A Specification Logic for Termination Reasoning

We propose a logical framework for specifying and proving assertions about program termination. Although termination of programs has been well studied, it is usually added as an external component to the specification logic. Here we propose to integrate termination requirements directly into our specification logic, as temporal constraints for each phase of every method. Our temporal constraints can specify a strict decrease in a bounded measure for termination proofs and the unreachability of method exit for non-termination proofs. Furthermore, our termination-infused logic can leverage richer specification logics to help conduct more complex termination reasoning for programs with structural specification, heap manipulation, exception handling, and multiple phases. We expect our termination reasoning to directly benefit from any future improvements to our specification mechanism because it is fully integrated into our specification logic. Through an experimental evaluation, we report on the usability and practicality of a verification system, based on separation logic, that has been enhanced with our termination constraints.