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π-calculus, Session Types research at Imperial College

Denotational and Operational Preciseness of Subtyping: A Roadmap
Mariangiola DEZANI-CIANCAGLINI , Silvia GHILEZAN , Svetlana JAKSIC , Jovanka PANTOVIC , Nobuko YOSHIDA
Theory and Practice of Formal Methods: Essays Dedicated to Frank de Boer on the Occasion of His 60th Birthday (Theory and Practice of Formal Methods) p. 155 - 172

The notion of subtyping has gained an important role both in theoretical and applicative domains: in lambda and concurrent calculi as well as in object-oriented programming languages. The soundness and the completeness, together referred to as the preciseness of subtyping, can be considered from two different points of view: denotational and operational. The former preciseness is based on the denotation of a type, which is a mathematical object describing the meaning of the type in accordance with the denotations of other expressions from the language. The latter preciseness has been recently developed with respect to type safety, i.e. the safe replacement of a term of a smaller type when a term of a bigger type is expected.

The present paper shows that standard proofs of operational preciseness imply denotational preciseness and gives an overview on this subject.

@inproceedings{DGJPY2016,
  author = {Mariangiola Dezani-Ciancaglini and Silvia Ghilezan and Svetlana Jaksic and Jovanka Pantovic and Nobuko Yoshida},
  title = {{Denotational and Operational Preciseness of Subtyping: A Roadmap}},
  booktitle = {Theory and Practice of Formal Methods: Essays Dedicated to Frank de Boer on the Occasion of His 60th Birthday},
  series = {LNCS},
  volume = {9660},
  pages = {155--172},
  publisher = {Springer},
  year = 2016
}
@inproceedings{DGJPY2016,
  author = {Mariangiola Dezani-Ciancaglini and Silvia Ghilezan and Svetlana Jaksic and Jovanka Pantovic and Nobuko Yoshida},
  title = {{Denotational and Operational Preciseness of Subtyping: A Roadmap}},
  booktitle = {Theory and Practice of Formal Methods: Essays Dedicated to Frank de Boer on the Occasion of His 60th Birthday},
  series = {LNCS},
  volume = {9660},
  pages = {155--172},
  publisher = {Springer},
  doi = "10.1007/978-3-319-30734-3_12",
  year = 2016
}