Progress in Theoretical Computer Science

Canonical Equational Proofs

Authors: Bachmair

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About this book

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.

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Buy this book

eBook $69.99 net
( price for USA )
  • ISBN 978-1-4684-7118-2
  • digitally watermarked, no DRM
  • included format: PDF
  • eBooks can be used on all Reading Devices
Softcover $99.00 net
( price for USA )
  • ISBN 978-0-8176-3555-8
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days

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Bibliographic Information

Bibliographic Information
Book Title
Canonical Equational Proofs
Series Title
Progress in Theoretical Computer Science
Copyright
1991
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-1-4684-7118-2
DOI
10.1007/978-1-4684-7118-2
Softcover ISBN
978-0-8176-3555-8
Edition Number
1
Topics