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Easy lambda-terms are not always simple
Published online by Cambridge University Press: 23 February 2012
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.
- 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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