Re: DownValues and Cases

*To*: mathgroup at smc.vnet.net*Subject*: [mg70785] Re: [mg70759] DownValues and Cases*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Fri, 27 Oct 2006 00:28:39 -0400 (EDT)*References*: <3282293.2074281161897563457.JavaMail.root@vms073.mailsrvcs.net> <B866860F-D756-42CE-A711-88777642D815@mimuw.edu.pl>

Of course I really meant: h = {HoldPattern[f[x_]] :> 1, HoldPattern[g[x_]] :> 2, b :> 3}; in which case you get: Cases[h, (x_ :> _) :> Level[x, -1]] {{x, _, x_, 1}, {x, _, x_, 2}, {}} Of course one can construct even more artificial examples where even my method will not produce the wanted result, namely, when the list h already contains something of the form Hold[f[a]]:>b, which we do not wish to pick up. One could modify it for such cases but then one could again construct examples where the new method would fail. I doubt that a completely universal and fail proof method could be found to deal with all such cases. Andrzej On 27 Oct 2006, at 11:43, Andrzej Kozlowski wrote: > That will, of course, solve the problem you asked about, concerning > DownValues. But it would not solve the more general problem with > HoldPattern (admittedly one that is not very likely to occur > naturally) . Suppose we have the definitions > > f[x_] := 1; g[x_] := 2; > > and consider the list > > h = {HoldPattern[f[x_]] :> 1, HoldPattern[g[x_]] :> 2, b -> 3}; > > Suppose we are only interesting in extracting information about f, > in the way you originally wanted. This will do it: > > > > Cases[h /. HoldPattern -> Hold, (Hold[f[x_]] :> y_) -> > {x, y}, Infinity] > > > {{x_, 1}} > > > > but this will do something rather different: > > > > Cases[h, (x_ :> _) :> Level[x, -1]] > > > {{x, _, x_, 1}, {x, _, x_, 2}} > > > > That's what I meant when I wrote "the most accurate way" - the way > that will allow you to pick up exactly the pattern you want when > similar ones are present. > > Andrzej Kozlowski > > > On 27 Oct 2006, at 06:19, Bruce Colletti wrote: > >> Andrezj >> >> Your reply, and that of another, has gripped and led me the >> statement below (crafted with Wolfram Tech Support's help): >> >> Cases[h, (x_ :> _) :> Level[x, -1]] >> >> This is likewise appealing...but does it suffer a flaw not found >> in your solutions? >> >> Thanks. >> >> Bruce >> >> ===================== >> From: Andrzej Kozlowski <akoz at mimuw.edu.pl> To: mathgroup at smc.vnet.net >> Subject: [mg70785] Re: [mg70759] DownValues and Cases >> >> >> On 26 Oct 2006, at 22:54, Andrzej Kozlowski wrote: >> >>> >>> On 26 Oct 2006, at 15:39, Bruce Colletti wrote: >>> >>>> 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}} >>>> >>> >>> This is rather tricky. The problem is how to force the >>> PatternMatcher to interpret HoldPattenr literally rather than as >>> the pattern to be held. Note that: >>> >>> Cases[h, (Verbatim[HoldPattern[f[2]]] :> y_) -> {x, y}, >>> Infinity] >>> >>> {{x, 5}} >>> >>> works, but: >>> >>> >>> Cases[h, (Verbatim[HoldPattern[f[x_]]] :> y_) -> {x, y}, >>> Infinity] >>> >>> {} >>> >>> doesn't, because now x_ is also interpreted literally rather than >>> as a pattern. So you have got to somehow to avoid using HoldPattern >>> directly in your pattern (this is now rally getting confusing), for >>> example like this: >>> >>> >>> Cases[h, (p_ :> y_) /; Head[p] === HoldPattern :> >>> {p[[1,1]], y}, Infinity] >>> >>> {{1, 3.5}, {2, 5}, {_, 0}} >>> >>> There are probably more elegant ways but none comes to my mind just >>> now. >>> >>> Andrzej Kozlowski >> >> >> A more compact way to do the above is: >> >> Cases[h, (p_HoldPattern :> y_) :> {p[[1, 1]], y}, Infinity] >> >> >> But, it seems to me that the most accurate way to match expressions >> with Head HoldPattern, as you wanted to do, is to first replace >> HoldPattern by something like Hold or Unevaluated: >> >> >> Cases[h /. HoldPattern -> Hold, >> (Hold[f[x_]] :> y_) -> {x, y}, Infinity] >> >> >> {{1, 3.5}, {2, 5}, {_, 0}} >> >> >> Andrzej Kozlowski >> >

**Re: DownValues and Cases**

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**Re: DownValues and Cases**

**Re: DownValues and Cases**