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MathGroup Archive 2006

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RE: pattern matching: rules that stop other rules?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71633] RE: [mg71596] pattern matching: rules that stop other rules?
  • From: "David Park" <djmp at earthlink.net>
  • Date: Sat, 25 Nov 2006 05:37:14 -0500 (EST)

First, if you use Mathematica in its standard default mode, spaces are
automatically inserted where appropriate and adding additional space usually
does little for readability except between larger chuncks of input.

f[x_] := 0

Next, check the attributes of If.

Attributes[If]
{HoldRest, Protected}

So the If statement will not evaluate f[2], at least not until it determines
that p is False. If you want f[2] to be evaluated you can specifically
Evaluate it.

If[p, 1, Evaluate@f[2]]
If[p, 1, 0]

A replacement rule will replace within held expressions.

If you use your own function instead of If, then none of the arguments are
held, unless you give your function one of the held attributes, and then all
arguments are automatically evaluated.

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/


From: croddie at princeton.edu [mailto:croddie at princeton.edu]

Hello. I've been using Mathamatica for quite a while but without ever
finding out how the language works fundamentally, which I'm trying to
do now. I'd be grateful for some help in understanding patterns - it
seems like a powerful idea to me. There is something I can't work out.

Define a function f [x_]:=0 say
Now If [ p, 1, f [ 2] ] evaluates to itself. So the rule in the
definition is not applied to f [ 2 ].

Replace If with some other undefined function, say qwerty, and you get
qwerty [ p, 1, 0] not surprisingly. And If [ p, 1, f [ 2] ] /. f
[x_]->0 returns If [ p, 1, 0 ].

Is there a rule associated with If that stops a rule (if that's the
right expression) from being applied inside it? Can users write such
rules?

Thanks for any help.



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