Baffled By Underscore Pattern Matching

• To: mathgroup at smc.vnet.net
• Subject: [mg45992] Baffled By Underscore Pattern Matching
• From: Harold.Noffke at wpafb.af.mil (Harold Noffke)
• Date: Mon, 2 Feb 2004 05:20:27 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```MathGroup:

In my study of Mathematica 5.0, I have reached "The Mathematica Book >
Principals of Mathematica > Patterns > 2.3.8 Functions with Variable
Numbers of Arguments".  The In[1]/Out[1] example I understand, but the
In[2,3]/Out[3] example (discussed below) has me totally mystified.

As printed, we have ...

In[2]:= h[a___, x_, b___, x_, c___] := hh[x] h[a, b, c]

In[3]:= h[2, 3, 2, 4, 5, 3]

Out[3]= h[4, 5] hh[2] hh[3]

Now let's make a change to In[2] ...

In[4]:= Clear[h, hh]

In[5]:= h[a___, x_, b___, x_, c___] := hh[x] h[{a}, {b}, {c}]

In[6]:= h[2, 3, 2, 4, 5, 3]

Out[6]= h[{}, {3}, {4, 5, 3}] hh[2]

I did a Trace on this pattern match problem, and found only that
doublets were pulled out on each iteration.  In order to understand
what is happening here, I think I need to understand the matching
process at a level of granularity finer than Trace can supply.  I
don"t have a clear mental picture of how In[5] manipulates the number
stream which feeds into it from In[6].  I have no idea of how the
In[6] lists came to contain the numbers they do.

Any help, pointers to tutorial papers, or more illuminating examples
will be greatly appreciated.

Thanks.
Harold

```

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