Abstract
Craig’s Interpolation Theorem is an important meta- theoretical result for several logics. Here we describe a formalisation of the result for first-order intuitionistic logic without function symbols or equality, with the intention of giving insight into how other such results in proof theory might be mechanically verified, notable cut-admissibility. We use the package Nominal Isabelle, which easily deals with the binding issues in the quantifier cases of the proof.
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References
Boulmé, S.: A Proof of Craig’s Interpolation Theorem in Coq (1996), citeseer.ist.psu.edu/480840.html
Coq Development Team. The Coq Proof Assistant Reference Manual Version 8.1 (2006), http://coq.inria.fr/V8.1/refman/index.html
Gabbay, M.J., Pitts, A.M.: A new approach to abstract syntax involving binders. In: 14th Annual Symposium on Logic in Computer Science, pp. 214–224. IEEE Computer Society Press, Washington (1999)
Jhala, R., Majumdar, R., Xu, R.-G.: State of the union: Type inference via craig interpolation. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 553–567. Springer, Heidelberg (2007)
McKinna, J., Pollack, R.: Pure type systems formalized. In: Bezem, M., Groote, J.F. (eds.) TLCA 1993. LNCS, vol. 664, pp. 289–305. Springer, Heidelberg (1993)
McMillan, K.L.: Applications of craig interpolants in model checking. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 1–12. Springer, Heidelberg (2005)
Nipkow, T., Paulson, L., Wenzel, M.: A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg (2005)
Nipkow, T.: Structured proofs in isar/hol. In: Geuvers, H., Wiedijk, F. (eds.) TYPES 2002. LNCS, vol. 2646, pp. 259–278. Springer, Heidelberg (2003)
Pfenning, F.: Structural cut elimination i. intuitionistic and classical logic. Information and Computation (2000)
Ridge, T.: Craig’s interpolation theorem formalised and mechanised in Isabelle/HOL. Arxiv preprint cs.LO/0607058, 2006 - arxiv.org (2006)
Takeuti, G.: Proof Theory. Studies in Logic and the Foundations of Mathematics, vol. 81. North-Holland Publishing Company, Amsterdam (1975)
Tasson, C., Urban, C.: Nominal techniques in Isabelle/HOL. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 38–53. Springer, Heidelberg (2005)
Troelstra, A.S., Schwichtenberg, H.: Basic Proof Theory, 2nd edn. Cambridge Tracts in Computer Science, vol. 43. Cambridge University Press, Cambridge (2000)
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Chapman, P., McKinna, J., Urban, C. (2008). Mechanising a Proof of Craig’s Interpolation Theorem for Intuitionistic Logic in Nominal Isabelle. In: Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M., Wiedijk, F. (eds) Intelligent Computer Mathematics. CICM 2008. Lecture Notes in Computer Science(), vol 5144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85110-3_5
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DOI: https://doi.org/10.1007/978-3-540-85110-3_5
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