Programming language semantics and closed applicative languages

This paper proposes axioms to define a sequence of language-classes; the most general is that of "programming language", the most restricted has some simple and attractive properties. Here "language" is used in its traditional sense as referring to a set of interpreted expressions. We are concerned with the syntax of an expression only to the degree needed to relate its structure to its "meaning". A clear distinction is drawn between a "language" and the many possible "realizations" of that language.