An Overview of Nominal-Typing versus Structural-Typing in OOP

TL;DR

This paper compares nominal and structural typing in object-oriented programming, emphasizing the mathematical modeling of nominality and subtyping, and contrasting these concepts with their structural counterparts.

Contribution

It provides a detailed overview of nominal and structural typing notions in OOP, highlighting their differences through formal definitions and illustrative examples.

Findings

NOOP model formalizes inheritance and subtyping in nominal OOP

Contrasts between nominal and structural typing clarified

Appendix illustrates concepts with code examples

Abstract

NOOP is a mathematical model of nominally-typed OOP that proves the identification of inheritance and subtyping in mainstream nominally-typed OO programming languages and the validity of this identification. This report gives an overview of the main notions in OOP relevant to constructing a mathematical model of OOP such as NOOP. The emphasis in this report is on defining nominality, nominal typing and nominal subtyping of mainstream nominally-typed OO languages, and on contrasting the three notions with their counterparts in structurally-typed OO languages, i.e., with structurality, structural typing and structural subtyping, respectively. An additional appendix demonstrates these notions and other related notions, and the differences between them, using some simple code examples. A detailed, more technical comparison between nominal typing and structural typing in OOP is presented in other publications.