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.
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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.-----
Maybe something like:
total-price cost-per-item number-of-items shipping-cost-per-item rush-cost = cost-per-item number-of-items * shipping-cost-per-item number-of-items * + rush-cost +
This doesn't seem super great; it could be refactored to use each thing once, but it's late and I can't think of any better example.-----
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