Re: Re: DownValues and Cases

On 27 Oct 2006, at 20:58, Carl Woll wrote:

> 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.
> In this case you can apply Verbatim to just the head HoldPattern,
> but then you still need a HoldPattern to prevent f[x_] from
> evaluating. So:
>
> In[18]:=
> Cases[h, (Verbatim[HoldPattern][HoldPattern[f[x_]]] :> y_) -> {x,
> y}, Infinity]
> Out[18]=
> {{1, 3.5}, {2, 5}, {_, 0}}
>
> Carl Woll
> Wolfram Research
>

Yes, of course! . I actually thought about wrapping Verbatim around
the Head, but then realized that f[x] would then evaluate and at this
point gave up the idea. It did not occur to me to use a second
HoldPattern.

Andrzej Kozlowski

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