Re: DownValues and Cases

• To: mathgroup at smc.vnet.net
• Subject: [mg70777] Re: [mg70759] DownValues and Cases
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 27 Oct 2006 00:28:22 -0400 (EDT)
• References: <200610260639.CAA19605@smc.vnet.net> <EA3D6F5B-C921-45E7-9AB3-DACF16C63276@mimuw.edu.pl>

```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

```

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