Lambda the Ultimate

Is anyone aware of concrete term rewriting systems in a form of computer languages? It seems to me as a very promising area as a programming paradigm, yet there is no sign of it as far as I have searched the web. There is no sign of it even on wiki page of programming paradigms, even generally. Are we looking at yet unrevealed area of programming? By my personal opinion, term rewriting might be a way humans think at some higher abstraction level, above all the neural networks native to the human brain. Term rewriting essence seems so natural to me as a thinking framework for solving math, physics, chemistry or logic problems, that I'm surprised there are no implementations of it in a form of programming languages.

Does anyone know of any implementation? And should term rewriting be accepted as a different programming paradigm?

Thank you,
Ivan