The disclosed embodiments provide a system that facilitates the development and execution of a software program. During runtime of the software program, the system obtains a function call associated with an overloaded function and a generic type hierarchy that lacks contravariance. Next, the system determines an applicability of an implementation of the overloaded function to the function call. Finally, the system selects the implementation for invocation by the function call based on the determined applicability and a partial order of implementations for the overloaded function.