Canonical Equational Proofs

  • Leo Bachmair

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

Table of contents

  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

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.


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

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