Coinductive Proofs for Temporal Hyperliveness
Temporal logics for hyperproperties have recently emerged as an expressive specification technique for relational properties of reactive systems. While the model checking problem for such logics has been widely studied, there is a scarcity of deductive proof systems for temporal hyperproperties. In...
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| Abstract | Temporal logics for hyperproperties have recently emerged as an expressive specification technique for relational properties of reactive systems. While the model checking problem for such logics has been widely studied, there is a scarcity of deductive proof systems for temporal hyperproperties. In particular, hyperproperties with an alternation of universal and existential quantification over system executions are rarely supported. In this paper, we focus on hyperproperties of the form ∀*∃*ψ, where ψ is a safety relation. We show that hyperproperties of this class – which includes many hyperliveness properties of interest – can always be approximated by coinductive relations. This enables intuitive proofs by coinduction. Based on this observation, we define HyCo (Hyperproperties, Coinductively), a mechanized framework to reason about temporal hyperproperties within the Coq proof assistant. We detail the construction of HyCo, provide a proof of its soundness, and exemplify its use by applying it to the verification of reactive systems modeled as imperative programs with nondeterminism and I/O. |
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| AbstractList | Temporal logics for hyperproperties have recently emerged as an expressive specification technique for relational properties of reactive systems. While the model checking problem for such logics has been widely studied, there is a scarcity of deductive proof systems for temporal hyperproperties. In particular, hyperproperties with an alternation of universal and existential quantification over system executions are rarely supported. In this paper, we focus on hyperproperties of the form ∀*∃*ψ, where ψ is a safety relation. We show that hyperproperties of this class – which includes many hyperliveness properties of interest – can always be approximated by coinductive relations. This enables intuitive proofs by coinduction. Based on this observation, we define HyCo (Hyperproperties, Coinductively), a mechanized framework to reason about temporal hyperproperties within the Coq proof assistant. We detail the construction of HyCo, provide a proof of its soundness, and exemplify its use by applying it to the verification of reactive systems modeled as imperative programs with nondeterminism and I/O. Temporal logics for hyperproperties have recently emerged as an expressive specification technique for relational properties of reactive systems. While the model checking problem for such logics has been widely studied, there is a scarcity of deductive proof systems for temporal hyperproperties. In particular, hyperproperties with an alternation of universal and existential quantification over system executions are rarely supported. In this paper, we focus on hyperproperties of the form ∀ * ∃ * ψ, where ψ is a safety relation. We show that hyperproperties of this class – which includes many hyperliveness properties of interest – can always be approximated by coinductive relations. This enables intuitive proofs by coinduction. Based on this observation, we define HyCo ( Hy perproperties, Co inductively), a mechanized framework to reason about temporal hyperproperties within the Coq proof assistant. We detail the construction of HyCo, provide a proof of its soundness, and exemplify its use by applying it to the verification of reactive systems modeled as imperative programs with nondeterminism and I/O. |
| ArticleNumber | 53 |
| Author | Correnson, Arthur Finkbeiner, Bernd |
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(e_1_2_2_33_1) e_1_2_2_11_1 e_1_2_2_10_1 e_1_2_2_30_1 e_1_2_2_31_1 e_1_2_2_19_1 e_1_2_2_32_1 e_1_2_2_18_1 Barthe Gilles (e_1_2_2_4_1) 2013 e_1_2_2_17_1 e_1_2_2_16_1 e_1_2_2_35_1 e_1_2_2_15_1 Esparza Javier (e_1_2_2_23_1) |
| References_xml | – reference: Michael R. Clarkson and Fred B. Schneider. 2008. Hyperproperties. In 2008 21st IEEE Computer Security Foundations Symposium. 51–65. https://doi.org/10.1109/CSF.2008.7 10.1109/CSF.2008.7 – reference: Gilles Barthe, Boris Köpf, Federico Olmedo, and Santiago Zanella Béguelin. 2013. Probabilistic Relational Reasoning for Differential Privacy. ACM Trans. Program. Lang. Syst., 35, 3 (2013), 9:1–9:49. https://doi.org/10.1145/2492061 10.1145/2492061 – reference: Li-yao Xia, Yannick Zakowski, Paul He, Chung-Kil Hur, Gregory Malecha, Benjamin C. Pierce, and Steve Zdancewic. 2019. Interaction trees: representing recursive and impure programs in Coq. Proc. ACM Program. Lang., 4, POPL (2019), Article 51, dec, 32 pages. https://doi.org/10.1145/3371119 10.1145/3371119 – reference: R. Beutner and B. Finkbeiner. 2022. Prophecy Variables for Hyperproperty Verification. In 2022 2022 IEEE 35th Computer Security Foundations Symposium (CSF) (CSF). 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Lang., 3, POPL (2019), 33:1–33:31. https://doi.org/10.1145/3290346 10.1145/3290346 – reference: Thibault Dardinier and Peter Müller. 2024. Hyper Hoare Logic: (Dis-)Proving Program Hyperproperties. Proc. ACM Program. Lang., 8, PLDI (2024), Article 207, jun, 25 pages. https://doi.org/10.1145/3656437 10.1145/3656437 – reference: Michael R. Clarkson, Bernd Finkbeiner, Masoud Koleini, Kristopher K. Micinski, Markus N. Rabe, and César Sánchez. 2014. Temporal Logics for Hyperproperties. In Proc. POST. 265–284. – reference: Timos Antonopoulos, Paul Gazzillo, Michael Hicks, Eric Koskinen, Tachio Terauchi, and Shiyi Wei. 2017. Decomposition instead of self-composition for proving the absence of timing channels. In Proceedings of the 38th ACM SIGPLAN Conference on Programming Language Design and Implementation, PLDI 2017, Barcelona, Spain, June 18-23, 2017, Albert Cohen and Martin T. Vechev (Eds.). 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