A Rely-Guarantee Framework for Proving Deadlock Freedom Under Causal Consistency

Jones’ rely-guarantee framework (originally developed to enable reasoning about partial correctness) has been extended in several works to additionally enable reasoning about deadlock freedom. However, these frameworks were originally developed for the strong memory model known as sequential consistency (SC). Under SC, all threads are assumed to read from the most recent write to each shared location, which is too strong for most modern multithreaded systems. In recent work, we have shown that rules for rely-guarantee can be adapted to cope with weaker causally consistent memory models (e.g., strong release-acquire), while preserving most of its core rules. This framework is modular and can be instantiated to different memory models. The only adaptation necessary is at the level of atomic statements (reads and writes), which require introduction of new assertions and associated proof rules that must be proved sound with respect to the operational semantics of the memory model at hand. In this paper, we show that it is possible to also further extend the framework to cope with deadlock freedom under causal consistency, taking inspiration from the aforementioned extensions to rely-guarantee reasoning for SC. We exemplify our technique on a short but challenging protocol for synchronising initialisation.