An unexpected behavior of PatternTest in Mathematica

Question

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__}]

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.

What is wrong with my interpretation of the code?

Answer 1

The documentation for PatternTest (aka ?) says

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

Thus your code will not work as you hoped.

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}}}

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}, {}}}