> f a -> f b)
-> (forall a b. a -> f b -> f a) -> Functor f
<$ :: forall a b. a -> I b -> I a
$c<$ :: forall a b. a -> I b -> I a
fmap :: forall a b. (a -> b) -> I a -> I b
$cfmap :: forall a b. (a -> b) -> I a -> I b
Functor, forall a. Eq a => a -> I a -> Bool
forall a. Num a => I a -> a
forall a. Ord a => I a -> a
forall m. Monoid m => I m -> m
forall a. I a -> Bool
forall a. I a -> Int
forall a. I a -> [a]
forall a. (a -> a -> a) -> I a -> a
forall m a. Monoid m => (a -> m) -> I a -> m
forall b a. (b -> a -> b) -> b -> I a -> b
forall a b. (a -> b -> b) -> b -> I a -> b
forall (t :: * -> *).
(forall m. Monoid m => t m -> m)
-> (forall m a. Monoid m => (a -> m) -> t a -> m)
-> (forall m a. Monoid m => (a -> m) -> t a -> m)
-> (forall a b. (a -> b -> b) -> b -> t a -> b)
-> (forall a b. (a -> b -> b) -> b -> t a -> b)
-> (forall b a. (b -> a -> b) -> b -> t a -> b)
-> (forall b a. (b -> a -> b) -> b -> t a -> b)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. t a -> [a])
-> (forall a. t a -> Bool)
-> (forall a. t a -> Int)
-> (forall a. Eq a => a -> t a -> Bool)
-> (forall a. Ord a => t a -> a)
-> (forall a. Ord a => t a -> a)
-> (forall a. Num a => t a -> a)
-> (forall a. Num a => t a -> a)
-> Foldable t
product :: forall a. Num a => I a -> a
$cproduct :: forall a. Num a => I a -> a
sum :: forall a. Num a => I a -> a
$csum :: forall a. Num a => I a -> a
minimum :: forall a. Ord a => I a -> a
$cminimum :: forall a. Ord a => I a -> a
maximum :: forall a. Ord a => I a -> a
$cmaximum :: forall a. Ord a => I a -> a
elem :: forall a. Eq a => a -> I a -> Bool
$celem :: forall a. Eq a => a -> I a -> Bool
length :: forall a. I a -> Int
$clength :: forall a. I a -> Int
null :: forall a. I a -> Bool
$cnull :: forall a. I a -> Bool
toList :: forall a. I a -> [a]
$ctoList :: forall a. I a -> [a]
foldl1 :: forall a. (a -> a -> a) -> I a -> a
$cfoldl1 :: forall a. (a -> a -> a) -> I a -> a
foldr1 :: forall a. (a -> a -> a) -> I a -> a
$cfoldr1 :: forall a. (a -> a -> a) -> I a -> a
foldl' :: forall b a. (b -> a -> b) -> b -> I a -> b
$cfoldl' :: forall b a. (b -> a -> b) -> b -> I a -> b
foldl :: forall b a. (b -> a -> b) -> b -> I a -> b
$cfoldl :: forall b a. (b -> a -> b) -> b -> I a -> b
foldr' :: forall a b. (a -> b -> b) -> b -> I a -> b
$cfoldr' :: forall a b. (a -> b -> b) -> b -> I a -> b
foldr :: forall a b. (a -> b -> b) -> b -> I a -> b
$cfoldr :: forall a b. (a -> b -> b) -> b -> I a -> b
foldMap' :: forall m a. Monoid m => (a -> m) -> I a -> m
$cfoldMap' :: forall m a. Monoid m => (a -> m) -> I a -> m
foldMap :: forall m a. Monoid m => (a -> m) -> I a -> m
$cfoldMap :: forall m a. Monoid m => (a -> m) -> I a -> m
fold :: forall m. Monoid m => I m -> m
$cfold :: forall m. Monoid m => I m -> m
Foldable, Functor I
Foldable I
forall (t :: * -> *).
