Covariance and Controvariance: a fresh look at an old issue (a primer in advanced type systems for learning functional programmers)

摘要

Twenty years ago, in an article titled "Covariance and contravariance:conflict without a cause", I argued that covariant and contravariantspecialization of method parameters in object-oriented programming haddifferent purposes and deduced that, not only they could, but actually theyshould both coexist in the same language. In this work I reexamine the result of that article in the light of recentadvances in (sub-)typing theory and programming languages, taking a fresh lookat this old issue. Actually, the revamping of this problem is just an excuse for writing anessay that aims at explaining sophisticated type-theoretic concepts, in simpleterms and by examples, to undergraduate computer science students and/orwilling functional programmers. Finally, I took advantage of this opportunity to describe some undocumentedadvanced techniques of type-systems implementation that are known only to fewinsiders that dug in the code of some compilers: therefore, even expertlanguage designers and implementers may find this work worth of reading.