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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/7885

Title: Uniform Normalisation beyond Orthogonality
Authors: Khasidashvili, Zurab
Ogawa, Mizuhito
Oostrom, Vincent van
Issue Date: 2001
Publisher: Springer
Magazine name: Lecture Notes in Computer Science
Volume: 2051
Start page: 122
End page: 136
DOI: 10.1007/3-540-45127-7_11
Abstract: A rewrite system is called uniformly normalising if all its steps are perpetual, i.e. are such that if s → t and s has an infinite reduction, then t has one too. For such systems termination (SN) is equivalent to normalisation (WN). A well-known fact is uniform normalisation of orthogonal non-erasing term rewrite systems, e.g. the λI-calculus. In the present paper both restrictions are analysed. Orthogonality is seen to pertain to the linear part and non-erasingness to the non-linear part of rewrite steps. Based on this analysis, a modular proof method for uniform normalisation is presented which allows to go beyond orthogonality. The method is shown applicable to biclosed first- and second-order term rewrite systems as well as to a λ-calculus with explicit substitutions.
Rights: This is the author-created version of Springer, Zurab Khasidashvili, Mizuhito Ogawa, and Vincent van Oostrom , Lecture Notes in Computer Science, 2051, 2001, 122-136. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/3-540-45127-7_11
URI: http://hdl.handle.net/10119/7885
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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