Interpretations of Extensible Objects and Types

We present a type-theoretic encoding of extensible objects and types. The ambient theory is a higher-order-calculus with poly-morphic types, recursive types and operators, and subtyping. Using this theory, we give a type preserving and computationally adequate translation of a full-edged object calculus that includes object extension and override. The translation specializes to calculi of nonextensible objects and validates the expected subtyping relationships.