A historical example of what one can do with limited memory is the Sinclair Scientific calculator (http://files.righto.com/calculator/sinclair_scientific_simul...). It doesn't use RAM at all, doing everything in registers.

If it would have had RAM, one could have used it to implement a memory or to implement a 'normal' infix UI.

And no, it isn't cheating that it uses a CPU designed for calculators. At best, that keeps the ROM space needed down, but I doubt that, given its somewhat weird instruction set.