We describe the foundations of Obj +a , a framework, or generic calculus, for modeling object-calculi. This framework is essentially a detailed formal operational semantics of object based languages, in the style of the Lambda Calculus of Objects. As a formalism for specication Obj +a is arranged in modules, permitting a natural classication of many object-based calculi according to their features. In particular there are modules for calculi of non-mutable objects (i.e., functional object-calculi) and for calculi of mutable objects (i.e., imperative object-calculi). As a computational formalism Obj +a is based on rewriting rules. Classical rst-order term rewriting systems are not appropriate since we want to reect aspects of implementation practice such as sharing, cycles in data structures and mutation. Therefore we dene the notion of addressed terms, and develop the corresponding notion of addressed term rewriting. CONTENTS 2 Contents 1 Introduction 3 1.1 Ad...