In recent work we have proposed a novel approach to define idealized type systems for object-oriented languages, based on abstract compilation ofprograms into Horn formulas which are interpreted w.r.t. the coinductive (that is, the greatest) Herbrand model. In this paper we investigate how this approach can be applied also inthe presence of imperative features. This is made possible by considering a natural translation of Static Single Assignment intermediate form programs into Horn formulas, where φ functionscorrespond to union types.

This paper presents a new type analysis for logic programs. The analysis is performed with a priori type definitions; and type expressions are formed from a fixed alphabet of type constructors. Non-discriminative union is used to join type information from different sources without loss of precision. An operation that is performed repeatedly during an analysis is to detect if a fixpoint has been reached. This is reduced to checking the emptiness of types. Due to the use of non-discriminative union, the fundamental problem of checking the emptiness of types is more complex in the proposed type analysis than in other type analyses with a priori type definitions. The experimental results, however, show that use of tabling reduces the effect to a small fraction of analysis time on a set of benchmarks.