Abstract types defined as classes of variables

The concept of “type” has been used without a precise definition in discussions about programming languages for 20 years. Before the concept of user defined data types was introduced, a definition was not necessary for discussions of specific programming languages. The meaning of the term was implicit in the small list of possible types supported by the language. There was even enough similarity between different languages so that this form of definition allowed discussions of languages in general. The need for a widely accepted definition of type became clear in discussions of languages that allow users to add to the set of possible types without altering the compiler. In such languages, the concept of type is no longer implicitly defined by the set of built-in types. A consistent language must be based on a clearer definition of the notion of type than we now have.