我正在研究"现实世界的哈斯克尔"，任务是制作head, tail, last,的安全版本，init.我在前三个上取得了成功，但Maybe类型类在init上杀死了我。
这是我的代码：
-- safeInit
safeInit :: [a] -> Maybe [a]
safeInit [] = Nothing
safeInit (x:xs) = if null xs
then Just [x]
else x : (safeInit xs)
以下是加载到 GHCI 时产生的错误(该函数从原始文件的第 23 行开始：
[1 of 1] Compiling Main ( ch04.exercises.hs, interpreted )
> ch04.exercises.hs:27:26: error:
> • Couldn't match expected type ‘Maybe [a]’ with actual type ‘[a]’
> • In the expression: x : (safeInit xs)
> In the expression: if null xs then Just [x] else x : (safeInit xs)
> In an equation for ‘safeInit’:
> safeInit (x : xs) = if null xs then Just [x] else x : (safeInit xs)
> • Relevant bindings include
> xs :: [a] (bound at ch04.exercises.hs:25:13)
> x :: a (bound at ch04.exercises.hs:25:11)
> safeInit :: [a] -> Maybe [a] (bound at ch04.exercises.hs:24:1) | 27 | else x : (safeInit xs) |
> ^^^^^^^^^^^^^^^^^
>
> ch04.exercises.hs:27:31: error:
> • Couldn't match expected type ‘[a]’ with actual type ‘Maybe [a]’
> • In the second argument of ‘(:)’, namely ‘(safeInit xs)’
> In the expression: x : (safeInit xs)
> In the expression: if null xs then Just [x] else x : (safeInit xs)
> • Relevant bindings include
> xs :: [a] (bound at ch04.exercises.hs:25:13)
> x :: a (bound at ch04.exercises.hs:25:11)
> safeInit :: [a] -> Maybe [a] (bound at ch04.exercises.hs:24:1) | 27 | else x : (safeInit xs) |
> ^^^^^^^^^^^ Failed, no modules loaded.
无论如何，我用Just标记或不标记最后两行的x或xs，我都会得到不同但非常相关的输入错误。 我缺少将"可能"类型与列表一起使用的哪些微妙之处？
这不起作用的主要原因是因为您的表达式x : safeInit xs不会进行类型检查。事实上，safeInit xs是一个Maybe [a]，但是(:)有类型(:) :: a -> [a] -> [a]，所以类型不匹配。
还有一个语义错误。如果null xs是True，那么你应该返回Just []而不是Just [x]，因为x是列表中的最后一个元素。
你可以利用fmap :: Functor f => (a -> b) -> f a -> f b(所以对于f ~ Maybe，fmap是fmap :: (a -> b) -> Maybe a -> Maybe b(，来改变包装在Just中的值：
safeInit :: [a] -> Maybe [a]
safeInit [] = Nothing
safeInit [_] = Just []
safeInit (x:xs) =fmap (x:)(safeInit xs)但这会导致Just中值的大量包装和解包。这也意味着对于无限列表，它将陷入无限循环。我们可以简单地检查列表是否至少包含 on 元素，然后执行 init 逻辑作为我们包装在Just中的函数的结果：
safeInit :: [a] -> Maybe [a]
safeInit [] = Nothing
safeInit (x:xs) =Just (go xs x)
where go [] _ = []
go (x2:xs) x = x : go xs x2一个有趣的问题是如何用foldr来写safeInit。除了谜题的乐趣之外，这还允许它作为"好消费者"参与GHC中的列表融合优化，这在某些情况下可以提高性能。我们从Willem Van Onsem回答中的第一个(天真(版本开始：
safeInit0 :: [a] -> Maybe [a]
safeInit0 [] = Nothing
safeInit0 [_] = Just []
safeInit0 (x:xs) = fmap (x:) (safeInit0 xs)
这样做的第一个问题是它的形状不太像褶皱：它有单独的[p]和p:q:rs的情况。修补此问题的一个经典技巧是传递一个携带列表中前一个值的Maybe。
safeInit1 :: [a] -> Maybe [a]
safeInit1 xs0 = go xs0 Nothing
where
-- This first case only happens when
-- the whole list is empty.
go [] Nothing = Nothing
go [] (Just x) = Just [x]
go (x:xs) Nothing = go xs (Just x)
go (x:xs) (Just prev) = (prev:) <$> go xs (Just x)
下一个问题是语义上的：它不适用于无限或部分定义的参数。我们想要
safeInit [1..] = Just [1..]
但在这种情况下safeInit1会有所不同，因为fmapMaybe论证必然是严格的。但事实证明，我们可以使用一些信息：在这种情况下，fmap只会应用于Just值。练习：证明这一点。
我们将利用这一点，以一种奇怪的方式将Maybe [a]表示为(Bool, [a])，其中Nothing表示为(False, [])，Just xs表示为(True, xs)。现在我们可以更懒了：
safeInit2 :: [a] -> Maybe [a]
safeInit2 xs = case helper2 xs of
(False, _) -> Nothing
(True, xs) -> Just xs
helper2 :: [a] -> (Bool, [a])
helper2 xs0 = go xs0 Nothing
where
go [] Nothing = (False, [])
go [] _ = (True, [])
go (x:xs) mb = case mb of
Nothing -> (True, rest)
Just p -> (True, p:rest)
where
rest = snd (go xs (Just x))
现在这正好是折叠的形状：
safeInit3 :: [a] -> Maybe [a]
safeInit3 xs = case helper3 xs of
(False, _) -> Nothing
(True, xs) -> Just xs
helper3 :: [a] -> (Bool, [a])
helper3 xs0 = foldr go stop x0 Nothing
where
stop Nothing = (False, [])
stop _ = (True, [])
go x r mb = case mb of
Nothing -> (True, rest)
Just p -> (True, p:rest)
where
rest = snd (r (Just x))
您可能会担心所有这些中间Maybe和对会导致性能问题，但实际上GHC能够将它们全部优化，产生非常类似于Willem Van Onsem的优化实现的东西。