Construction of a cms on a given cpo

Baier, Christel ; Majster-Cederbaum, Mila

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URN: urn:nbn:de:bsz:180-madoc-17562
Document Type: Working paper
Year of publication: 1995
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Mathematik und Informatik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Informatik > Technical Reports
Subject: 004 Computer science, internet
Subject headings (SWD): Metrik <Mathematik> , Vollständige Halbordnung
Abstract: In dealing with denotational semantics of programming languages partial orders resp. metric spaces have been used with great benefit in order to provide a meaning to recursive and repetitive constructs. This paper presents two methods to define a metric on a subset M of a cpo D such that M is a complete metric spaces and the metric semantics on M coincides with the cpo semantics on D when the same semantic operators are used. The first method is to add a 'length' on a cpo which means a function &#961; : D &#8594; IN 0 &cup;{&#8734;} of increasing power. The second is based on the ideas of [9] and uses pseudo rank orderings, i.e. monotone sequences of monotone functions &piv;n : D &#8594; D. We show that SFP domains can be characterized as special kinds of rank orderded cpo's. We also discuss the connection between the Lawson topology and the topology induced by the metric.
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