Uniform Abstraction, Atomicity and Contractions in the Comparative Semantics of Concurrent Prolog

This paper shows the equivalence of two semantics for a version of Concurrent Prolog with non-flat guards: an operational semantics based on a transition system and a denotational semantics which is a metric semantics (the domains are metric spaces). We do this in the following manner: First an uniform language £ is considered, that is a language where the atomic actions have arbitrary interpretations. For this language we prove that a denotational semantics is correct with respect to the operational semantics. This result relies on Banach's fixed point theorem. Techniques stemming from imperative languages are used. Then we show how to translate a Concurrent Prolog program to a program in £ by selecting certain basic sets for £ and then instantiating the interpretation function for the atomic actions. In this way we induce the two semantics for Concurrent Prolog and the equivalence between the two semantics. Remark: an extended abstract of this report will appear in Proc. Fifth Generation Computer Systems 1988 (FGCS '88), December 1988, Tokyo, Japan.