SUMMARY
We present the first formalization of implementation strategies for first-class continuations. The formalization hinges on abstractmachines for continuation-passing style (CPS) programs with a specialtreatment for the current continuation, accounting for the essence offirst-class continuations. These abstract machines are proven equivalentto a standard, substitution-based abstract machine. The proof techniqueswork uniformly for various representations of continuations. As a byproduct, we also present a formal proof of the two folklore theorems that onecontinuation identifier is enough for second-class continuations and thatsecond-class continuations are stackable.A large body of work exists on implementing continuations, but it is predominantly empirical and implementation-oriented. In contrast, our formalization abstracts the essence of first-class continuations and providesa uniform setting for specifying and formalizing their representation.