Glossary
A reflex mate is an inverse mate problem (i.e. you force the opponent to checkmate you) where both sides must checkmate (by reflex) whenever a mate in one is possible.
In retros, the reflex condition applies to any proof game. This is an additional constraint on legal proof games because they have to avoid situations where a mate in one is possible.
Here is an example:
404 - N. Plaksine Europe Echecs 283, 07/1982 In memoriam Roger Diot
6+13. Reflex mate in 1
Here the forward stipulation is easily answered with 1. Bb2! forcing the reflex 1 ... Qa2xb2 mate.
The interesting problem is to find how the position can be reached by a legal game without any earlier mate in one opportunity. Only the last few moves are problematic. See full solution if you cannot find them.
The first reflex problem was published by B. G. Laws in a 1893 British Chess Mag. issue. I don't know who first used the reflex condition in retros.
There exists a direct reflex stipulation (as opposed to inverse), recently invented by Jean Zeller. Here the goal is checkmate, but whenever it is possible (for any side) to play a so-called helping move that grants the opponent with a mate in one oportunity, one is under the obligation of playing it "by reflex" (unless one can already mate in one).