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Completeness of Cyclic Proofs for Symbolic Heaps with Inductive Definitions

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Programming Languages and Systems (APLAS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11893))

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Abstract

Separation logic is successful for software verification in both theory and practice. Decision procedure for symbolic heaps is one of the key issues. This paper proposes a cyclic proof system for symbolic heaps with general form of inductive definitions called cone inductive definitions, and shows its soundness and completeness. Cone inductive definitions are obtained from bounded-treewidth inductive definitions by imposing some restrictions for existentials, but they still include a wide class of recursive data structures. The completeness is proved by using a proof search algorithm and it also gives us a decision procedure for entailments of symbolic heaps with cone inductive definitions. The time complexity of the algorithm is nondeterministic double exponential. A prototype system for the algorithm has been implemented and experimental results are also presented.

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Acknowledgments

We would like to thank Prof. Kazushige Terui for valuable discussions. This is partially supported by Core-to-Core Program (A. Advanced Research Networks) of the Japan Society for the Promotion of Science.

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Authors and Affiliations

  1. National Institute of Informatics/Sokendai, Hayama, Japan

    Makoto Tatsuta

  2. Nagoya University, Nagoya, Japan

    Koji Nakazawa

  3. Toho University, Tokyo, Japan

    Daisuke Kimura

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  1. Makoto Tatsuta
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  2. Koji Nakazawa
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  3. Daisuke Kimura
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Correspondence to Makoto Tatsuta .

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  1. University of Kaiserslautern, Kaiserslautern, Germany

    Anthony Widjaja Lin

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Tatsuta, M., Nakazawa, K., Kimura, D. (2019). Completeness of Cyclic Proofs for Symbolic Heaps with Inductive Definitions. In: Lin, A. (eds) Programming Languages and Systems. APLAS 2019. Lecture Notes in Computer Science(), vol 11893. Springer, Cham. https://doi.org/10.1007/978-3-030-34175-6_19

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  • DOI: https://doi.org/10.1007/978-3-030-34175-6_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-34174-9

  • Online ISBN: 978-3-030-34175-6

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