模式匹配中的Monoid mempty [英] Monoid mempty in pattern matching

问题描述

我试着编写一个类似于 Prelude 中广义的最大函数。我的第一个naiv方法看起来像这样：

maximum'::（F.Foldable a，Ord b）=> a b - >也许b

最大'mempty = Nothing

最大'xs = Just $ F.foldl1 max xs

然而，当我测试它时总会返回 Nothing 不管输入如何：

>最大'[1,2,3]

> Nothing

现在我想知道是否有可能获得Monoid类型实例的空值。我写的一个测试函数可以正常工作：

getMempty ::（Monoid a）=> a - > a


getMempty _ = mempty

> getMempty [1,2,3]

> []

我已经看到了这两个问题，但我没有弄清楚答案如何解决我的问题：

在Haskell中使用Maybe编写最大Monoid

空集上的Haskell模式匹配

如何重写最大值函数以使其正常工作？
CA McCann在他的评论中指出，你不能在值上模式匹配，只有模式。

方程最大值'mempty = Nothing 实际上等价于方程最大值'x = Nothing 。参数被绑定到一个名字上，返回 Nothing 。

这是一种让代码有效的方法： （ab），幺半群（ab））=>（b）等式（ab） a b - >也许b
最大'xs
| xs == mempty = Nothing
|否则=只需$ F.foldl1 max xs

即。您可以将 xs 与 mempty 进行比较。请注意，我们需要一个 Monoid 约束来获得值 mempty :: ab 和 Eq 约束，以便能够进行比较。

另一个更优雅的解决方案是使用fold来区分在空的和非空的情况之间：

 最大''::（F.Foldable a，Ord b）=> a b  - >也许b 
最大''xs = F.foldl max'Nothing xs 
 where max'Nothing x = Just x 
 max'（Just y）x = Just $ max xy 
  

I tried to write a generalized maximum function similar to the one in Prelude. My first naiv approach looked like this:
maximum' :: (F.Foldable a, Ord b) => a b -> Maybe b
maximum' mempty = Nothing
maximum' xs = Just $ F.foldl1 max xs

However, when I test it it always returns Nothing regardless of the input:
> maximum' [1,2,3]
> Nothing

Now I wonder whether it's possible to obtain the empty value of a Monoid type instance. A test function I wrote works correctly:
getMempty :: (Monoid a) => a -> a
getMempty _ = mempty

> getMempty [1,2,3]
> []

I had already a look at these two questions but I didn't figure out how the answers solve my problem:
Write a Maximum Monoid using Maybe in Haskell
Haskell Pattern Matching on the Empty Set

How would I rewrite the maximum' function to get it to work ?

解决方案

As C. A. McCann points out in his comment, you can't pattern match on values, only patterns.

The equation maximum' mempty = Nothing is actually equivalent to the equation maximum' x = Nothing. The argument gets bound to a name and Nothing is returned.

Here's a way to make your code work:

maximum' :: (F.Foldable a, Ord b, Eq (a b), Monoid (a b)) => a b -> Maybe b
maximum' xs
  | xs == mempty = Nothing
  | otherwise    = Just $ F.foldl1 max xs

I.e. you can compare the value xs against mempty. Note that we need a Monoid constraint to be able to get at the value mempty :: a b and an Eq constraint to be able to compare as well.

An other, more elegant, solution would be to use a fold to differentiate between the empty and non-empty cases:

maximum'' :: (F.Foldable a, Ord b) => a b -> Maybe b
maximum'' xs = F.foldl max' Nothing xs
  where max' Nothing x = Just x
        max' (Just y) x = Just $ max x y

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