An Asynchronous soundness theorem for concurrent separation logic
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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.
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