This paper presents an imperative object calculus,
designed to support class-based programming via a combination of
extensible objects and encapsulation.  This calculus simplifies the
language presented in Fisher's Thesis in that, like C++ and
Java, it chooses to support an imperative semantics instead of
method specialization.  We show how Java-style classes and ``mixins''
may be coded in this calculus, prove a soundness theorem (via a subject
reduction property), and give a sound and complete typing algorithm.