Authors: Dezani-Ciancaglini, Mariangiola
Ghilezan, Silvia 
Jakšić, Svetlana
Pantović, Jovanka
Yoshida, Nobuko
Title: Denotational and operational preciseness of subtyping: A roadmap
Journal: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume: 9660
First page: 155
Last page: 172
Conference: Frank de Boer on the Occasion of His 60th Birthday, 2016; Porto; Portugal; 5 July 2016 through 5 July 2016
Issue Date: 1-Jan-2016
Rank: M33
ISBN: 978-3-319-30733-6
ISSN: 0302-9743
DOI: 10.1007/978-3-319-30734-3_12
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.
Publisher: Springer Link
Project: COST IC1201 BETTY, IC1402 ARVI and DART
Representations of logical structures and formal languages and their application in computing 
Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 
EPSRC EP/K011715/1, EP/K034413/1, and EP/L00058X/1

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