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A Coq Implementation of the Program Algebra in Jifeng He’s New Roadmap for Linking Theories of Programming

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Theories of Programming and Formal Methods

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14080))

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Abstract

Jifeng He has proposed a roadmap for linking theories of programming and presents an algebra of programs capable of generating both denotational and operational representations from the refinement relation. In this paper, we implement this algebra of programs and its refinement relation using the interactive theorem prover Coq. Encoding the algebra into CIC (Calculus of Inductive Constructions), the main formalism in Coq, facilitates machine-aided interactive proving for the properties of programs using predefined algebraic laws. The implementation of the algebra for finite programs enables us to prove that every finite program can be reduced to the normal form and to check the refinement between two finite programs. The implementation of the algebra for infinite programs supports formalizing recursive programs with one variable and checking the refinement between one finite and one infinite program. Then, we present examples of proving the refinement relationship between two finite programs and a finite program and an infinite program.

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Notes

  1. 1.

    https://github.com/DonnotPanic/Program-Algebra-in-Jifeng/blob/main/ProgramAlgebra.v.

  2. 2.

    https://github.com/DonnotPanic/Program-Algebra-in-Jifeng/blob/main/testAlt.v.

  3. 3.

    https://github.com/DonnotPanic/Program-Algebra-in-Jifeng/blob/main/testGCD.v.

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Acknowledgment

We would like to express our sincere gratitude to Simon Foster for his exceptional contribution to this paper. His valuable insights and expert guidance have greatly enhanced the quality of our work, and we are truly appreciative of his dedication and commitment to this project. Without his suggestions and feedback, the paper would not have been as comprehensive and insightful as it is now.

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Authors and Affiliations

  1. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China

    Rundong Mu & Qin Li

Authors
  1. Rundong Mu
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  2. Qin Li
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Correspondence to Qin Li .

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Editors and Affiliations

  1. London South Bank University, London, UK

    Jonathan P. Bowen

  2. East China Normal University, Shanghai, China

    Qin Li

  3. University of Macau, Macau, China

    Qiwen Xu

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Mu, R., Li, Q. (2023). A Coq Implementation of the Program Algebra in Jifeng He’s New Roadmap for Linking Theories of Programming. In: Bowen, J.P., Li, Q., Xu, Q. (eds) Theories of Programming and Formal Methods. Lecture Notes in Computer Science, vol 14080. Springer, Cham. https://doi.org/10.1007/978-3-031-40436-8_15

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  • DOI: https://doi.org/10.1007/978-3-031-40436-8_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-40435-1

  • Online ISBN: 978-3-031-40436-8

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