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A formal hierarchy of weak memory models

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Abstract

We present in this paper a formal generic framework, implemented in the Coq proof assistant, for defining and reasoning about weak memory models. We first present the three axioms of our framework, with several examples as illustration and justification. Then we show how to implement several existing weak memory models in our framework, and prove formally that our implementation is equivalent to the native definition for each of these models.

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Notes

  1. By linear order, we mean a relation r that is irreflexive (i.e. ∀x.¬((x,x)∈r)), transitive (i.e. ∀xyz.(x,y)∈r∧(y,z)∈r⇒(x,z)∈r) and total (i.e. ∀xy.(x,y)∈r∨(y,x)∈r).

  2. Note that these are not G. Winskel’s event structures.

  3. We omit the axioms Atomicity and Termination.

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Acknowledgements

We thank the anonymous reviewers of several versions of this paper for their helpful and insightful reviews. We thank Gérard Boudol, Damien Doligez, Matthew Hague, Maurice Herlihy, Xavier Leroy, Luc Maranget, Susmit Sarkar and Peter Sewell for invaluable discussions and comments, Assia Mahboubi and Vincent Siles for advice on the Coq development, and Thomas Braibant, Matt Lewis, Jules Villard and Boris Yakobowski for comments on a draft.

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Authors and Affiliations

  1. INRIA, Rocquencourt, France

    Jade Alglave

  2. Oxford University, Oxford, UK

    Jade Alglave

  3. Queen Mary University of London, London, UK

    Jade Alglave

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  1. Jade Alglave
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Correspondence to Jade Alglave.

Appendix: Tables of notations

Appendix: Tables of notations

Table 1 Table of notations for events and pairs of events
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Table 2 Table of relations
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Table 3 Notations to extract pairs from po
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Alglave, J. A formal hierarchy of weak memory models. Form Methods Syst Des 41, 178–210 (2012). https://doi.org/10.1007/s10703-012-0161-5

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