Coinduction in Uniform: Foundations for Corecursive Proof Search with Horn Clauses

Basold, Henning, Komendantskaya, Ekaterina and Li, Yue (2019) Coinduction in Uniform: Foundations for Corecursive Proof Search with Horn Clauses. Caires, Luís (ed.) In Programming Languages and Systems - 28th European Symposium on Programming, ESOP 2019, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019, Proceedings. vol. 11423 LNCS, Springer. pp. 783-813 . (doi:10.1007/978-3-030-17184-1_28).

Record type: Conference or Workshop Item (Paper)

Abstract

We establish proof-theoretic, constructive and coalgebraic foundations for proof search in coinductive Horn clause theories. Operational semantics of coinductive Horn clause resolution is cast in terms of coinductive uniform proofs; its constructive content is exposed via soundness relative to an intuitionistic first-order logic with recursion controlled by the later modality; and soundness of both proof systems is proven relative to a novel coalgebraic description of complete Herbrand models.

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Published date: 2019

Additional Information: Publisher Copyright: © The Author(s) 2019.

Venue - Dates: 28th European Symposium on Programming, ESOP 2019 Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019, , Prague, Czech Republic, 2019-04-06 - 2019-04-11

Keywords: Coalgebra, Coinduction, Fibrations, Horn clause logic, Intuitionistic logic, Löb modality, Uniform proofs

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