Why Nominal-Typing Matters in Mainstream OOP

The statements ‘inheritance is not subtyping’ and ‘mainstream OO languages unnecessarily place restrictions over inheritance’ have rippled as mantras through the PL research community for years. Many mainstream OO developers and OO language designers, however, do not accept these statements. In nominally-typed OO languages that these developers and language designers are dearly familiar with, inheritance simply is subtyping; and they believe OO type inheritance is an inherently nominal notion, not a structural one. Nominally-typed OO languages, such as Java, C#, C++, and Scala, are among the most used programming languages today. However, the value of nominal typing to mainstream OO developers, as a means for designing robust OO software, seems to be in wait for full appreciation among PL researchers—thereby perpetuating an unnecessary schism between many OO developers and language designers and many OO PL researchers, with each side discounting, if not even disregarding, the views of the other. In this essay we strengthen and complement earlier efforts to demonstrate the semantic value of nominal typing by presenting a technical comparison between nominal OO type systems and structural OO type systems. Recently, a domain-theoretic model of nominally-typed OOP was compared to well-known models of structurally-typed OOP. Combined, these comparisons provide both a clear technical account and a deep mathematical account of the relation between nominal and structural OO type systems that have not been presented before, and they help demonstrate the key value of nominal typing and nominal subtyping to OO developers and language designers. We believe a clearer understanding of the key semantic advantage of pure nominal OO typing over pure structural OO typing can help remedy the existing schism. We believe future foundational OO PL research, to further its relevance to mainstream OOP, should be based less on structural models of OOP and more on nominal ones instead.