Oostrom, Uniform normalisation beyond orthogonality (2001)
| Venue: | Proceedings of the Twelfth International Conference on Rewriting Techniques and Applications (RTA ’01), Lecture Notes in Computer Science (2001 |
| Citations: | 4 - 0 self |
BibTeX
@INPROCEEDINGS{Khasidashvili01oostrom,uniform,
author = {Zurab Khasidashvili and Mizuhito Ogawa and Vincent Van Oostrom},
title = {Oostrom, Uniform normalisation beyond orthogonality},
booktitle = {Proceedings of the Twelfth International Conference on Rewriting Techniques and Applications (RTA ’01), Lecture Notes in Computer Science (2001},
year = {2001},
pages = {122--136},
publisher = {Springer}
}
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Abstract
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. 1
