License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2023.32
URN: urn:nbn:de:0030-drops-180164
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18016/
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Blot, Valentin

Diller-Nahm Bar Recursion

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LIPIcs-FSCD-2023-32.pdf (0.6 MB)

Abstract

We present a generalization of Spector’s bar recursion to the Diller-Nahm variant of Gödel’s Dialectica interpretation. This generalized bar recursion collects witnesses of universal formulas in sets of approximation sequences to provide an interpretation to the double-negation shift principle. The interpretation is presented in a fully computational way, implementing sets via lists. We also present a demand-driven version of this extended bar recursion manipulating partial sequences rather than initial segments. We explain why in a Diller-Nahm context there seems to be several versions of this demand-driven bar recursion, but no canonical one.

BibTeX - Entry

@InProceedings{blot:LIPIcs.FSCD.2023.32,
  author =	{Blot, Valentin},
  title =	{{Diller-Nahm Bar Recursion}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{32:1--32:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18016},
  URN =		{urn:nbn:de:0030-drops-180164},
  doi =		{10.4230/LIPIcs.FSCD.2023.32},
  annote =	{Keywords: Dialectica, Bar recursion}
}

Keywords: Dialectica, Bar recursion
Collection: 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)
Issue Date: 2023
Date of publication: 28.06.2023

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