Abstract
Deterministic conditional rewrite systems permit extra variables on the right-hand sides of the rules. If such a system is quasi-reductive or quasi-simplifying, then it is terminating and has a computable rewrite relation. This paper provides new criteria for showing quasi-reductivity and quasi-simplifyingness. In this context, another criterion from [ALS94] will be rectified and a claim in [MAR96] will be refuted. Moreover, we will investigate under which conditions the properties exhibit a modular behavior.
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References
Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theoretical Computer Science (1999) (to appear)
Avenhaus, J., LorÃa-Sáenz, C.: On conditional rewrite systems with extra variables and deterministic logic programs. In: Pfenning, F. (ed.) LPAR 1994. LNCS (LNAI), vol. 822, pp. 215–229. Springer, Heidelberg (1994)
Bergstra, J.A., Klop, J.W.: Conditional rewrite rules: Confluence and termination. Journal of Computer and System Sciences 32(3), 323–362 (1986)
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)
Dershowitz, N.: Termination of rewriting. Journal of Symbolic Computation 3(1), 69–116 (1987)
Ganzinger, H.: Order-sorted completion: The many-sorted way. Theoretical Computer Science 89, 3–32 (1991)
Gramlich, B.: Abstract relations between restricted termination and confluence properties of rewrite systems. Fundamenta Informaticae 24, 3–23 (1995)
Hanus, M.: The integration of functions into logic programming: From theory to practice. The Journal of Logic Programming 19&20, 583–628 (1994)
Kaplan, S.: Simplifying conditional term rewriting systems: Unification, termination and confluence. Journal of Symbolic Computation 4(3), 295–334 (1987)
Kurihara, M., Ohuchi, A.: Modularity of simple termination of term rewriting systems with shared constructors. Theoretical Computer Science 103, 273–282 (1992)
Krishna Rao, M.R.K.: Modular proofs for completeness of hierarchical term rewriting systems. Theoretical Computer Science 151, 487–512 (1995)
Marchiori, M.: Unravelings and ultra-properties. Technical Report 8, Dept. of Pure and Applied Mathematics, University of Padova, Italy (1995)
Marchiori, M.: Unravelings and ultra-properties. In: Hanus, M., RodrÃguez-Artalejo, M. (eds.) ALP 1996. LNCS, vol. 1139, pp. 107–121. Springer, Heidelberg (1996)
Marchiori, M.: On deterministic conditional rewriting. Computation Structures Group, Memo 405. MIT Laboratory for Computer Science, Cambridge (1997)
Middeldorp, A.: Modular properties of conditional term rewriting systems. Information and Computation 104(1), 110–158 (1993)
Middeldorp, A., Zantema, H.: Simple termination of rewrite systems. Theoretical Computer Science 175(1), 127–158 (1997)
Ohlebusch, E.: Modular Properties of Composable Term Rewriting Systems. PhD thesis, Universität Bielefeld (1994)
Ohlebusch, E.: Transforming conditional rewrite systems with extra variables into unconditional systems. In: Proceedings of the 6th International Conference on Logic for Programming and Automated Reasoning. LNCS (LNAI). Springer, Berlin (1999) (to appear)
Zantema, H.: Termination of term rewriting: Interpretation and type elimination. Journal of Symbolic Computation 17, 23–50 (1994)
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Ohlebusch, E. (1999). On Quasi-Reductive and Quasi-Simplifying Deterministic Conditional Rewrite Systems. In: Middeldorp, A., Sato, T. (eds) Functional and Logic Programming. FLOPS 1999. Lecture Notes in Computer Science, vol 1722. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10705424_12
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DOI: https://doi.org/10.1007/10705424_12
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