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Intersection Types and Lambda Theories

M. Dezani-Ciancaglini·S. Lusin
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Abstract

We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation of an arbitrary simple easy term is any filter which can be described in an uniform way by a predicate. This allows us to prove the consistency of a well-know lambda theory: this consistency has interesting consequences on the algebraic structure of the lattice of lambda theories.

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M. Dezani-Ciancaglini, S. Lusin. 2002-11-12. Intersection Types and Lambda Theories. https://arxiv.org/abs/cs/0211011

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