This book is about the use of techniques and tools for the design and implementation of computer systems and software that are free from logical or functional flaws (in the sense of functional requirements). The word rigorous in the title of this book is justified by the fact that the arguments for such fault freeness have their roots in computer science, logic and mathematics rather than in empirical and statistical studies. In this sense this book will address concepts and techniques for fault avoidance rather than fault tolerance (which in itself represents a rich and very important area in computer system and software engineering).

The use of mathematical methods in the development of software is essential when reliable systems are sought; in particular they are now strongly recommended by the official norms adopted in the production of critical software. Program Verification is the area of computer science that studies mathematical methods for checking that a program conforms to its specification. This text is a self-contained introduction to program verification using logic-based methods, presented in the broader context of formal methods for software engineering. The idea of specifying the behaviour of individual software components by attaching contracts to them is now a widely followed approach in program development, which has given rise notably to the development of a number of behavioural interface specification languages and program verification tools. A foundation for the static verification of programs based on contract-annotated routines is laid out in the book. These can be independently verified, which provides a modular approach to the verification of software. The text assumes only basic knowledge of standard mathematical concepts that should be familiar to any computer science student. It includes a self-contained introduction to propositional logic and first-order reasoning with theories, followed by a study of program verification that combines theoretical and practical aspects - from a program logic (a variant of Hoare logic for programs containing user-provided annotations) to the use of a realistic tool for the verification of C programs (annotated using the ACSL specification language), through the generation of verification conditions and the static verification of runtime errors.