  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
\emph{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 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 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 a clear and deep account for the
relation between nominal and structural OO type systems that has 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.
