Using methods drawn from Game Semantics, we build a sound and computationally adequate model of a simple calculus that includes both subtyping and recursive types. Our model solves recursive type equations up to equality, and is shown to validate a subtyping rule for recursive types proposed by Amadio and Cardelli.

We investigated a multistate cluster of Escherichia coli O157:H7 isolates; pulsed-field gel electrophoresis subtyping, using a single enzyme, suggested an epidemiologic association. An investigation and additional subtyping, however, did not support the association. Confirmating E. coli O157 clusters with two or more restriction endonucleases is necessary before public health resources are allo...

CDuce is a functional programming language featuring overloaded functions and a rich type system with recursive types, subtyping, union, negation and intersection types. The boolean constructors have a set-theoretic behaviour defined via a semantic interpretation of the types. The Cπ-calculus is an extension of the π-calculus that enriches Pierce and Sangiorgi π-calculus subtyping with union, i...

We show that the first-order theory of structural subtyping of non-recursive types is decidable. Let Σ be a language consisting of function symbols (representing type constructors) and C a decidable structure in the relational language L containing a binary relation ≤. C represents primitive types; ≤ represents a subtype ordering. We introduce the notion of Σ-term-power of C, which generalizes ...

We present a calculus with dependent types, subtyping and late-bound overloading. Besides its theoretical interest this work is motivated by several practical needs that range from the definition of logic encodings, to proof specialization and reuse, and to object-oriented extension of the SML module system. The theoretical study of this calculus is not straightforward. While confluence is rela...

While developing their software, professional object-oriented (OO) software developers keep in their minds an image of the subtyping relation between types in their software. The goal of this paper is to present an observation about the graph of the subtyping relation in Java, namely the observation that, after the addition of generics—and of wildcards, in particular—to Java, the graph of the s...

To reason about the correctness of a method when cross-type aliases are possible, one must not only consider all possible patterns of aliasing among the method’s arguments, but all possible ways in which these types’ abstract (specification-only) fields may be aliased. Because of the large number of such aliasing possibilities, and because of the complications they cause for reasoning, cross-ty...

Solving systems of subtype constraints (or subtype inequalities) is in the core of eecient type reconstruction in modern object-oriented languages with subtyping and inheritance, two problems known polynomial time equivalent. It is important to know how diierent combinations of type constructors innuence the complexity of the problem. We show the NP-hardness of the satissability problem for sub...