New Definition of the Subtype Relation

摘要

The use of hierarchy is an important component of object-oriented design.Hierarchy allows the use of type families, in which higher level supertypes capture the behavior that all of their subtypes have in common. For this methodology to be effective, it is necessary to have a clear understanding of how subtypes and supertypes are related. This paper presents a new definition of the subtype relation that ensures that any property proved about supertype objects also holds for subtype objects. It also discusses the ramifications of the definition on the design of type families.