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Abstract: . We prove a version of the Standardization Theorem and the Discrete Normalization Theorem in stable Deterministic Residual Structures, Abstract Reduction Systems with axiomatized notions of residual , which model orthogonal rewrite systems. The latter theorem gives a strategy for construction of reductions L'evy-equivalent (or permutation-equivalent) to a given, finite or infinite, regular (or semi-linear) reduction, based on the neededness concept of Huet and L'evy. This and other results... (Update)
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.... Curry and Feys [Bar84] or L evy s Optimality Theorem [L ev78, L ev80] can be proven using only the abstract framework of DFSs [GK96, KG96]. Furthermore, by using the DFS axioms alone, one can interpret DFSs into non duplicating, also called affine, DFSs with zig zag as the...
...abstract reduction systems, such as Newman s Lemma. We are currently working on a more expressive set of axioms, based on those given in [12] for finitary systems. 4.1 Axioms for abstract systems A transfinite abstract reduction system consists of a complete ultrametric...
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7: Computations in orthogonal rewriting systems (context) - Huet, L'evy - 1991
6: An abstract standardisation theorem - Gonthier, L'evy et al. - 1992
6: Combinatory Reduction System (context) - Klop - 1980
BibTeX entry: (Update)
Khasidashvili Z., Glauert J. R. W. Discrete normalization and Standardization in Deterministic Residual Structures. In proc. of ALP'96, Springer LNCS, vol. 1139, M. Hanus, M. Rodr'iguez-Artalejo, eds. 1996, p.135-149. http://citeseer.ist.psu.edu/khasidashvili96discrete.html More
@inproceedings{ khasidashvili96discrete,
author = "Zurab Khasidashvili and John R. W. Glauert",
title = "Discrete Normalization and Standardization in Deterministic Residual Structures",
booktitle = "Algebraic and Logic Programming",
pages = "135-149",
year = "1996",
url = "citeseer.ist.psu.edu/khasidashvili96discrete.html" }
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259 Combinatory Logic (context) - Curry, Feys - 1958
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174 Combinatory Reduction Systems (context) - Klop - 1980
171 A needed narrowing strategy - Antoy, Echahed et al. - 1994
130 Full abstraction in the lazy lambda calculus (context) - Abramsky, Ong - 1993
102 Computations in Orthogonal Rewriting Systems (context) - Huet, L'evy - 1991
71 Transfinite reductions in orthogonal term rewriting - Kennaway, Klop et al. - 1995
70 An algorithm for optimal lambda calculus reduction (context) - Lamping - 1990
67 Computational semantics of term rewriting systems (context) - Boudol - 1985
63 Optimal reductions in the Lambda-calculus (context) - L'evy - 1980
61 Term Graph Rewriting: Theory and Practice (context) - Sleep, Plasmeijer et al. - 1993
57 Confluence for Abstract and Higher-Order Rewriting (context) - Van Oostrom - 1994
46 Orthogonal higher-order rewrite systems are confluent (context) - Nipkow - 1993
44 Programming in Equational Logic: Beyond Strong Sequentiality - Sekar, Ramakrishnan - 1993
35 An abstract Standardisation theorem - Gonthier, L'evy et al. - 1992
33 Sequentiality in Orthogonal Term Rewriting Systems (context) - Klop, Middeldorp - 1991
31 Confluence and normalisation for higher-order rewriting (context) - Van Raamsdonk - 1996
28 Needed Reduction and spine strategies for the lambda calculu.. (context) - Barendregt, Kennaway et al. - 1987
27 The Church-Rosser theorem in Orthogonal Combinatory Reductio.. (context) - Khasidashvili - 1992
25 Optimal normalization in orthogonal term rewriting systems - Khasidashvili - 1993
24 A Sequential Reduction Strategy - Antoy, Middeldorp - 1994
23 Minimal and optimal computations of recursive programs (context) - Berry, L'evy - 1979
23 Meaningless terms in rewriting - Kennaway, van Oostrom et al. - 1996
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18 On higher order recursive program schemes (context) - Khasidashvili - 1994
17 An abstract form of the Church-Rosser theorem (context) - Hindley - 1969
17 Discovering needed reductions using type theory - Gardner - 1994
14 Relative normalization in deterministic residual structures - Khasidashvili
14 Interaction Systems II: the practice of optimal reductions - Asperti, Laneve - 1996
14 Neededness is hypernormalizing in regular combinatory reduct.. (context) - Kennaway, Sleep - 1989
13 ese de l'Universit'e de Paris VII (context) - strat'egie, Th - 1992
11 Relative Normalization in Orthogonal Expression Reduction Sy.. - Khasidashvili - 1994
9 the interpretation of recursive polyadic program schemes (context) - On - 1975
8 Compilation and Programming Techniques (context) - Functional - 1994
8 An algebraic interpretation of the fiK-calculus; and an appl.. (context) - L'evy - 1976
6 Sequential evaluation strategy for parallel-or and related r.. (context) - Kennaway - 1989
5 Set theoretic models of lambda calculus: theories (context) - Longo - 1983
5 Minimal and optimal relative normalization in Expression Red.. (context) - Khasidashvili - 1994
3 Computing in unpredictable environments: semantics - Lisper
2 Zig-zag and extraction families in nonduplicating stable Det.. - Khasidashvili, Glauert
2 Relative normalization in stable deterministic residual stru.. - Khasidashvili - 1996
2 Discrete normalization and standardization in stable determi.. - Khasidashvili, Glauert - 1996
1 This article was processed using the L A T E X macro package.. (context) - transition, TCS - 1989
1 of the 19 th International Colloquium on Trees in Algebra an.. (context) - Kirchner - 1996
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