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A Proof System for MSVL Programs in Coq

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Structured Object-Oriented Formal Language and Method (SOFL+MSVL 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10189))

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Abstract

In this paper, we propose a semi-automatic proof approach for programs written in Modeling, Simulation and Verification Language (MSVL) based on the interactive theorem prover Coq. To this end, first, the syntax and semantics of MSVL are briefly introduced, and the specification and proof tactics of Coq are described. Further, an axiomatic system of MSVL programs is specified in Coq. Based on these, MSVL programs and related properties can be recognized in Coq so that theorems to be proved can be formalised and the verification can be conducted when proof tactics are provided in the Coq prover. Finally, an example is given to illustrate how our proposed approach works.

The research is supported by the National Natural Science Foundation of China under Grant Nos. 61133001, 61572386, 61420106004 and 91418201.

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Authors and Affiliations

  1. Institute of Computing Theory and Technology, Xidian University, Xi’an, 710071, China

    Lin Qian, Zhenhua Duan, Nan Zhang & Cong Tian

Authors
  1. Lin Qian
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  2. Zhenhua Duan
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  3. Nan Zhang
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  4. Cong Tian
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Corresponding author

Correspondence to Zhenhua Duan .

Editor information

Editors and Affiliations

  1. Hosei University, Tokyo, Japan

    Shaoying Liu

  2. Xidian University, Xi'an, Shaanxi, China

    Zhenhua Duan

  3. Xidian University, Xi'an, China

    Cong Tian

  4. Nihon University, Tokyo, Japan

    Fumiko Nagoya

Appendices

A Appendix: State Axioms and inference rules

Axioms

figure x

Inference Rules

figure y

B Appendix: Axioms and inference rules Over Intervals

Axioms

figure z

Inference Rules

figure aa

C Appendix: Deducting Frog Routing Problem in Coq

figure ab

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Qian, L., Duan, Z., Zhang, N., Tian, C. (2017). A Proof System for MSVL Programs in Coq. In: Liu, S., Duan, Z., Tian, C., Nagoya, F. (eds) Structured Object-Oriented Formal Language and Method. SOFL+MSVL 2016. Lecture Notes in Computer Science(), vol 10189. Springer, Cham. https://doi.org/10.1007/978-3-319-57708-1_8

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  • DOI: https://doi.org/10.1007/978-3-319-57708-1_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57707-4

  • Online ISBN: 978-3-319-57708-1

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