Canonical Equational Proofs

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.

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