Last active
August 24, 2020 02:37
-
-
Save sordina/b194dea474c3038a67bfcfd1f70e1396 to your computer and use it in GitHub Desktop.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
{-# LANGUAGE FunctionalDependencies #-} | |
{-# LANGUAGE MultiParamTypeClasses #-} | |
{-# LANGUAGE UndecidableInstances #-} | |
{-# LANGUAGE FlexibleInstances #-} | |
{-# LANGUAGE FlexibleContexts #-} | |
{-# LANGUAGE GADTs #-} | |
-- Wrong! | |
class K k a b c d e | e -> b where (...) :: k a b -> k c d -> k c e | |
instance {-# OVERLAPS #-} (a~d2, b~e2, d1~e1) => K (->) a b c (d1->d2) (e1->e2) where g ... f = \x -> g ... (f x) | |
instance {-# OVERLAPPING #-} (a~d, b~e) => K (->) a b c d e where g ... f = g . f | |
plus2 :: Int -> Int | |
plus2 = succ ... succ | |
add :: Int -> Int -> Int | |
add = succ ... (+) | |
-- Compositional version of C: | |
-- Non-Recursive instance (b ~ c, b' ~ c', b'' ~ a, c'' ~ a') => J (a -> a') (b -> (b' -> b'')) (c -> c' -> c'') where f .... g = \x -> f .... (g x) | |
-- instance (c ~ (b -> k), J a b' k ) => J a (b -> b') c where f .... g = \x -> f .... (g x) | |
-- instance (J a b' c', c ~ (b -> c') ) => J a (b -> b') c where f .... g = \x -> f .... (g x) | |
infixl 1 .... | |
class J f g h | f g -> h where (....) :: f -> g -> h | |
instance (J a b' c', b ~ c ) => J a (b -> b') (c -> c') where f .... g = \x -> f .... (g x) | |
instance {-# INCOHERENT #-} ( a ~ b', b ~ c, a' ~ c') => J (a -> a') (b -> b') (c -> c') where f .... g = f . g | |
foo1, foo2, foo3 :: Int -> Int | |
foo1 = succ | |
foo2 = succ .... succ | |
foo3 = succ .... (succ .... succ :: Int -> Int) | |
-- instance (J a@(String -> String) b'@(Char -> String) c'@(Char->String), b@Int ~ c@Int) | |
-- => J a@(String -> String) (b@Int -> b'@(Char -> String)) (c@Int -> c'@(Char -> String)) where f .... g = \x -> f .... (g x) | |
add' :: Int -> Int -> Int | |
add' = (succ :: Int -> Int) .... ((+) :: Int -> Int -> Int) | |
tada' :: Int -> Char -> String | |
tada' = (take 3 :: String -> String) .... (replicate :: Int -> Char -> String) | |
-- mul' :: Int -> Int -> Int -> Int | |
-- mul' = succ .... (\x y z -> x + y * z) | |
-- From https://gist.github.com/i-am-tom/8ce5fd5dbce2a71fe604934d774a08f8: | |
infixl 1 .~ | |
class C f g h | f g -> h where (.~) :: f -> g -> h | |
-- (a -> a') (b -> a) (b -> a') | |
-- instance (a ~ b', b ~ c, a' ~ c') => C (a -> a') (b -> b') (c -> c') where (f .~ g) a = f .~ g a -- Simple version | |
-- instance (k ~ (a -> h), C f g h) => C f (a -> g) k where (f .~ g) a = f .~ g a | |
instance (C a b' c', b ~ c) => C a (b -> b') (c -> c') where (f .~ g) a = f .~ g a | |
instance {-# InCoHeReNt #-} (a ~ c, b ~ d) => C (a -> b) c d where (.~) = ($) | |
foo :: Int | |
foo = succ .~ 2 | |
tada :: Int -> a -> [a] | |
tada = take 3 .~ replicate | |
greet :: String -> String -> String | |
greet = (++ "!") .~ \fore sur -> fore <> " " <> sur | |
mul :: Int -> Int -> Int -> Int | |
mul = succ .~ (\x y z -> x + y * z) | |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment