LIPIcs.CSL.2013.395.pdf
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Proving Strong Normalisation via Non-deterministic Translations into Klop's Extended lambda-Calculus
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Computer Science Logic 2013 (CSL 2013)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Computer Science Logic (CSL) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2013-09-02
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Kentaro Kikuchi. Proving Strong Normalisation via Non-deterministic Translations into Klop's Extended lambda-Calculus. In Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 23, pp. 395-414, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
https://doi.org/10.4230/LIPIcs.CSL.2013.395
https://doi.org/10.4230/LIPIcs.CSL.2013.395
Abstract
In this paper we present strong normalisation proofs using a technique of non-deterministic translations into Klop's extended lambda-calculus. We first illustrate the technique by showing strong normalisation of a typed calculus that corresponds to natural deduction with general elimination rules. Then we study its explicit substitution version, the type-free calculus of which does not satisfy PSN with respect to reduction of the original calculus; nevertheless it is shown that typed terms are strongly normalising with respect to reduction of the explicit substitution calculus. In the same framework we prove strong normalisation of Sørensen and Urzyczyn's cut-elimination system in intuitionistic sequent calculus.
Keywords
- Strong normalisation
- Klop's extended lambda-calculus
- Explicit substitution
- Cut-elimination
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