The Calculus of Inductive Constructions (CIC) is a powerful type system, featuring dependent types and inductive deenitions, that forms the basis of proof-assistant systems such as Coq and Lego. We extend CIC with constructor subtyping, a basic form of subtyping in which an inductive type is viewed as a subtype of another inductive type if has more elements than. It is shown that the calculus i...

The most prominent proposals of subtyping for asynchronous session types are by Mostrous and Yoshida for binary sessions, by Chen et al. for binary sessions under the assumption that every message emitted is eventually consumed, and by Mostrous et al. for multiparty session types. We prove that, differently from what stated or conjectured in above proposals, all of these three subtyping relatio...

Object-oriented software development is characterized by the repeated reenement of spec-iications and software components. The reenement of speciications is facilitated by the use of speciication languages which support subtyping based on the principle of substi-tutability. In this paper we propose to specify concurrent systems by types represented as expressions of a process calculus. These ty...

We present a statically typed, class-based object oriented language where classes are first class polymorphic values. A main contribution of this work is the design of a type system that combines first class polymorphic values with structural equirecursive types and admits a subtyping algorithm which is arguably much simpler than existing alternatives. Our development is modular and can be easi...

Subtyping judgments of the polymorphic second-order typed-calculus F extended by recursive types and diierent known inference rules for these types could be interpreted in S2S, M.Rabin's monadic second-order theory of two successor functions. On the one hand, this provides a comprehensible model of the parametric and inheritance polymorphisms over recursive types, on the other, proves that the ...

Algorithms for checking subtyping between recursive types lie at the core of many programming language implementations. But the fundamental theory of these algorithms and how they relate to simpler declarative speci cations is not widely understood, due in part to the di culty of the available introductions to the area. This tutorial paper o ers an \end-to-end" introduction to recursive types a...

Subtyping is an important feature of semantic approaches to conceptual schema design and, more recently, object-oriented database design. However the relational model does not directly support subtyping, and CASE tools for mapping conceptual to relational schemas typically provide only very weak support for mapping subtypes. This paper surveys some of the main issues related to conceptual speci...

We deene an extension of a second-order type system with records, subtyping and record concatenation. This system can model the most important concepts of object-oriented languages. The novelty in our approach is that concatenation is only permitted if the types on common elds agree. We give examples of how object-oriented concepts can be modeled and show how the system can be translated to a t...

In this report, a number of completeness results are given that are useful for database integration on the schema level and the instance level. Type equivalence and subtyping are proven sound and complete w.r.t. a model-theoretic semantics. Furthermore, a set of type transformations is introduced that is proven sound and complete w.r.t. data capacity. These completeness results imply that if da...

We extend the Abadi-Cardelli calculus of primitive objects with object extension. We enrich object types with a more precise, uniform, and exible type structure. This enables to type object extension under both width and depth subtyping. Objects may also have extend-only or virtual contra-variant methods and read-only co-variant methods. The resulting subtyping relation is richer, and types of ...