Abstract
Context-sensitive rewriting is a refined form of rewriting which explores a smaller reduction space by imposing some fixed restrictions on the replacements. Any Term Rewriting System (TRS) can be given a context-sensitive rewrite relation. In this paper, we formulate conditions to guarantee the confluence of this relation. Moreover, for a confluent TRS, we are able to give sufficient conditions to ensure that the (eventually obtained) computed value of a given expression can be reached by using context-sensitive rewriting, thus leading to more efficient and still complete computations.
This work has been partially supported by CICYT under grant TIC 95-0433-C03-03.
Preview
Unable to display preview. Download preview PDF.
References
N. Dershowitz. Termination of rewriting. Journal on Symbolic Computation 3:69–115, 1987.
N. Dershowitz and J.P. Jouannaud. Rewrite Systems. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B: Formal Models and Semantics, pages 243–320. Elsevier, Amsterdam and The MIT Press, Cambridge, MA, 1990.
H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification. Volume 6 of EATCS Monographs on Theoretical Computer Science. Springer-Verlag, Berlin, 1985.
D.P. Friedman and D.S. Wise. CONS should not evaluate its arguments. In S. Michaelson and R. Milner, editors, Automata, Languages and Programming, pages 257–284, Edinburgh University Press, 1976.
G. Huet. Confluent reductions: abstract properties and applications to term rewriting systems. Journal of the ACM 27:797–821, 1980.
G. Huet and J.J. Lévy. Computations in orthogonal term rewriting systems. In J.L. Lassez and G. Plotkin, editors, Computational logic: essays in honour of J. Alan Robinson, MIT Press, Cambridge, MA, 1991.
J.F.Th. Kamperman and H.R. Walters. Lazy Rewriting and Eager Machinery. In J. Hsiang, editor, Proc. of the 6th International Conference on Rewriting Techniques and Applications, RTA '95, LNCS 914:147–162, Springer-Verlag, Berlin, 1995.
R. Lalement. Computation as Logic. Masson-Prentice Hall International, 1993.
S. Lucas. Fundamentals of context-sensitive rewriting. In M. Bartosek, J. Staudek and J. Wiedermann, editors, Proc. of XXII Seminar on Current Trends in Theory and Practice of Informatics, SOFSEM'95, LNCS 1012:405–412, Springer-Verlag, Berlin, 1995.
S. Lucas. Termination of context-sensitive rewriting by rewriting. In F. Meyer auf der Heide and B. Monien, editors, Proc. of 23rd. International Colloquium on Automata, Languages and Programming, ICALP'96, LNCS 1099:122–133, Springer-Verlag, Berlin, 1996.
L. Maranget. Optimal Derivations in Weak Lambda-calculi and in Orthogonal Term Rewriting Systems In Conference Record of the 18th ACM Symposium on Principles of Programming Languages, pages 255–269, ACM Press, 1990.
A. Mycroft. The theory and practice of transforming call-by-need into call-by-value. In Proc. of the fourth International Symposium on Programming, LNCS 83:269–281, Springer-Verlag, Berlin, 1980.
M.H.A. Newman. On theories with a combinatorial definition of ‘equivalence'. Ann. Math., 43:223–243, 1942.
C. Reade. Elements of Functional Programming. Addison-Wesley Publishing Company, 1987.
J.E. Stoy. Denotational semantics: the Scott-Strachey approach to programming language theory. The MIT Press, Cambridge MA, 1977.
J. Vuillemin Correct and optimal implementation of recursion in a simple programming language. JCSS 9(3):332–354, 1974.
P. Wadler. Strictness Analysis on Non-Flat Domains (by Abstract Interpretation over Finite Domains). In S. Abramsky and C. Hankin, editors, Abstract Interpretation of Declarative Languages, Ellis Horwood Ltd., John Wiley and sons, pages 266–275, 1987.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lucas, S. (1996). Context-sensitive computations in confluent programs. In: Kuchen, H., Doaitse Swierstra, S. (eds) Programming Languages: Implementations, Logics, and Programs. PLILP 1996. Lecture Notes in Computer Science, vol 1140. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61756-6_100
Download citation
DOI: https://doi.org/10.1007/3-540-61756-6_100
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61756-3
Online ISBN: 978-3-540-70654-0
eBook Packages: Springer Book Archive