Higher-order subtyping

AbstractSystem F⩽ω is an extension with subtyping of the higher-order polymorphic λ-calculus —an orthogonal combination of Girard's system Fω with Cardelli and Wegner's Kernel Fun variant of System F⩽. We develop the fundamental metatheory of this calculus: decidability of β-conversion on well-kinded types, elimination of the “cut-rule” of transitivity from the subtype relation, and the soundness, completeness, and termination of algorithms for subtyping and typechecking