> For example, I once wrote a library for a computing in particular area of mathematics, but I also wanted to see some symbolic equations. I just changed the basic evaluation semantics of my numeric operators to operate on symbols as well as numbers and to run some simplification logic and boom.

This is very much something I find fascinating (and a reason I’m quite excited by Julia). Can you point me to any examples where you feel this has been tastefully done? (yours or otherwise)