I dont think so... I know Reflective higher order calculus is currently even been developed by a team of developers from pyrofex and Rchain community.
for the record Jason Knight rho calc is not theoritical... check out Rchain developers
My answer would be a question: "FOR WHAT?!?"
Outside of purely scientific endeavors -- and even then -- what POSSIBLE purpose would it serve? 99%+ of programming would likely never have any legitimate reason for the subject to even come up.
In what scenario would it actually be useful? I mean the only place it would come close might be 3d programming, and that's all -- for better or worse -- gone over to matrices.
The only time you see anything of that nature mentioned being in the theoretical BS you find in a college setting, and not in practical application. The typical textbook rubbish written by career educators who know jack about s*, used by them to make programming sound all lofty and high-brow. It isn't.
Mark
I think I can answer with both "I don't know rho calculus" and "no it is not common".
I base this on two things:
I'm rather curious though where this question is coming from. Why would a specialized field of math be popular? Should it be? Why do you care?