import Test.QuickCheck

-- Bool

xor :: Bool -> Bool -> Bool
xor x y = (x || y) && not(x && y)

xor2 :: Bool -> Bool -> Bool
xor2 True True = False
xor2 True False = True
xor2 False True = True
xor2 False False = False

prop_xor2 x y =
  xor x y == xor2 x y

prop_xor_neq x y =
  xor x y == (not(x == y))


-- Integer

sq :: Integer -> Integer
sq n  =  n * n

mymax :: Integer -> Integer -> Integer
mymax x y
  | x >= y     = x
  | otherwise  = y

prop_mymax_assoc x y z =
  mymax x (mymax y z) == mymax (mymax x y) z

pow x 0  =  1
pow x n | n > 0  =  x * pow x (n-1)

sumTo :: Integer -> Integer
sumTo 0  =  0
sumTo n | n > 0  =  n + sumTo (n-1)

prop_sumTo n =
  n >= 0  ==>  sumTo n == n*(n+1) `div` 2