Shostak's Congruence Closure as Completion
نویسنده
چکیده
Shostak's congruence closure algorithm is demystiied, using the framework of ground completion on (possibly nonterminating, non-reduced) rewrite rules. In particular, the canonical rewriting relation induced by the algorithm on ground terms by a given set of ground equations is precisely constructed. The main idea is to extend the signature of the original input to include new constant symbols for nonconstant subterms appearing in the input. A byproduct of this approach is (i) an algorithm for associating a connuent rewriting system with possibly nonterminating ground rewrite rules, and (ii) a new quadratic algorithm for computing a canonical rewriting system from ground equations.
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