For a process language with action refinement and synchronization both an operational and a denotational semantics are given. The operational semantics is based on an SOS-style transition system specification involving syntactical refinement sequences. The denotational semantics is an interleaving model which uses semantical refinement ‘environments'. It identifies those statements which are equal under all refinements. The denotational model is shown to be fully abstract with respect to the operational one. The underlying metric machinery is exploited to obtain this full abstractness result. Usually, action refinement is treated either in a model with some form of true concurrency, or, when an interleaving model is applied, by assuming that the refining statements are atomized. We argue that an interleaving model without such atomization is attractive as well.

A comparative semantic study is made of two notions in concurrency, viz. atomicity and action refinement. Parallel composition is modeled by interleaving, and refinement is taken in the version where actions are refined by atomized statements. The bi

The Centre for Mathematics and Computer

Transition systems as proposed by Hennessy & Plotkin are defined for a series of three languages featuring concurrency.The first has shuffle and local nondeterminancy, the second synchronization merge and local nondeterminacy, and the third synchronization merge and global nondeterminacy.The languages are all uniform in the sense that the elementary actions are uninterpreted.Throughout, infinite behaviour is taken into account and modelled with infinitary languages in the sense of Nivat.A comparison with denotational semantics is provided.For the first two languages, a linear time model suffices; for the third language a braching time model with processes in the sense of De Bakker & Zucker is described.In the comparison an important role is played by an intermediate semantics in the style of Hoare & Olderog's specification oriented semantics.A variant on the notion of ready set is employed here.Precise statements are given relating the various semantics in terms of a number of abstraction operators.

A general framework for the denotational treatment of concurrency is introduced. The key idea is the notion of process which is element of a domain obtained as solution of a domain equation in the style as considered previously by Plotkin. We use tools from metric topology as advocated by Nivat to solve this equation, show how operations upon processes can be defined conveniently, and illustrate the approach with the definition of a variety of concepts as encountered in the study of concurrency. Only few proofs of the supporting mathematical theory are given; full proofs will appear in the final version of the paper.

The proof theory of structured programming insofar as concerned with flow of control is investigated. Various proof rules for the while, repeat-until and simple iteration statements - all essentially variants of Hoare's original while rule - are analyzed with respect to their soundness and adequacy. Next, a recently proposed proof rule for recursive procedures due to Dijkstra is - after correction - shown to be a simple instance of Scott's induction rule. Finally, Manna & Pnueli's rule for total correctness of the while statement is formally justified using the Hitchcock & Park theory of program termination based on well-founded relations.