Typing Classes and Mixins with Intersection Types
This work addresses type safety for mixins in languages like Java and C#, offering a solution without recursive or F-bounded types, but it is incremental as it builds on existing intersection type systems.
The authors tackled the problem of typing classes and mixins in object-oriented programming by developing an intersection type system for a lambda-calculus with records, which preserves types under reduction and expansion, and adapted this to Java and C# without requiring new language features.
We study an assignment system of intersection types for a lambda-calculus with records and a record-merge operator, where types are preserved both under subject reduction and expansion. The calculus is expressive enough to naturally represent mixins as functions over recursively defined classes, whose fixed points, the objects, are recursive records. In spite of the double recursion that is involved in their definition, classes and mixins can be meaningfully typed without resorting to neither recursive nor F-bounded polymorphic types. We then adapt mixin construct and composition to Java and C#, relying solely on existing features in such a way that the resulting code remains typable in the respective type systems. We exhibit some example code, and study its typings in the intersection type system via interpretation into the lambda-calculus with records we have proposed.