haskell - 创建 Haskell 'init' 函数的安全版本

Question

我正在研究“真实世界 Haskell”，任务是制作 head, tail, last, 的安全版本。和 init.我在前三个上成功了，但是 Maybe typeclass 在 init 上杀了我.
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)

这是加载到 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.

我以任何方式标记或不标记 x或 xs在最后两行 Just ，我得到了不同但非常相关的打字错误。我错过了在列表中使用 Maybe 类型的哪些微妙之处？

Answer 1

这不起作用的主要原因是因为你的表达 x : safeInit xs不会类型检查。确实，safeInit xs是 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 null xs是 True ，那么你应该返回 Just []而不是 Just [x] , 从此x是列表中的最后一个元素。
您可以使用 fmap :: Functor f => (a -> b) -> f a -> f b (所以对于 f ~ Maybe ， fmap 是 fmap :: (a -> b) -> Maybe a -> Maybe b )，改变包裹在 Just 中的值:

safeInit :: [a] -> Maybe [a]
safeInit [] = Nothing
safeInit [_] = Just []
safeInit (x:xs) = fmap (x:) (safeInit xs)

但这将导致 Just 中值的大量包装和展开.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一个元素，然后执行初始化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