{-# LANGUAGE ViewPatterns #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TupleSections #-}

module Main where
import Text.ParserCombinators.Parsec (many1, sepBy1, string, noneOf, char, digit, spaces, sepEndBy, Parser, (<|>), parse, letter)
import Control.Monad (void)
import Prelude
import qualified Data.Set as Set
data Term = Var String | App Term Term | Lam String Term deriving (Eq)
instance Show Term where
    show (Var x) = x
    show (App x y) = show x ++ show y
    show (Lam x y) = "(λ"++x++". "++show y++")"

parens :: Parser a -> Parser a
parens p = char '(' *> spaces *> p <* spaces <* char ')'

var :: Parser Term
var = Var <$> many1 letter

lam :: Parser Term
lam = Lam <$> (char 'λ' *> spaces *> (many1 letter)) <*> (spaces *> string "." *> spaces *> term)

app :: Parser Term
app = foldl1 App <$> sepBy1 (var <|> parens term) spaces

term :: Parser Term
term = lam <|> app <|> var

fv :: Term -> Set.Set String
fv (Var x) = Set.singleton x
fv (Lam x m) = x `Set.delete` (fv m)
fv (App m1 m2) = (fv m1) `Set.union` (fv m2)

pickFresh :: Set.Set String -> String -> String
pickFresh s = pickFresh'
  where
    pickFresh' n | n `Set.notMember` s = n
    pickFresh' n = pickFresh' $ n ++ "'"

subst :: Term -> String -> Term -> Term
subst n x (Var e)
    | x == e = n
    | otherwise = Var e
subst n x (App m1 m2) = App (subst n x m1) (subst n x m2)
subst n x (Lam y m)
    | x == y = Lam y m
    | y `Set.notMember` (fv n) = Lam y (subst n x m)
    | otherwise = Lam y' (subst n x (subst (Var y') y m))
  where
    y' = pickFresh ((fv n) `Set.union` (fv m)) y

normalstep :: Term -> Maybe Term
normalstep (App (Lam x m) n) = Just (subst n x m)
normalstep (Lam x m) = normalstep m >>= return . Lam x
normalstep (App m n) | normalstep m == Nothing = normalstep n >>= return . App m
normalstep (App m n) = normalstep m >>= return . (`App` n)
normalstep _ = Nothing

repeatedly :: (a -> Maybe a) -> a -> [a]
repeatedly f = repeatedly'
  where
    repeatedly' x =
        x : case f x of
            Nothing -> []
            Just y -> repeatedly' y

eval s = last <$> repeatedly normalstep <$> parse term "" s 

main = do 
	contents <- getContents 
	putStrLn $ show $ eval contents