Fmap在包含单个元素和列表的列表上

Question

我有这样的数据结构

data ShoppingList a
  = Empty
  | Item a 
  | Listofitems [ShoppingList a]
  deriving (Show)

我正在尝试为此编写fmap

instance Functor ShoppingList where
  fmap f Empty    = Empty
  fmap f (Item i) = Item (f i)
  fmap f (Listofitems [Empty]) = Empty
  fmap f (Listofitems ((Item a):Listofitems [as])) = Listofitems $ (fmap f (Item a)) (fmap f Listofitems [as])

这是我到目前为止所写的，但它没有编译，请你帮我理解这里的问题是什么，解释会很棒。我得到的两个错误

src\Ml.hs:19:33: error:
    * Couldn't match expected type `[ShoppingList a]'
                  with actual type `ShoppingList a0'
    * In the pattern: Listofitems [as]
      In the pattern: (Item a) : Listofitems [as]
      In the pattern: Listofitems ((Item a) : Listofitems [as])
    * Relevant bindings include
        a :: a (bound at src\Ml.hs:19:30)
        f :: a -> b (bound at src\Ml.hs:19:8)
        fmap :: (a -> b) -> ShoppingList a -> ShoppingList b
          (bound at src\Ml.hs:16:3)
   |
19 |   fmap f (Listofitems ((Item a):Listofitems [as])) = Listofitems $ (fmap f (Item a)) (fmap f Listofitems [as])
   |                                 ^^^^^^^^^^^^^^^^

src\Ml.hs:19:68: error:
    * Couldn't match expected type `b -> [ShoppingList b]'
                  with actual type `ShoppingList b'
    * The function `fmap' is applied to three arguments,
      but its type `(a -> b) -> ShoppingList a -> ShoppingList b'
      has only two
      In the second argument of `($)', namely
        `(fmap f (Item a)) (fmap f Listofitems [as])'
      In the expression:
        Listofitems $ (fmap f (Item a)) (fmap f Listofitems [as])
    * Relevant bindings include
        f :: a -> b (bound at src\Ml.hs:19:8)
        fmap :: (a -> b) -> ShoppingList a -> ShoppingList b
          (bound at src\Ml.hs:16:3)
   |
19 |   fmap f (Listofitems ((Item a):Listofitems [as])) = Listofitems $ (fmap f (Item a)) (fmap f Listofitems [as])
   |                                                                    ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

基本上如果我有一个list = [Item Apple，Empty，[Item Banana，Empty]]我希望fmap（++ M）列表返回[Item AppleM .Empty。[Item BananaM，Empty]]

Answer 1

Note on the data type

首先，您的数据类型过于复杂。项目列表确实应该是一个列表，所以你可以定义data ShoppingList' a = ShoppingList' [a]，因为你正在使用你的列表。没有必要嵌套购物清单。

Solution to your question

但是，如果您需要这种方式，这是一个解决方案。注意我假设您不需要ShoppingLists列表，因为您的数据定义中已经有一个列表。所以你可以打电话

--fmap :: (a -> b) -> ShoppingList a -> ShoppingList b
fmap _ Empty = Empty
fmap f (Item i) = Item (f i)
fmap f (Listofitems ls) = Listofitems $ map (fmap f) ls


>>fmap (++ "M") $ Listofitems [Item "Apple", Empty, Listofitems [Item "Banana", Empty]]
Listofitems [Item "AppleM",Empty,Listofitems [Item "BananaM",Empty]]

注意：

• 你的字符串需要引号，
• 你需要在Listofitems上调用它

还要记住，如果需要性能，String追加操作对于长字符串效率不高