Re: Problem with evaluation of delayed rules

*To*: mathgroup at smc.vnet.net*Subject*: [mg21579] Re: Problem with evaluation of delayed rules*From*: Bojan Bistrovic <bojanb at physics.odu.edu>*Date*: Sat, 15 Jan 2000 02:04:22 -0500 (EST)*Organization*: Old Dominion Universityaruba*References*: <85mkef$1og@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Eckhard Hennig wrote: > > 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 > You could use the "/. If -> MyIf /. MyIf -> If" trick and map a "Hold" function before the transformation to the places yuo don't want evaluated: MapAt[ReleaseHold,MapAt[Hold,Out[3],{1}]/.If->MyIf/.MyIf->If,{1}] If "Hold" doesn't do the trick, the, you can try with HoldForm or Unevaluated or something else. There was a talk about working with unevaluated expressions on 1999 developers conference; here's the link: http://library.wolfram.com/conferences/devconf99/withoff/index2.html http://library.wolfram.com/conferences/devconf99/withoff/index.html The first one is HTML and the secon one is .nb format Bye, Bojan -- ------------------------------------------------------------- Bojan Bistrovic, bojanb at physics.odu.edu Old Dominion University, Physics Department, Norfolk, VA -------------------------------------------------------------