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Logical inconsistency

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1229] Logical inconsistency
• From: jorma.virtamo at vtt.fi (Jorma Virtamo)
• Date: Fri, 26 May 1995 03:39:58 -0400

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


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