Shematization of infinite sets of rewrite rules. Applications to the divergence of completion processes
Résumé
Infinite sets of rewrite rules may be generated by completion of term rewriting systems or by a narrowing process for solving equations in equational theories. This is a severe limitation to the practical use of these processes. We propose in this paper a formalism to deal with the problem of divergence, namely the definition of melta-rules (rules with meta-variables), together with the derived notions of met-rewriting and meta-narrowing. We show how to use meta-rules for deciding the validity or satisfiability of an equation in the equational theory defined by the infinite set of rules. We define a sound and complete schematization of the infinite set of rules to ensure that the set of meta-rules and the infinite set of rules can be used equivalently.