The Perl code reads exactly from the piece definition, adding a few $ symbols, a *, and semi's. It makes every condition explicit, and don't rely on narrowing constraints and order of definition. So I'm pretty sure that's a correct implementation.

I suppose there are multiple versions of Ackerman's idea, all working in the same way, but different in detail.

—John

VSarkiss was just trying to rewrite what you wrote more cleanly. But do a search for Ackermann's function and you consistently come up with the function as I wrote it.

Incidentally as noted in this biography, what Ackermann actually came up with was a function of 3 variables. This was later simplified by Rosza Peter then Raphael Robinson into the current textbook form which I wrote.