MultiJava is a conservative extension of the Java programming language that adds symmetric multiple dispatch and open classes. Among other benefits, multiple dispatch provides a solution to the binary method problem. Open classes provide a solution to the extensibility problem of object-oriented programming languages, allowing the modular addition of both new types and new operations to an existing type hierarchy. This article illustrates and motivates the design of MultiJava and describes its modular static typechecking and modular compilation strategies. Although MultiJava extends Java, the key ideas of the language design are applicable to other object-oriented languages, such as C # and C++, and even, with some modifications, to functional languages such as ML. This article also discusses the variety of application domains in which MultiJava has been successfully used by others, including pervasive computing, graphical user interfaces, and compilers.

For a number of programming languages, among them Eiffel, C, Java, and Ruby, Hoare-style logics and dynamic logics have been developed. In these logics, pre- and postconditions are typically formulated using potentially effectful programs. In order to ensure that these pre- and postconditions behave like logical formulae (that is, enjoy some kind of referential transparency), a notion of purity is needed. Here, we introduce a generic framework for reasoning about purity and effects. Effects are modelled abstractly and axiomatically, using Moggi’s idea of encapsulation of effects as monads. We introduce a dynamic logic (from which, as usual, a Hoare logic can be derived) whose logical formulae are pure programs in a strong sense. We formulate a set of proof rules for this logic, and prove it to be complete with respect to a categorical semantics. Using dynamic logic, we then develop a relaxed notion of purity which allows for observationally neutral effects such writing on newly allocated memory.