A lambda calculus of objects with self-inflicted extension

In this paper we investigate, in the context of functional prototype-based languages, objects which might extend themselves upon receiving a message. The possibility for an object of extending its own "self", referred to by Cardelli, as a self-inflicted operation, is novel in the context of typed object-based languages. We present a sound type system for this calculus which guarantees that evaluating a well-typed expression will never yield a message-not-found runtime error. We give several examples which illustrate the increased expressive power of our system with respect to existing calculi of objects. The new type system allows also for a flexible width-subtyping, still permitting sound method override, and a limited form of object extension. The resulting calculus appears to be a good starting point for a rigorous mathematical analysis of class-based languages.