In the PL community, when we want to communicate an algorithm in a paper in something like code, we will say something to the effect of C-style pseudo code. This serves two roles: 1) everyone "knows" C so you don't have to explain your notation very well, and 2) we will skip over all the ickiness of C (hence the C-like).

I get the impression that the work here is more about thinking and iterating on paper, not just communicating on paper, which, IMHO, is a very niche use case that most people aren't going to run into. We don't do anything in our C-style pseudo codes but present.