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

Twenty years ago, in an article titled "Covariance and contravariance: conflict without a cause", I argued that covariant and contravariant specialization of method parameters in object-oriented programming had different purposes and deduced that, not only they could, but actually they should both coexist in the same language. In this work I reexamine the result of that article in the light of recent advances in (sub-)typing theory and programming languages, taking a fresh look at this old issue. Actually, the revamping of this problem is just an excuse for writing an essay that aims at explaining sophisticated type-theoretic concepts, in simple terms and by examples, to undergraduate computer science students and/or willing functional programmers. Finally, I took advantage of this opportunity to describe some undocumented advanced techniques of type-systems implementation that are known only to few insiders that dug in the code of some compilers: therefore, even expert language designers and implementers may find this work worth of reading

Set-theoretic foundation of parametric polymorphism and subtyping

International audienc

Building a Typed Scripting Language

Since the 1990s, scripting languages (e.g. Python, Ruby, JavaScript, and many others) have gained widespread popularity. Features such as ad-hoc data manipulation, dynamic structural typing, and terse syntax permit rapid engineering and improve developer productivity. Unfortunately, programs written in scripting languages execute slower and are less scalable than those written in traditional languages (such as C or Java) due to the challenge of statically analyzing scripting languages' semantics. Although various research projects have made progress on this front, corner cases in the semantics of existing scripting languages continue to defy static analysis and software engineers must generally still choose between program performance and programmer performance when selecting a language. We address that dichotomy in this dissertation by designing a scripting language with the intent of statically analyzing it. We select a set of core primitives in which common language features such as object-orientation and case analysis can be encoded and give a sound and decidable type inference system for it. Our type theory is based on subtype constraint systems but is also closely related to abstract interpretation; we use this connection to guide development of the type system and to employ a novel type soundness proof strategy based on simulation. At the heart of our approach is a type indexed record we call the onion which supports asymmetric concatenation and dispatch; we use onions to formally encode a variety of features, including records, operator overloading, objects, and mixins. An optimistic call-site polymorphism model defined herein captures the ad-hoc, case-analysis-based reasoning often used in scripting languages. Although the language in this dissertation uses a particular set of core primitives, the strategy we use to design it is general: we demonstrate a simple, formulaic process for adding features such as integers and state