Abstract. Compiler correctness proofs for higher-order concurrent languages are difficult: they involve establishing a termination-preserving refinement between a concurrent high-level source language and an implementation that uses low-level shared memory primitives. However, existing logics for proving concurrent refinement either neglect properties such as termination, or only handle first-order state. In this paper, we address these limitations by extending Iris, a recent higher-order concurrent separation logic, with support for reasoning about terminationpreserving refinements. To demonstrate the power of these extensions, we prove the correctness of an efficient implementation of a higher-order, session-typed language. To our knowledge, this is the first program logic capable of giving a compiler correctness proof for such a language. The soundness of our extensions and our compiler correctness proof have been mechanized in Coq.
We present Polaris, a concurrent separation logic with support for probabilistic reasoning. As part of our logic, we extend the idea of coupling, which underlies recent work on probabilistic relational logics, to the setting of programs with both probabilistic and non-deterministic choice. To demonstrate Polaris, we verify a variant of a randomized concurrent counter algorithm and a two-level concurrent skip list. All of our results have been mechanized in Coq.1 Of course, a real scheduler is unlikely to behave in such an adversarial way. However, if the timing of operations can depend on random values, effects like this can arise even with non-adversarial schedulers, as discussed in §5. 2 However, it requires O (log 2 (n)) bits to store the count. Nevertheless, it uses less space than other alternatives for decreasing contention (e.g., having each thread maintain its own local counter).
Read-Copy-Update (RCU) is a technique for letting multiple readers safely access a data structure while a writer concurrently modifies it. It is used heavily in the Linux kernel in situations where fast reads are important and writes are infrequent. Optimized implementations rely only on the weaker memory orderings provided by modern hardware, avoiding the need for expensive synchronization instructions (such as memory barriers) as much as possible.Using GPS, a recently developed program logic for the C/C++11 memory model, we verify an implementation of RCU for a singlylinked list assuming "release-acquire" semantics. Although releaseacquire synchronization is stronger than what is required by real RCU implementations, it is nonetheless significantly weaker than the assumption of sequential consistency made in prior work on RCU verification. Ours is the first formal proof of correctness for an implementation of RCU under a weak memory model.
A number of tools have been developed for carrying out separation-logic proofs mechanically using an interactive proof assistant. One of the most advanced such tools is the Iris Proof Mode (IPM) for Coq, which offers a rich set of tactics for making separation-logic proofs look and feel like ordinary Coq proofs. However, IPM is tied to a particular separation logic (namely, Iris), thus limiting its applicability. In this paper, we propose MoSeL, a general and extensible Coq framework that brings the benefits of IPM to a much larger class of separation logics. Unlike IPM, MoSeL is applicable to both affine and linear separation logics (and combinations thereof), and provides generic tactics that can be easily extended to account for the bespoke connectives of the logics with which it is instantiated. To demonstrate the effectiveness of MoSeL, we have instantiated it to provide effective tactical support for interactive and semi-automated proofs in six very different separation logics.
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