11 - The Four Classes of Rules Generated from Lemmas

Abstract

This chapter discusses the four classes of rules generated from lemmas. The four classes of rules are REWRITE, META, ELIM, and GENERALIZE. REWRITE rules are by far the most common, the most useful, and the most complicated kind of rule used by the system. The kind of REWRITE rule generated from a given formula depends on the syntactic form of the formula. One treats the submitted formula as a conjunction and generates a rule for each of the conjuncts. If a given conjunct cannot be encoded as a type prescription, one tries to generate a compound recognizer rule. If that fails, one tries to generate a linear arithmetic rule. If that fails, one tries to generate a replacement rule. Sometimes, it is impossible to generate any rule for a conjunct and this is reported. Despite the priorities, almost all REWRITE rules are replacement rules. Replacement rules are the most common form of REWRITE rules. They permit the rewriter to simplify the terms by replacing subterms with equivalent ones.