Metric semantics from partial order semantics

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 of a complete partial order such that is a complete metric spaces and the metric semantics on coincides with the partial order semantics on when the same semantic operators are used. The first method is to add a ‘length’ on a complete partial order which means a function of increasing power. The second is based on the ideas of 11] and uses pseudo rank orderings, i.e. monotone sequences of monotone functions . 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. Received 11 July 1995 / 1 August 1996