Abstract
We present a confluence tool for left-linear term rewrite systems. The tool proves confluence by using Hindley’s commutation theorem together with three commutation criteria, including Church-Rosser modulo associative and/or commutative theories. Despite a small number of its techniques, experiments show that the tool is comparable to recent powerful confluence tools.
Supported by JSPS KAKENHI Grant Number 25730004 and Core to Core Program.
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Notes
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All problems and results are available at the tool website (see the URL in Section 1).
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References
Hindley, J.R.: The Church-Rosser Property and a Result in Combinatory Logic. Ph.D. thesis, University of Newcastle-upon-Tyne (1964)
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)
Jouannaud, J.P., Kirchner, H.: Completion of a set of rules modulo a set of equations. SIAM J. Comput. 15(4), 1155–1194 (1986)
Rubio, A.: A fully syntactic AC-RPO. Inf. Comput. 178(2), 515–533 (2002)
Plotkin, G.: Building in equational theories. Mach. Intell. 7, 73–90 (1972)
Schulz, K.: Word unification and transformation of generalized equations. In: Abdulrab, H., Pecuchet, J.-P. (eds.) IWWERT 1991. LNCS, vol. 677, pp. 150–176. Springer, Heidelberg (1993)
Schmidt, R.A.: \(E\)-Unification for subsystems of \(S4\). In: Nipkow, T. (ed.) RTA 1998. LNCS, vol. 1379, pp. 106–120. Springer, Heidelberg (1998)
Peterson, G., Stickel, M.: Complete sets of reductions for some equational theories. J. ACM 28(2), 233–264 (1981)
Aoto, T., Yoshida, J., Toyama, Y.: Proving confluence of term rewriting systems automatically. In: Treinen, R. (ed.) RTA 2009. LNCS, vol. 5595, pp. 93–102. Springer, Heidelberg (2009)
Huet, G.: Confluent reductions: abstract properties and applications to term rewriting systems. J. ACM 27(4), 797–821 (1980)
Toyama, Y.: Commutativity of term rewriting systems. In: Fuchi, K., Kott, L. (eds.) Programming of Future Generation Computers II, pp. 393–407. North-Holland, Amsterdam (1988)
van Oostrom, V.: Developing developments. Theoret. Comput. Sci. 175(1), 159–181 (1997)
van Oostrom, V.: Confluence by decreasing diagrams. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 306–320. Springer, Heidelberg (2008)
Aoto, T.: Automated confluence proof by decreasing diagrams based on rule-labelling. In: Lynch, C. (ed.) RTA 2010, LIPIcs, vol. 6, pp. 7–16 (2010)
Pottier, L.: Minimal solutions of linear diophantine systems: bounds and algorithms. In: Book, R.V. (ed.) Rewriting Techniques and Applications. LNCS, vol. 488, pp. 162–173. Springer, Heidelberg (1991)
Ohlebusch, E.: Modular Properties of Composable Term Rewriting Systems. Ph.D. thesis, Universität Bielefeld (1994)
Zankl, H., Felgenhauer, B., Middeldorp, A.: CSI – a confluence tool. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE-23. LNCS, vol. 6803, pp. 499–505. Springer, Heidelberg (2011)
Hirokawa, N., Middeldorp, A.: Decreasing diagrams and relative termination. J. Autom. Reason. 47(4), 481–501 (2011)
Durán, F., Meseguer, J.: A Church-Rosser checker tool for conditional order-sorted equational maude specifications. In: Ölveczky, P.C. (ed.) WRLA 2010. LNCS, vol. 6381, pp. 69–85. Springer, Heidelberg (2010)
Aoto, T., Toyama, Y.: A reduction-preserving completion for proving confluence of non-terminating term rewriting systems. LMCS 8(1), 1–29 (2012)
Toyama, Y.: On the Church-Rosser property for the direct sum of term rewriting systems. J. ACM 34(1), 128–143 (1987)
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We are grateful for the detailed comments of the anonymous reviewers, which helped us to improve the presentation.
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Shintani, K., Hirokawa, N. (2015). CoLL: A Confluence Tool for Left-Linear Term Rewrite Systems. In: Felty, A., Middeldorp, A. (eds) Automated Deduction - CADE-25. CADE 2015. Lecture Notes in Computer Science(), vol 9195. Springer, Cham. https://doi.org/10.1007/978-3-319-21401-6_8
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DOI: https://doi.org/10.1007/978-3-319-21401-6_8
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