Local scoping of pattern names in rules--or not

*To*: mathgroup at smc.vnet.net*Subject*: [mg120642] Local scoping of pattern names in rules--or not*From*: Kris Carlson <carlsonkw at gmail.com>*Date*: Sun, 31 Jul 2011 23:37:32 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Hi, I am writing a function to find the shortest paths from a source vertex to a target in a directed graph. The actual application of this is identifying possible circuits in the spinal cord where an electrical stimulator interferes with pain signals and alleviates the pain. To find direct connections from source to target, even with 11K connections, is trivial, but it's less so with intermediate nodes, variable path length in the # of vertices, and recurrence. I could not find a built-in shortest paths function with variable path length, or in Combinatorica. If you know of one please let me know. Sometimes the local scoping in Rule and Cases works and sometimes not. I'd like to have a better understanding of this. Here is what Tech Support wrote me a while ago after some initial confusion about the cause and solution themselves, and a toy example: Thank you for the email. I apologize for not providing explanations in my notebook for what exactly Mathematica is doing. In fact I have figured out that it is not a problem with your variables being symbols or lists but rather that of evaluating the Rule itself. For some reason, even when the variables are locally scoped, Mathematica is evaluating their values before the rule is evaluated. Using a Rule Delayed (:>) solves this problem and the results are as expected. I have inserted my comments/explanations in the attached notebook. In[558]:= aList=Range[10];n=7; In[563]:= f1[list1_List]:=Module[{},Cases[aList,n_/;n>3->50]] f2[list1_List]:=Module[{},Cases[aList,n_->{a,n,b}]] (* local scoping doesn't work as intended *) In[565]:= f3[list1_List]:=Module[{},Cases[aList,n_:>{a,n,b}]] In[564]:= f1[aList] Out[564]= {50,50,50,50,50,50,50} In[562]:= f2[aList] Out[562]= {{a,7,b},{a,7,b},{a,7,b},{a,7,b},{a,7,b},{a,7,b},{a,7,b},{a,7,b},{a,7,b},{a,7,b}} In[566]:= f3[aList] Out[566]= {{a,1,b},{a,2,b},{a,3,b},{a,4,b},{a,5,b},{a,6,b},{a,7,b},{a,8,b},{a,9,b},{a,10,b}} Thanks, Kris