The text begins by analyzing existing object-oriented languages, paying special attention to their type systems and impediments to expressiveness. It then examines two key features: subtypes and subclasses. After a brief introduction to the lambda calculus, it presents a prototypical object-oriented language, SOOL, with a simple type system similar to those of class-based object-oriented languages in common use. The text offers proof that the type system is sound by showing that the semantics preserves typing information. It concludes with a discussion of desirable features, such as parametric polymorphism and a MyType construct, that are not yet included in most statically typed object-oriented languages. Copyright (C) Muze Inc. 2005. For personal use only. All rights reserved.