Canonical Equational Proofs

By Leo Bachmair and Bachmair

Book Overview

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.

• Format: Paperback
• Language: English
• ISBN: 0817635556
• ISBN13: 9780817635558
• Release Date: June 1991
• Publisher: Birkhauser
• Length: 138 Pages
• Weight: 1.00 lbs.
• Dimensions: 0.3" x 6.1" x 9.2"