Prolog, Mercury and the termination problem

This paper shortly introduces the two logic programming languages Prolog and Mercury. On this background we introduce the problem of analysing termination of programs. Then we present Mercury's termination analyser, that the authors of the language incorporated into its compiler. We will also discuss the proposition based on the same method analyser for Prolog's predicates

Classes of Terminating Logic Programs

Termination of logic programs depends critically on the selection rule, i.e. the rule that determines which atom is selected in each resolution step. In this article, we classify programs (and queries) according to the selection rules for which they terminate. This is a survey and unified view on different approaches in the literature. For each class, we present a sufficient, for most classes even necessary, criterion for determining that a program is in that class. We study six classes: a program strongly terminates if it terminates for all selection rules; a program input terminates if it terminates for selection rules which only select atoms that are sufficiently instantiated in their input positions, so that these arguments do not get instantiated any further by the unification; a program local delay terminates if it terminates for local selection rules which only select atoms that are bounded w.r.t. an appropriate level mapping; a program left-terminates if it terminates for the usual left-to-right selection rule; a program exists-terminates if there exists a selection rule for which it terminates; finally, a program has bounded nondeterminism if it only has finitely many refutations. We propose a semantics-preserving transformation from programs with bounded nondeterminism into strongly terminating programs. Moreover, by unifying different formalisms and making appropriate assumptions, we are able to establish a formal hierarchy between the different classes.Comment: 50 pages. The following mistake was corrected: In figure 5, the first clause for insert was insert([],X,[X]

Termination Analysis for Mercury

Since the late eighties, much progress has been made in the theory of termination analysis for logic programs. However, from a practical point of view, the significance of much of the work on termination is hard to judge, since experimental evaluations rarely get published. Here we describe and evaluate a termination analyzer for Mercury, a strongly typed and moded logicfunctional programming language. Mercury's high degree of referential transparency and the guaranteed availability of reliable mode information simplify the termination analysis of Mercury compared with that of other logic programming languages. We describe our termination analyzer, which uses a variant of a method developed by Plumer. It deals with full Mercury, including modules, declarative input/output, the foreign language interface, and higher-order features. In spite of these obstacles, it produces high-quality termination information, comparable to the results recently obtained by Lindenstrauss and Sagiv. Most i..