# Canonical Equational Proofs

• Leo Bachmair
Book

Part of the Progress in Theoretical Computer Science book series (PTCS)

1. Front Matter
Pages i-x
2. Leo Bachmair
Pages 1-11
3. Leo Bachmair
Pages 13-38
4. Leo Bachmair
Pages 39-71
5. Leo Bachmair
Pages 73-98
6. Leo Bachmair
Pages 99-115
7. Back Matter
Pages 117-137

### Introduction

Equations occur in many computer applications, such as symbolic compu­ tation, functional programming, abstract data type specifications, program verification, program synthesis, and automated theorem proving. Rewrite systems are directed equations used to compute by replacing subterms in a given formula by equal terms until a simplest form possible, called a normal form, is obtained. The theory of rewriting is concerned with the compu­ tation of normal forms. We shall study the use of rewrite techniques for reasoning about equations. Reasoning about equations may, for instance, involve deciding whether an equation is a logical consequence of a given set of equational axioms. Convergent rewrite systems are those for which the rewriting process de­ fines unique normal forms. They can be thought of as non-deterministic functional programs and provide reasonably efficient decision procedures for the underlying equational theories. The Knuth-Bendix completion method provides a means of testing for convergence and can often be used to con­ struct convergent rewrite systems from non-convergent ones. We develop a proof-theoretic framework for studying completion and related rewrite­ based proof procedures. We shall view theorem provers as proof transformation procedures, so as to express their essential properties as proof normalization theorems.

### Keywords

equation function proof theorem verification

#### Authors and affiliations

• Leo Bachmair
• 1
1. 1.Department of Computer ScienceState University of New York at Stony BrookStony BrookUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4684-7118-2
• Copyright Information Birkhäuser Boston 1991
• Publisher Name Birkhäuser Boston
• eBook Packages
• Print ISBN 978-0-8176-3555-8
• Online ISBN 978-1-4684-7118-2
• Buy this book on publisher's site