An imperative formal calculus for Java

This paper presents a formal imperative calculus to formalize the semantics of class-based object-oriented programming languages. The tractability of this approach is demonstrated by our formalization of a core subset of the Java programming language called Cool: Core Object-Oriented Language. Cool is relatively small but retains many of modern class-based object-oriented languages' key features, including classes, inheritance, objects, virtual functions and dynamic method dispatch etc. The technical contribution of this paper can be summarized as: first, this paper formalizes a syntactic specification for Cool; second, this paper presents static semantics for Cool via typing rules, and its operational semantics via small-step transition relation. Finally, this paper proves that the formal calculus proposed is type safe.