Precise Inference of Polymorphic Constrained Types

This paper develops a precise polymorphic type inference algorithm. Several methods for polymorphic type inference have been developed, including let-polymorphism and flow-based approaches such as Agesen’s Cartesian Product Algorithm (CPA). In this paper we focus on the flow-based variety. There is a class of polymorphic behavior which CPA misses: so-called data polymorphism. In the context of imperative object-oriented languages such as Java, data polymorphism is in fact quite common. This paper develops a new extension to CPA, DCPA, which improves on CPA by accurately and efficiently analyzing data polymorphic programs. We develop DCPA in a type-constraint-based setting, prove its type-soundness, and implement the algorithm for the full Java language to test its feasibility in practice. Our test implementation is used to statically verify the correctness of Java downcasts. Initial benchmark results are given which show the algorithm has considerable promise, both in terms of precision and efficiency.