Analysis of Polymorphically Typed Logic Programs Using ACI-Unification

Analysis of (partial) groundness is an important application of abstract interpretation. There are several proposals for improving the precision of such an analysis by exploiting type information, icluding our own work with Hill and King, where we had shown how the information present in the type declarations of a program can be used to characterise the degree of instantiation of a term in a precise and yet inherently finite way. This approach worked for polymorphically typed programs as in Goedel or HAL. Here, we recast this approach following works by Codish, Lagoon and Stuckey. To formalise which properties of terms we want to characterise, we use labelling functions, which are functions that extract subterms from a term along certain paths. An abstract term collects the results of all labelling functions of a term. For the analysis, programs are executed on abstract terms instead of the concrete ones, and usual unification is replaced by unification modulo an equality theory which includes the well-known ACI-theory. Thus we generalise the works by Codish, Lagoon and Stuckey w.r.t. the type systems considered and relate the works among each other.