-- This is the arith.hs that was handed out in the lecture.

data Expr			-- introduce a new type, Expr
   = Literal Int		-- an Expr can be (Literal i) where i is an Int
   | Negated Expr
   | Sum Expr Expr
   | Difference Expr Expr
   | Product Expr Expr
   | Quotient Expr Expr
   | Remainder Expr Expr

instance Show Expr		-- how to print Exprs
  where
    showsPrec _ (Literal      x) s = shows x s
    showsPrec _ (Negated      e) s = "-" ++ shows e s
    showsPrec _ (Sum        e f) s = "(" ++ shows e ("+" ++ shows f (")" ++ s))
    showsPrec _ (Difference e f) s = "(" ++ shows e ("-" ++ shows f (")" ++ s))
    showsPrec _ (Product    e f) s = "(" ++ shows e ("*" ++ shows f (")" ++ s))
    showsPrec _ (Quotient   e f) s = "(" ++ shows e ("/" ++ shows f (")" ++ s))
    showsPrec _ (Remainder  e f) s = "(" ++ shows e ("%" ++ shows f (")" ++ s))

value (Literal      x) = x
value (Negated      e) = 0 - value e
value (Sum        e f) = value e   +   value f
value (Difference e f) = value e   -   value f
value (Product    e f) = value e   *   value f
value (Quotient   e f) = value e `div` value f
value (Remainder  e f) = value e `mod` value f

main = putStrLn (shows e (" == " ++ shows (value e) ""))
  where e = Product (Difference (Literal 1) (Literal 2))
                    (Sum (Literal 3) (Literal 4))