compressor/limiter questions

I've read the manual and online discussion about the compressor/limiter, but they explain the controls in terms of the resulting sound. I'm looking for a technical explanation in terms of the exact effect on the signal. That is, what the settings do exactly to a note's envelope. This is what I've gathered so far, can anyone confirm or correct this?

Any amplitude above the amplitide set by THRESH is decreased, by an amount determined by the COMP setting. The range of reduction is from zero (not at all), to complete reduction all the way down to the Theshold amplitude.

This reduction, however, is subject to the RESP setting. This setting seems to control two independent things. Couldn't it actually be split into two dials? From what I can tell, a fast setting means reduction will occur on all amplitudes immediately after a note attack, but will preserve a note's natural decay and release. A slow setting will reduce only amplitudes which occur some time after a note's initial attack, but will not preserve the note's natural decay and release. Instead, it will increase amplitude of decaying notes up to the threshold level, for a variable length of time.

Gain is applied after all the other controls, and simply raises or lowers the entire resulting signal.

Is this correct? Can anyone add anything? Thanks!!!