Foundations of Algebraic Specification and Formal Software Development

Description

This book provides foundations for software specification and formal software development from the perspective of work on algebraic specification, concentrating on developing basic concepts and studying their fundamental properties. These foundations are built on a solid mathematical basis, using elements of universal algebra, category theory and logic, and this mathematical toolbox provides a convenient language for precisely formulating the concepts involved in software specification and development. Once formally defined, these notions become subject to mathematical investigation, and this interplay between mathematics and software engineering yields results that are mathematically interesting, conceptually revealing, and practically useful. The theory presented by the authors has its origins in work on algebraic specifications that started in the early 1970s, and their treatment is comprehensive. This book contains five kinds of material: the requisite mathematical foundations; traditional algebraic specifications; elements of the theory of institutions; formal specification and development; and proof methods. While the book is self-contained, mathematical maturity and familiarity with the problems of software engineering is required; and in the examples that directly relate to programming, the authors assume acquaintance with the concepts of functional programming. The book will be of value to researchers and advanced graduate students in the areas of programming and theoretical computer science. Front Matter....Pages i-xvi Universal algebra....Pages 15-39 Simple equational specifications....Pages 41-95 Category theory....Pages 97-153 Working within an arbitrary logical system....Pages 155-228 Structured specifications....Pages 229-258 Parameterisation....Pages 259-292 Formal program development....Pages 293-324 Behavioural specifications....Pages 325-399 Proofs for specifications....Pages 401-484 Working with multiple logical systems....Pages 485-532 Back Matter....Pages 533-581