main :: IO ()
main = do
  -- right length
  quickCheck $ forAll genPos $ \n -> (toInteger . length . grayCode) n == 2 ^ n
  -- right elements, and sorted
  quickCheck $
    forAll genPos $ \n -> map fromBaseTwo (grayRead n) == [0 .. 2 ^ n - 1]
  -- test in base 10
  quickCheck $ forAll genPos $ \n -> n == (n `fromBase` 10) `inBase` 10
  -- test in all bases
  quickCheck $
    forAll genPos $ \d ->
      forAll (genBaseD d) $ \n -> n == (n `fromBase` d) `inBase` d