# Fundamental Proof Methods in Computer Science: A Computer-Based Approach

## Book Description

**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.

### Table of Contents

Part I Introduction

Chapter 1 An Overview Of Fundamental Proof Methods

Chapter 2 Introduction To Athena

Part II Fundamental Proof Methods

Chapter 3 Proving Equalities

Chapter 4 Sentential Logic

Chapter 5 First-Order Logic

Chapter 6 Implication Chaining

Part III Proofs About Fundamental Datatypes

Chapter 7 Organizing Theory Development With Athena Modules

Chapter 8 Natural Number Orderings

Chapter 9 Integer Representations And Proof Mappings

Chapter 10 Fundamental Discrete Structures

Part IV Proofs About Algorithms

Chapter 11 A Binary Search Algorithm

Chapter 12 A Fast Exponentiation Algorithm

Chapter 13 Euclidâ€™S Algorithm For Greatest Common Divisors

Part V Proofs At An Abstract Level

Chapter 14 Abstract Structures

Chapter 15 Abstract Algorithms

Chapter 16 Algorithms On Memory Abstractions

Part VI Proofs About Programming Languages

Chapter 17 A Correctness Proof For A Toy Compiler

Chapter 18 A Simple Imperative Programming Language

Appendix A Athena Reference

Appendix B Logic Programming And Prolog

Appendix C Pizza, Recursion, And Induction

Appendix D Automated Theorem Proving

Appendix E Solutions To Selected Exercises

## Book Details

- Title: Fundamental Proof Methods in Computer Science: A Computer-Based Approach
- Author: David Musser, Konstantine Arkoudas
- Length: 976 pages
- Edition: 1
- Language: English
- Publisher: The MIT Press
- Publication Date: 2017-05-05
- ISBN-10: 0262035537
- ISBN-13: 9780262035538

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