Polymorphic Rewriting Conserves Algebraic Strong Normalization

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-η rewriting of mixed terms is also strongly normalizing. The result is obtained using a technique which generalizes Girard's "candidats de reductibilité", introduced in the original proof of strong normalization for the polymorphic lambda calculus.