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.

/pdf/the-theory-and-practice-of-concurrency-1kzi2sg7cs.pdf

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

The following problem is investigated in the 
paper: what structures can be uniquely defined, by algorithmic 
properties? The algorithmic propertifa are represented in this 
paper as open formulae of the logic of effective definitions. This 
approach can be viewed as an alternative way of defining abstract 
data types.

Implicit definability of algebraic structurs by means of program properties

We develop an algebraic theory for the top-down design of communicating systems in which levels of abstraction are represented by algebras, and their stepwise refinements are represented by homomorphisms. Particular attention is paid to the equational specification of these levels of abstraction. A number of examples are included for illustration, most notably a top-down design for a communication protocol.

Top-down design and the algebra of communicating processes

Promise Theory bridges the worlds of semantics and dynamics to describe interactions between autonomous agencies within a system. It provides a semi-formal language for modelling intent and its outcome, which results in a chemistry for cooperative behaviour. This book is aimed at scientists and engineers. It introduces readers to promises in a practical manner, keeping within the paradigm of `voluntary cooperation'. The book draws on examples from the real world, with a special emphasis on computers and information systems.

Promise Theory: Principles and Applications (Volume 1)

Ready-trace semantics for concrete process algebra with the priority operator

We consider processes that have transitions labeled with atomic actions, and states labeled
with formulas over a propositional logic. These state labels are called signals. A process in a
parallel composition may proceed conditionally, dependent on the presence of a signal in
the process in parallel. This allows a natural treatment of signal observation.

Jan A. Bergstra

Papers

Implicit definability of algebraic structurs by means of program properties

Top-down design and the algebra of communicating processes

Promise Theory: Principles and Applications (Volume 1)

Ready-trace semantics for concrete process algebra with the priority operator

Process Algebra with Propositional Signals