module Main where
import Prelude hiding(reverse)
import Test.QuickCheck

-- Basic definition of reverse
reverse :: [a] -> [a]
reverse [] = []
reverse (x:xs) = reverse xs ++ [x]

-- Faster implementation of reverse
revHelper :: [a] -> [a] -> [a]
revHelper [] ys = ys
revHelper (x:xs) ys = revHelper xs (x:ys)

reverse2 :: [a] -> [a]
reverse2 xs = revHelper xs []

-- reversing a string twice is identity
prop_revrev :: [Int] -> Bool
prop_revrev xs = reverse (reverse xs) == xs

-- reverse2 is equivalent to reverse
prop_revrev2 :: [Int] -> Bool
prop_revrev2 xs = reverse2 xs == reverse xs

-- revHelper is related to reverse and concatenation
prop_revrevh :: [Int] -> [Int] -> Bool
prop_revrevh xs ys = reverse xs ++ ys == revHelper xs ys

main = do
    quickCheck prop_revrev
    quickCheck prop_revrev2
    quickCheck prop_revrevh