Blanchette, J., Böhme, S., Popescu, A. et al. (1 more author) (2017) Encoding monomorphic and polymorphic types. Logical Methods in Computer Science, 12 (4). pp. 1-52. ISSN 1860-5974
Abstract
Many automatic theorem provers are restricted to untyped logics, and existing translations from typed logics are bulky or unsound. Recent research proposes monotonicity as a means to remove some clutter when translating monomorphic to untyped first-order logic. Here we pursue this approach systematically, analysing formally a variety of encodings that further improve on efficiency while retaining soundness and completeness. We extend the approach to rank-1 polymorphism and present alternative schemes that lighten the translation of polymorphic symbols based on the novel notion of "cover". The new encodings are implemented in Isabelle/HOL as part of the Sledgehammer tool. We include informal proofs of soundness and correctness, and have formalised the monomorphic part of this work in Isabelle/HOL. Our evaluation finds the new encodings vastly superior to previous schemes.
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Copyright, Publisher and Additional Information: | © J. C. Blanchette, S. Böhme, A. Popescu, and N. Smallbone. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (http://creativecommons.org/licenses/by/4.0) | ||||
Keywords: | Computer Science; Logic in Computer Science | ||||
Dates: |
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Institution: | The University of Sheffield | ||||
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) | ||||
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Depositing User: | Symplectic Sheffield | ||||
Date Deposited: | 21 Oct 2022 12:10 | ||||
Last Modified: | 21 Oct 2022 12:10 | ||||
Status: | Published | ||||
Publisher: | Centre pour la Communication Scientifique Directe (CCSD) | ||||
Refereed: | Yes | ||||
Identification Number: | https://doi.org/10.2168/lmcs-12(4:13)2016 | ||||
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