Functor t
-> Foldable t
-> (forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> t a -> f (t b))
-> (forall (f :: * -> *) a. Applicative f => t (f a) -> f (t a))
-> (forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> t a -> m (t b))
-> (forall (m :: * -> *) a. Monad m => t (m a) -> m (t a))
-> Traversable t
forall (m :: * -> *) a. Monad m => I (m a) -> m (I a)
forall (f :: * -> *) a. Applicative f => I (f a) -> f (I a)
forall (m :: * -> *) a b. Monad m => (a -> m b) -> I a -> m (I b)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> I a -> f (I b)
sequence :: forall (m :: * -> *) a. Monad m => I (m a) -> m (I a)
$csequence :: forall (m :: * -> *) a. Monad m => I (m a) -> m (I a)
mapM :: forall (m :: * -> *) a b. Monad m => (a -> m b) -> I a -> m (I b)
$cmapM :: forall (m :: * -> *) a b. Monad m => (a -> m b) -> I a -> m (I b)
sequenceA :: forall (f :: * -> *) a. Applicative f => I (f a) -> f (I a)
$csequenceA :: forall (f :: * -> *) a. Applicative f => I (f a) -> f (I a)
traverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> I a -> f (I b)
$ctraverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> I a -> f (I b)
Traversable)
newtype K a i = K {forall a i. K a i -> a
unK :: a} deriving (forall a b. (a -> b) -> K a a -> K a b
forall a a b. a -> K a b -> K a a
forall a a b. (a -> b) -> K a a -> K a b
forall (f :: * -> *).
(forall a b. (a -> b) -> f a -> f b)
-> (forall a b. a -> f b -> f a) -> Functor f
<$ :: forall a b. a -> K a b -> K a a
$c<$ :: forall a a b. a -> K a b -> K a a
fmap :: forall a b. (a -> b) -> K a a -> K a b
$cfmap :: forall a a b. (a -> b) -> K a a -> K a b
Functor, forall a a. Eq a => a -> K a a -> Bool
forall a a. Num a => K a a -> a
forall a a. Ord a => K a a -> a
forall m a. Monoid m => (a -> m) -> K a a -> m
forall a m. Monoid m => K a m -> m
forall a a. K a a -> Bool
forall a a. K a a -> Int
forall a a. K a a -> [a]
forall a a. (a -> a -> a) -> K a a -> a
forall a m a. Monoid m => (a -> m) -> K a a -> m
forall a b a. (b -> a -> b) -> b -> K a a -> b
forall a a b. (a -> b -> b) -> b -> K a a -> b
forall (t :: * -> *).
(forall m. Monoid m => t m -> m)
-> (forall m a. Monoid m => (a -> m) -> t a -> m)
-> (forall m a. Monoid m => (a -> m) -> t a -> m)
-> (forall a b. (a -> b -> b) -> b -> t a -> b)
-> (forall a b. (a -> b -> b) -> b -> t a -> b)
-> (forall b a. (b -> a -> b) -> b -> t a -> b)
-> (forall b a. (b -> a -> b) -> b -> t a -> b)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. t a -> [a])
-> (forall a. t a -> Bool)
-> (forall a. t a -> Int)
-> (forall a. Eq a => a -> t a -> Bool)
-> (forall a. Ord a => t a -> a)
-> (forall a. Ord a => t a -> a)
-> (forall a. Num a => t a -> a)
-> (forall a. Num a => t a -> a)
-> Foldable t
product :: forall a. Num a => K a a -> a
$cproduct :: forall a a. Num a => K a a -> a
sum :: forall a. Num a => K a a -> a
$csum :: forall a a. Num a => K a a -> a
minimum :: forall a. Ord a => K a a -> a
$cminimum :: forall a a. Ord a => K a a -> a
maximum :: forall a. Ord a => K a a -> a
$cmaximum :: forall a a. Ord a => K a a -> a
elem :: forall a. Eq a => a -> K a a -> Bool
$celem :: forall a a. Eq a => a -> K a a -> Bool
length :: forall a. K a a -> Int
$clength :: forall a a. K a a -> Int
null :: forall a. K a a -> Bool
$cnull :: forall a a. K a a -> Bool
toList :: forall a. K a a -> [a]
$ctoList :: forall a a. K a a -> [a]
foldl1 :: forall a. (a -> a -> a) -> K a a -> a
$cfoldl1 :: forall a a. (a -> a -> a) -> K a a -> a
foldr1 :: forall a. (a -> a -> a) -> K a a -> a
$cfoldr1 :: forall a a. (a -> a -> a) -> K a a -> a
foldl' :: forall b a. (b -> a -> b) -> b -> K a a -> b
$cfoldl' :: forall a b a. (b -> a -> b) -> b -> K a a -> b
foldl :: forall b a. (b -> a -> b) -> b -> K a a -> b
$cfoldl :: forall a b a. (b -> a -> b) -> b -> K a a -> b
foldr' :: forall a b. (a -> b -> b) -> b -> K a a -> b
$cfoldr' :: forall a a b. (a -> b -> b) -> b -> K a a -> b
foldr :: forall a b. (a -> b -> b) -> b -> K a a -> b
$cfoldr :: forall a a b. (a -> b -> b) -> b -> K a a -> b
foldMap' :: forall m a. Monoid m => (a -> m) -> K a a -> m
$cfoldMap' :: forall a m a. Monoid m => (a -> m) -> K a a -> m
foldMap :: forall m a. Monoid m => (a -> m) -> K a a -> m
$cfoldMap :: forall a m a. Monoid m => (a -> m) -> K a a -> m
fold :: forall m. Monoid m => K a m -> m
$cfold :: forall a m. Monoid m => K a m -> m
Foldable, forall a. Functor (K a)
forall a. Foldable (K a)
forall a (m :: * -> *) a. Monad m => K a (m a) -> m (K a a)
forall a (f :: * -> *) a. Applicative f => K a (f a) -> f (K a a)
forall a (m :: * -> *) a b.
