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URN: urn:nbn:de:0030-drops-46320
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A Direct Version of Veldman's Proof of Open Induction on Cantor Space via Delimited Control Operators

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Abstract

First, we reconstruct Wim Veldman's result that Open Induction on Cantor space can be derived from Double-negation Shift and Markov's Principle. In doing this, we notice that one has to use a countable choice axiom in the proof and that Markov's Principle is replaceable by slightly strengthening the Double-negation Shift schema. We show that this strengthened version of Double-negation Shift can nonetheless be derived in a constructive intermediate logic based on delimited control operators, extended with axioms for higher-type Heyting Arithmetic. We formalize the argument and thus obtain a proof term that directly derives Open Induction on Cantor space by the shift and reset delimited control operators of Danvy and Filinski.

BibTeX - Entry

@InProceedings{ilik_et_al:LIPIcs:2014:4632,
  author =	{Danko Ilik and Keiko Nakata},
  title =	{{A Direct Version of Veldman's Proof of Open Induction on Cantor Space via Delimited Control Operators}},
  booktitle =	{19th International Conference on Types for Proofs and Programs (TYPES 2013)},
  pages =	{188--201},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-72-9},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{26},
  editor =	{Ralph Matthes and Aleksy Schubert},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4632},
  URN =		{urn:nbn:de:0030-drops-46320},
  doi =		{10.4230/LIPIcs.TYPES.2013.188},
  annote =	{Keywords: Open Induction, Axiom of Choice, Double Negation Shift, Markov's Principle, delimited control operators}
}

Keywords: Open Induction, Axiom of Choice, Double Negation Shift, Markov's Principle, delimited control operators
Seminar: 19th International Conference on Types for Proofs and Programs (TYPES 2013)
Issue date: 2014
Date of publication: 2014


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