Abstract
We present a framework for studying equational specifications that partially specify functions over built-in structures. Using an order-sorted approach we are able to suitably assign semantics to such specifications in a denotational as well as an operational way. The operationalization, based on a combination of order-sorted and constraint based reasoning, enables us to generalize some basic results from classical rewrite theory.
This research was supported by the Deutsche Forschungsgemeinschaft, SFB 314, Proj. D4.
Preview
Unable to display preview. Download preview PDF.
References
J. Avenhaus and K. Becker, Conditional rewriting modulo a built-in algebra, SEKI Report SR-92-11.
J. Avenhaus and K. Madlener, Term rewriting and equational reasoning, in: R. B. Banerji, ed., Formal Techniques in Artificial Intelligence (Amsterdam, 1990) pp. 1–43.
L. Bachmair and N. Dershowitz, Completion for rewriting modulo a congruence, Theor. Comp. Science 67 (1989) pp. 173–201.
K. Becker, Proving ground confluence and inductive validity in constructor based equational specifications, TAPSOFT '93, LNCS 668 (Berlin, 1993) pp. 46–60.
M. Broy and M. Wirsing, Generalized heterogenous algebras and partial interpretations, in: Proc. 8th CAAP, LNCS 159 (Berlin, 1983) pp. 1–34.
M. Broy, C. Pair and M. Wirsing, A systematic study of models of abstract data types, Theor. Comp. Science 33 (1984) pp. 139–174.
N. Dershowitz and J. P. Jouannaud, Rewriting systems, in: J. van Leeuwen, ed., Handbook of Theoretical Computer Science, Vol. B (Amsterdam, 1990) pp. 241–320.
N. Dershowitz and M. Okada, A rationale for conditional equational rewriting, Theoret. Comput. Science 75(1/2) (1990) pp. 111–137.
N. Dershowitz, S. Mitra and G. Sivakumar, Decidable matching for convergent systems, in: CADE 11, LNCS 607 (Berlin, 1992) pp. 589–602.
G. Huet, Confluent reductions: abstract properties and applications to term rewriting systems, J. of the ACM 27 (1980) pp. 797–821.
J. Jaffar and J.-L. Lassez, Constraint logic programming, in ACM Symp. on Principles of Progr. Languages '87 (1987) pp. 111–119.
J.-P. Jouannaud and H. Kirchner, Completion of a set of rules modulo a set of equations, SIAM J. on Comp. 15 (1986) pp. 1155–1194.
S. Kaplan and C. Choppy, Abstract rewriting with concrete operators, in: 3rd RTA '89, LNCS 355, (Berlin, 1989) pp. 178–185.
D. Kapur and D.R. Musser, Inductive reasoning for incomplete specifications, in: Proc. IEEE Symposium on LICS (Cambridge MA, 1986) pp. 367–377.
C. Kirchner, H. Kirchner and M. Rusinowitch, Deduction with symbolic constraints, Revue d'Intelligence Artificielle 4 (1990) pp. 9–52.
G. Smolka, W. Nutt, J.A. Goguen and J. Meseguer, Order-sorted equational computation, in: CREAS (San Diego, 1989) pp. 297–367.
S.G. Vorobyov, Conditional rewrite rule systems with built-in arithmetic and induction, in: 3rd RTA '89, LNCS 355, (Berlin, 1989) pp. 492–512.
M. Wirsing, Algebraic specification, in: J. van Leeuwen, ed., Handbook of Theoretical Computer Science, Vol. B (Amsterdam, 1990) pp. 675–788.
C.-P. Wirth and B. Gramlich, A constructor-based approach for positive/negative conditional equational specifications, CTRS 92, LNCS 656 (Berlin, 1993) pp. 198–212.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Avenhaus, J., Becker, K. (1994). Operational specifications with built-ins. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds) STACS 94. STACS 1994. Lecture Notes in Computer Science, vol 775. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57785-8_147
Download citation
DOI: https://doi.org/10.1007/3-540-57785-8_147
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57785-0
Online ISBN: 978-3-540-48332-8
eBook Packages: Springer Book Archive