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

@article{Frisch2008SemanticSD,
  title={Semantic subtyping: Dealing set-theoretically with function, union, intersection, and negation types},
  author={Alain Frisch and Giuseppe Castagna and V{\'e}ronique Benzaken},
  journal={J. ACM},
  year={2008},
  volume={55},
  pages={19:1-19:64}
}
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. 

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