A theory of higher-order subtyping with type intervals

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

Type Inference and Subtyping for Higher-Order Generative Communication

Models for generative communication use a common space, where concurrent agents put or retrieve data; data extraction is controlled by various kinds of filtering techniques, usually based on the structure of the data itself. However, for higher-order communication, i.e. when the data consists of software fragments, such techniques are not appropriate: structural information does not reflect the...

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...

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...