Semantics of the Domain of Flow Diagrams

Abstract

A domain of flow diagrams similar to that proposed by Scott, a domain of linear flow diagrams proposed by Goguen et al, a domain of decision table diagrams involving infinitary branching, and a domain of processes based on the ideas of Milner and Bekic are each provided with a direct semantics, closely related to partial-function semantics, and a continuation semantics similar to that developed by Morris and Wadsworth. It is shown that there is a variety of meaning-preserving continuous functions among these language-like domains, that every direct semantics possesses an “equivalent” continuation semantics, and that there is a particular continuation semantics which always gives distinct meanings to distinct processes. The proofs utilize the algebraic methods of Goguen et al, which are extended to continuous algebras with operations whose arguments can be Indexed by mflmte sets or even domains. © 1977, ACM. All rights reserved.