Polymorphic Constraint-Based Type Inference for Objects

Constraint-based type inference infers types with subtyping constraints. Such types can capture detailed data and control flow information about the analyzed program. In the presence of polymorphism, existing constraint-based type inference algorithms sacrifice much precision for efficiency. This paper presents both theoretical and practical results on developing precise and efficient polymorphic constraint-based type inference for object-oriented languages. We develop a novel theoretical framework for polymorphic constraint-based type inference. A concrete type inference algorithm can be obtained by instantiating the framework with a particular strategy for handling polymorphism. We define well-known algorithms such as Shivers’ nCFA and Agesen’s Cartesian Product Algorithm (CPA) as instantiations of the framework. We prove the soundness of the framework, which entails the soundness of every algorithm defined as an instantiation of the framework. Using the framework, we develop a novel algorithm, Data Polymorphic CPA (DCPA), which extends Agesen’s CPA Algorithm to achieve high precision in the presence of Data Polymorphism. We further study the construction of practical constraint-based type inference systems for realistic programming languages. We have constructed a type inference system for the full Java language. The system includes implementations of the 0CFA, CPA and DCPA algorithms, and it incorporates a number of novel implementation techniques for achieving scalability. The system is used to statically verify the correctness of Java downcasts. Benchmark results on realistic Java applications show that the DCPA algorithm has good precision and efficiency: it is significantly more accurate than existing algorithms and its efficiency is comparable to CPA.