A Core Calculus for Mixin-Types

The programming construct mixin was invented to implement modules that provide the mechanism of abstracting uniform extensions and modifications to superclasses. One approach to implement a mixin is to parameterize a superclass of a generic class using a type parameter; however, this approach lacks the ability to declare a mixin that is also used as a type. In this paper, we propose a programming language McJava, an extension of Java that is equipped with mixin-types, a mechanism to declare a mixin that is also used as a type. Then, we develop Core McJava, a core language for McJava, and show its type soundness theorem. This core language is based on Featherweight Java (FJ), a minimum core calculus for Java. FJ is a very small subset of Java. Focusing on a few key issues, we have developed a flexible subtyping relation among mixin compositions.