Denotational and Operational Preciseness of Subtyping: A Roadmap

Dedicated to Frank de Boer on the Occasion of His 60th Birthday
  • Mariangiola Dezani-Ciancaglini
  • Silvia Ghilezan
  • Svetlana Jakšić
  • Jovanka Pantović
  • Nobuko Yoshida
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9660)


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.


Operational Soundness Characteristic Context Union Type Reduction Rule Characteristic Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Mariangiola Dezani-Ciancaglini
    • 1
  • Silvia Ghilezan
    • 2
  • Svetlana Jakšić
    • 2
  • Jovanka Pantović
    • 2
  • Nobuko Yoshida
    • 3
  1. 1.Università di TorinoTurinItaly
  2. 2.Univerzitet u Novom SaduNovi SadSerbia
  3. 3.Imperial College LondonLondonUK

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