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Standardization and Evaluation in Combinatory Reduction Systems (2000)  (Make Corrections)  (3 citations)
J.B. Wells, Robert Muller



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Abstract: A rewrite system has standardization i for any rewrite sequence there is an equivalent one which contracts the redexes in a standard order. Standardization is extremely useful for finding normalizing strategies and proving that a rewrite system for a programming language is sound with respect to the language's operational semantics. Although for some rewrite systems the standard-order can be simple, e.g., left-to-right or outermost-first, many systems need a more delicate order. There are... (Update)

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...two worked examples of a general framework that supports rigorous proofs of standardization theorems. The framework, developed in [WM00], is abstract enough to handle a large class of languages, yet it is nevertheless concrete enough that the programming language theorist...

...part of the theorem is as for TRSs. For a proof of the rst part for left linear fully extended (orthogonal) CRSs see [18, Sect. 7.7. 3] [26]) By the correspondence between CRSs and P 2 RSs this suces for our purposes. STD even holds for PRSs [22, Cor. 1.5] ut Proof. of...

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BibTeX entry:   (Update)

J. B. Wells and Robert Muller. Standardization and evaluation in combinatory reduction systems. Unpublished draft to be submitted, 2000. http://citeseer.ist.psu.edu/wells00standardization.html   More

@misc{ wells00standardization,
  author = "J. Wells and R. Muller",
  title = "Standardization and evaluation in combinatory reduction systems",
  note = "Unpublished draft to be submitted.",
  year = "2000",
  url = "citeseer.ist.psu.edu/wells00standardization.html" }
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30   Combinatory Reduction Systems (context) - Klop - 1980
28   Studies in Logic and the Foundations of Mathematics (context) - Curry, Feys - 1958
28   Needed reduction and spine strategies for the lambda calculu.. (context) - Barendregt, Kennaway et al. - 1987
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18   Sequentiality in orthogonal term rewriting systems (context) - Klop, Middeldorp - 1991
15   Context-sensitive conditional expression reduction systems - Khasidashvili, van Oostrom - 1995
14   Higher-order narrowing with denitional trees (context) - Hanus, Prehofer - 1999
14   Combinatory Reduction Systems: Introduction and survey - Klop, van Oostrom et al. - 1993
13   Practical Foundations of Mathematics (context) - Taylor - 1999
9   Con uence and Normalisation for Higher-Order Rewriting (context) - van Raamsdonk - 1996
8   Discrete normalization and standardization in deterministic .. - Khasidashvili, Glauert
8   Standardization theorem revisited - Suzuki
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6   Con uence for Abstract and Higher-Order Rewriting (context) - van Oostrom - 1994
5   Computational Logic: Essays in Honor of Alan Robinson (context) - Lassez, Plotkin - 1991
4   Minimal and optimal relative normalization in orthogonal exp.. - Glauert, Kenneway et al. - 2000
4   Compilation of Combinatory Reduction Systems - Kahrs - 1994
4   Description Abstraite des Systemes de Reecriture (context) - Melli - 1996
4   Minimal and optimal relative normalization in orthogonal exp.. - Glauert, Khasidashvili - 1996
2   Ecient Functional Programming: Compilation and Programming T.. (context) - ocker - 1994
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1   Two applications of standardization and evaluation in Combin.. - Muller, Wells - 2000

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