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Uniform normalisation beyond orthogonality

By Z. Khasidashvili, M. Ogawa and V. van Oostrom


A rewrite system is called uniformly normalising if all its\ud steps are perpetual, i.e. are such that if s → t and s has an infinite reduction,\ud then t has one too. For such systems termination (SN) is equivalent\ud to normalisation (WN). A well-known fact is uniform normalisation of\ud orthogonal non-erasing term rewrite systems, e.g. the λ/-calculus. In the\ud present paper both restrictions are analysed. Orthogonality is seen to\ud pertain to the linear part and non-erasingness to the non-linear part of\ud rewrite steps. Based on this analysis, a modular proof method for uniform\ud normalisation is presented which allows to go beyond orthogonality.\ud The method is shown applicable to biclosed first- and second-order term\ud rewrite systems as well as to a λ-calculus with explicit substitutions

Topics: Wijsbegeerte
Year: 2000
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