Property Types: Semantic Programming for Java

Dependent types have been proposed for functional programming languages as a means of expressing semantically rich properties as types. In this paper, we consider the problem of bringing semantic programming based on dependent types to an object-oriented language. A type-theoretically light extension to Java (with generics) is proposed, called property types. These are types indexed not by other types (as in Java with generics) but by immutable expressions. We consider programming with two examples of property types: a property type HasFactors〈long x,Set a〉, expressing that the elements of a are the multiplicative prime factors of x; and a property type Sorted〈List l〉, expressing that l is sorted.