Unified classical logic completeness: a coinductive pearl

Blanchette, Jasmin Christian, Popescu, Andrei and Traytel, Dmitriy (2014) Unified classical logic completeness: a coinductive pearl. Automated Reasoning: 7th International Joint Conference, IJCAR 2014, Held as Part of the Vienna Summer of Logic, VSL 2014, Vienna, Austria, July 19-22, 2014. Proceedings. In: 7th International Joint Conference on Automated Reasoning (IJCAR), 19-22 Jul 2014, Vienna, Austria. ISBN 9783319085869. ISSN 0302-9743

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Abstract

Codatatypes are absent from many programming languages and proof assistants. We make a case for their importance by revisiting a classic result: the completeness theorem for first-order logic established through a Gentzen system. The core of the proof establishes an abstract property of possibly infinite derivation trees, independently of the concrete syntax or inference rules. This separation of concerns simplifies the presentation. The abstract proof can be instantiated for a wide range of Gentzen and tableau systems as well as various flavors of first order logic. The corresponding Isabelle/HOL formalization demonstrates the recently introduced support for codatatypes and the Haskell code generator.

Item Type: Conference or Workshop Item (Paper)
Additional Information: Online ISBN: 9783319085876
Published paper appears in: Automated Reasoning, Volume 8562 of the series Lecture Notes in Computer Science, pp 46-60, 2014
Research Areas: A. > School of Science and Technology > Computer Science > Foundations of Computing group
Item ID: 15290
Notes on copyright: The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-08587-6_4
Useful Links:
Depositing User: Andrei Popescu
Date Deposited: 23 Apr 2015 14:02
Last Modified: 03 Apr 2019 11:14
URI: https://eprints.mdx.ac.uk/id/eprint/15290

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