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MathGroup Archive 1991

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Re: math2.0 rule ordering

  • To: mathgroup at yoda.ncsa.uiuc.edu
  • Subject: Re: math2.0 rule ordering
  • From: Frank Zizza <willamu!pioneer!zizza at uunet.UU.NET>
  • Date: Wed, 7 Aug 91 14:05:17 PDT

	I have found that the order in which rules are assigned can  
be important.  (I have not worked with version 2.0 yet, my experience  
is only with version 1.2) Consider the following:

Mathematica (sun4) 1.2 (June 13, 1990) [With pre-loaded data]
by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin,
   S. Omohundro, D. Ballman and J. Keiper
with I. Rivin and D. Withoff
Copyright 1988,1989,1990 Wolfram Research Inc.

In[1]:= f[2] := 2

In[2]:= f[x_] := single    


In[3]:= f[x__] := double

In[4]:= f[x___] := triple

In[5]:= ?f
f
f/: f[2] := 2
 

f/: f[x_] := single
 

f/: f[x__] := double
 

f/: f[x___] := triple
 


In[5]:= g[x___] := triple

In[6]:= g[x__] := double

In[7]:= g[x_] := single

In[8]:= g[2] := 2

In[9]:= ?g
g
g/: g[2] := 2
 

g/: g[x___] := triple
 

g/: g[x__] := double
 

g/: g[x_] := single

This shows that the most specific rule is positioned first but that  
the rules that contain pattern blanks are ordered as they were  
entered.  Presumably Mathematica cannot decide how these rules should  
be ordered.  I cannot test your code (for MoreGeneralThan) because it  
relies on Mathematica 2.0 constructions but I would GUESS that based  
on the above Mathematica session it would also return False for  
MoreGeneralThan[f[x_], f[x___]].  (I would be interested to hear the  
result of such a test.)  


	If Mathematica 2.0 does in general place the rule for f[x_]  
before f[x___] as your calculations show, then we can argue that if  
it did not place the rule for f[x_] first, that rule would never be  
used since f[a] matches the pattern f[x___].

Frank Zizza
zizza at willamette.edu





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