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Normalization, Approximation, and Semantics for Combinator Systems

By Steffen Van Bakel and Maribel Fernández


This paper studies normalization of typeable terms and the relation between approximation semantics and filter models for Combinator Systems. It presents notions of approximants for terms, intersection type assignment, and reduction on type derivations; the last will be proved to be strongly normalizable. With this result, it is shown that, for every typeable term, there exists an approximant with the same type, and a characterization of the normalization behaviour of terms using their assignable types is given. Then the two semantics are defined and compared, and it is shown that the approximants semantics is fully abstract but the filter semantics is not. Introduction In this paper we will focus on the relation between two approaches for semantics in the framework of Combinator Systems (CS), being the filter semantics, obtained by interpreting terms by the set of intersection types that can be assigned to them, and the approximants semantics, where terms are interpreted by the set o..

Year: 2003
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