Difunctorial Semantics of Object Calculus

Authors:
Johan Glimming;Neil Ghani
Affiliations:
Department of Numerical Analysis and Computer Science, Stockholm University, Sweden;Department of Mathematics and Computer Science, University of Leicester, United Kingdom
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2005

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Abstract

In this paper we give a denotational model for Abadi and Cardelli's first order object calculus FOb"1"+"x"@m (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.