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Normalisation by Random Descent

Vincent van Oostrom and Yoshihito Toyama

Proceedings of the 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016), Leibniz International Proceedings in Informatics 52, pp. 32:1 – 32:18, 2016.

Abstract

We present abstract hyper-normalisation results for strategies. These results are then applied to term rewriting systems, both first and higher-order. For example, we show hyper-normalisation of the left—outer strategy for, what we call, left—outer pattern rewrite systems, a class comprising both Combinatory Logic and the lambda-calculus but also systems with critical pairs. Our results apply to strategies that need not be deterministic but do have Newman’s random descent property: all reductions to normal form have the same length, with Huet and Lévy’s external strategy being an example. Technically, we base our development on supplementing the usual notion of commutation diagram with a notion of order, expressing that the measure of its right leg does not exceed that of its left leg, where measure is an abstraction of the usual notion of length. We give an exact
characterisation of such global commutation diagrams, for pairs of reductions, by means of local ones, for pairs of steps, we dub Dyck diagrams.

 

  PDF |    doi:10.4230/LIPIcs.FSCD.2016.32  |  © Creative Commons License CC-BY

BibTeX 

@inproceedings{VvOYT-FSCD16,
author = "Vincent van Oostrom and Yoshihito Toyama",
title = "Normalisation by Random Descent",
booktitle = "Proceedings of the 1st International Conference on Formal Structures for
Computation and Deduction (FSCD 2016)",
pages = "32:1-32:18",
series = "Leibniz International Proceedings in Informatics (LIPIcs)",
volume = 52,
editor = "Delia Kesner and Brigitte Pientka",
publisher = "Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik",
year = 2016
}
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