I do Bret Victor style interactive programming environments. I've developed a set of tricks over the years and they are all quite simple. It really is programming in the classic sense and not so much Greek symbols on the whiteboard.
also, what I do is not very well understood, so there is no good theory for it yet and a lot of open questions to investigate. So its more experiment and measure vs. find a proof that will tell you for sure the right thing to do.
> I've developed a set of tricks over the years and they are all quite simple.
Actually, so is Earley parsing. The more I study this little piece of CS, the more I see how simple this really is. This is why it feels so much like math to me: hard at the beginning, then something "clicks" and everything becomes simpler.
Your "set of tricks" are probably similar. Knowing nothing about them, I'd bet their simplicity is rooted in some deep, abstract, yet simple math, just waiting to be formalized:
> what I do is not very well understood, so there is no good theory for it yet and a lot of open questions to investigate.
And how do you plan to further your understanding, or finding good theories? It can't be just psychology and cognitive science. I'm sure there will be some math involved, including proofs.
My set of tricks is more like: trace dependencies for work as it is done, put work on dirty list when dependency changes, redo work, + some tricks to optimize previous steps. It is really hard to interpret that as math, especially if the word "math" is to remain meaningful and useful. It is all math at some level, but so is everything.
also, what I do is not very well understood, so there is no good theory for it yet and a lot of open questions to investigate. So its more experiment and measure vs. find a proof that will tell you for sure the right thing to do.