Infinite Values in Hierarchical Imperative Types

Abstract

A system of hierarchical imperative types is extended to allow infinite values. The general structure of value assignments to types in the context of a hierarchy is considered, and it is shown that a smallest and largest such exist. A method for obtaining intermediate value assignments is investigated, and a general characterization of the infinite values allowable in programming languages is presented. Finally, the set of rational values is demonstrated to be appropriate for our imperative hierarchy. Programs can then work on infinite imperative data structures which are allocated lazily during execution.