Infinitary rewriting: meta-theory and convergence

Kahrs, Stefan (2007) Infinitary rewriting: meta-theory and convergence. Acta Informatica, 44 (2). pp. 91-121. ISSN 0001-5903. (doi:https://doi.org/10.1007/s00236-007-0043-2) (Full text available)

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Official URL http://dx.doi.org/10.1007/s00236-007-0043-2

Abstract

When infinitary rewriting was introduced by Kaplan et.al. at the beginning of the 1990s, its term universe was explained as the metric completion of a metric on finite terms. The motivation for this connection to topology was that it allowed to import other well-studied notions from metric spaces, in particular the notion of convergence as a replacement for normalisation. This paper generalises the approach by parameterising it with a term metric, and applying the process of metric completion not only to terms but also to operations on and relations between terms. The resulting meta-theory is studied, leading to a revised notion of infinitary rewrite system. For these systems a method is devised to prove their convergence.

Item Type:	Article
Uncontrolled keywords:	rewriting topology infinitary
Subjects:	Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
Divisions:	Faculties > Sciences > School of Computing > Theoretical Computing Group
Depositing User:	Mark Wheadon
Date Deposited:	24 Nov 2008 18:05 UTC
Last Modified:	28 Jun 2017 01:06 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/14587 (The current URI for this page, for reference purposes)