Abstract
A lambda term is k-duplicating if every occurrence of a lambda abstractor binds at most k variable occurrences. We prove that the problem of higher order matching where solutions are required to be k-duplicating (but with no constraints on the problem instance itself) is decidable. We also show that the problem of higher order matching in the affine lambda calculus (where both the problem instance and the solutions are constrained to be 1-duplicating) is in NP, generalizing de Groote’s result for the linear lambda calculus [4].
Supported by KBN grant 8T 11C 04319
This is a preview of subscription content, log in via an institution to check access.
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
Hubert Comon, Yan Jurski, Higher-Order Matching and Tree Automata, Proc. 11th Int’l Workshop Computer Science Logic, CSL’97, Mogens Nielsen, Wolfgang Thomas, eds., Aarhus, Denmark, August 1997, LNCS 1414, Springer-Verlag, 1998, 157–176.
Nachum Dershowitz, Zohar Manna, Proving termination with multiset orderings, Comm. Assoc. for Computing Machinery, 6(22), 465–476, 1979.
Giles Dowek, Third order matching is decidable, Proc. 7th IEEE Symp. Logic in Computer Science, LICS’92, IEEE Press, 1992, 2–10, also in Annals of Pure and Applied Logic, 69, 1994, 135–155.
Philippe de Groote, Linear Higher-Order Matching Is NP-Complete, Proc. 11th Int’l Conf. Rewriting Techniques and Applications, RTA 2000, Leo Bachmair, ed., Norwich, UK, July 10–12, 2000, LNCS 1833, Springer-Verlag, 2000, 127–140.
Jordi Levy, Linear Second Order Unification, Proc. 7th Int’l Conf. Rewriting Techniques and Applications, RTA’96, H. Ganzinger, ed., New Brunswick, NJ, 1996, LNCS 1103, Springer-Verlag, 1996, 332–346.
Ralph Loader, Higher Order β Matching is Undecidable, October 2001, manuscript.
Harry G. Mairson, A Simple Proof of a Theorem of Statman, Theoretical Computer Science, 103, 1992, 213–226.
Vincent Padovani, Decidability of All Minimal Models, Proc. 3rd Int’l Workshop Types for Proofs and Programs, TYPES’95, Stefano Berardi, Mario Coppo, eds., Torino, Italy, 1995, LNCS 1158, Springer-Verlag, 1996, 201–215.
Vincent Padovani, On equivalence classes of interpolation equations, Proc.Int’l Conf. Typed Lambda Calculi and Applications, TLCA’95, M. Dezani-Ciancaglini, G. Plotkin, eds., LNCS 902, Springer-Verlag, 1995, 335–349.
Vincent Padovani, Decidability of fourth-order matching, Mathematical Structures in Computer Science, 3(10), 2000, 361–372.
Manfred Schmidt-Schauß, Klaus U. Schulz, Decidability of bounded higher order unification, technical report Frank-report-15, Institut für Informatik, J. W. Goethe-Universität, Frankfurt am Main, 2001.
Aleksy Schubert, Linear interpolation for the higher order matching problem, Proc. 7th Int’l Joint Conf. Theory and Practice of Software Development, TAP-SOFT’97, M. Bidoit, M. Dauchet, eds., LNCS 1214, Springer-Verlag, 1997.
Richard Statman, The Typed λ-Calculus is Not Elementary Recursive, Theoretical Computer Science, 15, 1981, 73–81.
Sergei Vorobyov, The “Hardest” Natural Decidable Theory, Proc. 12th Annual IEEE Symp. Logic in Computer Science, LICS’97, IEEE Press, 1997, 294–305.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dougherty, D., Wierzbicki, T. (2002). A Decidable Variant of Higher Order Matching. In: Tison, S. (eds) Rewriting Techniques and Applications. RTA 2002. Lecture Notes in Computer Science, vol 2378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45610-4_24
Download citation
DOI: https://doi.org/10.1007/3-540-45610-4_24
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43916-5
Online ISBN: 978-3-540-45610-0
eBook Packages: Springer Book Archive