Higher-order intersection types and multiple inheritance

We study a natural generalization of System F ! with intersection types, establishing basic structural properties and constructing a semantic model based on partial equivalence relations to prove the soundness of typing. As an application of this calculus, we deene a simple typed model of object-oriented programming with multiple inheritance. One of the rst applications of subtyping in-calculi was modeling the reenement of interfaces in object-oriented programming languages Cardelli, 1984]. The formal subtype relation ? ` S T models the assertion that the objects in some collection S provide more services than those in T, so that it is safe to use a member of S in any context where a member of T is expected. Subtyping itself is a straightforward concept, but it took years to build full-scale models of real object-oriented languages on this foundation. Treating the interaction between interface reenement and encapsulation of objects has required higher-order gener-Using these techniques, a number of fairly complete \foundational object models" related to those found in lan-Current work in this area also includes models of the object-oriented features in languages such as CLOS Castagna et al., 1995, Castagna, 1992], which are less closely related to the results described here. The common goal of these studies is to prove the safety of a type system describing a set of high-level syntactic constructs for object encapsulation, message passing, and inheritance. Most proceed either by mapping the high-level syntax directly into a deno-tational model and proving the soundness of this interpretation using standard semantic techniques or by reasoning directly on the operational semantics of the source calculus. Others translate the high-level syntax into a more conventional-calculus, whose own

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