Explain this DSP notation

Question

I'm trying to implement this extenstion of the Karplus-Strong plucked string algorithm, but I don't understand the notation there used. Maybe it will take years of study, but maybe it won't - maybe you can tell me.

I think the equations below are in the frequency domain or something. Just starting with the first equation, H_p(z), the pick direction lowpass filter. For one direction you use p = 0, for the other, perhaps 0.9. This boils down to to 1 in the first case, or 0.1 / (1 - 0.9 z^-1) in the second.

Now, I feel like this might mean, in coding terms, something towards:

H_p(float* input, int time) {
  if (downpick) {
    return input[time];
  } else {
    return some_function_of(input[t], input[t-1]);
  }
}

Can someone give me a hint? Or is this futile and I really need all the DSP background to implement this? I was a mathematician once...but this ain't my domain.