Abstract. We define a small functional calculus that expresses class-based object oriented features and is modelled on the similar calculi of Featherweight Java [34] and Middleweight Java [15], which are ultimately based upon the Java programming language. We define a predicate system, similar to the one defined in [10], and show subject reduction and expansion, and argue that program analysis systems can be built on top of this system. Generalising the concept of approximant from the Lambda Calculus, we show that all expressions that we can assign a predicate to have an approximant that satisfies the same predicate. From this, a characterisation of (head-)normalisation follows. 1

This paper will show the usefulness and elegance of strict intersection types; these are strict in the sense that they are the representatives of equivalence classes of types in the BCD-system [Barendregt et al. 1983]. We will focus on the essential intersection type assignment for the Lambda Calculus; we will briefly compare this with other existing systems. The system is