A Recipe for Raw Types

The design of GJ (Bracha, Odersky, Stoutamire and Wadler), an extension of Java with parametric polymorphism, was significantly affected by the issue of compatibility between legacy Java code and new GJ code. In particular, the introduction of raw types made it easier to interface polymorphic code with monomorphic code. In GJ, for example, a polymorphic class List, parameterized by the element type X, provides not only parameterized types such as List or List but also the raw type List; then, a Java class using List can be compiled without adding element types to where List is used. Raw types, therefore, can reduce (or defer, at least) programmers’ burden of modifying their old Java code to match with new polymorphic code. From the type-theoretic point of view, raw types are close to existential types in the sense that clients using a raw type C expect some implementation of a polymorphic class of the same name C. Unlike ordinary existential types, however, raw types allow several unsafe operations such as coercion from the raw type List, whose element type is abstract, to List for any concrete type T. In this paper, basing on Featherweight GJ, proposed by the authors as a tiny core language of GJ, we formalize a type system and direct reduction semantics of raw types. The bottom type, which is subtype of any type, plays a key role in our type-preserving reduction semantics. In the course of the work, we have found a flaw in the typing rules from the GJ specification; type soundness is proved with respect to a repaired version of the type system.