Abstract

The intersection type discipline (ITD) is well-established for the Lambda Calculus (LC) and the functional programming paradigm. It has also been extended to Term Rewriting Systems (TRS) and more recently to object calculi and sequent calculi. We continue this trend by applying the techniques of ITD to the analysis of the (class based) object-oriented (OO) programming paradigm: specifically, we study a small core calculus for Java which is a restriction of Featherweight Java by removing casts. Our main contribution is an approximation result for this programming model, demonstrating a direct correspondence between types and the functional behaviour of programs. This opens the possibility for type-based abstract interpretation and termination analysis for OO. We achieve this result by defining a notion of reduction on type derivations that is strongly normalising, a technique which has also been used for LC and TRS. Finally, we show how the approximation result facilitates a type-based characterisation of (weak) normalisation and termination. We also discuss the relationship between our calculus and TRS, highlighting how our result extends previous work in this area.

Citations