On the Refinement Calculus gives one view of the development of the refinement calculus and its attempt to bring together - among other things - Z specifications and Dijkstra's programming language. It is an excellent source of reference material for all those seeking the background and mathematical underpinnings of the refinement calculus.

This book contains enough mnaterial for three complete courses of study. It provides an introduction to the world of logic, sets and relations. It explains the use of the Znotation in the specification of realistic systems. It shows how Z specifications may be refined to produce executable code; this is demonstrated in a selection of case studies. The essentials of specification, refinement and proof are covered, revealing techniques never previously published. Exercises, Solutions and set of Tranparencies are available via http://www.comlab.ox.ac.uk/usingz.html

The goal of this book is to provide a comprehensive and systematic introduction to the important and highly applicable method of data refinement and the simulation methods used for proving its correctness. The authors concentrate in the first part on the general principles needed to prove data refinement correct. They begin with an explanation of the fundamental notions, showing that data refinement proofs reduce to proving simulation. The book's second part contains a detailed survey of important methods in this field, which are carefully analysed, and shown to be either incomplete, with counterexamples to their application, or to be always applicable whenever data refinement holds. This is shown by proving, for the first time, that all these methods can be described and analysed in terms of two simple notions: forward and backward simulation. The book is self-contained, going from advanced undergraduate level and taking the reader to the state of the art in methods for proving simulation.

Much current research in computer science is concerned with two questions: is a program correct? And how can we improve a correct program preserving correctness? This latter question is known as the refinement of programs and the purpose of this book is to consider these questions in a formal setting. In fact, correctness turns out to be a special case of refinement and so the focus is on refinement. Although a reasonable background knowledge is assumed from mathematics and CS, the book is a self-contained introduction suitable for graduate students and researchers coming to this subject for the first time. There are numerous exercises provided of varying degrees of challenge.

Providing a thorough treatment of most elementary program development techniques, this revised edition covers topics such as procedures, parameters, recursion and data refinement, with the integration of specification, development and coding, based on ordinary (classical) logic.

Provides an integrated coverage of random/probabilistic algorithms, assertion-based program reasoning, and refinement programming models, providing a focused survey on probabilistic program semantics. This book illustrates, by examples, the typical steps necessary to build a mathematical model of any programming paradigm.

The stepwise refinement method postulates a system construction route that starts with a high-level specification, goes through a number of provably correct development steps, and ends with an executable program. The contributions to this volume survey the state of the art in this extremely active research area. The world's leading specialists in concurrent program specification, verification, and the theory of their refinement present latest research results and surveys of the fields. State-based, algebraic, temporal logic oriented and category theory oriented approaches are presented. Special attention is paid to the relationship between compositionality and refinement for distributed programs. Surveys are given of results on refinement in partial-order based approaches to concurrency. A unified treatment is given of the assumption/commitment paradigm in compositional concurrent program specification and verification, and the extension of these to liveness properties. Latest results are presented on specifying and proving concurrent data bases correct, and deriving network protocols from their specifications.

Refinement types can be the vector that brings formal verification into mainstream software development. This happy outcome hinges upon the design and implementation of refinement type systems that can be retrofitted to existing languages, or co-designed with new ones.In this book, the authors catalyze the development of such systems by distilling the ideas developed in the sprawling literature on the topic into a coherent and unified tutorial that explains the key ingredients of modern refinement type systems, by showing how to implement a refinement type checker.Inspired by the nanopass framework for teaching compilation the authors show how to implement refinement types via a progression of languages that incrementally add features to the language or type system.The readily accessible book provides the reader with an insightful introduction into Refinement Types using an innovative tutorial style that enables fast learning. Furthermore, the accompanying software implementation allows readers to work on practical real-world examples.

Refinement is one of the cornerstones of the formal approach to software engineering, and its use in various domains has led to research on new applications and generalisation. This book brings together this important research in one volume, with the addition of examples drawn from different application areas. It covers four main themes: - data refinement and its application to Z; - generalisations of refinement that change the interface and atomicity of operations; - refinement in Object-Z; - and modelling state and behaviour by combining Object-Z with CSP. Refinement in Z and Object-Z: Foundations and Advanced Applications provides an invaluable overview of recent research for academic and industrial researchers, lecturers teaching formal specification and development, industrial practitioners using formal methods in their work, and postgraduate and advanced undergraduate students.

On the Refinement Calculus gives one view of the development of the refinement calculus and its attempt to bring together - among other things - Z specifications and Dijkstra's programming language. It is an excellent source of reference material for all those seeking the background and mathematical underpinnings of the refinement calculus.