Coviarance and Contravariance : Connict without a Cause Covariance and Contravariance: Connict without a Cause

In type theoretic research on object-oriented programming the \covariance versus con-travariance issue" is a topic of continuing debate. In this short note we argue that covari-ance and contravariance appropriately characterize two distinct and independent mechanisms. The so-called contravariance rule correctly captures the substitutivity, or subtyping relation (that establishes which sets of codes can replace in every context another given set). A covariant relation, instead, characterizes the specialization of code (i.e. the deeni-tion of new code that replaces the old one in some particular cases). Therefore, covariance and contravariance are not opposing views, but distinct concepts that each have their place in object-oriented systems and that both can (and should) be type safely integrated in an object-oriented language. We also show that the independence of the two mechanisms is not characteristic of a particular model but is valid in general, since covariant specialization is present also in record-based models, but is hidden by a deeciency of all calculi that realize this model. As an aside, we show that the &-calculus CGL92] can be taken as the basic calculus both for an overloading-based and for a record-based model. In that case, one not only obtains a more uniform vision of object-oriented type theories but, in the case of the record-based approach, one also gains multiple dispatching, which is not captured by the existing record-based models.