A Lambda Calculus of Objects and Method Specialization

This paper presents an untyped lambda calculus, extended with object primitives that reflect the capabilities of so-called delegation-based object-oriented languages. A type inference system allows static detection of errors, such as message not understood, while at the same time allowing the type of an inherited method to be specialized to the type of the inheriting object. Type soundness, in the form of a `subject-reduction' theorem, is proved and examples illustrating the expressiveness of the pure calculus are presented.