License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2021.19
URN: urn:nbn:de:0030-drops-134531
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13453/
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Dinis, Bruno ; Miquey, Étienne

Realizability with Stateful Computations for Nonstandard Analysis

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LIPIcs-CSL-2021-19.pdf (0.7 MB)

Abstract

In this paper we propose a new approach to realizability interpretations for nonstandard arithmetic. We deal with nonstandard analysis in the context of intuitionistic realizability, focusing on the Lightstone-Robinson construction of a model for nonstandard analysis through an ultrapower. In particular, we consider an extension of the λ-calculus with a memory cell, that contains an integer (the state), in order to indicate in which slice of the ultrapower ℳ^{ℕ} the computation is being done. We shall pay attention to the nonstandard principles (and their computational content) obtainable in this setting. We then discuss how this product could be quotiented to mimic the Lightstone-Robinson construction.

BibTeX - Entry

@InProceedings{dinis_et_al:LIPIcs:2021:13453,
  author =	{Bruno Dinis and {\'E}tienne Miquey},
  title =	{{Realizability with Stateful Computations for Nonstandard Analysis}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{19:1--19:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Christel Baier and Jean Goubault-Larrecq},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13453},
  URN =		{urn:nbn:de:0030-drops-134531},
  doi =		{10.4230/LIPIcs.CSL.2021.19},
  annote =	{Keywords: realizability, nonstandard analysis, states, glueing, ultrafilters, Łoś' theorem}
}

Keywords: realizability, nonstandard analysis, states, glueing, ultrafilters, Łoś' theorem
Collection: 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)
Issue Date: 2021
Date of publication: 13.01.2021

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