We propose and study coercive subtyping, a formal extension with subtyping of dependent type theories such as Martin-LL of's type theory NPS90] and the type theory UTT Luo94]. In this approach, subtyping with speciied implicit coercions is treated as a feature at the level of the logical framework; in particular, subsumption and coercion are combined in such a way that the meaning of an object ...

Behavioural typing and subtyping has proved to be a very useful concept for the support of incremental reuse in the area of object-oriented (O-O) languages. With the emergence of formalisms integrating the O-O approach and concurrency, the question arises how behavioural subtyping may be supported by such formalisms. We present a formal framework for the definition of behavioural subtyping in O...

Usually subtyping relations are defined either syntactically by a formal system or semantically by an interpretation of types in an untyped denotational model. In this work we show how to define a subtyping relation semantically, for a language whose operational semantics is driven by types; we consider a rich type algebra, with product, arrow, recursive, intersection, union and complement type...

F is a typed λ-calculus with subtyping and bounded polymorphism. Typechecking for F is known to be undecidable, because the subtyping relation on types is undecidable. Fμ is an extension of F with recursive types. In this paper, we show how symbolic labelled transition system techniques from concurrency theory can be used to reason about subtyping for Fμ . We provide a symbolic labelled transit...

There is a great divide between the study of the foundations of object-oriented languages and the practice of mainstream object-oriented languages like JAVA[AG98] and C++[Str97]. One of the most striking examples of this divide is the rôle that class inheritance plays in defining subtyping relations. In most foundational descriptions of OO languages, and in the language designs that these studi...

Nominal and structural subtyping each have their own strengths and weaknesses. Nominal subtyping allows programmers to explicitly express design intent, and, when types are associated with run time tags, enables run-time type tests and external method dispatch. On the other hand, structural subtyping is flexible and compositional, allowing unanticipated reuse. To date, nearly all object-oriente...

Subtyping relations for the π-calculus are usually de-fined in a syntactic way, by means of structural rules. Wepropose a semantic characterisation of channel types anduse it to derive a subtyping relation.The type system we consider includes read-only andwrite-only channel types, as well as boolean combinationsof types. A set-theoretic interpretation of types is pro...

Subtyping of union types can be fairly complex due to interactions with function and pair types. Furthermore, this interaction turns out to depend on the calculus considered: for instance, a call-by-value calculus and a call-by-name calculus will have different possible subtyping rules. In order to abstract ourselves away from this dependence, we consider a fairly large family of calculi. We de...

We propose and study coercive subtyping, a formal extension with subtyping of dependent type theories such as Martin-LL of's type theory 38] and the type theory UTT 30]. In this approach, subtyping with speciied implicit coercions is treated as a feature at the level of the logical framework; in particular, the meaning of an object being in a supertype is given by coercive deenition rules for t...