A textbook that teaches students to read and write proofs using Athena.
Proof is the primary vehicle for knowledge generation in mathematics. In computer science, proof has found an additional use: verifying that a particular system (or component, or algorithm) has certain desirable properties. This book teaches students how to read and write proofs using Athena, a freely downloadable computer language. Athena proofs are machine-checkable and written in an intuitive natural-deduction style. The book contains more than 300 exercises, most with full solutions. By putting proofs into practice, it demonstrates the fundamental role of logic and proof in computer science as no other existing text does. Guided by examples and exercises, students are quickly immersed in the most useful high-level proof methods, including equational reasoning, several forms of induction, case analysis, proof by contradiction, and abstraction/specialization. The book includes auxiliary material on SAT and SMT solving, automated theorem proving, and logic programming.
The book can be used by upper undergraduate or graduate computer science students with a basic level of programming and mathematical experience. Professional programmers, practitioners of formal methods, and researchers in logic-related branches of computer science will find it a valuable reference.
Konstantine Arkoudas is a Senior Research Scientist and Software Architect at Bloomberg.
David Musser is Professor Emeritus of Computer Science at Rensselaer Polytechnic Institute.
This book serves as both an encyclopedic manual of proof tools and techniques, and as a well-written inspirational manifesto explaining why it is important to think about and work with proofs.
Fundamental Proof Methods in Computer Science is well thought out and carefully written. The text introduces formal notation from the outset, and employs it throughout the presentation. No other book that I know of brings with it the formalism necessary for mechanized logic processing. This is a significant contribution to the teaching of applications of formal logic in problems relevant to computer science.
Rex Page, Professor Emeritus, School of Computer Science, University of Oklahoma, coauthor of Discrete Mathematics Using a Computer
Working through the exercises in the book will help programmers think rigorously about their code. While learning Athena and going through hundreds of problems is a difficult task, it will lead not only to more correct code, but will help programmers to decompose the code into coherent subcomponents. My professional life would have been easier if this book was available when I was young.
Alexander Stepanov, coauthor of Elements of Programming and From Mathematics to Generic Programming
Fundamental Proof Methods in Computer Science…is a positively marvelous book, one symbiotically united with the long-standing Athena environment, by our lights among the best mechanical proof assistants available at this time, especially when proof pedagogy is a requirement for such an assistant.