A Comparison of NOOP to Structural Domain-Theoretic Models of OOP

TL;DR

This paper compares the NOOP domain-theoretic model of object-oriented programming, which includes nominal type information, with structural models, providing a mathematical understanding of their differences.

Contribution

It offers a detailed comparison between NOOP and existing structural models, clarifying the relationship between nominal and structural OO type systems.

Findings

NOOP incorporates full nominal type information.

The comparison reveals precise mathematical relations between models.

Clarifies the distinction between nominal and structural typing in OOP.

Abstract

Mainstream object-oriented programming languages such as Java, C#, C++ and Scala are all almost entirely nominally-typed. NOOP is a recently developed domain-theoretic model of OOP that was designed to include full nominal information found in nominally-typed OOP. This paper compares NOOP to the most widely known domain-theoretic models of OOP, namely, the models developed by Cardelli and Cook, which were structurally-typed models. Leveraging the development of NOOP, the comparison presented in this paper provides a clear and precise mathematical account for the relation between nominal and structural OO type systems.