Subtyping for Object Type Constructors

Object type constructors have been introduced as an approach to adding container object types to a language with type inference. Useful subtyping for object type constructors requires a flexible subtype rule for type constructors that is not simply the pointwise extension of subtyping for types. At the same time, subtyping should avoid requiring run-time type checks, as in the Java subtype rule for arrays. An extension of object type constructors is considered to allow this subtyping, extending the kinds of object type constructors with polarities that allow this subtyping without jeopardizing soundness.