Subtyping and Inheritance for Inductive Types

Inheritance and subtyping are key features of object-oriented languages. We show that there are corresponding (or, more precisely, dual) notions for inductive or algebraic datatypes: there is a natural notion of subtyping for these types and an associated form of code reuse (inheritance) for programs on these types. Inheritance and subtyping for inductive types not only suggest possible extensions of functional programming languages, but also provide a new perspective on inheritance as we know it from object-oriented languages, which may help in getting a better understanding of this notion.