Higher-order subtyping and its decidability

Decidability of Higher-Order Subtyping with Intersection Types

The combination of higher-order subtyping with intersection types yields a typed model of object-oriented programming with multiple inheritance 11]. The target calculus, F ! ^ , a natural generalization of Girard's system F ! with intersection types and bounded polymorphism, is of independent interest, and is our subject of study. Our main contribution is the proof that subtyping in F ! ^ is de...

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

Decidability of higher-order matching

We show that the higher-order matching problem is decidable using a game-

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...