In q it's just {(q%x),z%q:-.5y+signum[y]sqrt(yy)-4xz}

This is easy to see is correct.

How do you know that Joy is correct?

I'm trying to mentally execute this. I know I haven't seen Joy before, but I've used Forth, Postscript and Lisp, so I feel like I have a lot to stand on:

- cons seems to have the same meaning in lisp, so x y cons -> (x . y) or in Erlangish, [x|y] right?

- x [y] dip seems to be y x

- [x] [y] infra seems to be the same as [x y]

- swap, first, pop, sqrt all seem reasonable

- wouldn't [] cons cons cons dup* be better than the extra list with [i] map ] infra first? it's not really clear to me what [i] map is doing... I see how the values have to flow, but it feels like it should be redundant.

I feel like it's immediately a lot more (mental) work. It reminds me of tracing forth code before I just gave in and started using variables like a normal person.

Is this really the best way to be introduced to Joy? Is this a typical problem that Joy programmers feel is the right way to program (and the right solution?) Am I missing something here?