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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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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