Institut de Mathématiques de Marseille, UMR 7373


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Refutation of Sallé’s Longstanding Conjecture

Jeudi 15 février 11:00-12:30 - Giulio MANZONETTO - LIPN, Paris 13

Refutation of Sallé’s Longstanding Conjecture

Résumé : 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. We will first show that Morris’s theory satisfies the omega-rule. We will then demonstrate that the two aforementioned theories actually coincide, thus disproving Sallé’s conjecture. The proof technique we develop is general enough to provide as a byproduct a new characterization, based on bounded eta-expansions, of the least extensional equality between Böhm trees.

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