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Refutation of Sallé's Longstanding Conjecture

Authors Benedetto Intrigila, Giulio Manzonetto, Andrew Polonsky



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Benedetto Intrigila
Giulio Manzonetto
Andrew Polonsky

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Benedetto Intrigila, Giulio Manzonetto, and Andrew Polonsky. Refutation of Sallé's Longstanding Conjecture. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 20:1-20:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.FSCD.2017.20

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.
Keywords
  • lambda calculus
  • observational equivalence
  • Böhm trees
  • omega-rule

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