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Canonical equational proofs [electronic resource] / Leo Bachmair.

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Equations occur in many computer applications, such as symbolic compu℗Ư 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...

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Bachmair, Leo
Format: Electronic eBook
Language:English
Published: Boston : Birkhäuser, 1991.
Series:Progress in theoretical computer science.
Subjects:
Rewriting systems (Computer science)
Equations.

MARC

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245 1 0 |a Canonical equational proofs  |h [electronic resource] /  |c Leo Bachmair. 
260 |a Boston :  |b Birkhäuser,  |c 1991. 
300 |a 1 online resource (x, 135 pages) :  |b illustrations. 
336 |a text  |b txt  |2 rdacontent. 
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490 1 |a Progress in theoretical computer science. 
500 |a Based in part on author's thesis (Ph. D.)--University of Illinois at Urbana-Champaign, 1987. 
504 |a Includes bibliographical references (pages 117-127) and index. 
505 0 |a 1 Equational Proofs -- 1.1. Introduction -- 1.2. Terms -- 1.3. Equations -- 1.4. Orderings -- 1.5. Proofs -- 2 Standard Completion -- 2.1. Basic Completion -- 2.2. Proof Transformation -- 2.3. Proof Simplification -- 2.4. Fairness and Correctness -- 2.5. Standard Completion -- 2.6. Critical Pair Criteria -- 3 Extended Completion -- 3.1. Rewriting Modulo a Congruence -- 3.2. The Left-Linear Rule Method -- 3.3. Church-Rosser Systems -- 3.4. Extended Completion -- 3.5. The Extended Rule Method -- 3.6. Associative-Commutative Completion -- 3.7. The Protected Rule Method -- 3.8. Extended Critical Pair Criteria -- 4 Ordered Completion -- 4.1. Ordered Completion -- 4.2. Construction of Convergent Rewrite Systems -- 4.3. Refutational Theorem Proving -- 4.4. Horn Clauses with Equality -- 5 Proof by Consistency -- 5.1. Consistency and Ground Reducibility -- 5.2. Proof by Consistency -- 5.3. Refutation Completeness -- 5.4. Covering Sets. 
520 |a Equations occur in many computer applications, such as symbolic compu℗Ư 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℗Ư 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℗Ư 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℗Ư struct convergent rewrite systems from non-convergent ones. We develop a proof-theoretic framework for studying completion and related rewrite℗Ư 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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