Special relations in automated deduction
Journal of the ACM (JACM) - The MIT Press scientific computation series
A computational logic handbook
A computational logic handbook
Functional instantiation in first-order logic
Artificial intelligence and mathematical theory of computation
Computer-Aided Reasoning: An Approach
Computer-Aided Reasoning: An Approach
Structured Theory Development for a Mechanized Logic
Journal of Automated Reasoning
Parameterized congruences in ACL2
ACL2 '06 Proceedings of the sixth international workshop on the ACL2 theorem prover and its applications
Double rewriting for equivalential reasoning in ACL2
ACL2 '06 Proceedings of the sixth international workshop on the ACL2 theorem prover and its applications
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
Theorem Proving with the Real Numbers
Theorem Proving with the Real Numbers
A Formalization of Powerlist Algebra in ACL2
Journal of Automated Reasoning
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Traditionally, a conditional rewrite rule directs replacement of one term by another term that is provably equal to it, perhaps under some hypotheses. This paper generalizes the notion of rewrite rule to permit the connecting relation to be merely an equivalence relation. We then extend the algorithm for applying rewrite rules. Applications of these generalized rewrite rules are only admissible in certain equivalential contexts, so the algorithm tracks which equivalence relations are to be preserved and admissible generalized rewrite rules are selected according to this context. We introduce the notions of congruence rule and refinement rule. We also introduce the idea of generated equivalences, corresponding to a new equivalence relation generated by a set of pre-existing ones. Generated equivalences are used to give the rewriter broad access to admissible generalized rewrite rules. We discuss the implementation of these notions in the ACL2 theorem prover. However, the discussion does not assume familiarity with ACL2, and these ideas can be applied to other reasoning systems as well.