Rewriting modulo a Rewrite System Universit a Degli Studi Di Pisa Dipartimento Di Informatica Rewriting modulo a Rewrite System

We introduce rewriting with two sets of rules, the rst interpreted equationally and the second not. A semantic view considers equational rules as deening an equational theory and reduction rules as deening a rewrite relation modulo this theory. An operational view considers both sets of rules as similar. We introduce suucient properties for these two views to be equivalent (up to diierent notions of equivalence). The paper ends with a collection of example showing the eeectiveness of this approach. Abstract. We introduce rewriting with two sets of rules, the rst interpreted equationally and the second not. A semantic view considers equational rules as deening an equational theory and reduction rules as deening a rewrite relation modulo this theory. An operational view considers both sets of rules as similar. We introduce suucient properties for these two views to be equivalent (up to diierent notions of equivalence). The paper ends with a collection of example showing the eeectiveness of this approach.