Relating Semantic Models for the Object Calculus

Abadi and Cardelli have investigated several versions of the c-calculus, a calculus for describing central features of object-oriented programs, with particular emphasis on various type systems. In this paper we study the properties of a denotational semantics due to Abadi and Cardelli vis-a-vis the notion of observational congruence for the calculus Ob 1 . In particular, we prove that the denotational semantics based on partial equivalence relations is correct with respect to observational congruence. By means of a counter-example, we argue that the denotational model is not fully abstract with respect to observational congruence. In fact, the model is able to distinguish objects that have the same behaviour in every Ob 1 -context.