An Experiment in Domain Refinement: Type Domains and Type Representations for Logic Programs

We apply the methodology of domain refinement to systematically derive domains for type analysis. Domains are built by iterative application of the Heyting completion operator to a given set of basic types. We give a condition on the type system which assures that two steps of iteration are sufficient to reach the fixpoint. Moreover, we provide a general representation for type domains through transfinite formulas. Finally, we show a subset of finite formulas which can be used as a computationally feasible implementation of the domains and we define the corresponding abstract operators.