Re: Pure Functions in rules

*To*: mathgroup at smc.vnet.net*Subject*: [mg15962] Re: Pure Functions in rules*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Fri, 19 Feb 1999 03:26:52 -0500*Organization*: Universitaet Leipzig*References*: <7ag34l$aie@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi Will, the behaviour is correct because you have to use RuleDelayed[] and {1,2,3}/.m_List:>(2*#& /@ m) works as expected. You can see what's happen with Trace[{1,2,3}/.m_List->((2*#)& /@ m)] The rhs of Rule[] is evaluated first and gives the final replacement m_List -> m, because the pure function maps to a symbol. If you have a function f[m_List] defined just the same happens (m_List -> f[m]) but since m is not a list Mathematica leaves the result unevaluated until ReplaceAll[] insert the list in the argument of f[]. Now the pattern for f[m_List] matches and f[] can multiply the list entries by two. It is a good rule for the design of replacment rules to use RuleDelayed[] when in the left hand side of the rule contain a pattern. Hope that helps Jens Will Self wrote: > > It appears that I cannot depend on using a pure function > in a pattern-matching rule. > > Here I am trying to convince reluctant students that they're > better off learning to use Mathematica than doing things > by hand, and we run across something like this, and in a > much more complicated situation where the trouble was > hard to isolate. > > I am quite frankly incensed by the behavior shown in > In/Out 80, below. Look at these examples: --- snip snap - snip snapp - snip snap --- > > In[79]:= {1,2,3}/.m_List->f[m] > Out[79]= {2,4,6} > > Now try this: > > In[80]:= {1,2,3}/.(m_List->(2*#& /@ m)) > Out[80]= {1,2,3} > > Does anyone (say, at WRI for example) care to comment on > this? > > Will Self