Very nice. I tried several times without success to come up with a good non-recursive solution. The above not only is short, but it really does the binary search, and applying standard golfing techniques, it comes up a winner at 55:

sub f{
($s,$t)=@_;$t=$$t{$$t{d}gt$s?l:r}while$t&&$$t{d}ne$s;$t
}
[download]

(Or 57 if you add my to kill side effects. Still better than anything I thought of.)

Note that this is much less readable than what tye wrote, but every transformation is fairly mechanical compression of the code...