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Since the early seventies concepts of specification have become central in the whole area of computer science. Especially algebraic specification techniques for abstract data types and software systems have gained considerable importance in recent years. They have not only played a central role in the theory of data type specification, but meanwhile have had a remarkable influence on programming language design, system architectures, arid software tools and environments. The fundamentals of algebraic specification lay a basis for teaching, research, and development in all those fields of computer science where algebraic techniques are the subject or are used with advantage on a conceptual level. Such a basis, however, we do not regard to be a synopsis of all the different approaches and achievements but rather a consistently developed theory. Such a theory should mainly emphasize elaboration of basic concepts from one point of view and, in a rigorous way, reach the state of the art in the field. We understand fundamentals in this context as: 1. Fundamentals in the sense of a carefully motivated introduction to algebraic specification, which is understandable for computer scientists and mathematicians. 2. Fundamentals in the sense of mathematical theories which are the basis for precise definitions, constructions, results, and correctness proofs. 3. Fundamentals in the sense of concepts from computer science, which are introduced on a conceptual level and formalized in mathematical terms.
List of contents
1 Informal Introduction to Abstract Modules.- 1A: Towards Modularization in Software Development.- 1B: Modules and Modularization in Programming and Specification Languages.- 1C: Concepts for Abstract Modules and Modular Systems.- 1D: Informal Introduction to Algebraic Specification of Modules and Modular Systems.- 1E: Abstract Data Types and Abstract Modules.- 1F: Bibliographic Notes.- 2 Module Specifications.- 2A: Syntax of Module Specifications.- 2B: Restriction Construction and Conservative Functors.- 2C: Semantics and Correctness of Module Specifications.- 2D: Modular Specification of an Airport Schedule: Part 1.- 3 Basic Operations on Module Specifications.- 3A: Composition.- 3B: Union.- 3C: Actualization.- 3D: Distributive Laws.- 3E: Modular Specification of an Airport Schedule System: Part 2.- 4 General Operations on Module Specifications.- 4A: General Notion of Operations.- 4B: Clean Operations.- 4C: Renaming, Partial Composition and Recursion.- 4D: Product and Iteration.- 4E: Bibliographic Notes for Chapters 2, 3, and 4.- 5 Refinement, Interface Specifications, and Realizations.- 5A: Refinement.- 5B: Interface Specifications.- 5C: Realization.- 5D: Modular Specification of an Airport Schedule System: Part 3.- 6 Development Categories, Simulation, and Transformation.- 6A: Development Categories.- 6B: Compatibility of Operations with Development Steps.- 6C: Simulation.- 6D: Transformations.- 6E: Bibliographic Notes for Chapters 5 and 6.- 7 Constraints.- 7A: Concepts of Constraints.- 7B: Logic of Constraints.- 7C: Specifications with Constraints.- 7D: Parameterized Specifications with Constraints.- 8 Module Specifications and Operations with Constraints.- 8A: Module Specifications with Constraints.- 8B: Composition with Constraints.- 8C: Union with Constraints.-8D: Actualization with Constraints.- 8E: Modular Specification of an Airport Schedule System: Part 4.- 8F: Discussion and Bibliographic Notes for Chapters 7 and 8.- 9 Abstract ACT ONE and ACT TWO.- 9A: Abstract Specifications with Constraints.- 9B: Abstract ACT ONE.- 9C: Abstract ACT TWO.- 9D: Modular Specification of an Airport Schedule System: Part 5.- 9E: Bibliographic Notes for Chapter 9.- 10 Summary of Basic Notions.- 10A: Summary of Equational Specifications.- 10B: Summary of Parameterized Specifications.- 10C: Basic Concepts from Category Theory.
