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Easy lambda-terms are not always simple

Published online by Cambridge University Press:  23 February 2012

Alberto Carraro  and
Antonino Salibra
Alberto Carraro
Affiliation:
DAIS, Università Ca’ Foscari Venezia, via Torino 155, 30172 Mestre, Italy. acarraro@dsi.unive.it, salibra@dsi.unive.it PPS, Université Paris Diderot, 175 rue de Chevaleret, 75013 Paris, France
Antonino Salibra
Affiliation:
DAIS, Università Ca’ Foscari Venezia, via Torino 155, 30172 Mestre, Italy. acarraro@dsi.unive.it, salibra@dsi.unive.it
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Abstract

A closed λ-term M is easy if, for any other closed term N, the lambda theory generated by M = N is consistent. Recently, it has been introduced a general technique to prove the easiness of λ-terms through the semantical notion of simple easiness. Simple easiness implies easiness and allows to prove consistency results via construction of suitable filter models of λ-calculus living in the category of complete partial orderings: given a simple easy term M and an arbitrary closed term N, it is possible to build (in a canonical way) a non-trivial filter model which equates the interpretation of M and N. The question whether easiness implies simple easiness constitutes Problem 19 in the TLCA list of open problems. In this paper we negatively answer the question providing a non-empty co-r.e. (complement of a recursively enumerable) set of easy, but not simple easy, λ-terms.

Keywords

Lambda calculuseasy lambda-termssimple easy lambda-termsfilter modelsris models
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 46 , Issue 2: 12th Italian Conference on Theoretical Computer Science (ICTCS) , April 2012 , pp. 291 - 314
Copyright
© EDP Sciences 2012

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