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DownValues and Cases

• To: mathgroup at smc.vnet.net
• Subject: [mg70759] DownValues and Cases
• From: Bruce Colletti <vze269bv at verizon.net>
• Date: Thu, 26 Oct 2006 02:39:08 -0400 (EDT)

Re Mathematica 5.2 under WinXP.

The results of the first two Cases statements leads me to anticipate {{1,3.5}, {2,5}, {_,0}} as the output of the third.  

The output of the fourth Cases statement confirms this expectation.

Unfortunately, the output of the third statement is the empty list.  

Why so?  I've reviewed a related mid-July MathGroup thread, but don't see the answer (if it's there at all). 

Thankx.

Bruce

--------------------------

f at 1=3.5;
f@2=5;
f[_]:=0;
h=DownValues@f

Out[4]={HoldPattern[f[1]] :> 3.5, HoldPattern[f[2]] :> 5, HoldPattern[f[_]] :> 0}

Cases[h,HoldPattern[f[x_]] -> x,Infinity]
Out[5]={1,2,_}

Cases[h,(_ :> y_) -> y,Infinity]
Out[6]={3.5,5,0}

Cases[h,(HoldPattern[f[x_]] :> y_) -> {x,y},Infinity]
Out[7]={}

Cases[{a :> 4,b :> 5, c :> 6},(x_ :> y_) -> {x,y}]
Out[8]={{a,4},{b,5},{c,6}}

• Follow-Ups:
  • Re: DownValues and Cases
    • From: Oyvind Tafjord <tafjord@wolfram.com>
  • Re: DownValues and Cases
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>