Opening -- Discrete Mathematics -- Numbers -- Sets -- Cartesians -- Types -- Functions -- A ?-Calculus -- Algebras -- Mathematical Logic -- Simple RSL -- Atomic Types and Values in RSL -- Function Definitions in RSL -- Property-Oriented and Model-Oriented Abstraction -- Sets in RSL -- Cartesians in RSL -- Lists in RSL -- Maps in RSL -- Higher-Order Functions in RSL -- Specification Types -- Types in RSL -- Specification Programming -- Applicative Specification Programming -- Imperative Specification Programming -- Concurrent Specification Programming -- And So On! -- Etcetera!.

The art, craft, discipline, logic, practice, and science of developing large-scale software products needs a believable, professional base. The textbooks in this three-volume set combine informal, engineeringly sound practice with the rigour of formal, mathematics-based approaches. Volume 1 covers the basic principles and techniques of formal methods abstraction and modelling. First this book provides a sound, but simple basis of insight into discrete mathematics: numbers, sets, Cartesians, types, functions, the Lambda Calculus, algebras, and mathematical logic. Then it trains its readers in basic property- and model-oriented specification principles and techniques. The model-oriented concepts that are common to such specification languages as B, VDM-SL, and Z are explained here using the RAISE specification language (RSL). This book then covers the basic principles of applicative (functional), imperative, and concurrent (parallel) specification programming. Finally, the volume contains a comprehensive glossary of software engineering, and extensive indexes and references. These volumes are suitable for self-study by practicing software engineers and for use in university undergraduate and graduate courses on software engineering. Lecturers will be supported with a comprehensive guide to designing modules based on the textbooks, with solutions to many of the exercises presented, and with a complete set of lecture slides.