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Abstract
We present the first formalization of implementation strategies<br /> for first-class continuations. The formalization hinges on abstract<br />machines for continuation-passing style (CPS) programs with a special<br />treatment for the current continuation, accounting for the essence of<br />first-class continuations. These abstract machines are proven equivalent<br />to a standard, substitution-based abstract machine. The proof techniques<br />work uniformly for various representations of continuations. As a byproduct<br />, we also present a formal proof of the two folklore theorems that one<br />continuation identifier is enough for second-class continuations and that<br />second-class continuations are stackable.<br />A large body of work exists on implementing continuations, but it is <br />predominantly empirical and implementation-oriented. In contrast, our <br />formalization abstracts the essence of first-class continuations and provides<br />a uniform setting for specifying and formalizing their representation.
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