2-stage Fixed-point Iteration in a Modiied Plotkin Powerdomain
نویسنده
چکیده
Powerdomains are used both when describing the semantics of non-deterministic programming languages and when doing abstract interpretation of deterministic programming languages. In the latter case, the restrictions imposed on sets in the usual powerdomain constructions can lead to less precise results than desired. We show a variant of the Plotkin (convex) powerdomain which impose fewer restrictions on the sets used. In this powerdomain, however, point-wise extensions of continuous functions are not necessarily continuous, and hence the least xed-point of a function might be diierent from the limit of the sequence obtained by iterated application of the function to the least element in the powerdomain. We solve this problem by showing that a 2-stage process involving limits in two diierent orderings will yield the least xed-point. We show an example of an analysis that beneet from the extended precision obtained by using the new powerdomain construction.
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