Concurrent Separation Logic Meets Template Games

An old dream of concurrency theory and programming language semantics has been to uncover the fundamental synchronization mechanisms which regulate situations as different as game semantics for higher-order programs, and Hoare logic for concurrent programs with shared memory and locks. In this paper, we establish a deep and unexpected connection between two recent lines of work on concurrent separation logic (CSL) and on template game semantics for differential linear logic (DiLL). Thanks to this connection, we reformulate in the purely conceptual style of template games for DiLL the asynchronous and interactive interpretation of CSL designed by Melli`es and Stefanesco. We believe that the analysis reveals something important about the secret anatomy of CSL, and more specifically about the subtle interplay, of a categorical nature, between sequential composition, parallel product, errors and locks.