Mathematica 中 PatternTest 的意外行为 [英] An unexpected behavior of PatternTest in Mathematica

问题描述

我正在研究玩具问题，以帮助我理解 Mathematica 中模式匹配的想法.以下代码的行为不符合我的预期，我无法弄清楚我对 PatternTest 的理解有什么问题.

I am working on toy problems to help me assimilate the idea of pattern matching in Mathematica. The following code does not behave as I expected, and I could not figure out what is wrong with my understanding of PatternTest.

MatchQ[{2, 1, 2, 5}, {x__?(FromDigits[{#}] > 3 &), y__}]

我希望这段代码可以检查列表 {2,1,2,5} 是否可以写成两个连续的(非空)序列，以便我们从第一个序列大于 3.由于 {Sequence[2,1],Sequence[2,5]} 是重写列表的一种方法，使得 FromDigits[{2,1}]>3 成立，我希望该代码返回值 True.然而，事实并非如此.

I expected this piece of code to check if the list {2,1,2,5} can be written as two consecutive (non-empty) sequences such that the integer we get from the first sequence is greater than 3. Since {Sequence[2,1],Sequence[2,5]} is one way to rewrite the list such that FromDigits[{2,1}] > 3 holds, I expected that code to return the value True. However, that is not the case.

我对代码的解释有什么问题?

What is wrong with my interpretation of the code?

推荐答案

PatternTest 的文档(又名 ?)说

在__?test这样的形式中，序列中的每个元素都与__匹配应用测试时必须产生 True.

In a form such as __?test every element in the sequence matched by __ must yield True when test is applied.

因此您的代码将无法如您所愿.

Thus your code will not work as you hoped.

查看模式如何工作的一个好方法是使用 ReplaceList.与您的代码接近的东西是

A good way to see how a pattern is working is to use ReplaceList. Something close to your code is

In[1]:= ReplaceList[{3, 4, 2, 1}, 
          {___, x__?(FromDigits[{##}] > 3 &), y___} :> {{x}, {y}}]

Out[1]= {{{4}, {2, 1}}}

但是，如果您使用 条件 (/;) 而不是模式测试，然后你可以得到你正在寻找的行为

However, if you use Condition (/;) instead of pattern test, then you can get the behaviour that you were looking for

In[2]:= ReplaceList[{3, 4, 2, 1}, 
          {___, x__, y___} :> {{x}, {y}} /; FromDigits[{x}] > 3]

Out[2]= {{{3, 4}, {2, 1}}, {{3, 4, 2}, {1}}, {{3, 4, 2, 1}, {}}, 
         {{4}, {2, 1}}, {{4, 2}, {1}}, {{4, 2, 1}, {}}, {{2, 1}, {}}}

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