Automatic Termination Analysis of Programs Containing Arithmetic Predicates

For logic programs with arithmetic predicates, showing termination is not easy, since the usual order for the integers is not well-founded. A new method, easily incorporated in the TermiLog system for automatic termination analysis, is presented for showing termination in this case. The method consists of the following steps: First, a finite abstract domain for representing the range of integers is deduced automatically. Based on this abstraction, abstract interpretation is applied to the program. The result is a finite number of atoms abstracting answers to queries which are used to extend the technique of query-mapping pairs. For each query-mapping pair that is potentially non-terminating, a bounded (integer-valued) termination function is guessed. If traversing the pair decreases the value of the termination function, then termination is established. Simple functions often suffice for each query-mapping pair, and that gives our approach an edge over the classical approach of using a single termination function for all loops, which must inevitably be more complicated and harder to guess automatically. It is worth noting that the termination of McCarthy's 91 function can be shown automatically using our method. In summary, the proposed approach is based on combining a finite abstraction of the integers with the technique of the query-mapping pairs, and is essentially capable of dividing a termination proof into several cases, such that a simple termination function suffices for each case. Consequently, the whole process of proving termination can be done automatically in the framework of TermiLog and similar systems.Comment: Appeared also in Electronic Notes in Computer Science vol. 3

A General Framework for Automatic Termination Analysis of Logic Programs

This paper describes a general framework for automatic termination analysis of logic programs, where we understand by ``termination'' the finitenes s of the LD-tree constructed for the program and a given query. A general property of mappings from a certain subset of the branches of an infinite LD-tree into a finite set is proved. From this result several termination theorems are derived, by using different finite sets. The first two are formulated for the predicate dependency and atom dependency graphs. Then a general result for the case of the query-mapping pairs relevant to a program is proved (cf. \cite{Sagiv,Lindenstrauss:Sagiv}). The correctness of the {\em TermiLog} system described in \cite{Lindenstrauss:Sagiv:Serebrenik} follows from it. In this system it is not possible to prove termination for programs involving arithmetic predicates, since the usual order for the integers is not well-founded. A new method, which can be easily incorporated in {\em TermiLog} or similar systems, is presented, which makes it possible to prove termination for programs involving arithmetic predicates. It is based on combining a finite abstraction of the integers with the technique of the query-mapping pairs, and is essentially capable of dividing a termination proof into several cases, such that a simple termination function suffices for each case. Finally several possible extensions are outlined

Proving Correctness and Completeness of Normal Programs - a Declarative Approach

We advocate a declarative approach to proving properties of logic programs. Total correctness can be separated into correctness, completeness and clean termination; the latter includes non-floundering. Only clean termination depends on the operational semantics, in particular on the selection rule. We show how to deal with correctness and completeness in a declarative way, treating programs only from the logical point of view. Specifications used in this approach are interpretations (or theories). We point out that specifications for correctness may differ from those for completeness, as usually there are answers which are neither considered erroneous nor required to be computed. We present proof methods for correctness and completeness for definite programs and generalize them to normal programs. For normal programs we use the 3-valued completion semantics; this is a standard semantics corresponding to negation as finite failure. The proof methods employ solely the classical 2-valued logic. We use a 2-valued characterization of the 3-valued completion semantics which may be of separate interest. The presented methods are compared with an approach based on operational semantics. We also employ the ideas of this work to generalize a known method of proving termination of normal programs.Comment: To appear in Theory and Practice of Logic Programming (TPLP). 44 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

CP debugging tools: Clarification of functionalities and selection of the tools

Abstract is not available

On Language Processors and Software Maintenance

This work investigates declarative transformation tools in the context of software maintenance. Besides maintenance of the language specification, evolution of a software language requires the adaptation of the software written in that language as well as the adaptation of the software that transforms software written in the evolving language. This co-evolution is studied to derive automatic adaptations of artefacts from adaptations of the language specification. Furthermore, AOP for Prolog is introduced to improve maintainability of language specifications and derived tools.Die Arbeit unterstützt deklarative Transformationswerkzeuge im Kontext der Softwarewartung. Neben der Wartung der Sprachbeschreibung erfordert die Evolution einer Sprache sowohl die Anpassung der Software, die in dieser Sprache geschrieben ist als auch die Anpassung der Software, die diese Software transformiert. Diese Koevolution wird untersucht, um automatische Anpassungen von Artefakten von Anpassungen der Sprachbeschreibungen abzuleiten. Weiterhin wird AOP für Prolog eingeführt, um die Wartbarkeit von Sprachbeschreibungen und den daraus abgeleiteten Werkzeugen zu erhöhen

Directional Types and the Annotation Method

This paper shows that the annotation proof method, proposed by Deransart for proving declarative properties of logic programs, is also applicable for proving correctness of directional types. In particular, the sufficient correctness criterion of well-typedness by Bronsard et al, turns out to be a specialization of the annotation method. The comparison shows a general mechanism for construction of similar specializations, which is applied to derive yet another concept of well-typedness. The usefulness of the new correctness criterion is shown on examples of Prolog programs, where the traditional notion of well-typedness is not applicable. We further show that the new well-typing condition can be applied to different execution models. This is illustrated by an example of an execution model where unification is controlled by directional types, and where our new well-typing condition is applied to show the absence of deadlock. / 1. INTRODUCTIO