Typed interpretations of extensible objects

Finding typed encodings of object-oriented into procedural or functional programming sheds light on the theoretical foundations of object-oriented languages and their specific typing constructs and techniques. This article describes a type preserving and computationally adequate interpretation of a full-fledged object calculus that supports message passing and constructs for object update and extension. The target theory is a higher-order λ-calculus with records and recursive folds/unfolds, polymorphic and recursive types, and subtyping. The interpretation specializes to calculi of nonextensible objects, and validates the expected subtyping relationships.