LIPIcs.RTA.2012.288.pdf
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Meaningless Sets in Infinitary Combinatory Logic
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23rd International Conference on Rewriting Techniques and Applications (RTA'12) (RTA 2012)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Rewriting Techniques and Applications (RTA) - License:
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
- Publication Date: 2012-05-29
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Paula Severi and Fer-Jan de Vries. Meaningless Sets in Infinitary Combinatory Logic. In 23rd International Conference on Rewriting Techniques and Applications (RTA'12). Leibniz International Proceedings in Informatics (LIPIcs), Volume 15, pp. 288-304, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)
https://doi.org/10.4230/LIPIcs.RTA.2012.288
Abstract
In this paper we study meaningless sets in infinitary combinatory logic. So far only a handful of meaningless sets were known. We show that there are uncountably many meaningless sets. As an application to the semantics of finite combinatory logics, we show that there exist uncountably many combinatory algebras that are not a lambda algebra. We also study ways of weakening the axioms of meaningless sets to get, not only sufficient, but also necessary conditions for having confluence and normalisation.
Subject Classification
Keywords
- Infinitary Rewriting
- Combinatory Logic
- Meaningless Sets
- Confluence
- Normalisation
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