Abstract
Matching is a solving process which is crucial in declarative (rule-based) programming languages. In order to apply rules, one has to match the left-hand side of a rule with the term to be rewritten. In several declarative programming languages, programs involve operators that may also satisfy some structural axioms. Therefore, their evaluation mechanism must implement powerful matching algorithms working modulo equational theories. In this paper, we show the existence of an equational theory where matching is decidable (resp. finitary) but matching in presence of additional (free) operators is undecidable (resp. infinitary). The interest of this result is to easily prove the existence of a frontier between matching and matching with free operators.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
F. Baader and K. U. Schulz. Unification in the union of disjoint equational theories: Combining decision procedures. JSC, 21(2):211–243, February 1996.
A. Boudet. Combining unification algorithms. JSC, 16(6):597–626, 1993.
H.-J. Bürckert. Matching — A special case of unification? JSC, 8(5):523–536, 1989.
N. Dershowitz and J.-P. Jouannaud. Rewrite Systems. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, chapter 6, pages 244–320. Elsevier Science Publishers B. V. (North-Holland), 1990.
S. Eker. Fast matching in combination of regular equational theories. In J. Meseguer, editor, First Intl. Workshop on Rewriting Logic and its Applications, volume 4. Electronic Notes in Theoretical Computer Science, September 1996.
J.-P. Jouannaud and Claude Kirchner. Solving equations in abstract algebras: a rule-based survey of unification. In Jean-Louis Lassez and G. Plotkin, editors, Computational Logic. Essays in honor of Alan Robinson, chapter 8, pages 257–321. The MIT press, Cambridge (MA, USA), 1991.
C. Kirchner and H. Kirchner, editors. Second Intl. Workshop on Rewriting Logic and its Applications, Electronic Notes in Theoretical Computer Science, Pont-à-Mousson (France), September 1998. Elsevier.
T. Nipkow. Combining matching algorithms: The regular case. JSC, 12:633–653, 1991.
Ch. Ringeissen. Combining decision algorithms for matching in the union of disjoint equational theories. Information and Computation, 126(2):144–160, May 1996.
Ch. Ringeissen. Matching with Free Function Symbols — A Simple Extension of Matching? (Full Version), 2001. Available at: http://www.loria.fr/~ringeiss.
M. Schmidt-Schauβ. Unification in a Combination of Arbitrary Disjoint Equational Theories. JSC, 8(1 & 2):51–99, 1989.
P. Szabó. Unifikationstheorie erster Ordnung. PhD thesis, Universität Karlsruhe, 1982.
E. Tidén. First-order unification in combinations of equational theories. PhD thesis, The Royal Institute of Technology, Stockholm, 1986.
K. Yelick. Unification in combinations of collapse-free regular theories. JSC, 3(1 & 2):153–182, April 1987.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ringeissen, C. (2001). Matching with Free Function Symbols — A Simple Extension of Matching?. In: Middeldorp, A. (eds) Rewriting Techniques and Applications. RTA 2001. Lecture Notes in Computer Science, vol 2051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45127-7_21
Download citation
DOI: https://doi.org/10.1007/3-540-45127-7_21
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42117-7
Online ISBN: 978-3-540-45127-3
eBook Packages: Springer Book Archive