Difunctorial Semantics of Object Calculus

In this paper we give a denotational model for Abadi and Cardelli’s first order object calculus FOb1+×μ (without subtyping) in the category pCpo. The key novelty of our model is its extensive use of recursively defined types, supporting self-application, to model objects. At a technical level, this entails using some sophisticated techniques such as Freyd’s algebraic compactness to guarantee the existence of the denotations of the object types. The last sections of the paper demonstrates that the canonical recursion operator inherent in our semantics is potentially useful in object-oriented programming. This is witnessed by giving a straightforward translation of algebraic datatypes into so called wrapper classes.