--the quickcheck
prop_polyListValue :: [Integer] -> Integer -> Bool
prop_polyListValue [] _ = True
prop_polyListValue pl n
    | plv == pv = True
    | otherwise = False
        where
            plv = polyListValue pl n
            pv = polyValue p n
            p = polyListToPoly pl

--functions used in quickcheck

--polyValue from assignment 3
polyValue :: Poly -> Integer -> Integer
polyValue X n = n
polyValue (Coef x) _ = x
polyValue (Sum x y) n = (polyValue x n) + (polyValue y n)
polyValue (Prod x y) n = (polyValue x n) * (polyValue y n)

polyListValue :: [Integer] -> Integer -> Integer
polyListValue [] _ = 0
polyListValue pl n = hormeth pl n
    where
        hormeth (x:[]) n = x
        hormeth (x:xs) n = (hormeth xs n) * n + x

polyListToPoly :: [Integer] -> Poly
polyListToPoly [] = (Coef 0)
polyListToPoly (x:xs) = Sum (Prod (Coef x) (indexDegree (length xs))) (polyListToPoly xs)
    where indexDegree a =
                        if a == 0 then Coef 1
                        else Prod X (indexDegree (a - 1))