[rer0tsaz]

Yes, that is the point I tried to make. Use simple, constrained forms such as (C) "for(int i = 0; i < n; i++) { ... }" with n an int and no modification of i in the body, or (Python) "for e in l:" where l is a list that is not modified in the body. Then your code is very easy to analyze, not just in theory but also in practice for compilers, tools and people reading your code. Many language designers have realized this and provide special syntax for this very common case. I'm not aware of any language that has special syntax for primitive recursion, but it's an interesting idea.

My apologies for making an absolute statement with unclear terms, thus inviting uncharitable interpretations.

[mafribe]

I agree, that simple loops that you describe are easier to analyse than full recursion.

But simple loops are not as expressive as full loops (where you can modify the loop variable). As a simple example, try to phrase the Euclid's algorithm for computing the GCD using "for(int i = 0; i < n; i++) { ... }" where "i" is not modified in the loop body.

[rer0tsaz]

Just use n = max(a, b). Of course that doesn't help you much unless you're adhering to strict safety standards (e.g. power of ten rules), it just shifts the burden of proof from termination to correctness. And there's no such trick with the Ackermann function.

I'm really just advocating a rule of least power. Don't go into full general recursion just because you can.