An Asynchronous soundness theorem for concurrent separation logic

Abstract

Concurrent separation logic (CSL) is a specification logic for concurrent imperative programs with shared memory and locks. In this paper, we develop a concurrent and interactive account of the logic inspired by asynchronous game semantics. To every program C, we associate a pair of asynchronous transition systems C S and C L which describe the operational behavior of the Code when confronted to its Environment or Frame -both at the level of machine states (S) and of machine instructions and locks (L). We then establish that every derivation tree π of a judgment Γ {P }C{Q} defines a winning and asynchronous strategy π Sep with respect to both asynchronous semantics C S and C L . From this, we deduce an asynchronous soundness theorem for CSL, which states that the canonical map L : C S → C L from the stateful semantics C S to the stateless semantics C L satisfies a basic fibrational property. We advocate that this provides a clean and conceptual explanation for the usual soundness theorem of CSL, including the absence of data races.