Subtyping in Java is a Fractal

TL;DR

This paper observes that the subtyping relation in Java and similar OO languages with generics and wildcards forms a fractal pattern, complicating mental models but potentially aiding developers with better tools and understanding.

Contribution

It introduces the novel fractal perspective of the subtyping relation in Java and other OO languages with generics, enhancing understanding and tooling for developers.

Findings

Subtyping graphs become fractals after adding generics and wildcards.

This fractal shape applies to Java, C#, C++, and Scala.

The fractal model can improve IDE support and developer intuition.

Abstract

While developing their software, professional object-oriented (OO) software developers keep in their minds an image of the subtyping relation between types in their software. The goal of this paper is to present an observation about the graph of the subtyping relation in Java, namely the observation that, after the addition of generics---and of wildcards, in particular---to Java, the graph of the subtyping relation is no longer a simple directed-acyclic graph (DAG), as in pre-generics Java, but is rather a fractal. Further, this observation equally applies to other mainstream nominally-typed OO languages (such as C#, C++ and Scala) where generics and wildcards (or some other form of 'variance annotations') are standard features. Accordingly, the shape of the subtyping relation in these OO languages is more complex than a tree or a simple DAG, and indeed is also a fractal. Given the popularity of fractals, the fractal observation may help OO software developers keep a useful and intuitive mental image of their software's subtyping relation, even if it is a little more frightening, and more amazing one than before. With proper support from IDEs, the fractal observation can help OO developers in resolving type errors they may find in their code in lesser time, and with more confidence.