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Questions about rules

  • To: mathgroup at
  • Subject: Questions about rules
  • From: Jean-Paul Roy <roy at>
  • Date: Thu, 7 Jan 93 14:59:57 +0100

3 packages of questions to Mma gurus about RULES (version 2.1).

A) I want my program to dynamically generate rules. Say that a global variable
z has value 3 at some moment, and the function foo is undefined:

z = 3; x = 10;
  Information :: symbol foo not found
What then must my running *program* do to get after execution :

  foo[x_] := x + 1 /; x < 3

where the 3 stands for the value of z at the moment of the definition of foo. 
I want exactly *this*, not a more complicated form with Evaluate[z]. I tried 
many forms with DownValues, Hold, ... but couldn't get the desired result.

B) I suppose it's the same problem if I want to generate a new rule like:

bar[x_] := Which[x < 1, 3, x < 2, 6, True, 9]

where 3 stands for z, 6 for 2z and 9 for 3z ? The 'True' may also
cause problems. I'm trying in A) and B) to generate piecewise curves from
interpolation points.

Notice that z and x both have values when the rule is generated (this is 
normal for z but may cause problems for x, as I want to capture the value of z 
but not the value of x).

Maybe am I trying to practise Lisp macros in Mma ? Apparently I didn't get 
the right way to do it. Anyway, being able to dynamically build rules is
very important, and we should be able to do it *easily*...

C) What am I missing here ? The variable n is unbound but declared Integer:

n /: IntegerQ[n] = True;

1 + Sin[n Pi] /. Sin[k_Integer Pi]->0
   (* unchanged *)
1 + Sin[n Pi] /. Sin[k_ Pi] -> 0
   (* 0 but not always correct *)
Replace[Sin[n Pi],Sin[n_ Pi] -> 0 /; IntegerQ[n]]
   (* obsolete warning, result 0 *)
Replace[Sin[n Pi],Sin[k_ Pi] -> 0 /; IntegerQ[k]]
   (* obsolete warning, result Fail *)
1/Sqrt[x] /. Sqrt[y_]->2
   (* unchanged *)
1/Sqrt[x] /. Sqrt[x]->2
   (* unchanged but 1+Sqrt[x] /. Sqrt[x]->2 is correct, result 3 !!! *)
*Please* explain me...

          Jean-Paul Roy
          Departement d'Informatique
          Faculte des Sciences de Nice
          [roy at]

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