The semantics of the combination of atomized statements and parallel choice

Abstract

Abstract In this paper we define a uniform language ℒ that is an extension of the language underlying the process algebra PA . One of the main extensions of this language over PA is given by so-called atomizing brackets. If we place these brackets around a statement then we treat this statement as an atomic action. Put differently, these brackets remove all interleaving points. We present a transition system for the language and derive its operational semantics. We show that there are several options for defining a transition system such that the resulting operational semantics is a conservative extension of the semantics for PA . We define a semantic domain and a denotational model for the language. Next we define a closure operator on the semantic domain and show how to use this closure operator to derive a fully abstract denotational semantics. Then the algebraic theory of the language is considered. We define a collection of axioms and a term rewrite system based on these axioms. Using this term rewrite system we are able to identify normal forms for the language. It is shown that these axioms capture the denotational equality. It follows that if two terms are provably equal then they have the same operational semantics. Finally, we show how to extend the axiomatization in order to axiomatize its operational equivalence.