Erik Meijer - Contravariance is the Dual of Covariance Implies Iterable is the Dual of Observable (Making Money Using Math)

Every developer that has ever dealt with contra- and covariance in a modern OO language with generics, shivers with fear when they have to deal with these concepts in their code (except of course in Dart language, where all generic types are covariant).

Typically the solution is to click, click, click, click on the “suggested fix” by the IDE until the error messages finally go away. To add insult to injury, all this panic is for nothing since typically at runtime all generics are erased anyway, so all thus type torture really didn’t matter in the end (except in .NET where generics is reified). However, fear no more!

In this talk we will provide trauma recovery therapy for victims of variance by explaining the concepts from first principles using real world examples such as vending machines and garbage cans. For additional fun, we will throw in some good old imperative side-effects and show how the simplest possible covariant type of getters ()=>T and the simplest contra-variant type of setters T=>() are essentially the same as Iterator[+T] and Observer[-T].

Add a pinch of self-application on top of that, and we discover that Iterable[+T] boils down to Iterator[Iterator[T]] = ()=>(()=>T) and Observable[+T] boils down to Observer[Observer[T]] = (T=>())=>(). Lambdas all the way down, and all arrows reversed.

In case you wondered why Scala uses +T for covariance and -T for contravariance, and why a contravariant type in a contravariant position becomes a covariant type, well, that is all part of the magic of the Curry-Howard isomorphism, but we’ll have to leave that for another talk. The most amazing thing of all however is that companies like Netflix are powered by this exact duality in the form of RxJava. And after this talk, you too will know how to make money using math.