Limiting itself to reversible operations gives some mathematical niceties, but also locks out a lot of things.

When I did something similar, I was thinking about perfect hashing, where the set of inputs is known ahead of time. The usual approach uses a constant array, but I wanted to - in particular, if the inputs are already small integers, if I could compact them further (obviously this is possible: hash -= hash > > gap_index). I sat down and wrote out a list of ... probably 100? ... primitive operations (some of which are admittedly redundant with each other, but which are useful thinking of separately). And then I got bored and never did anything with the project.