Uniform Normalisation beyond Orthogonality
نویسندگان
چکیده
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 nonlinear 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 firstand second-order term rewrite systems as well as to a λ-calculus with explicit substitutions.
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