This paper unveils and motivates an ambitious programme of hidden algebraic research in software engineering, beginning with our general goals, continuing with an overview of results, and including some future plans. The main contribution is powerful hidden coinduction techniques for proving behavioral correctness of concurrent systems; several mechanical proofs are given using OBJ3. We also show how modularization, bisimulation, transition systems, concurrency and combinations of the functional, constraint, logic and object paradigms fit into hidden algebra. 1. Introduction

Circular coinduction is a technique for behavioral reasoning that extends cobasis coinduction to specifications with circularities. Because behavioral satisfaction is not recursively enumerable, no algorithm can work for every behavioral statement. However, algorithms using circular coinduction can prove every practical behavioral result that we know. This paper proves the correctness of circular coinduction and some consequences.

Abstract: Verifying design instead of code can be an effective and practical approach to obtaining verified software. This paper argues that proof scores are an attractive method for verifying design, in that they achieve a balance in which the respective capabilities of humans and machines are utilized optimally. 1 Verifying Code or Design Although creation of a verifying compiler is a difficult challenge, recent developments suggest that there are ways to make it easier. Systems that generate lexical analyzers and parsers already have a long history (e.g. Lex and Yacc), and recent work of Sorin Lerner [23] shows that the same can be done for compiler backends; there is also work suggesting that code generation modules can be automatically generated (e.g. using intermediate languages). Unfortunately, a great number of different compilers are needed in today’s software world, and the underlying machine architectures are evolving, as are the languages, so it would be difficult to create verifying compilers for all useful combinations of language and platform, and code verification for such tools still remains very difficult. Major impediments include the unsolvability of discovering loop invariants, the potential unsolvability of loop once they are found, and the further difficulties raised by interactivity, nondeterminism, concurrency, distribution, active agents, and unreliable communication. A long term approach is to use high level, application specific source languages, in order to greatly simplify source program verification by eliminating many obscure features of current languages. In the meantime, a currently feasible approach is to verify the design of software, instead of its code; experience shows that design verification often leads to better design, and nearly always leads to greater conceptual clarity. An aditional motivation is that the main sources of errors in software are in areas other than code, namely, requirements, specification, and design. 2

iii This thesis describes a theory for representing, manipulating, and reasoning about structured pieces of knowledge in open collaborative systems. The theory’s design is motivated by both its general model as well as its target user commu-nity. Its model is structured information, with emphasis on classification, relative structure, equivalence, and interpretation. Its user community is meant to be non-mathematicians and non-computer scientists that might use the theory via computational tool support once inte-grated with modern design and development tools. This thesis discusses a new logic called kind theory that meets these challenges. The core of the work is based in logic, type theory, and universal algebras. The theory is shown to be efficiently implementable, and several parts of a full realization have already been constructed and are reviewed. Additionally, several software engineering concepts, tools, and technologies have been con-structed that take advantage of this theoretical framework. These constructs are discussed as well, from the perspectives of general software engineering and applied formal methods. Acknowledgements iv I am grateful to my initial primary adviser, Prof. K. Mani Chandy, for bringing me to Caltech and his willingness to let me explore many unfamiliar research fields of my own choosing. I am also appreciative of my second adviser, Prof. Jason Hickey, for his support, encouragement, feedback, and patience through the later years of my work. If Jason had not appeared at Caltech in Autumn of 1999, I may well have not finished my Ph.D. I am very much in debt to Joseph Goguen whose inspiring work started me on the path of using algebras and categories. José Meseguer and Francisco (Paco) Duran have been of tremendous help and inspiration in my use of Maude and rewriting logic.

The use of semiotics has been proposed in studying the ways in which information is mediated in computer systems, particularly in user interfaces.