Abstract
Designing concurrent objects for non-volatile memory (NVM) is challenging since designers must take both inter-thread synchronization and durability into account. To simplify development, a number of libraries have been developed to support transformations to durability. In this paper, we study one such library, Mirror\documentclass[12pt]{minimal}
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\begin{document}$$\textsf{Mirror} $$\end{document}, which offers a technique for transforming linearizable (lock-free) concurrent data structures into a durably linearizable version. We aimed to prove soundness of Mirror\documentclass[12pt]{minimal}
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\begin{document}$$\textsf{Mirror} $$\end{document} using the interactive proof assistant KIV, but in doing so discovered a subtle bug: Mirror\documentclass[12pt]{minimal}
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\begin{document}$$\textsf{Mirror} $$\end{document} can only be shown to correctly implement a durable compare_exchange_weak instruction rather than a durable compare_exchange_strong, as claimed in the original paper. Unlike the compare_exchange_strong instruction, compare_exchange_weak may fail spuriously. It turns out that the bug in Mirror\documentclass[12pt]{minimal}
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\begin{document}$$\textsf{Mirror} $$\end{document}’s implementation is difficult to fix, thus, we only provide a formal proof that Mirror\documentclass[12pt]{minimal}
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\begin{document}$$\textsf{Mirror} $$\end{document} implements compare_exchange_weak. Our proof is via refinement against an abstract persistency library, PLib\documentclass[12pt]{minimal}
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\begin{document}$$\textsf{PLib} $$\end{document}, that we developed in prior work. We split the proof into two steps via a new intermediate specification IMirror\documentclass[12pt]{minimal}
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\begin{document}$$\textsf{IMirror} $$\end{document}: we prove forward simulation between Mirror\documentclass[12pt]{minimal}
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\begin{document}$$\textsf{Mirror} $$\end{document} and IMirror\documentclass[12pt]{minimal}
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\begin{document}$$\textsf{IMirror} $$\end{document} and backward simulation between IMirror\documentclass[12pt]{minimal}
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\begin{document}$$\textsf{IMirror} $$\end{document} and PLib\documentclass[12pt]{minimal}
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\begin{document}$$\textsf{PLib} $$\end{document}. Since any implementation of PLib\documentclass[12pt]{minimal}
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\begin{document}$$\textsf{PLib} $$\end{document} is guaranteed to ensure correct transformations to durability, we conclude that Mirror\documentclass[12pt]{minimal}
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\begin{document}$$\textsf{Mirror} $$\end{document} continues to support this property.