Abstract
We continue here a study of properties of rewrite systems that are not necessarily terminating, but allow for infinite derivations that have a limit. In particular, we give algebraic semantics for theories described by such systems, consider sufficient completeness of hierarchical systems, suggest practical conditions for the existence of a limit and for its uniqueness, and extend the ideas to conditional rewriting.
This research supported in part by the U.S. National Science Foundation under Grant DCR 85-13417 and by the European Communities under ESPRIT project 432 (METEOR).
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References
J. Goguen, J. Thatcher, E. Wagner, Initial algebra semantics and continuous algebras, JACM 24(1), pp.69–95 (1977)
N. Dershowitz, Termination of rewritting, J. of Symbolic Computation, 3(1&2), pp. 69–115; 4(3), pp. 409–410 (1987).
N. Dershowitz, J.-P. Jouannaud, Rewriting systems, in Handbook of Theoretical Computer Science, J. van Leeuwen, ed., North-Holland, Amsterdam (to appear 1989).
N. Dershowitz, S. Kaplan, Rewrite, rewrite, rewrite, rewrite, rewrite, Principles of Programming Languages, pp. 250–259, Austin, TX (1989).
H. Ehrig, F. Parisi-Presicce, P. Boehm, C. Rieckhoff, C. Dmitrovici, and M. Große-Rhode, Algebraic data type and process specifications based on projection spaces. In Recent Trends in Data Type Specifications: Selected Papers from the Fifth Workshop on Specification of Abstract Data Types, Gullane, Scotland. Lecture Notes in Computer Science 332, Springer, pp. 23–43 (1988).
G. Huet, Confluent reductions: abstract properties and applications to term rewriting systems, JACM 27, 4, pp. 797–821 (1980).
G. Huet, D. C. Oppen, Equations and rewrite rules: A survey, in Formal Language Theory: Perspectives and Open Problems, R. Book, ed., Academic Press, New York, pp. 349–405 (1980).
S. Kaplan, Conditional rewrite rules, TCS 33, pp. 175–193 (1984).
S. Kaplan, J.-L. Rémy, Completion algorithms for conditional rewriting systems, in Resolution of Equations in Algebraic Structures, H. Ait-Kaci & M. Nivat, eds., Academic Press, pp. 141–170 (1989).
J.-W. Klop, Term rewriting systems: a tutorial, Bulletin of the EATCS, 32, pp. 143–183 (1987).
B. Moeller, On the specification of infinite objects — ordered and continuous models of algebraic types, Acta Informatica (1984).
S. Narain, LOG(F): An optimal combination of logic programming, rewriting and lazy evaluation, Ph.D. thesis, Department of Computer Science, UCLA, Los Angeles, CA (1988).
M. Nivat, On the interpretation of recursive polyadic program schemes, Symposium Math. 15, pp. 255–281, Rome (1975).
M. J. O'Donnell, Computing in systems described by equations, Lecture Notes in Computer Science 58, Springer (1977).
D. Scott, Data types as lattices, SIAM Journal of Computing 5 (1976)
J. Stoy, Denotational semantics: The Scott-Strachey approach to programming languages, M.I.T. Press, Cambridge (1977)
A. Tarlecki, M. Wirsing, Continuous abstract data types, Fundamenta Informaticae 9, pp. 95–126 (1986).
M. Wirsing, Algebraic specification, in Handbook of Theoretical Computer Science, J. van Leeuwen, ed., North-Holland, Amsterdam (to appear 1989).
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Dershowitz, N., Kaplan, S., Plaisted, D.A. (1989). Infinite normal forms. In: Ausiello, G., Dezani-Ciancaglini, M., Della Rocca, S.R. (eds) Automata, Languages and Programming. ICALP 1989. Lecture Notes in Computer Science, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035765
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DOI: https://doi.org/10.1007/BFb0035765
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