Atomic refinement in process description languages

Abstract

The hierarchical development of concurrent systems is investigated in a linguistic approach, by introducing a a new combinator for action refinement that substitutes a process for an action. In this way, the classic horizontal modularity is amalgamated with the new vertical one. The semantic definitions have been driven by two methodological criteria arising from a quest for compositionality that enforce to consider as atomic the behaviour of the processes refining actions. The first criterion requires that refinement must preserve the structure of the semantic object to be refined; the second one calls for a compositional refinement operation at the semantic level. Thus, refinement is not syntactic substitution, rather it is a compositional operation, which results to be context-free graph replacement of transition systems for transitions. The operational semantics implements this operation through states which are sort of stacks, used to make atomic the behaviour of processes refining actions; the denotational one uses tags expressing the start and the end of atomic sequences. Moreover, we define equivalences on both semantics, based on strong and rooted branching bisimulations, and we prove them congruences with respect to all the combinators of the language, and coincident.