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Problem with evaluation of delayed rules

  • To: mathgroup at
  • Subject: [mg21505] Problem with evaluation of delayed rules
  • From: Eckhard Hennig <hennig at>
  • Date: Fri, 14 Jan 2000 02:43:25 -0500 (EST)
  • Organization: ITWM
  • Sender: owner-wri-mathgroup at

Hi, I would greatly appreciate any elegant solutions to the following type
of problem.

Assume that we have a list of symbols, e.g.

In[1]:= symbols = {a, b, c, d};

and that we have the following expression that involves a function (here
"If") with HoldXXX attribute (HoldAll, HoldRest, ...).

In[2]:= expr = If[x > 0, Difference[1, 2], Difference[3, 4]];

In the above expression, I want to replace all objects of the form
Difference[i, j] by differences of the two entries i and j from the list
"symbols". If I use a delayed rule as follows

In[3]:= expr /. Difference[x_, y_] :> symbols[[x]] - symbols[[y]]

then this is what I get:

Out[3]= If[x > 0, symbols[[1]] - symbols[[2]], symbols[[3]] - symbols[[4]]]

Due to the HoldXXX attribute of the "If" function, the right-hand side of
the delayed rule remains unevaluated. However, I need the result of the rule
to be evaluated BEFORE it is inserted into expr, i.e. the result I want for
In[3] is:

Out[3new]= If[x > 0, a - b, c - d]

Does there exist any (simple) approach to forcing Mathematica 3.0/4.0 to
simplify the result of a delayed rule as soon as the rule applies to a
subexpression of a held expression (please note the conditions below)? One
may argue that it doesn't make a difference in the end whether result of
rewriting expr is given in the form of Out[3] or Out[3new]. Well, the
difference comes in as soon as you clear the value of "symbols" with
Clear[symbols] and then evaluate Out[3] for some x.

Condition 1: Temporarily removing any HoldXXX attributes from expr or any of
its subexpressions is not a solution because I only want the results of
rules to be simplified. No further simplification of held subexpressions
must be performed after rule application. For example,

  Out[3] /. If -> MyIf /. MyIf -> If

yields Out[3new], but this approach does not count as a solution.

Condition 2: The solution must not be limited to a predefined set of
functions with HoldXXX attribute, say If and Which.

Best regards,


Dipl.-Ing. Eckhard Hennig      mailto:hennig at
Institut fuer Techno- und Wirtschaftsmathematik e.V. (ITWM)
Erwin-Schroedinger-Strasse,  67663 Kaiserslautern,  Germany
  Voice: +49-(0)631-205-3126    Fax: +49-(0)631-205-4139

     ITWM - Makers of Analog Insydes for Mathematica

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