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

According to ADO [6] a data structure is a many-sorted algebra tha t satisfies various equations and conditional equations. Several author s [3], [4], [5], [8], [9] have emphasised that visible and non-visible sort s should be distinguished ;objects that belong to an invisible sort show a so-called observable behaviour and all of the authors mentioned point ou t that on these sorts terminal equivalence rather than initial equivalenc e is the more interesting congruence relation. Objects that have indistinguishable observable behaviour are made equivalent in this terminal congruence. We have in mind to present the reader with a survey of some terminolog y and several new definitions, notably that of an I/0-computable data structure. We shall define I/0-equivalence and prove that for each data structure A ther e is a computable data structure B that is I/O-equivalent to A. This very simpl e result may prove to be significant. First of all it shows the adequacy of th e concept of an I/0-computable data structure, as in principle all such dat a structures can practically exist. Moreover this fact suggests that both initia l and terminal semantics of equations may differ from what actually occurs in a n implementation. This means that both should be considered as theoretica l concepts that can be used to describe a data structure, given certain purposes. Certainly this result gives a post facto justification of the restrictio n to computable algebras that was made in 11] and l2]. Some technical terms have to be introduced in our discussion now. Let A be an algebra with sort s We assume A to be finitely generated by its finite signature E (i .e. The terminology visible-invisible being not so pleasant in the long run, w e propose to call the visible sorts I/O-sorts and the invisible sorts interna l sorts. Elements of I/O-sorts can be seen as tokens on which an equalit y relation is fixed. Elements of the internal sorts are the true data structures. It is on the internal sorts that investigating the variety of congruenc e relations that respect the I/0-behaviour (i .e. the word problem on the I/0-sorts) is interesting .

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I/O-computable data structures

We illustrate the difference between sequential composition in process algebra axiomatisations like ACP and action prefixing in process calculi like CCS. We define both early and late input in a general framework extending ACP, and consider various subalgebras, some very close to value passing CCS, another one close to CSP.

On sequential composition, action prefixes and process prefix

We develop an algebraic framework for the description and analysis of financial behaviours, that is, behaviours that consist of transferring certain amounts of money at planned times. To a large extent, analysis of financial products amounts to analysis of such behaviours. We formalize the cumulative interest compliant conservation requirement for financial products proposed by Wesseling and van den Bergh by an equation in the framework developed and define a notion of financial product behaviour using this formalization. We also present some properties of financial product behaviours. The development of the framework has been influenced by previous work on the process algebra ACP.

/pdf/timed-tuplix-calculus-and-the-wesseling-and-van-den-bergh-3ed5um1tkm.pdf

Timed tuplix calculus and the Wesseling and van den Bergh equation

We investigate basic issues concerning stored threads and their execution, building upon Maurer's model for computers and the thread algebra of Bergstra et al. We show among other things that a single thread can control the execution on a Maurer machine of any executable finite-state thread stored in the memory of the Maurer machine. We also relate stored threads with programs as considered in the program algebra of Bergstra et al. The work is intended as a preparation for the development of a formal approach to model micro-architectures and to verify their correctness and anticipated speed-up results.

/pdf/maurer-computers-with-single-thread-control-59spygyacb.pdf

Maurer Computers with Single-Thread Control

We consider a model of the real time process algebra of [1,2,3] based on the nonstandard reals. As a subalgebra, we obtain a theory in which the urgent actions of ATP, TiCCS, TeCCS can be modeled.

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Jan A. Bergstra

Papers

I/O-computable data structures

On sequential composition, action prefixes and process prefix

Timed tuplix calculus and the Wesseling and van den Bergh equation

Maurer Computers with Single-Thread Control

Real time process algebra with infinitesimals