@webhat Yeah, I heard it called [reverse] Polish notation as well, or prefix notation. The problem arises that people want to write factorial as 5! not ! 5 (maybe you could get a lisper to write (fact 5)), or worse, people including lispers want to write 2/3 and so forth.
So each token has a nud (prefix notation host language thing to do) and a led (infix or left-binding host language thing to do), and you compare the current right binding power with tokens' left binding powers or something...