Java Integers

Abstract

Specification languages typically offer idealistic data types that are not available in programming languages. For example, the integer data types available in the specification languages UML/OCL, Z, B, and Java Card DL (which can also be seen as a specification language) are isomorphic to the mathematical integers ℤ having an infinite domain. On the other hand, the built-in integer types in Java and many other programming languages have finite domains. As a consequence the semantics of data types on specification and implementation level differ (at least on the boundaries of the domain).

In this section we clarify the quite subtle relation between integer data types in Java Card DL and Java. It turns out that the Java integers are not a refinement of the type integer in Java Card DL but a so-called retrenchment which constitutes a generalisation of refinement. Note, that the problems and solutions given in this section are not restricted to Java Card DL and Java. They analogously apply to other specification languages like e.g., UML/OCL, Z and B and to several programming languages like e.g., C and C++.

This section may also serve as a lightweight introduction to refinement and retrenchment (for a more detailed and systematic introduction we recommend [Derrick and Boiten, 2001] and [Banach and Poppleton, 1998], respectively). This section is based on material published in [Beckert and Schlager, 2004, 2005, Schlager, 2002].