The Braga Method: Extracting Certified Algorithms from Complex Recursive Schemes in Coq

Larchey-Wendling, Dominique; Monin, Jean-François

doi:10.1142/9789811236488_0008

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2024

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Cited by 2 publications

References 14 publications

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Mechanised Uniform Interpolation for Modal Logics K, GL, and iSL

Férée,

Giessen,

Gool

et al. 2024

Automated Reasoning

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The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal logics, namely: (1) the modal logic K, for which a pen-and-paper proof exists; (2) Gödel-Löb logic GL, for which our formalisation clarifies an important point in an existing, but incomplete, sequent-style proof; and (3) intuitionistic strong Löb logic iSL, for which this is the first proof-theoretic construction of uniform interpolants. Our work also yields verified programs that allow one to compute the propositional quantifiers on any formula in this logic.

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