Approximation and Filter Semantics for Combinator Systems ? Extended

This paper studies the relation between approximation semantics and filter models for Combinator Systems. It presents notions of approximants for terms, intersection type assignment, and using a strong normalization result of [4], it is proved that, for every typeable term, there exists an approximant of that term with the same type. Also 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.