Parameterized Memory Models and Concurrent Separation Logic (extended version)

Formal reasoning about concurrent programs is usually done with the assumption that the underlying memory model is sequentially consistent, i.e. the execution outcome is equivalent to an interleaving of instructions according to the program order. However, memory models in reality are weaker in order to accommodate compiler and hardware optimizations. To simplify the reasoning, many memory models provide a guarantee that data-race-free programs behave in a sequentially consistent manner, the so-called DRFguarantee. The DRF-guarantee removes the burden of reasoning about relaxations when the program is well-synchronized. In this paper, we formalize relaxed memory models by giving a parameterized operational semantics to a concurrent programming language. Behaviors of a program under a relaxed memory model are defined as behaviors of a set of related programs under the sequentially consistent model. This semantics is parameterized in the sense that different memory models can be obtained by using different relations between programs. We present one particular relation that we believe accounts for the majority of memory models and sequential optimizations. We then show that the derived semantics has the DRF-guarantee, using a notion of race-freedom captured by an operational grainless semantics. Our grainless semantics also bridges concurrent separation logic (CSL) and relaxed memory models naturally, which allows us to finally prove the folklore theorem that CSL is sound with relaxed memory models.