A Mechanized Model of the Theory of Objects

In this paper we present a formalization of Abadi's and Cardelli's theory of ob jects in the interactive theorem prover Isabelle/HOL. Our motivation is to build a mechanized HOL-framework for the analysis of a functional calculus for distributed ob jects. In particular, we present (a) a formal model of ob jects and its operational semantics based on de Bruijn indices (b) a parallel reduction relation for ob jects (c) the proof of confluence for the theory of ob jects reusing Nipkow's HOL-framework for the lambda calculus. We expect this framework to be highly reusable and allow further development and mechanized proofs of various aspects of ob ject theory, e.g., distribution, aspect orientation, typing.