A logical view of types

Abstract

People working in the areas of data abstraction, databases, and conceptual modeling have argued at considerable length over the meanings of such terms as “abstraction” and “type.”* Rather than add to this debate by offering yet another set of definitions, in the paragraphs below we shall attempt to show how ordinary predicate calculus can be used to talk about most (perhaps all) the notions for which the terms “abstraction” and “type” are currently being used in various quarters of computer science. We do not intend to argue that predicate calculus is a suitable tool for implementing types, but rather that it provides a well-understood, uniform conceptual framework and notation for describing and precisely comparing various ideas on typing—and that special notations developed for this purpose are therefore unnecessary.