Scott encoding ... again

scottaststuff.hs

data Expr = Var Int | Application Expr Expr | Abstraction Int Expr deriving (Show, Eq, Ord)

zeroExpr :: Expr
zeroExpr = Abstraction 0 (Abstraction 1 (Var 0))

succExpr :: Expr -> Expr
succExpr num = Abstraction 0 (Abstraction 1 (Application (Var 1) num))

isScottNum :: Expr -> Bool
isScottNum (Abstraction a (Abstraction b (Var c)))                 | a == c && a /= b = True           -- Zero
isScottNum (Abstraction a (Abstraction b (Application (Var c) d))) | b == c           = isScottNum d   -- Succ
isScottNum _                                                                          = False          -- otherwise

decodeScottNum :: Expr -> Maybe Int
decodeScottNum (Abstraction a (Abstraction b (Var c)))                 | a == c && a /= b = Just 0                    -- Zero
decodeScottNum (Abstraction a (Abstraction b (Application (Var c) d))) | b == c           = (+1) <$> decodeScottNum d -- Succ
decodeScottNum _                                                                          = Nothing                   -- otherwise