We present the a-calculus, a calculus of communicating systems in which one can naturally express processes which have changing structure. Not only may the component agents of a system be arbitrarily linked, but a communication between neighbours may carry information which changes that linkage. The calculus is an extension of the process algebra CCS, following work by Engberg and Nielsen, who added mobility to CCS while preserving its algebraic properties. The rr-calculus gains simplicity by removing all distinction between variables and constants; communication links are identified by names, and computation is represented purely as the communication of names across links. After an illustrated description of how the n-calculus generalises conventional process algebras in treating mobility, several examples exploiting mobility are given in some detail. The important examples are the encoding into the n-calculus of higher-order functions (the I-calculus and combinatory algebra), the transmission of processes as values, and the representation of data structures as processes. The paper continues by presenting the algebraic theory of strong bisimilarity and strong equivalence, including a new notion of equivalence indexed by distinctions-i.e., assumptions of inequality among names. These theories are based upon a semantics in terms of a labeled transition system and a notion of strong bisimulation, both of which are expounded in detail in a companion paper. We also report briefly on work-in-progress based upon the corresponding notion of weak bisimulation, in which internal actions cannot be observed. 0 1992 Academic Press, Inc.

A calculus of mobile processes, II

An Introduction to MultiAgent Systems.

From the Publisher:
Since the introduction of Hoares' Communicating Sequential Processes notation, powerful new tools have transformed CSP into a practical way of describing industrial-sized problems. This book gives you the fundamental grasp of CSP concepts you'll need to take advantage of those tools.Part I provides a detailed foundation for working with CSP, using as little mathematics as possible. It introduces the ideas behind operational, denotational and algebraic models of CSP. Parts II and III go into greater detail about theory and practice. Topics include: parallel operators, hiding and renaming, piping and enslavement, buffers and communication, termination and sequencing, and semantic theory. Three detailed practical case studies are also presented.For anyone interested in modeling sequential processes.

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The Theory and Practice of Concurrency

Publisher Summary
This chapter focuses on rewrite systems, which are directed equations used to compute by repeatedly replacing sub-terms of a given formula with equal terms until the simplest form possible is obtained. As a formalism, rewrite systems have the full power of Turing machines and may be thought of as nondeterministic Markov algorithms over terms rather than strings. The theory of rewriting is in essence a theory of normal forms. To some extent, it is an outgrowth of the study of A. Church's Lambda Calculus and H. B. Curry's Combinatory Logic. The chapter discusses the syntax and semantics of equations from the algebraic, logical, and operational points of view. To use a rewrite system as a decision procedure, it must be convergent. The chapter describes this fundamental concept as an abstract property of binary relations. To use a rewrite system for computation or as a decision procedure for validity of identities, the termination property is crucial. The chapter presents the basic methods for proving termination. The chapter discusses the question of satisfiability of equations and the convergence property applied to rewriting.

CHAPTER 6 – Rewrite Systems

We survey the literature available on the topic of domain-specific languages as used for the construction and maintenance of software systems. We list a selection of 75 key publications in the area, and provide a summary for each of the papers. Moreover, we discuss terminology, risks and benefits, example domain-specific languages, design methodologies, and implementation techniques.

https://people.cis.ksu.edu/~schmidt/505f14/Lectures/DSLbib.pdf

Domain-specific languages: an annotated bibliography

Top-down design and the algebra of communicating processes

The following fundamental theorem about the adequacy of the algebraic specification methods for data abstractions is proved. Let A be a data type with n subtypes. Then A is computable if, and only if, A possesses an equational specification, involving at most 3( n + 1) hidden operators and 2( n + 1) axioms, which defines it under initial and final algebra semantics simultaneously.

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The completeness of the algebraic specification methods for computable data types

Analytic execution architectures have been proposed as a means to conceptualize the cooperation between components such as programs, threads, states and services. Interface groups provide a technique to combine interface elements into interfaces with the exibility to distinguish between permission and obligation and between promise and expectation which all come into play when component interfaces are specied.

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Interface Groups for Analytic Execution Architectures

This paper provides a systematic and full treatment of mode transfer operators in process algebra, including complete axiomatizations, operational rules, analysis of expressive power and extensions with timing features. In particular, we study a disrupt operator and an interrupt operator.

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Mode transfer in process algebra

In a previous paper, we developed an algebraic theory about threads and multi-threading based on the assumption that a deterministic interleaving strategy determines how threads are interleaved. The theory includes interleaving operators for a number of plausible deterministic interleaving strategies. The interleaving of different threads constitutes a multi-thread. Several multi-threads may exist concurrently on a single host in a network, several host behaviors may exist concurrently in a single network on the internet, etc. In the current paper, we assume that the above-mentioned kind of interleaving is also present at these other levels. We extend the theory developed so far with features to cover the multi-level case. We use the resulting theory to develop a simplified formal representation schema of systems that consist of several multi-threaded programs on various hosts in different networks. We also investigate the connections of the resulting theory with the algebraic theory of processes known as ACP.

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Jan A. Bergstra

Papers

Top-down design and the algebra of communicating processes

The completeness of the algebraic specification methods for computable data types

Interface Groups for Analytic Execution Architectures

Mode transfer in process algebra

Thread Algebra with Multi-Level Strategies