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

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.