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Avoid iteration in pattern test?

• To: mathgroup at smc.vnet.net
• Subject: [mg132157] Avoid iteration in pattern test?
• From: Yi Wang <tririverwangyi at gmail.com>
• Date: Mon, 6 Jan 2014 02:30:34 -0500 (EST)
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• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-outx@smc.vnet.net
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Dear all,

I wonder if one can stop pattern test from unnecessary iteration. For example

ClearAll[x, a, b, c, d, f]
x /: f_ x := "matched" /; !FreeQ[f, d]

Trace[a b c x]

One can find that Mathematica first tests if a*b*c is free of d. Then it tests if a*b is free of d, if a*c is free of d, ...

However, we know that if a*b*c is free of d, all the sub-sequences are free of d. Thus is it possible to rewrite the above rule, to stop Mathematica from wasting the efforts?

Thanks a lot!
Yi

PS: currently, I have a workaround -- to hold evolution of x when no match. However, it makes things complicated and less automatic.

x /: f_ x := If[!FreeQ[f, d], "matched", f Hold[x]]

• Follow-Ups:
  • Re: Avoid iteration in pattern test?
    • From: Carl K Woll <carlw@wolfram.com>