Yves Caseau

Efficient handling of multiple inheritance hierarchies

Dealing with multiple inheritance hierarchies is a problem both for designers of compilers for object-oriented languages supporting multiple inheritance and for users who have to model complex hierarchical data with languages where classes are not first-class objects (such as C++). We propose here two techniques that yield a new way of encoding a multiple inheritance hierarchy. We first give a proven algorithm to incrementally transform any hierarchy into a lattice. We then develop a technique, called compact hierarchical encoding, which provides constant time for subsumption between two nodes of the lattice, using the codes as a representation of the associated order (transitive closure). The encoding builds a lattice mapping to a powerset inclusion lattice and can thus be implemented efficiently using bit-vectors. It offers an interesting alternative to the modulation technique proposed by [ABL89], because it produces more compact encoding on complex hierarchies that are frequent in object-oriented applications.

Attaching Second-Order Types to Methods in an Object-Oriented Language

This paper proposes an extension of the notion of method as it is currently used in most object-oriented languages. We define polymethods as methods that we can attach directly to types, as opposed to classes and that we can describe with a second-order type. Two benefits result from this extension; first, the expressive power of the language is improved with better modeling abilities. Next, second-order types yield a more powerful (precise) type inference, which extends the range of static type checking in a truly extensible object-oriented language. We first show that extensible object-oriented languages present many difficulties for static type-checking and that second-order types are necessary to get stronger type-checking. We illustrate how to combine polymethods through type inheritance and propose a technique based on abstract interpretation to derive a second-order type for new polymethods.