More Pattern Match Understanding Problems

*To*: mathgroup at smc.vnet.net*Subject*: [mg46620] More Pattern Match Understanding Problems*From*: Harold.Noffke at wpafb.af.mil (Harold Noffke)*Date*: Wed, 25 Feb 2004 13:07:12 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

MathGroup: In the Mathematica 5 Book, Section 2.3.8, "Functions with Variable Numbers of Arguments," there are three examples of using ReplaceList to understand pattern matching (In/Out-4,5,6). I understand In/Out-4 and In/Out-6 if I assume the Mathematica explanation (immediately below) refers only to "labeled blanks" when it says "blanks" ... When you use multiple blanks, there are often several matches that are possible for a particular expression. In general, Mathematica tries first those matches that assign the shortest sequences of arguments to the first <labeled?> multiple blanks that appear in the pattern. When I examine In/Out-5, however, my understanding breaks down when I see that the answer Mathematica gives is g[a,b,c,d], which is the longest (not the shortest) sequence assigned to the labeled blank x__. In[5]:= ReplaceList[f[a, b, c, d], f[___, x__] -> g[x]] Out[5]= {g[a,b,c,d], g[b,c,d], g[c,d], g[d]} Therefore, I conclude my reasoning is incorrect. Can anyone provide some guidance on how to think through In/Out-4,5,6 without assuming labeled multiple-blanks have priority over unlabeled ones? Thanks. Harold