Semantic subtyping: Dealing set-theoretically with function, union, intersection, and negation types

Subtyping relations are usually defined either syntactically by a formal system or semantically by an interpretation of types into an untyped denotational model. This work shows how to define a subtyping relation semantically in the presence of Boolean connectives, functional types and dynamic dispatch on types, without the complexity of denotational models, and how to derive a complete subtyping algorithm.