Lambda the Ultimate

Multiple Dispatch as Dispatch on Tuples, by Gary T. Leavens and Todd D. Millstein:

Many popular object-oriented programming languages, such as C++, Smalltalk-80, Java, and Eiffel, do not support multiple dispatch. Yet without multiple dispatch, programmers find it difficult to express binary methods and design patterns such as the "visitor" pattern. We describe a new, simple, and orthogonal way to add multimethods to single-dispatch object-oriented languages, without affecting existing code. The new mechanism also clarifies many differences between single and multiple dispatch.

Multimethods and multiple dispatch has been discussed numerous times here on LtU. While the theory has been fully fleshed out to the point of supporting full-fledged type systems for multiple dispatch, there has always remained a conceptual disconnect between multimethods and the OO model, namely that methods are supposed to be messages sends to objects with privileged access to that object's internal state. Multimethods would seem to violate encapsulation inherent to objects, and don't fit with the conceptual messaging model.

This paper goes some way to solving that disconnect, as multiple dispatch is simply single dispatch on a distinct, primitive class type which is predicated on N other class types and thus supporting N-ary dispatch. This multiple dispatch support can also be retrofitted to an existing single-dispatch languages without violating its existing dispatch model.