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Problem with evaluation of delayed rules
*To*: mathgroup at smc.vnet.net
*Subject*: [mg21505] Problem with evaluation of delayed rules
*From*: Eckhard Hennig <hennig at itwm.uni-kl.de>
*Date*: Fri, 14 Jan 2000 02:43:25 -0500 (EST)
*Organization*: ITWM
*Sender*: owner-wri-mathgroup at wolfram.com
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,
Eckhard
-----------------------------------------------------------
Dipl.-Ing. Eckhard Hennig mailto:hennig at itwm.uni-kl.de
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
http://www.itwm.uni-kl.de/as/employees/hennig.html
ITWM - Makers of Analog Insydes for Mathematica
http://www.itwm.uni-kl.de/as/products/ai
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