Type inference, abstract interpretation and strictness analysis

AbstractFilter domains (Coppo et al.,1984) can be seen as abstract domains for the interpretation of (functional) type-free programming languages. What is remarkable is the fact that in filter domains the interpretation of a term is given by the set of its types in the intersection type discipline with inclusion, thus reducing the computation of an abstract interpretation to typechecking. As a main example, an abstract filter domain for strictness analysis of type-free functional languages is presented. The inclusion relation between types representing strictness properties has a complete recursive axiomatization. Type inference rules cannot be complete (strictness being a Π01 property), but a complete extension of the type inference system is presented