Subjective Simulation as a Notion of Morphism for Composing Concurrent Resources

Abstract: Recent approaches to verifying programs in separation logics for concurrency have used state transition systems (STSs) to specify the atomic operations of programs. A key challenge in the setting has been to compose such STSs into larger ones, while enabling programs specified under one STS to be linked to a larger one, without reverification. This paper develops a notion of morphism between two STSs which permits such lifting. The morphisms are a constructive form of simulation between the STSs, and lead to a general and concise proof system. We illustrate the concept and its generality on several disparate examples, including staged construction of a readers/writers lock and its proof, and of proofs about quiescence when concurrent programs are executed without external interference.