Abstract
We adopt the untyped imperative object calculus of Abadi and<br />Cardelli as a minimal setting in which to study problems of compilation<br />and program equivalence that arise when compiling object oriented<br />languages. We present both a big-step and a small-step<br />substitution-based operational semantics for the calculus. Our first<br />two results are theorems asserting the equivalence of our substitution based semantics with a closure-based semantics like that given by Abadi and Cardelli. Our third result is a direct proof of the correctness of compilation to a stack-based abstract machine via a small-step decompilation algorithm. Our fourth result is that contextual equivalence of objects coincides with a form of Mason and Talcott's CIU<br />equivalence; the latter provides a tractable means of establishing operational equivalences. Finally, we prove correct an algorithm, used in<br />our prototype compiler, for statically resolving method offsets. This is<br />the first study of correctness of an object-oriented abstract machine,<br />and of operational equivalence for the imperative object calculus.
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