Pré-Publication, Document De Travail Année : 2026

Bidirectional Interpolation for the Lambda-Calculus – Revisiting and Formalising Craig-Čubrić Interpolation

Résumé

Craig's Interpolation theorem has a wide range of applications, from mathematical logic to computer science. Proof-theoretic techniques for establishing interpolation usually follow a method first introduced by Maehara for the Sequent Calculus and then adapted by Prawitz to Natural Deduction. The result can be strengthened to a proof-relevant version, taking proof terms into account: this was first established by Čubrić in the simply-typed lambda-calculus with sums and more recently in linear, classical and intuitionistic sequent calculi. We give a new proof of Čubrić's proof-relevant interpolation theorem by building on principles of bidirectional typing, and formalise it in Rocq.

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hal-05526634 , version 1 (25-02-2026)

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  • HAL Id : hal-05526634 , version 1

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Meven Lennon-Bertrand, Alexis Saurin. Bidirectional Interpolation for the Lambda-Calculus – Revisiting and Formalising Craig-Čubrić Interpolation. 2026. ⟨hal-05526634⟩
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