Super interesting! I like how you can zoom into the system, almost like using a microscope to see how code works.
One thing that isn't quite clear from your examples here (and maybe that wasn't the point, but I am wondering): why have a different stack when a function is called? Your examples would work fine if they used the same stack. That is, if functions used the same stack, `1+` could be defined as `1 +`.
Perhaps it would be more clear if an example used two variables, or used the same variable twice.
Is it that you're trying to reduce stack juggling? That's hard to understand from simple examples (that you need to have to grok the syntax). Maybe compare something like finding the hypotenuse of a right triangle given the two other sides. Without naming arguments, you'd have to do something like:
hypot = dup * swap dup * + sqrt
But with named arguments:
hypot x y = x x * y y * + sqrt
That seems a little easier to read, but even the original isn't so complicated. Is there an example that makes it more obvious why it's better? Even your `square` example is more tokens than with stack juggling (without arguments, `square = dup *` is just four tokens, compared to six with named arguments). I'd say the with-arguments one is easier to read, but I've far less familiar with stack-based postfix programming.
Yeah, some other polynomial might be a better example. The Pythagorean formula has a clean separation when it comes to which args each term uses. How about the roots of a quadratic equation when you start out with a, b and c on the stack?
You're right that in general any such example can be refactored to reduce stack operations. That's even a fun game for many Forth programmers to play. (We lispers have our own equivalents.) But it usually makes the code less comprehensible, in my experience.