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Machine-Assisted Proofs for Institutions in Coq

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Theoretical Aspects of Software Engineering (TASE 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13299))

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Abstract

The theory of institutions provides an abstract mathematical framework for specifying logical systems and their semantic relationships. Institutions are based on category theory and have deep roots in a well-developed branch of algebraic specification. However, there are no machine-assisted proofs of correctness for institution-theoretic constructions—chiefly satisfaction conditions for institutions and their (co)morphisms—making them difficult to incorporate into mainstream formal methods. This paper therefore provides the details of our approach to formalizing a fragment of the theory of institutions in the Coq proof assistant. We instantiate this framework with the institutions \( FOPEQ \) for first-order predicate logic and \( EVT \) for the Event-B specification language, both of which will serve as an illustration and evaluation of the overall approach.

Funded by the Irish Research Council (GOIPG/2019/4529).

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Notes

  1. 1.

    https://github.com/AlDanial/cloc.

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Authors and Affiliations

  1. Maynooth University, Maynooth, Ireland

    Conor Reynolds & Rosemary Monahan

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  1. Conor Reynolds
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  2. Rosemary Monahan
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Correspondence to Conor Reynolds .

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Editors and Affiliations

  1. IRIT, Toulouse, France

    Yamine Aït-Ameur

  2. Babeș-Bolyai University, Cluj-Napoca, Romania

    Florin Crăciun

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Reynolds, C., Monahan, R. (2022). Machine-Assisted Proofs for Institutions in Coq. In: Aït-Ameur, Y., Crăciun, F. (eds) Theoretical Aspects of Software Engineering. TASE 2022. Lecture Notes in Computer Science, vol 13299. Springer, Cham. https://doi.org/10.1007/978-3-031-10363-6_13

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  • DOI: https://doi.org/10.1007/978-3-031-10363-6_13

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