Polytool: Polynomial interpretations as a basis for termination analysis of logic programs

  • Authors:

  • Manh thang Nguyen;Danny De schreye;JÜrgen Giesl;Peter Schneider-kamp

  • Affiliations:

  • Department of computer science, k. u. leuven celestijnenlaan 200a, b-3001, heverlee, belgium (e-mail: danny.deschreye@cs.kuleuven.be);Department of computer science, k. u. leuven celestijnenlaan 200a, b-3001, heverlee, belgium (e-mail: danny.deschreye@cs.kuleuven.be);Lufg informatik ii, rwth aachen, ahornstr. 55, 52074 aachen, germany (e-mail: giesl@informatik.rwth-aachen.de);Department of mathematics and computer science, university of southern denmark, campusvej 55, dk-5230 odense m, denmark (e-mail: petersk@imada.sdu.dk)

  • Venue:
  • Theory and Practice of Logic Programming
  • Year:
  • 2011

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Abstract

Our goal is to study the feasibility of porting termination analysis techniques developed for one programming paradigm to another paradigm. In this paper, we show how to adapt termination analysis techniques based on polynomial interpretations—very well known in the context of term rewrite systems—to obtain new (nontransformational) termination analysis techniques for definite logic programs (LPs). This leads to an approach that can be seen as a direct generalization of the traditional techniques in termination analysis of LPs, where linear norms and level mappings are used. Our extension generalizes these to arbitrary polynomials. We extend a number of standard concepts and results on termination analysis to the context of polynomial interpretations. We also propose a constraint-based approach for automatically generating polynomial interpretations that satisfy the termination conditions. Based on this approach, we implemented a new tool, called Polytool, for automatic termination analysis of LPs.