Abstract
We develop a Coq formalization of the matrix interpretation method, which is a recently developed, powerful approach to proving termination of term rewriting. Our formalization is a contribution to the CoLoR project and allows to automatically certify matrix interpretation proofs produced by tools for proving termination. Thanks to this development the combination of CoLoR and our tool, TPA, was the winner in 2007 in the new certified category of the annual Termination Competition.
Some preliminary results of this paper were first announced in [14].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
The Coq proof assistant, http://coq.inria.fr
The RTA list of open problems, http://www.lsv.ens-cachan.fr/rtaloop
Termination competition, http://www.lri.fr/~marche/termination-competition
Termination problems data base, http://www.lri.fr/~marche/tpdb
Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theoretical Computer Science 236(1-2), 133–178 (2000)
Blanqui, F., Delobel, W., Coupet-Grimal, S., Hinderer, S., Koprowski, A.: CoLoR, a Coq library on rewriting and termination. In: 8th WST (2006)
Contejean, É., Courtieu, P., Forest, J., Pons, O., Urbain, X.: Certification of automated termination proofs. In: Konev, B., Wolter, F. (eds.) FroCoS 2007. LNCS(LNAI), vol. 4720, pp. 148–162. Springer, Heidelberg (to appear, 2007)
Contejean, E., Marché, C., Monate, B., Urbain, X.: The CiME rewrite tool, http://cime.lri.fr
Endrullis, J., Waldmann, J., Zantema, H.: Matrix interpretations for proving termination of term rewriting. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 574–588. Springer, Heidelberg (2006)
Endrullis, J., Waldmann, J., Zantema, H.: Matrix interpretations for proving termination of term rewriting. Journal of Automated Reasoning (accepted, 2007)
Giesl, J., Thiemann, R., Schneider-Kamp, P.: The dependency pair framework: Combining techniques for automated termination proofs. In: Baader, F., Voronkov, A. (eds.) LPAR 2004. LNCS (LNAI), vol. 3452, pp. 301–331. Springer, Heidelberg (2005)
Hirokawa, N., Middeldorp, A.: Tyrolean termination tool: Techniques and features. Information and Computation 205(4), 474–511 (2007)
Koprowski, A.: TPA: Termination proved automatically. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 257–266. Springer, Heidelberg (2006)
Koprowski, A., Zantema, H.: Certification of matrix interpretations in Coq. In: 9th WST (2007)
Koprowski, A., Zantema, H.: Certification of proving termination of term rewriting by matrix interpretations. Technical Report CS-Report 07/22, Eindhoven University of Technology (August 2007), http://www.win.tue.nl/~akoprows/papers/mint-cert-TR.pdf
Krauss, A.: Certified size-change termination. In: CADE 2007. LNCS (LNAI), vol. 4603, pp. 460–475. Springer, Heidelberg (2007)
Magaud, N.: Ring properties for square matrices. Coq contributions, http://coq.inria.fr/contribs-eng.html
Marché, C., Zantema, H.: The Termination Competition 2007. In: RTA 2007. LNCS, vol. 4533, pp. 303–313. Springer, Heidelberg (2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Koprowski, A., Zantema, H. (2008). Certification of Proving Termination of Term Rewriting by Matrix Interpretations. In: Geffert, V., Karhumäki, J., Bertoni, A., Preneel, B., Návrat, P., Bieliková, M. (eds) SOFSEM 2008: Theory and Practice of Computer Science. SOFSEM 2008. Lecture Notes in Computer Science, vol 4910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77566-9_28
Download citation
DOI: https://doi.org/10.1007/978-3-540-77566-9_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77565-2
Online ISBN: 978-3-540-77566-9
eBook Packages: Computer ScienceComputer Science (R0)