Anti-Symmetry of Higher-Order Subtyping

This paper shows that the subtyping relation of a higher-order lambda calculus, F ! , is anti-symmetric. It exhibits the rst such proof, establishing in the process that the subtyping relation is a partial order| reeexive, transitive and anti-symmetric. While a sub-typing relation is reeexive and transitive by deeni-tion, anti-symmetry is a derived property. The result, which may seem obvious to the non-expert, is technically challenging, and had been an open problem for almost a decade. In this context, typed operational semantics for subtyping ooers a powerful new technology to solve the problem. The paper also gives a presentation of F ! without-equality, apparently the rst such, and shows its equivalence with the traditional presentation.