A straightforward denotational semantics for non-determinate data flow programs

Data flow programming languages are especially amenable to mathematization of their semantics in the denotational style of Scott and Strachey. However, many real world programming problems, such as operating systems and data base inquiry systems, require a programming language capable of non-determinacy because of the non-determinate behavior of their physical environment. To date, there has been no satisfactory denotational semantics of programming languages with non-determinacy. This paper presents a straightforward denotational treatment of non-determinate data flow programs as functions from sets of tagged sequences to sets of tagged sequences. A simple complete partial order on such sets exists, in which the data flow primitives are continuous functions, so that any data flow program computes a well defined function.