Transition systems, metric spaces and ready sets in the semantics of uniform concurrency

AbstractTransition systems as proposed by Hennessy and Plotkin are defined for a series of three languages featuring concurrency. The first has shuffle and local nondeterminacy, 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 branching time model with processes in the sense of de Bakker and Zucker is described. In the comparison an important role is played by an intermediate semantics in the style of Hoare and Olderog's specification oriented semantics. A variant on the notion of ready set is employed here. Precise statements are given relating the various semantics terms of a number of abstraction operators

Some comments on CPO-semantics and metric space semantics for imperative languages

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Fifty years of Hoare's Logic

We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin

Computable concurrent processes

AbstractWe study relative computability for processes and process transformations, in general, and in particular the non-deterministic and concurrent processes which can be specified in terms of various fair merge constructs. The main result is a normal form theorem for these (relatively) computable process functions which implies that although they can be very complex when viewed as classical set-functions, they are all “loosely implementable” in the sense of Park (1980). The precise results are about the player model of concurrency introduced in Moschovakis (1991), which supports both fairness constructs and full recursion

Designing equivalent semantic models for process creation

Operational and denotational semantic models are designed for languages with process creation, and the relationships between the two semantics are investigated. The presentation is organized in four sections dealing with a uniform and static, a uniform and dynamic, a nonuniform and static, and a nonuniform and dynamic language, respectively. Here uniform/nonuniform refers to a language with uninterpreted/interpreted elementary actions, and static/dynamic to the distinction between languages with a fixed/growing number of parallel processes. The contrast between uniform and nonuniform is reflected in the use of linear time versus branching time models., the latter employing a version of Plotkin's resumptions. The operational semantics make use of Hennessy and Plotkin's transition systems. All models are built on metric structures, and involve continuations in an essential way. The languages studied are abstractions of the parallel object-oriented language POOL for which we have designed separate operational and denotational semantics in earlier work. The paper provides a full analysis of the relationship between the two semantics for these abstractions. Technically, a key role is played by a new operator which is able to decide dynamically whether it should act as sequential or parallel composition