Walther Recursion

Primitive recursion is a well known syntactic restriction on recursive deenitions which guarantees termination. Unfortunately many natural deenitions, such as the most common deenition of Euclid's GCD algorithm, are not primitive recursive. Walther has recently given a proof system for verifying termination of a broader class of deenitions. Although Walther's system is highly automatible, the class of acceptable deenitions remains only semi-decidable. Here we simplify Walther's calculus and give a syntactic criterion on deenitions which guarantees termination. This syntactic criteria generalizes primitive recursion and handles most of the examples given by Walther. We call the corresponding class of acceptable deenitions \Walther recursive".