Novel Uses of Category Theory in Modeling OOP

TL;DR

This paper explores four innovative ways to apply category theory concepts to model various aspects of object-oriented programming, offering a new mathematical perspective on OOP structures.

Contribution

It introduces four novel applications of category theory to model key OOP features like subtyping, generics, structural typing, and type erasure.

Findings

Operads effectively model Java subtyping.

Yoneda's lemma aids in representing generic types.

Adjoint functors provide a framework for Java erasure.

Abstract

An outline and summary of four new potential applications of category theory to OOP research are presented. These include (1) the use of operads to model Java subtyping, (2) the use of Yoneda's lemma and representable functors in the modeling of generic types in generic nominally-typed OOP, (3) using a combination of category presentations and cartesian closed categories to model structurally-typed OOP, and (4) the use of adjoint functors to model Java erasure.