We present a denotational semantics based on action traces, for parallel programs which share mutable data and synchronize using resources and conditional critical regions. We introduce a resource-sensitive logic for partial correctness, adapting separation logic to the concurrent setting, as proposed by O'Hearn. The logic allows program proofs in which "ownership" of a piece of state is deemed to transfer dynamically between processes and resources. We prove soundness of this logic, using a novel "local" interpretation of traces, and we show that every provable program is race-free.
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