Monad m =>
(a -> m b) -> K a a -> m (K a b)
forall a (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> K a a -> f (K a b)
forall (t :: * -> *).
Functor t
-> Foldable t
-> (forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> t a -> f (t b))
-> (forall (f :: * -> *) a. Applicative f => t (f a) -> f (t a))
-> (forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> t a -> m (t b))
-> (forall (m :: * -> *) a. Monad m => t (m a) -> m (t a))
-> Traversable t
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> K a a -> f (K a b)
sequence :: forall (m :: * -> *) a. Monad m => K a (m a) -> m (K a a)
$csequence :: forall a (m :: * -> *) a. Monad m => K a (m a) -> m (K a a)
mapM :: forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> K a a -> m (K a b)
$cmapM :: forall a (m :: * -> *) a b.
Monad m =>
(a -> m b) -> K a a -> m (K a b)
sequenceA :: forall (f :: * -> *) a. Applicative f => K a (f a) -> f (K a a)
$csequenceA :: forall a (f :: * -> *) a. Applicative f => K a (f a) -> f (K a a)
traverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> K a a -> f (K a b)
$ctraverse :: forall a (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> K a a -> f (K a b)
Traversable)
data E f = forall i. E {()
unE :: f i}
runE :: (f :=> b) -> E f -> b
runE :: forall (f :: * -> *) b. (f :=> b) -> E f -> b
runE f :=> b
f (E f i
x) = f :=> b
f f i
x
data A f = A {forall (f :: * -> *). A f -> forall i. f i
unA :: forall i. f i}
instance Eq a => Eq (K a i) where
K a
x == :: K a i -> K a i -> Bool
== K a
y = a
x forall a. Eq a => a -> a -> Bool
== a
y
K a
x /= :: K a i -> K a i -> Bool
/= K a
y = a
x forall a. Eq a => a -> a -> Bool
/= a
y
instance Ord a => Ord (K a i) where
K a
x < :: K a i -> K a i -> Bool
< K a
y = a
x forall a. Ord a => a -> a -> Bool
< a
y
K a
x > :: K a i -> K a i -> Bool
> K a
y = a
x forall a. Ord a => a -> a -> Bool
> a
y
K a
x <= :: K a i -> K a i -> Bool
<= K a
y = a
x forall a. Ord a => a -> a -> Bool
<= a
y
K a
x >= :: K a i -> K a i -> Bool
>= K a
y = a
x forall a. Ord a => a -> a -> Bool
>= a
y
min :: K a i -> K a i -> K a i
min (K a
x) (K a
y) = forall a i. a -> K a i
K forall a b. (a -> b) -> a -> b
$ forall a. Ord a => a -> a -> a
min a
x a
y
max :: K a i -> K a i -> K a i
max (K a
x) (K a
y) = forall a i. a -> K a i
K forall a b. (a -> b) -> a -> b
$ forall a. Ord a => a -> a -> a
max a
x a
y
compare :: K a i -> K a i -> Ordering
compare (K a
x) (K a
y) = forall a. Ord a => a -> a -> Ordering
compare a
x a
y
infixr 0 :->
infixr 0 :=>
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)
class HFunctor h where
hfmap :: (f :-> g) -> h f :-> h g
instance (Functor f) => HFunctor (Compose f) where hfmap :: forall (f :: * -> *) (g :: * -> *).
(f :-> g) -> Compose f f :-> Compose f g
hfmap f :-> g
f (Compose f (f i)
xs) = forall {k} {k1} (f :: k -> *) (g :: k1 -> k) (a :: k1).
f (g a) -> Compose f g a
Compose (forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap f :-> g
f f (f i)
xs)
infixl 5 :.:
data (:.:) f (g :: (Type -> Type) -> (Type -> Type)) (e :: Type -> Type) t = Comp (f (g e) t)