The Formal Semantics of Programming Languages provides the basic mathematical techniques necessary for those who are beginning a study of the semantics and logics of programming languages. These techniques will allow students to invent, formalize, and justify rules with which to reason about a variety of programming languages. Although the treatment is elementary, several of the topics covered are drawn from recent research, including the vital area of concurency. The book contains many exercises ranging from simple to miniprojects.Starting with basic set theory, structural operational semantics is introduced as a way to define the meaning of programming languages along with associated proof techniques. Denotational and axiomatic semantics are illustrated on a simple language of while-programs, and fall proofs are given of the equivalence of the operational and denotational semantics and soundness and relative completeness of the axiomatic semantics. A proof of Godel's incompleteness theorem, which emphasizes the impossibility of achieving a fully complete axiomatic semantics, is included. It is supported by an appendix providing an introduction to the theory of computability based on while-programs. Following a presentation of domain theory, the semantics and methods of proof for several functional languages are treated. The simplest language is that of recursion equations with both call-by-value and call-by-name evaluation. This work is extended to lan guages with higher and recursive types, including a treatment of the eager and lazy lambda-calculi. Throughout, the relationship between denotational and operational semantics is stressed, and the proofs of the correspondence between the operation and denotational semantics are provided. The treatment of recursive types - one of the more advanced parts of the book - relies on the use of information systems to represent domains. The book concludes with a chapter on parallel programming languages, accompanied by a discussion of methods for specifying and verifying nondeterministic and parallel programs.

Provability, Computability and Reflection

An essential introduction to the analysis and verification of control system software The verification of control system software is critical to a host of technologies and industries, from aeronautics and medical technology to the cars we drive. The failure of controller software can cost people their lives. In this authoritative and accessible book, Pierre-Loïc Garoche provides control engineers and computer scientists with an indispensable introduction to the formal techniques for analyzing and verifying this important class of software. Too often, control engineers are unaware of the issues surrounding the verification of software, while computer scientists tend to be unfamiliar with the specificities of controller software. Garoche provides a unified approach that is geared to graduate students in both fields, covering formal verification methods as well as the design and verification of controllers. He presents a wealth of new verification techniques for performing exhaustive analysis of controller software. These include new means to compute nonlinear invariants, the use of convex optimization tools, and methods for dealing with numerical imprecisions such as floating point computations occurring in the analyzed software. As the autonomy of critical systems continues to increase—as evidenced by autonomous cars, drones, and satellites and landers—the numerical functions in these systems are growing ever more advanced. The techniques presented here are essential to support the formal analysis of the controller software being used in these new and emerging technologies.

A handbook to the Coq software for writing and checking mathematical proofs, with a practical engineering focus. The technology of mechanized program verification can play a supporting role in many kinds of research projects in computer science, and related tools for formal proof-checking are seeing increasing adoption in mathematics and engineering. This book provides an introduction to the Coq software for writing and checking mathematical proofs. It takes a practical engineering focus throughout, emphasizing techniques that will help users to build, understand, and maintain large Coq developments and minimize the cost of code change over time. Two topics, rarely discussed elsewhere, are covered in detail: effective dependently typed programming (making productive use of a feature at the heart of the Coq system) and construction of domain-specific proof tactics. Almost every subject covered is also relevant to interactive computer theorem proving in general, not just program verification, demonstrated through examples of verified programs applied in many different sorts of formalizations. The book develops a unique automated proof style and applies it throughout; even experienced Coq users may benefit from reading about basic Coq concepts from this novel perspective. The book also offers a library of tactics, or programs that find proofs, designed for use with examples in the book. Readers will acquire the necessary skills to reimplement these tactics in other settings by the end of the book. All of the code appearing in the book is freely available online.

This text aims to provide an introduction to graph algorithms and data structures and an understanding of the basic properties of a broad range of fundamental graph algorithms. It is suitable for anyone with some basic programming concepts. It covers graph properties and types, graph search, directed graphs, minimal spanning trees, shortest paths, and networks.

Software programs are formal entities with precise meanings independent of their programmers, so the transition from ideas to programs necessarily involves a formalisation at some point. The first part of this graduate-level introduction to formal methods develops an understanding of what constitutes formal methods and what their place is in Software Engineering. It also introduces logics as languages to describe reasoning and the process algebra CSP as a language to represent behaviours. The second part offers specification and testing methods for formal development of software, based on the modelling languages CASL and UML. The third part takes the reader into the application domains of normative documents, human machine interfaces, and security. Use of notations and formalisms is uniform throughout the book. Topics and features: Explains foundations, and introduces specification, verification, and testing methods Explores various application domains Presents realistic and practical examples, illustrating concepts Brings together contributions from highly experienced educators and researchers Offers modelling and analysis methods for formal development of software Suitable for graduate and undergraduate courses in software engineering, this uniquely practical textbook will also be of value to students in informatics, as well as to scientists and practical engineers, who want to learn about or work more effectively with formal theories and methods. Markus Roggenbach is a Professor in the Dept. of Computer Science of Swansea University. Antonio Cerone is an Associate Professor in the Dept. of Computer Science of Nazarbayev University, Nur-Sultan. Bernd-Holger Schlingloff is a Professor in the Institut für Informatik of Humboldt-Universität zu Berlin. Gerardo Schneider is a Professor in the Dept. of Computer Science and Engineering of University of Gothenburg. Siraj Ahmed Shaikh is a Professor in the Institute for Future Transport and Cities of Coventry University. The companion site for the book offers additional resources, including further material for selected chapters, prepared lab classes, a list of errata, slides and teaching material, and virtual machines with preinstalled tools and resources for hands-on experience with examples from the book. The URL is: https://sefm-book.github.io

In any serious engineering discipline, it would be unthinkable to construct a large system without having a precise notion of what is to be built and without verifying how the system is expected to function. Software engineering is no different in this respect. Formal methods involve the use of mathematical notation and calculus in software development; such methods are difficult to apply to large-scale systems with practical constraints (e.g., limited developer skills, time and budget restrictions, changing requirements). Here Liu claims that formal engineering methods may bridge this gap. He advocates the incorporation of mathematical notation into the software engineering process, thus substantially improving the rigor, comprehensibility and effectiveness of the methods commonly used in industry. This book provides an introduction to the SOFL (Structured Object-Oriented Formal Language) method that was designed and industry-tested by the author. Written in a style suitable for lecture courses or for use by professionals, there are numerous exercises and a significant real-world case study, so the readers are provided with all the knowledge and examples needed to successfully apply the method in their own projects.

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.

This Festschrift was published in honor of Egon Börger on the occasion of his 75th birthday. It acknowledges Prof. Börger's inspiration as a scientist, author, mentor, and community organizer. Dedicated to a pioneer in the fields of logic and computer science, Egon Börger's research interests are unusual in scope, from programming languages to hardware architectures, software architectures, control systems, workflow and interaction patterns, business processes, web applications, and concurrent systems. The 18 invited contributions in this volume are by leading researchers in the areas of software engineering, programming languages, business information systems, and computer science logic.