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

Based on Simon's excellent solution here, I suggest:

Cases[DownValues[f], _?(FreeQ[#[[1]], Pattern | Blank] &)]