Polymorphic Rewriting Conserves Algebraic 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 has the Church-Rosser property (is confluent), then R + β + type-β + type-η rewriting of mixed terms has the Church-Rosser property too. η reduction does not commute with algebraic reduction, in general. However, using long normal forms, we show that if R is canonical (confluent and strongly normalizing) then equational provability from R + β + η + type-β + type-η is still decidable. Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-90-37. Revised: January 1992 This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/565 Polymorphic Rewriting Conserves Algebraic Confluence MS-CIS-90-37 LOGIC & COMPUTATION 21 Val Breazu-Tannen Jean Gallier Department of Computer and Information Science School of Engineering and Applied Science University of Pennsylvania Philadelphia, PA 19104-6389 Revised January 1992 Polymorphic Rewriting Conserves Algebraic Confluence Val BreazuTannen2 Jean Gallie? Department of Computer and Information Science University of Pennsylvania 200 South 33rd St., Philadelphia, PA 19104, USA Abstract. 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-sort.ed algebraic rewrite system R has the Church-Rosser property (is confluent), then R + p + type-B + type-17 rewriting of mixed terms has the Church-Rosser property too. q reduction does not commute with algebraic reduction, in general. However, using long normal forms, we show that if R is canonical (confluent and strongly normalizing) then equational provability from R + /3 + 11 + type-P + type-11 is stJill decidable. 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-sort.ed algebraic rewrite system R has the Church-Rosser property (is confluent), then R + p + type-B + type-17 rewriting of mixed terms has the Church-Rosser property too. q reduction does not commute with algebraic reduction, in general. However, using long normal forms, we show that if R is canonical (confluent and strongly normalizing) then equational provability from R + /3 + 11 + type-P + type-11 is stJill decidable.