Connectivity graphs: a method for proving deadlock freedom based on separation logic

We introduce the notion of a connectivity graph —an abstract representation topology concurrently interacting entities, which allows us to encapsulate generic principles reasoning about deadlock freedom . Connectivity graphs are parametric in their vertices (representing entities like threads and channels) edges references between entities) with labels interaction protocols). prove memory leak style progress preservation use separation logic as meta theoretic tool treat substructurally. To locally, we distill rules for local transformations that preserve acyclicity graph. global waiting induction principle acyclic graphs. mechanize our results Coq, instantiate method higher-order binary session-typed language obtain first mechanized proof freedom.