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 ρ : D → IN 0 ∪{∞} of increasing power. The second is based on the ideas of [9] and uses pseudo rank orderings, i.e. monotone sequences of monotone functions ϖn : D → 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.
Additional information:
Das Dokument wird vom Publikationsserver der Universitätsbibliothek Mannheim bereitgestellt.
![[img]](https://madoc.bib.uni-mannheim.de/style/images/fileicons/application_pdf.png)
Search Authors in