Subtyping + Extensionality: Confluence of beta-eta-top reduction in F<=

We contribute to the syntactic study of F≤, a variant of second order λ-calculus F which appears as a paradigmatic kernel language for polymorphism and subtyping. The type system of F≤ has a maximum type Top and bounded quantification. We endow this language with the familiar β-rules (for terms and types), to which we add extensionality rules: the η-rules (for terms and types), and a rule (top) which equates all terms of type Top. These rules are suggested by the axiomatization of cartesian closed categories. We show that this theory βηtop≤ is decidable, by exhibiting an effectively weakly normalizing and confluent rewriting system for it. Our proof of confluence relies on the confluence of a corresponding system on F1 (the extension of F with a terminal type), and follows a general pattern that we investigate for itself in a separate paper.