Higher-order subtyping

Decidable Higher Order Subtyping

This paper establishes the decidability of typechecking in Fω ∧ , a typed lambda calculus combining higher-order polymorphism, subtyping, and intersection types. It contains the first proof of decidability of subtyping for a higher-order system.

Polarized higher-order subtyping

Anti-symmetry of higher-order subtyping and equality by subtyping

This paper gives the first proof that the subtyping relation of a higherorder lambda calculus, F ≤, is anti-symmetric, establishing in the process that the subtyping relation is a partial order—reflexive, transitive, and anti-symmetric up to β-equality. While a subtyping relation is reflexive and transitive by definition, anti-symmetry is a derived property. The result, which may seem obvious t...

Typed operational semantics for higher-order subtyping

Bounded operator abstraction is a language construct relevant to object oriented programming languages and to ML2000, the successor to Standard ML. In this paper, we introduce Fω ≤, a variant of Fω <: with this feature and with Cardelli and Wegner’s kernel Fun rule for quantifiers. We define a typed operational semantics with subtyping and prove that it is equivalent with Fω ≤, using a Kripke m...

Syntactic Metatheory of Higher-Order Subtyping

We present a new proof of decidability of higher-order subtyping in the presence of bounded quantification. The algorithm is formulated as a judgement which operates on beta-eta-normal forms. Transitivity and closure under application are proven directly and syntactically, without the need for a model construction or reasoning on longest beta-reduction sequences. The main technical tool is here...