This IFIP report is a collection of fundamental, high-quality contributions on the algebraic foundations of system specification. The contributions cover and survey active topics and recent advances, and address such subjects as: the role of formal specification, algebraic preliminaries, partiality, institutions, specification semantics, structuring, refinement, specification languages, term rewriting, deduction and proof systems, object specification, concurrency, and the development process. The authors are well-known experts in the field, and the book is the result of IFIP WG 1.3 in cooperation with Esprit Basic Research WG COMPASS, and provides the foundations of the algebraic specification language CASL designed in the CoFI project. For students, researchers, and system developers.

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.

The aim of this book is to present fundamentals of algebraic specifications with respect to the following three aspects: fundamentals in the sense of a carefully motivated introduction to algebraic specifications, which is easy to understand for computer scientists and mathematicians; fundamentals in the sense of mathematical theories which are the basis for precise definitions, constructions, results, and correctness proofs; and fundamentals in the sense of concepts, which are introduced on a conceptual level and formalized in mathematical terms. The book is equally suitableas a text book for graduate courses and as a reference for researchers and system developers.

AMAST’s goal is to advance awareness of algebraic and logical methodology as part of the fundamental basis of software technology. Ten years and seven conferences after the start of the AMAST movement, I believe we are attaining this. The movement has propagated throughout the world, assembling many enthusiastic specialists who have participated not only in the conferences, which are now annual, but also in the innumerable other activities that AMAST promotes and supports. We are now facing the Seventh International Conference on Algebraic Methodology and Software Technology (AMAST’98). The previous meetings were held in Iowa City, USA (1989 and 1991), in Enschede, The Netherlands (1993), in Montreal, Canada (1995), in Munich, Germany (1996), and in Sydney, Australia (1997). This time it is Brazil’s turn, in a very special part of this colorful country – Amazonia. Thus, “if we have done more it is by standing on the shoulders of giants.” The effort started by Teodor Rus, Arthur Fleck, and William A. Kirk at AMAST’89 was consolidated in AMAST'91 by Teodor Rus, Maurice Nivat, Charles Rattray, and Giuseppe Scollo. Then came modular construction of the building, wonderfully carried out by Giuseppe Scollo, Vangalur Alagar, Martin Wirsing, and Michael Johnson, as Program Chairs of the AMAST conferences held between 1993 and 1997.

This book constitutes the thoroughly refereed post-workshop proceedings of the 15th International Workshop on Algebraic Development Techniques, WADT 2001, held jointly with the General Workshop of the ESPRIT Working Group CoFI in Genova, Italy, in April 2001. The book presents 16 papers selected from 32 workshop presentations. Among the topics addressed are formal specification, specification languages, term rewriting, and proof systems.

The AMAST movement was initiated in 1989 with the First International C- ference on Algebraic Methodology and Software Technology (AMAST), held on May 21{23in Iowa City, Iowa,and aimed at setting the development of software technology on a mathematical basis. The virtue of the software technology en- sioned by AMAST is the capability to produce software that has the following properties: (a) it is correct and its correctness can be proved mathematically, (b) it is safe, such that it can be used in the implementation of critical systems, (c) it is portable, i. e. , it is independent of computing platforms and language generations, and (d) it is evolutionary, i. e. , it is self-adaptable and evolves with the problem domain. Ten years later a myriad of workshops, conferences, and researchprogramsthat sharethe goalsof the AMAST movementhaveoccurred. This can be taken as proof that the AMAST vision is right. However, often the myriad of workshops, conferences, and research programs lack the clear obj- tives and the coordination of their goals towards the software technology en- sioned by AMAST. This can be taken as a proof that AMAST is still necessary.