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GPS\(+\): Reasoning About Fences and Relaxed Atomics

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Abstract

In order to support efficient compilation to modern architectures, mainstream programming languages, such as C/C\(++\) and Java, have adopted weak (or relaxed) memory models. According to these weak memory models, multithreaded programs are allowed to exhibit behaviours that would have been inconsistent under the traditional strong (i.e., sequentially consistent) memory model. This makes the task of reasoning about concurrent programs even more challenging. The GPS framework, developed by Turon et al. (ACM OOPSLA, pp 691–707, 2014), has made a step forward towards tackling this challenge for the release–acquire fragment of the C11 memory model. By integrating ghost states, per-location protocols and separation logic, GPS can successfully verify programs with release–acquire atomics. In this paper, we introduced GPS\(+\) to support a larger class of C11 programs, that is, programs with release–acquire atomics, relaxed atomics and release–acquire fences. Key elements of our proposed logic include two new types of assertions, a more expressive resource model and a set of new verification rules.

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Notes

  1. Here we explain these examples in an intuitive manner, leaving the formal introductions of syntax and semantics to the next section.

  2. Or via release sequences, which we do not consider in this paper.

  3. In GPS, \(|r|\) represents the duplicable part of \(r\): \(r=r\oplus |r|\). For duplicable items in \(r\), like atomic values and the known escrow set, stripping keeps them unchanged. That is, we have \(|r|.\varSigma =r.\varSigma \), and if \(\ell _\mathtt {at}\) is an atomic location in \(r\) we have \(|r|.\varPi (\ell _\mathtt {at})=r.\varPi (\ell _\mathtt {at})\). For non-duplicable items, like non-atomic values, stripping removes them. For example, if \(\ell _\mathtt {na}\) is a non-atomic location in \(r\) we have \(|r|.\varPi (\ell _\mathtt {na})=\bot \). The value \(\diamond \) of ghost type \(\mathsf {Tok}\) is also not duplicable, and all ghost locations of type \(\mathsf {Tok}\) will be set as empty after stripping: \(|r|.g(\mathsf {Tok})(-)=\xi \).

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Authors and Affiliations

  1. School of Computing, Teesside University, Middlesbrough, UK

    Mengda He, Shengchao Qin & João F. Ferreira

  2. Max Planck Institute for Software Systems (MPI-SWS), Kaiserslautern, Germany

    Viktor Vafeiadis

  3. HASLab/INESC TEC, Universidade do Minho, Braga, Portugal

    João F. Ferreira

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  1. Mengda He
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  2. Viktor Vafeiadis
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  3. Shengchao Qin
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  4. João F. Ferreira
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Correspondence to Mengda He.

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He, M., Vafeiadis, V., Qin, S. et al. GPS\(+\): Reasoning About Fences and Relaxed Atomics. Int J Parallel Prog 46, 1157–1183 (2018). https://doi.org/10.1007/s10766-017-0518-x

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