In object-oriented languages, overloaded methods with multiple dispatch extend the functionality of existing classes, and multiple inheritance allows a class to reuse code in multiple classes. However, both multiple dispatch and multiple inheritance introduce the possibility of ambiguous method calls that cannot be resolved at run time. To guarantee no ambiguous calls at run time, the overloaded method declarations should be checked statically.
In this paper, we present a core calculus for the Fortress programming language, which provides both multiple dispatch and multiple inheritance. While previous work proposed a set of static rules to guarantee no ambiguous calls at run time, the rules were parametric to the underlying programming language. To implement such rules for a particular language, the rules should be instantiated for the language. Therefore, to concretely realize the overloading rules for Fortress, we formally define a core calculus for Fortress and mechanize the calculus and its type safety proof in