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I am reading this page : https://reference.wolfram.com/language/tutorial/FunctionsWithVariableNumbersOfArguments.html

And I don't understand the example : h[a___, x_, b___, x_, c___] := hh[x] h[a, b, c]

At the exact first call, which vales take x,a,b,c on the call ? Because I am confused with thoose ___.

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  • $\begingroup$ In the linked page, there are explanations of those blanks right below this example. $\endgroup$
    – vapor
    Jun 2, 2017 at 10:33
  • $\begingroup$ A brief explanation: the two x_ represents any two duplicated elements, and a, b, c with blank null sequence pattern can represent anything. Together h will pick out duplicated elements regardless of their positions. If your first call refers to h[2, 3, 2, 4, 5, 3], then a is Sequence[](Nothing), b is 3, c is Sequence[4,5,3] and x is 2, the expression becomes ` hh[2] h[3,4,5,3]. Then the latter part can also be matched, with a` is Sequence[], b is Sequence[4,5], c is Sequence[] and x is 3, then the final answer is h[4, 5] hh[2] hh[3] $\endgroup$
    – vapor
    Jun 2, 2017 at 10:41
  • $\begingroup$ @happyfish I think the explanation in the reference might not be so clear. Why not post your comment as an answer? This question should be OK, IMO. $\endgroup$
    – LLlAMnYP
    Jun 2, 2017 at 11:04
  • $\begingroup$ When you say h will pick out duplicated elements. Here we have $2$ and $3$ that have two occurences. How the function knows $x=2$ and not $x=3$ for example ? Is it the first duplicated elements that the functions meet ? Then as $2$ is the first duplicated, the program knows that $a$ has to be nothing ? $\endgroup$
    – StarBucK
    Jun 2, 2017 at 11:27
  • $\begingroup$ So you are basically asking how pattern matching is implemented in mathematica? I do not have an answer. But you can look up algorithms that are commonly used, e.g. Thompson's construction $\endgroup$
    – vapor
    Jun 2, 2017 at 13:08

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