Typed Static Analysis: Application to the Groundness Analysis of Typed Prolog

We enrich the domain Pos used for the static analysis of Prolog programs by combining it with types. We adopt the prescriptive view on typing, and we assume that programs are well-typed in an already existing type system. Typed static analysis of Typed Prolog programs gives access to more refined properties than untyped analysis because types give information on the inductive structure of terms that untyped static analysis does not discover. The increased refinement is not in variables assigned to true (e.g., variable recognized as bound to ground terms), but rather in variables not assigned to true; they can be assigned a more informative value than false. For instance, the proposed analysis can show that a variable is bound to a nil-terminated list whose elements are not necessarily ground. We contend that this kind of property is sometimes more useful than groundness. Because

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