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arXiv · 2603.03083

Bidirectional Interpolation for the Lambda-Calculus: Revisiting and Formalising Craig-\v{C}ubri\'c Interpolation

Meven Lennon Bertrand·Alexis Saurin
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Abstract

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 \v{C}ubri\'c in the simply-typed lambda-calculus with sums and more recently in linear, classical and intuitionistic sequent calculi. We give a new proof of \v{C}ubri\'c's proof-relevant interpolation theorem by building on principles of bidirectional typing, and formalise it in Rocq.

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Meven Lennon Bertrand, Alexis Saurin. 2026-03-03. Bidirectional Interpolation for the Lambda-Calculus: Revisiting and Formalising Craig-\v{C}ubri\'c Interpolation. https://doi.org/10.4230/lipics.itp.2026.30

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