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Re: Logical inconsistency

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1249] Re: Logical inconsistency
• From: rubin at msu.edu (Paul A. Rubin)
• Date: Fri, 26 May 1995 07:00:31 -0400
• Organization: Michigan State University

In article <3q14ct$725 at news0.cybernetics.net>,
   jorma.virtamo at vtt.fi (Jorma Virtamo) wrote:
->
->The other day I tried to construct a rule that applies
->to patterns of type 
-> 
->  test = h[a] + h[1] + h[anything];
->
->i.e. a sum of functions with head h. The most natural thing
->to do is to define the general pattern by
->
->  patt = Plus[__h];
->
->However, when you check for the match, you find to your surprise:
->
->In[3]:=
->  MatchQ[test,patt]
->Out[3]=
->  False
->
->This happens because
->
->In[4]:=
->  patt
->Out[4]=
->  __h
->
->or more fully
->
->In[5]:=
->  patt // FullForm
->Out[5]=BlankSequence[h]
->
->Because BlankSequence as the argument of Plus is a
->unary argument, Plus "thinks" to be superfluous, and
->drops out. However, BlankSequence outspokenly stands
->for a *sequence* of arguments. Therefore, Plus should 
->make an exception to the rule Plus[expr] := expr.
->
->A workaround in this case seems to be  
->
->In[6]:=
->  patt=(pl_/; pl==Plus)[__h]; 
->
->In[7]:=
->  MatchQ[test,patt]
->Out[7]=
->  True
->
->
->Has anybody a comment?
->
->
->-- Jorma Virtamo
->
->
->============================================================     
->Jorma Virtamo
->VTT Information Technology / Telecommunications
->P.O. Box 1202,  FIN-02044 VTT,  Finland
->phone: +358 0 456 5612          fax: +358 0 455 0115
->email: jorma.virtamo at vtt.fi     web: http://www.vtt.fi/tte/
->============================================================

I think the key is not that Plus[x] == x but that the expression Plus[__h] 
is being evaluated at all.  You want to convey to Mathematica that Plus is 
part of the pattern; you can do that by wrapping it in Literal[], which 
prevents evaluation.  Just change the pattern creation line to 

   patt = Literal[Plus[__h]];

and you get what you want.

Paul

**************************************************************************
* Paul A. Rubin                                  Phone: (517) 432-3509   *
* Department of Management                       Fax:   (517) 432-1111   *
* Eli Broad Graduate School of Management        Net:   RUBIN at MSU.EDU    *
* Michigan State University                                              *
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Mathematicians are like Frenchmen:  whenever you say something to them,
they translate it into their own language, and at once it is something
entirely different.                                    J. W. v. GOETHE