On abstract normalisation beyond neededness
Abstract
We study normalisation of multistep strategies, strategies that reduce a set of redexes at a time, focussing on the notion of necessary sets, those which contain at least one redex that cannot be avoided in order to reach a normal form. This is particularly appealing in the setting of non-sequential rewrite systems, in which terms that are not in normal form may not have any needed redex. We first prove a normalisation theorem for abstract rewrite systems (ARS), a general rewriting framework encompassing many rewriting systems developed by P-A.Melli\`es in his PhD thesis. The theorem states that multistep strategies reducing so called necessary and never-gripping sets of redexes at a time are normalising in any ARS. Gripping refers to an abstract property reflecting the behavior of higher-order substitution. We then apply this result to the particular case of PPC, a calculus of patterns and to the lambda-calculus with parallel-or.
Cite
@article{arxiv.1412.2118,
title = {On abstract normalisation beyond neededness},
author = {Eduardo Bonelli and Delia Kesner and Carlos Lombardi and Alejandro Rios},
journal= {arXiv preprint arXiv:1412.2118},
year = {2016}
}