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.FSCD.2017.20
URN: urn:nbn:de:0030-drops-77236
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7723/
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Intrigila, Benedetto ; Manzonetto, Giulio ; Polonsky, Andrew

Refutation of Sallé's Longstanding Conjecture

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Abstract

The lambda-calculus possesses a strong notion of extensionality, called "the omega-rule", which has been the subject of many investigations. It is a longstanding open problem whether the equivalence obtained by closing the theory of Böhm trees under the omega-rule is strictly included in Morris's original observational theory, as conjectured by Sallé in the seventies. In a recent work, Breuvart et al. have shown that Morris's theory satisfies the omega-rule. In this paper we demonstrate that the two aforementioned theories actually coincide, thus disproving Sallé's conjecture.

BibTeX - Entry

@InProceedings{intrigila_et_al:LIPIcs:2017:7723,
  author =	{Benedetto Intrigila and Giulio Manzonetto and Andrew Polonsky},
  title =	{{Refutation of Sall{\'e}'s Longstanding Conjecture}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{20:1--20:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Dale Miller},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7723},
  URN =		{urn:nbn:de:0030-drops-77236},
  doi =		{10.4230/LIPIcs.FSCD.2017.20},
  annote =	{Keywords: lambda calculus, observational equivalence, B{\"o}hm trees, omega-rule}
}

Keywords: lambda calculus, observational equivalence, Böhm trees, omega-rule
Collection: 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)
Issue Date: 2017
Date of publication: 30.08.2017

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