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An Improved HHL Prover: An Interactive Theorem Prover for Hybrid Systems

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Formal Methods and Software Engineering (ICFEM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9407))

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Abstract

Hybrid systems are integrations of discrete computation and continuous physical evolution. To guarantee the correctness of hybrid systems, formal techniques on modelling and verification of hybrid systems have been proposed. Hybrid CSP (HCSP) is an extension of CSP with differential equations and some forms of interruptions for modelling hybrid systems, and Hybrid Hoare logic (HHL) is an extension of Hoare logic for specifying and verifying hybrid systems that are modelled using HCSP. In this paper, we report an improved HHL prover, which is an interactive theorem prover based on Isabelle/HOL for verifying HCSP models. Compared with the prototypical release in [22], the new HHL prover realises the proof system of HHL as a shallow embedding in Isabelle/HOL, rather than deep embedding in [22]. In order to contrast the new HHL prover in shallow embedding and the old one in deep embedding, we demonstrate the use of both variants on the safety verification of a lunar lander case study.

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Notes

  1. 1.

    The HHL prover in both embeddings, plus the corresponding models and proofs related to the case study, can be found at https://github.com/wangslyl/hhlprover.

  2. 2.

    The full version of both the operational semantics of HCSP and the specification logic HHL to be introduced next can be found at [17].

  3. 3.

    To distinguish from HOL, we wrap the arithmetic operators and FOL connectives with , and DC connectives with outside. For example, are HOL, FOL and DC conjunctions respectively.

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Acknowledgements

This paper is supported partly by “973 Program” under grant No. 2014CB340701, by NSFC under grants 91118007 and 91418204, by CDZ project CAP (GZ 1023), and by the CAS/SAFEA International Partnership Program for Creative Research Teams.

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Authors and Affiliations

  1. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China

    Shuling Wang, Naijun Zhan & Liang Zou

Authors
  1. Shuling Wang
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  2. Naijun Zhan
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  3. Liang Zou
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Correspondence to Shuling Wang .

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Editors and Affiliations

  1. Electronics and Computer Science, University of Southampton, Southampton, United Kingdom

    Michael Butler

  2. Université Paris-Sud, Orsay, France

    Sylvain Conchon

  3. Université Paris-Sud, Orsay, France

    Fatiha Zaïdi

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Wang, S., Zhan, N., Zou, L. (2015). An Improved HHL Prover: An Interactive Theorem Prover for Hybrid Systems. In: Butler, M., Conchon, S., Zaïdi, F. (eds) Formal Methods and Software Engineering. ICFEM 2015. Lecture Notes in Computer Science(), vol 9407. Springer, Cham. https://doi.org/10.1007/978-3-319-25423-4_25

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  • DOI: https://doi.org/10.1007/978-3-319-25423-4_25

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-25423-4

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