"How to Program an Infinite Abacus" defines register machines (a.k.a counter machines), and shows that they coincide with general recursive functions. "The comp

"How to Program an Infinite Abacus" defines register machines (a.k.a counter machines), and shows that they coincide with general recursive functions. "The complexity of loop programs" defines loop programs, and shows that the coincide with primitive recursive functions. (A key difference is whether loops are bounded or not.)