Bidirectional Interpolation for the Lambda-Calculus -- Revisiting and Formalising Craig-Čubrić Interpolation
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912940049825792 |
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| author | Bertrand, Meven Lennon Saurin, Alexis |
| author_facet | Bertrand, Meven Lennon Saurin, Alexis |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03083 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bidirectional Interpolation for the Lambda-Calculus -- Revisiting and Formalising Craig-Čubrić Interpolation Bertrand, Meven Lennon Saurin, Alexis Logic in Computer Science Programming Languages Logic F.4.1; I.2.3 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. |
| title | Bidirectional Interpolation for the Lambda-Calculus -- Revisiting and Formalising Craig-Čubrić Interpolation |
| topic | Logic in Computer Science Programming Languages Logic F.4.1; I.2.3 |
| url | https://arxiv.org/abs/2603.03083 |