Popescu, A. orcid.org/0000-0001-8747-0619 (2022) Rensets and renaming-based recursion for syntax with bindings. In: Blanchette, J., Kovács, L. and Pattinson, D., (eds.) Automated Reasoning: 11th International Joint Conference, IJCAR 2022, Haifa, Israel, August 8–10, 2022, Proceedings. 11th International Joint Conference, IJCAR 2022, 08-10 Aug 2022, Haifa, Israel. Lecture Notes in Computer Science (13385). Springer International Publishing , pp. 618-639. ISBN 9783031107689
Abstract
I introduce renaming-enriched sets (rensets for short), which are algebraic structures axiomatizing fundamental properties of renaming (also known as variable-for-variable substitution) on syntax with bindings. Rensets compare favorably in some respects with the well-known foundation based on nominal sets. In particular, renaming is a more fundamental operator than the nominal swapping operator and enjoys a simpler, equationally expressed relationship with the variable-freshness predicate. Together with some natural axioms matching properties of the syntactic constructors, rensets yield a truly minimalistic characterization of λ-calculus terms as an abstract datatype – one involving an infinite set of unconditional equations, referring only to the most fundamental term operators: the constructors and renaming. This characterization yields a recursion principle, which (similarly to the case of nominal sets) can be improved by incorporating Barendregt’s variable convention. When interpreting syntax in semantic domains, my renaming-based recursor is easier to deploy than the nominal recursor. My results have been validated with the proof assistant Isabelle/HOL.
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Item Type: | Proceedings Paper |
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Copyright, Publisher and Additional Information: | © 2022 The Author(s). Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 06 Oct 2022 14:50 |
Last Modified: | 06 Oct 2022 14:50 |
Status: | Published |
Publisher: | Springer International Publishing |
Series Name: | Lecture Notes in Computer Science |
Refereed: | Yes |
Identification Number: | 10.1007/978-3-031-10769-6_36 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:191500 |