Local Reasoning for Termination

In this paper, we bridge the gap between separation logic and transition invariants in order to obtain a uniform framework for proving total correctness of pointer programs. We introduce the concept of separated transition constraints to describe the local effect of pointer programs. Separated transition constraints provide a new view on locality by their non-tight interpretation. Furthermore, separated transition constraints constitute the basis for separated transition logic which enables local reasoning about relations over states of heap-manipulating programs. We put the framework of transition invariants to work with separated transition logic and obtain as a consequence a conservative extension of separation logic that is able to prove termination.