Polymorphic Rewriting Conserves Algebraic Strong Normalization and Confluence

We study combinations of many-sorted algebraic term rewriting systems and polymorphic lambda term rewriting. Algebraic and lambda terms are mixed by adding the symbols of the algebraic signature to the polymorphic lambda calculus, as higher-order constants. We show that if a many-sorted algebraic rewrite system R is strongly normalizing (terminating, noetherian), then R + β + η + type-β + type-η rewriting of mixed terms is also strongly normalizing. We obtain this results using a technique which generalizes Girard's "candidats de reductibilité", introduced in the original proof of strong normalization for the polymorphic lambda calculus. We also show that if a many-sorted algebraic rewrite system R has the Church-Rosser property (is confluent), then R + β + type-β + type-η rewriting of mixed terms has the ChurchRosser property too. Combining the two results, we conclude that if R is canonical (complete) on algebraic terms, then R + β + type-β + type-η is canonical on mixed terms. η reduction does not commute with a1gebraic reduction, in general. However, using long βnormal forms, we show that if R is canonical then R + β + η + type-β + type-η convertibility is still decidable. Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-89-27. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/782 POLYMORPHIC REWRITING CONSERVES ALGEBRAIC STRONG NORMALIZATION AND CONFLUENCE Val Breazu-Tannen and Jean Gallier MS-CIS-89-27 LOGIC & COMPUTATION 06 Department of Computer and Information Science School of Engineering and Applied Science University of Pennsylvania Philadelphia, PA 19104