Fundamental Proof Methods in Computer Science: A Computer-Based Approach
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.
Praise for Fundamental Proof Methods in Computer Science: A Computer-Based Approach
"[A] positively marvelous book. [ . . . ] Athena is by our lights the best mechanical proof assistant available at this time. [ . . . ] For those determined to teach or learn how to produce substantive proofs in the 21st century and beyond, FPMICS is peerless,and gradually digesting it, with Athena at one’s side along the way, will produce in the learner a deep understanding of proof in the context of both computer science and artificial intelligence 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.”—Selmer Bringsjord and Naveen Sundar Govindarajulu for Theory and Practice of Logic Programming
"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
"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 be able to think about and work with proofs."
―Peter Norvig, Director of Research, Google