2026-09-22T19:28:09Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:27004 2026-09-05T20:01:22Z ddc:004 open_access

Bidirectional Interpolation for the λ-Calculus: Revisiting and Formalising Craig-Čubrić Interpolation Lennon-Bertrand, Meven Saurin, Alexis Craig Interpolation Bidirectional Typing Typed Lambda Calculus 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 λ-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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Meven Lennon-Bertrand and Alexis Saurin 2026 Is Part Of LIPIcs, Volume 382, 17th International Conference on Interactive Theorem Proving (ITP 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITP.2026.30 urn:nbn:de:0030-drops-270049 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2026.30 eng https://creativecommons.org/licenses/by/4.0/legalcode