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Overloaded functions and methods with multiple dispatch are useful for extending the functionality of existing classes in an objectoriented language. However, such functions introduce the possibility of ambiguous calls that cannot be resolved at run time, and modular static checking that such ambiguity does not exist has proved elusive in the presence of multiple implementation inheritance. We present a core language for defining overloaded functions and methods that supports multiple dispatch and multiple inheritance, together with a set of restrictions on these definitions that can be statically and modularly checked. We have proved that these restrictions guarantee that no undefined nor ambiguous calls occur at run time, while still permitting various kinds of overloading.

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