{-# LANGUAGE GADTs #-}

data Expr a where
  I :: Int -> Expr Int
  Plus :: Expr Int -> Expr Int -> Expr Int
  Pair :: Expr a -> Expr b -> Expr (a, b)
  Fst :: Expr (a, b) -> Expr a
  Snd :: Expr (a, b) -> Expr b
deriving instance Show (Expr a)

data Value a where
  VI :: Int -> Value Int
  VPair :: Value a -> Value b -> Value (a, b)
deriving instance Show (Value a)

interpret :: Expr a -> Value a
interpret (I i) = VI i
interpret (Plus e1 e2) = case (interpret e1, interpret e2) of
                           (VI a, VI b) -> VI (a + b)
interpret (Pair e1 e2) = VPair (interpret e1) (interpret e2)
interpret (Fst e) = case interpret e of
                      VPair a _ -> a
interpret (Snd e) = case interpret e of
                      VPair _ b -> b

main :: IO ()
main = print $ interpret $ Plus (Fst (Pair (I 2) (I 3))) (I 4)