The Cartesian Product Algorithm: Simple and Precise Type Inference Of Parametric Polymorphism

Concrete types and abstract types are different and serve different purposes. Concrete types, the focus of this paper, are essential to support compilation, application delivery, and debugging in object-oriented environments. Concrete types should not be obtained from explicit type declarations because their presence limits polymorphism unacceptably. This leaves us with type inference. Unfortunately, while polymorphism demands the use of type inference, it has also been the hardest challenge for type inference. We review previous type inference algorithms that analyze code with parametric polymorphism and then present a new one: the cartesian product algorithm. It improves precision and efficiency over previous algorithms and deals directly with inheritance, rather than relying on a preprocessor to expand it away. Last, but not least, it is conceptually simple. The cartesian product algorithm has been used in the Self system since late 1993. We present measurements to document its performance and compare it against several previous algorithms.