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A Fine-Grained Semantics for Arrays and Pointers Under Weak Memory Models

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Formal Methods (FM 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14000))

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Abstract

Developers of concurrent code for multicore architectures must navigate weak memory models (wmms) – either directly at the hardware/assembly level or at a somewhat generalised software level – making the verification of concurrent code an even more difficult task. Semantic models based on a system-wide partial-ordering on events have been developed to define the behaviour of code executing under wmms, but typically require specialised assertion languages and inference techniques to reason about, and often apply to only rudimentary programming constructs. In this paper we present a generic but versatile abstract imperative language “IMP+ptr ” which includes pointers and arrays, from which can be built high-level imperative programming constructs for verifying abstract algorithmic logic, or low-level microassembly for, e.g., investigating hardware security vulnerabilities. The base language carefully controls the syntax of atomic instructions to allow program-level, algebraic reasoning about the additional nondeterminism inherent in programs executing under wmms. We show how arrays of pointers, aliasing, and linked lists may be affected by wmms, establishing a base from where we apply pre-existing verification results and techniques for sequential programs with nested parallelism.

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Notes

  1. 1.

    Although \({\varphi }^\succeq \) is infinite it reduces, for the purposes of calculating reordering, to a pointwise-check wrt. \({\textsc {g}} \), i.e., \( {\varphi _1}^\succeq \int {\varphi _2}^\succeq = \emptyset \iff \lnot (\varphi _1 \succeq \varphi _2 \vee \varphi _2 \succeq \varphi _1) \). For \(x,y \in \textsf{Var}\) it collapses to \(x \ne y\).

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Acknowledgements

We thank Duong Dinh for help with modelling Meltdown, and Scott Heiner, Roger Su, Kait Lam, Nicholas Coughlin, Kirsten Winter, Graeme Smith and the anonymous reviewers for feedback.

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  1. Defence Science and Technology Group and The University of Queensland, Brisbane, Australia

    Robert J. Colvin

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  1. University of Toronto, Toronto, ON, Canada

    Marsha Chechik

  2. RWTH Aachen University, Aachen, Germany

    Joost-Pieter Katoen

  3. University of Lübeck, Lübeck, Germany

    Martin Leucker

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Colvin, R.J. (2023). A Fine-Grained Semantics for Arrays and Pointers Under Weak Memory Models. In: Chechik, M., Katoen, JP., Leucker, M. (eds) Formal Methods. FM 2023. Lecture Notes in Computer Science, vol 14000. Springer, Cham. https://doi.org/10.1007/978-3-031-27481-7_18

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