drop dup dup * swap abs - swap dup * +
operation : stack
(init) : x y z
drop : x y
dup : x y y
dup : x y y y
* : x y (y^2)
swap : x (y^2) y
abs : x (y^2) |y|
- : x (y^2 - |y|)
swap : (y^2 - |y|) x
dup : " x x
* : " (x^2)
+ : y^2-|y|+x^2
The author's version requires rot_3 in order to deal with performing the computation in an awkward order. This version deals with each variable in order and in a more natural way. And replacing `dup * ` with `square` simplifies it a bit more (which is what you'd do in a language like Forth, you factor common operations into new words): : square dup *;
drop dup square swap abs - swap square +
operation : stack
(init) : x y z
drop : x y
dup : x y y
square : x y (y^2)
swap : x (y^2) y
abs : x (y^2) |y|
- : x (y^2 - |y|)
swap : (y^2 - |y|) x
square : " (x^2)
+ : y^2-|y|+x^2
Down to 9 ops, and reasonably clear at this point.It is great that the author brings the issue up, even saying "every kind of language has its strengths and weaknesses, but most language designers will lie to you about the latter"
I do believe that point-free-form holds much promise. Maybe there could be more support for it in more standard languages and programming support tools.
I think the problem with "drop dup dup × swap abs rot3 dup × swap − +" is that it gets too abstract. Even though it is very elegant and succinct, it takes effort to understand it. And if something is hard to understand it is also hard to find the errors it may have.
But this is my point—the effort it takes to understand it is, in some sense, a one-time effort. If you invest the up-front effort to learn how to read concatenative programs, then you gain a fluency that makes it easier to read other programs. (Our more familiar programming paradigms are just as opaque to a beginning programmer; recursion, which is so fundamentally intelligible to us, is a major obstacle to people first learning to program, but I think there are few who would say it's not worth it.)
One of the big goals of concatenative programming is refactorability, which Jtsummers beautifully showed at work in your sibling post: https://news.ycombinator.com/item?id=25261911 . If you can understand enough to refactor, then you can simplify it to the point where errors must be apparent.