Automated Termination Proofs for Logic Programs by Term Rewriting

There are two kinds of approaches for termination analysis of logic programs: "transformational" and "direct" ones. Direct approaches prove termination directly on the basis of the logic program. Transformational approaches transform a logic program into a term rewrite system (TRS) and then analyze termination of the resulting TRS instead. Thus, transformational approaches make all methods previously developed for TRSs available for logic programs as well. However, the applicability of most existing transformations is quite restricted, as they can only be used for certain subclasses of logic programs. (Most of them are restricted to well-moded programs.) In this paper we improve these transformations such that they become applicable for any definite logic program. To simulate the behavior of logic programs by TRSs, we slightly modify the notion of rewriting by permitting infinite terms. We show that our transformation results in TRSs which are indeed suitable for automated termination analysis. In contrast to most other methods for termination of logic programs, our technique is also sound for logic programming without occur check, which is typically used in practice. We implemented our approach in the termination prover AProVE and successfully evaluated it on a large collection of examples.Comment: 49 page

Using parametric set constraints for locating errors in CLP programs

This paper introduces a framework of parametric descriptive directional types for constraint logic programming (CLP). It proposes a method for locating type errors in CLP programs and presents a prototype debugging tool. The main technique used is checking correctness of programs w.r.t. type specifications. The approach is based on a generalization of known methods for proving correctness of logic programs to the case of parametric specifications. Set-constraint techniques are used for formulating and checking verification conditions for (parametric) polymorphic type specifications. The specifications are expressed in a parametric extension of the formalism of term grammars. The soundness of the method is proved and the prototype debugging tool supporting the proposed approach is illustrated on examples. The paper is a substantial extension of the previous work by the same authors concerning monomorphic directional types.Comment: 64 pages, To appear in Theory and Practice of Logic Programmin

Directional Type Inference for Logic Programs

. We follow the set-based approach to directional types proposed by Aiken and Lakshman [1]. Their type checking algorithm works via set constraint solving and is sound and complete for given discriminative types. We characterize directional types in model-theoretic terms. We present an algorithm for inferring directional types. The directional type that we derive from a logic program P is uniformly at least as precise as any discriminative directional type of P, i.e., any directional type out of the class for which the type checking algorithm of Aiken and Lakshman is sound and complete. We improve their algorithm as well as their lower bound and thereby settle the complexity (DEXPTIME-complete) of the corresponding problem. 1 Introduction Directional types form a type system for logic programs which is based on the view of a predicate as a directional procedure which, when applied to a tuple of input terms, generates a tuple of output terms. There is a rich literature on ty..