picking specific symbol definitions in mathematica (not transformation rules)

Question

I have a following problem.

f[1]=1;
f[2]=2;
f[_]:=0;

dvs = DownValues[f];

this gives

dvs = 
   {
      HoldPattern[f[1]] :         


        

Answer 1

Leonid, of course, completely answered the question about why your temporary solution works but HoldPattern does not. However, as an answer to your original problem of extracting the f[1] and f[2] type terms, his code is a bit ugly. To solve just the problem of extracting these terms, I would just concentrate on the structure of the left-hand-side of the definition and use the fact that FreeQ searches at all levels. So, defining

f[1] = 1;  f[2] = 2;  f[_] := 0;
dvs = DownValues[f];

All of the following

Select[dvs, FreeQ[#, Verbatim[_]] &]
Select[dvs, FreeQ[#, Verbatim[f[_]]] &]
Select[dvs, ! FreeQ[#, HoldPattern[f[_Integer]]] &]

yield the result

{HoldPattern[f[1]] :> 1, HoldPattern[f[2]] :> 2}

Provided there are no f[...] (or, for the first version, Blank[]) terms on the right-hand-side of the downvalues of f, then one of the above will probably be suitable.