Computational Soundness and Adequacy for Typed Object Calculus

By giving a translation from typed object calculus into Plotkin’s FPC, we demonstrate that every computationally sound and adequate model of FPC (with eager operational semantics), is also a sound and adequate model of typed object calculus. This establishes that denotational equality is contained in operational equivalence, i.e. that for any such model of typed object calculus, if two terms have equal denotations, then no program (or rather program context) can distinguish between those two terms. Hence we show that FPC models can be used in the study of program transformations (program algebra) for typed object calculus. Our treatment is based on self-application interpretation and subtyping is not considered. The typed object calculus under consideration is a variation of Abadi and Cardelli’s first-order calculus with sum and product types, recursive types, and the usual method update and method invocation in a form where the object types have assimilated the recursive types. As an additional result, we prove subject reduction for this calculus.