We design an invariance proof method for concurrent programs parameterised by a weak consistency model. The calculational design of the invariance proof method is by abstract interpretation of a truly parallel analytic semantics. This generalises the methods by Lamport and Owicki-Gries for sequential consistency. We use cat as an example of language to write consistency specifications of both concurrent programs and machine architectures.
Shared memory concurrency relies on synchronisation primitives: compare-and-swap, load-reserve/store-conditional (aka LL/SC), language-level mutexes, and so on. In a sequentially consistent setting, or even in the TSO setting of x86 and Sparc, these have well-understood semantics. But in the very relaxed settings of IBM R POWER R , ARM, or C/C++, it remains surprisingly unclear exactly what the programmer can depend on.This paper studies relaxed-memory synchronisation. On the hardware side, we give a clear semantic characterisation of the load-reserve/store-conditional primitives as provided by POWER multiprocessors, for the first time since they were introduced 20 years ago; we cover their interaction with relaxed loads, stores, barriers, and dependencies. Our model, while not officially sanctioned by the vendor, is validated by extensive testing, comparing actual implementation behaviour against an oracle generated from the model, and by detailed discussion with IBM staff. We believe the ARM semantics to be similar.On the software side, we prove sound a proposed compilation scheme of the C/C++ synchronisation constructs to POWER, including C/C++ spinlock mutexes, fences, and read-modify-write operations, together with the simpler atomic operations for which soundness is already known from our previous work; this is a first step in verifying concurrent algorithms that use load-reserve/storeconditional with respect to a realistic semantics. We also build confidence in the C/C++ model in its own terms, fixing some omissions and contributing to the C standards committee adoption of the C++11 concurrency model.
Concurrency in the Linux kernel can be a contentious topic. The Linux kernel mailing list features numerous discussions related to consistency models, including those of the more than 30 CPU architectures supported by the kernel and that of the kernel itself. How are Linux programs supposed to behave? Do they behave correctly on exotic hardware? A formal model can help address such questions. Better yet, an executable model allows programmers to experiment with the model to develop their intuition. Thus we offer a model written in the cat language, making it not only formal, but also executable by the herd simulator. We tested our model against hardware and refined it in consultation with maintainers. Finally, we formalised the fundamental law of the Read-Copy-Update synchronisation mechanism, and proved that one of its implementations satisfies this law.
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