>term rewriting
In uni we had to make a spreadsheet software.
I volunteered to do the formula parser, thinking it sounded like a fun challenge.
I was stumped for a week, until I realized I could rewrite the formulas into a form I knew how to parse. So it would rewrite 1+1 into ADD(1,1) and so on.
I also refused to learn regex, so the parsing code was "interesting" ;)
I recall a comment from a colleague. "Okay, Andy says it works. Don't touch it." XD
Guy from another group used regex and his solution was 20x shorter than mine.
Regular expressions are probably not enough for parsing formulas (depending of course on the exact task given), they usually are at least a context free language.