Abstract
Within the framework of Higher-Order Rewriting Systems proposed by van Oostrom, a sufficient condition for the unique normal form property is presented. This requires neither left-linearity nor termination of the system.
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References
H. P. Barendregt, editor. The Lambda Calculus, Its Syntax and Semantics. North Holland, 1984. revised edition.
J. A. Bergstra and J. W. Klop. Process algebra for synchronous communication. Information and Control, Vol. 60, pp. 109–137, 1984.
P. Chew. Unique normal forms in term rewriting systems with repeated variables. In the 13th STOC, pp. 7–18, 1981.
R. C. de Vrijer. Unique normal forms for combinatory logic with parallel conditional, a case study in conditional rewriting. Technical report, Vrije universiteit, Amsterdam, 1990.
J. W. Klop and R. C. de Vrijer. Unique normal forms for lambda calculas with surjective pairing. Information and Computation, Vol. 80, pp. 97–113, 1989.
J. W. Klop and R. de Vrijer. Extended term rewriting systems. In CTRS '90, pp. 26–50, 1990. LNCS 516.
J. W. Klop. Combinatory reduction systems, 1980. PhD thesis, Rijks universiteit Utrecht.
Z. Khasidashvili and V. van Oostrom. Context-sensitive conditional expression reduction systems. Electric Notes in Computer Science, Vol. 13, 1995.
C. LorÃa-Sáenz. A theoretical framework for reasoning about program construction based on extensions of rewrite systems, 1993. PhD thesis, Universität Kaiserslautern, Germany.
R. Mayr and T. Nipkow. Higher-order rewrite systems and their confluence. Technical Report 19433, Insitut für Informatik, TU München, 1994.
K. Mano and M. Ogawa. A new proof of Chew's theorem. In Theory of Rewriting Systems and Its Application, pp. 160–177, 1995. Research report 918, RIMS, Kyoto Univ, Kyoto.
T. Nipkow. Higher-order critical pairs. In LICS, pp. 342–349, 1991.
Y. Toyama and M. Oyamaguchi. Church-Rosser property and unique normal form property of non-duplicating term rewriting systems. In CTRS '94, pp. 316–331, 1994.
V. van Oostrom. Confluence for abstract and higher-order rewriting, 1994. PhD thesis, Vrije universiteit, Amsterdam.
V. van Oostrom and F. van Raamsdonk. Weak orthogonality implies confluence: The higher-order case. In 3rd Int. sympo. on Logical Foundations of Computer Science, pp. 379–392, 1994.
F. van Raamdonk. Confluence and normalisation of higher-order rewriting, 1996. PhD thesis, Vrije universiteit, Amsterdam.
D. A. Wolfram. The Clausal Theory of Types. Cambridge University Press, 1993.
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Mano, K., Ogawa, M. (1996). Unique normal form property of Higher-Order Rewriting Systems. In: Hanus, M., RodrÃguez-Artalejo, M. (eds) Algebraic and Logic Programming. ALP 1996. Lecture Notes in Computer Science, vol 1139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61735-3_18
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DOI: https://doi.org/10.1007/3-540-61735-3_18
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