Types as Intervals

Abstract

To accommodate polymorphic data types and operations, several computer scientists--most notably MacQueen, Plotkin, and Sethi--have proposed formalizing types as ideals. Although this approach is intuitively appealing, the resulting type system is both complex and restrictive because the type constructor that creates function types is not monotonic, and hence not computable. As a result, types cannot be treated as data values, precluding the formalization of type constructors and polymorphic program modules (where types are values) as higher order computable functions. Moreover, recursive definitions of new types do not necessarily have solutions.