Abstract
We introduce a new higher-order rewriting formalism, called Expression Reduction Systems with Patterns (ERSP), where abstraction is not only allowed on variables but also on nested patterns. These patterns are built by combining standard algebraic patterns with choice constructors used to denote different possible structures allowed for an abstracted argument. In other words, the non deterministic choice between different rewriting rules which is inherent to classical rewriting formalisms can be lifted here to the level of patterns. We show that confluence holds for a reasonable class of systems and terms.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
F. Baader and T. Nipkow. Term Rewriting and All That. Cambridge University Press, 1998.
H. Barendregt. The Lambda Calculus: Its Syntax and Semantics, volume 103 of Studies in Logic and the Foundations of Mathematics. North-Holland, 1984. Revised Edition.
F. Blanqui, J.-P. Jouannaud, and M. Okada. Inductive-Data-Type Systems. Theoretical Computer Science, 277, 2001.
E. Bonelli, D. Kesner, and A. Ríos. A de Bruijn notation for higher-order rewriting. In 11th RTA, LNCS 1833. 2000.
S. Cerrito and D. Kesner. Pattern matching as cut elimination. Theoretical Computer Science. To appear.
S. Cerrito and D. Kesner. Pattern matching as cut elimination. In 14th LICS. IEEE. 1999.
H. Cirstea. Calcul de réécriture: fondements et applications. Thèse de doctorat, Université Henri Poincaré — Nancy 1, 2000.
H. Cirstea and C. Kirchner. ρ-calculus, the rewriting calculus. In 5th CCL, 1998.
J. Forest. A weak calculus with explicit operators for pattern matching and substitution. In 13th RTA, LNCS 2378. 2002.
J. Forest and D. Kesner. Expression Reduction Systems with Patterns, 2003. Available on http://www.pps.jussieu.fr/~kesner/papers/.
J.-P. Jouannaud and A. Rubio. The higher-order recursive path ordering. In 14th LICS. IEEE. 1999.
D. Kesner, L. Puel, and V. Tannen. A Typed Pattern Calculus. Information and Computation, 124(1), 1996.
Z. Khasidashvili. Expression reduction systems. In Proceedings of IN Vekua Institute of Applied Mathematics, volume 36, Tbilisi, 1990.
C. Kirchner, H. Cirstea and L. Liquori. The Rho Cube. In FOSSACS’01, LNCS 2030. 2001.
J.-W. Klop. Combinatory Reduction Systems, volume 127 of Mathematical Centre Tracts. CWI, Amsterdam, 1980. PhD Thesis.
J.-W. Klop, V. van Oostrom, and F. van Raamsdonk. Combinatory reduction systems: introduction and survey. Theoretical Computer Science 121, 1993.
T. Nipkow. Higher-order critical pairs. In 6th LICS. IEEE. 1991.
The Objective Caml language, http://caml.inria.fr/.
M. Takahashi. Parallel Reductions in lambda-Calculus. Journal of Symbolic Computation, 7(2), 1989.
V. van Oostrom and F. van Raamsdonk. Weak orthogonality implies confluence: the higher-order case. In 3rd LFCS, LNCS 813. 1994.
F. van Raamsdonk. On termination of higher-order rewriting. In 12th RTA, LNCS 2051. 2001.
D. Wolfram. The Clausal Theory of Types, volume 21 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1993.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Forest, J., Kesner, D. (2003). Expression Reduction Systems with Patterns. In: Nieuwenhuis, R. (eds) Rewriting Techniques and Applications. RTA 2003. Lecture Notes in Computer Science, vol 2706. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44881-0_9
Download citation
DOI: https://doi.org/10.1007/3-540-44881-0_9
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40254-1
Online ISBN: 978-3-540-44881-5
eBook Packages: Springer Book Archive