Denotational semantics of a parallel object-oriented language

TLDR: A denotational model is presented for the language POOL, a parallel object-oriented language that is actually used to write programs for a parallel machine, and a new technique is developed to solve a wide class of such equations, including function space constructions.

Abstract: A denotational model is presented for the language POOL, a parallel object-oriented language. It is a syntactically simplified version of POOL-T, a language that is actually used to write programs for a parallel machine. The most important aspect of this language is that it describes a system as a collection of communicating objects that all have internal activities which are executed in parallel. To describe the semantics of this language we construct a mathematical domain of processes. This domain is obtained as a solution of a reflexive domain equation over a category of complete metric spaces. A new technique is developed to solve a wide class of such equations, including function space constructions. The desired domain is obtained as the fixed point of a contracting functor implicit in the equation. The domain is sufficiently rich to allow a fully compositional definition of the language constructs in POOL, including concepts such as object creation and method invocation by messages. The semantic equations give a meaning to each syntactic construct depending on the POOL object executing the construct, the environment constituted by the declarations, and a continuation, representing the actions to be performed after the execution of the current construct. After the process representing the execution of an entire program is constructed, a yield function can extract the set of possible execution sequences from it. A preliminary discussion is provided on how to deal with fairness. Full mathematical details are supplied, with the exception of the general domain construction, which is described elsewhere.