SKI combinators

Author: ZeppLu

Diff for: ski.hs

@@ -0,0 +1,39 @@
+-- TODO: add codewars link
+
+{-# LANGUAGE GADTs          #-}
+{-# LANGUAGE KindSignatures #-}
+{-# LANGUAGE DataKinds      #-}
+
+data SKI :: * -> * where
+    S  :: SKI ((a -> b -> c) -> (a -> b) -> a -> c)
+    K  :: SKI (a -> b -> a)
+    I  :: SKI (a -> a)
+    Ap :: SKI (a -> b) -> SKI (a) -> SKI (b)
+
+-- a convenient symbol to avoid tons of parentheses
+infixl <|
+(<|) = Ap
+
+instance Show (SKI c) where
+    show S        = "S"
+    show K        = "K"
+    show I        = "I"
+    show (Ap a b) = "(" ++ show a ++ " " ++ show b ++ ")"
+
+-- equality is guaranteed by type system
+-- you can check this by `Ap (Ap S K) _ == I`
+instance Eq (SKI c) where
+    a == b = True
+
+data Variables a = Sing a
+                 | Cons a (Variables a)
+
+--data Lambda :: Variables * -> * where
+--    Var :: a -> Lambda (Sing a)
+--    Abs :: a -> Lambda b -> Lambda (Just a)
+--    App :: Lambda a -> Lambda b -> Lambda c
+--
+--instance (Show a) => Show (Lambda (Maybe a)) where
+--    show (Var a) = show a
+--    show (Abs x y) = "(λ" ++ show x ++ ". " ++ show y++ ")"
+--    show (App a b) = "(" ++ show a ++ " " ++ show b ++ ")"