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 complete partial order \(D\) such that \(M\) is a complete metric spaces and the metric semantics on \(M\) coincides with the partial order semantics on \(D\) when the same semantic operators are used. The first method is to add a ‘length’ on a complete partial order which means a function \(\rho : D \to {\Bbb N} \cup \{\infty\}\) of increasing power. The second is based on the ideas of [11] and uses pseudo rank orderings, i.e. monotone sequences of monotone functions \(\pi_n : D \to D\). 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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Received 11 July 1995 / 1 August 1996
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Baier, C., Majster-Cederbaum, M. Metric semantics from partial order semantics. Acta Informatica 34, 701–735 (1997). https://doi.org/10.1007/s002360050104
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DOI: https://doi.org/10.1007/s002360050104