Uniform Normalisation beyond Orthogonality
Zurab Khasidashvili, Mizuhito Ogawa, Vincent van Oostrom · Institutional Repositories DataBase (IRDB) · 2000
. 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 innite 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 I-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 rst- and second-order term rewrite systems as well as to a -calculus with explicit substitutions. 1 Introduction Two classical results in the study of uniform normalisation are: { the I-calculus is uniformly normalising [7, p. 20, 7 XXV], and { non-erasing steps are perpetual in orthogonal TRSs [14,...