Haskell:如何证明(测试)自定义的 Monad 实例是否遵循 Monad 定律？

Question

不使用形式推导，如何测试自定义的Monad实例是否遵循Monad定律？

Answer 1

FWIW，这是我最近编写的一组 QuickCheck 属性，用于测试从 F 代数派生的 Maybe 实现的 Monad 定律:

testProperty "Monad left identity law" $ do
  a :: String <- arbitrary
  k :: String -> MaybeFix Integer <- (fromMaybe .) <$> arbitrary

  let left = return a >>= k
  let right = k a

  return $ left == right
,
testProperty "Monad right identity law" $ do
  m :: MaybeFix Integer <- fromMaybe <$> arbitrary

  let left = m >>= return
  let right = m

  return $ left == right
,
testProperty "Monad associativity law" $ do
  m :: MaybeFix String <- fromMaybe <$> arbitrary
  k :: String -> MaybeFix Integer <- (fromMaybe .) <$> arbitrary
  h :: Integer -> MaybeFix Ordering <- (fromMaybe .) <$> arbitrary

  let left = m >>= (\x -> k x >>= h)
  let right = (m >>= k) >>= h

  return $ left == right