In a theory of processes the names are atomic data items which can be exchanged and tested for identity. A well-known example of a calculus for name-passing is the π-calculus, where names additionally are used as communication ports. We provide complete axiomatisations of late and early bisimulation equivalences in such calculi. Since neither of the equivalences is a congruence we also axiomatise the corresponding largest congruences. We consider a few variations of the signature of the language; among these, a calculus of deterministic processes which is reminiscent of sequential functional programs with a conditional construct. Most of our axioms are shown to be independent. The axiom systems differ only by a few simple axioms and reveal the similarities and the symmetries of the calculi and the equivalences.

We give sound and complete proof systems for a variety of bisimulation based equivalences over a message-passing process algebra. The process algebra is a generalisation of pure CCS where the actions consist of receiving and sending messages or data on communication channels; the standard prefixing operator a:p is replaced by the two operators c?x:p and c!e:p and in addition messages can be tested by a conditional construct. The various proof systems are parameterised on auxiliary proof systems for deciding on equalities or more general boolean identities over the expression language for data. The completeness of these proof systems are thus relative to the completeness of the auxiliary proof systems.

ions for Value-Passing Systems ? Rance Cleaveland ?? and James Riely ??? 1 Dept. of Computer Science, N.C. State University, Raleigh, NC 27695-8206, USA 2 Dept. of Computer Science, University of N.C., Chapel Hill, NC 27599-3175, USA email: rance@csc.ncsu.edu, riely@cs.unc.edu Abstract. This paper presents a framework for the abstract interpretation of processes that pass values. We define a process description language that is parameterized with respect to the set of values that processes may exchange and show that an abstraction over values induces an abstract semantics for processes. Our main results state that if the abstract value interpretation safely/optimally approximates the ground interpretation, then the resulting abstracted processes safely/optimally approximate those derived from the ground semantics (in a precisely defined sense). As the processes derived from an abstract semantics in general have far fewer states than those derived from a concrete sem...

We develop a semantic theory based on testing for a minor variant of the ß-calculus. The resulting semantic equivalence can be characterised using of acceptance sets and can also be characterised as an equational theory. We define a class of interpretations for the ß-calculus and construct one which is fully-abstract. Moreover the interpretation we construct is initial in the class of all fully-abstract interpretations. This work has been supported by the ESPRIT/BRA CONCUR project 1 Introduction In [MPW92a], [MPW92b], a calculus of mobile processes, the ß-calculus, is presented. The first reference is an introduction to the calculus and the second develops a semantic theory based on bisimulations, [Mil89]. The ß-calculus is an extension of the process algebra CCS, a more primitive calculus for describing and manipulating processes which perform uninterpreted actions. In the ß-calculus these actions are now interpreted as either the input or output of values along channels. The p...

In this chapter we give a survey of the semantic theory for value-passing processes, focusing on bisimulation equivalences. The emphasis is on the symbolic method. Both operational and proof theoretic approaches are described and their expressiveness compared.

A general class of languages and denotational models for value-passing calculi based on the late semantic approach is defined. A concrete instantiation of the general syntax is given. This is a modification of the standard CCS according to the late approach. A denotational model for the concrete language is given, an instantiation of the general class. An equationally based proof system is defined and shown to be sound and complete with respect to the model.

Abstract. We present a streamlined theory of session types based on a simple yet general and expressive formalism whose main features are semantically characterized and where each design choice is semantically justified. We formally define the semantics of session types and use it to define the subsessioning relation. We give a coinductive characterization of subsessioning and describe algorithms to decide all the key relations defined in the article. We then apply the theory to statically ensure progress for a simple π-based process calculus, give examples, and discuss related work. 1.

Imposing certain restrictions on the transition system that defines the behaviour of a process allows us to characterize the readiness semantics of [OH86] by means of black--box testing experiments, or more precisely by lighted button testing experiments [BM92]. As divergence is considered we give the semantics as a preorder, the readiness preorder, which kernel coincides with the readiness equivalence of [OH86]. This leads to a bisimulation like characterization and a modal characterization of the semantics. A concrete

The language CRL allows to specify processes with data and to reason with them in an algebraic vein. This allows to express and reason about global correctness of systems. Sometimes, one only needs to analyse particular properties of CRL-processes. Modal logics are very convenient toexpressandverify such properties. Therefore, we de ne a modal logic for CRL. It is a branching time modal logic based on actions. It has future and past operators and it allows for reasoning about data, for instance using rst order quanti cation over data variables. It is shown that these modal formulae cannot distinguish between divergence sensitive branching bisimilar processes. The rst author is partly supported by the Netherlands Computer Science Research Foundation (SION) with nancial support of the Netherlands Organisation for Scienti c Research (NWO).

A simple untyped language based on CML, Concurrent ML, is defined and analysed. The language contains a spawn operator for initiating new independent threads of computation and constructs for the exchange of data between these threads. A denotational model for the language is presented where denotations correspond to computations of values rather than simply values. It is shown to be fully abstract with respect to a behavioural preorder based on contextual testing. 1 Introduction The language Concurrent ML (CML), [18], is one of a number of recent languages which seeks to combine aspects of functional and concurrent programming. Standard ML, [19], is augmented with the ability to spawn off new independent threads of computation. Further constructs are added to enable these threads to synchronise and exchange data on communication channels. As it includes higherorder objects, which can be exchanged between threads as data, new channel name generation, and the ability to form abstractio...