An Integrated Logic for Termination and Non-Termination Reasoning

We propose a logical framework for specifying and proving assertions about program termination and non-termination. Although program termination has been well studied, it is usually added as an external component to a specification logic. Here we propose to integrate termination requirements directly into our specification logic, as temporal constraints for each execution phase of every method. Our temporal constraints can specify a strict decrease in some bounded measure for termination proofs or the unreachability of method exit for nontermination proofs. The reasoning on these temporal constraints is supported by a novel temporal entailment procedure. Furthermore, our termination-enhanced logic can leverage on richer specification logics to help conduct more intricate termination reasoning for programs with heap manipulation or multiple terminating phases. Through a seamless integration into the specification logics, we expect our termination reasoning to benefit from any future improvements to our logics, and vice-versa. With an experimental evaluation, we report on the usability and practicality of our approach for capturing both termination and non-termination reasoning for an existing verification system.