Formalizing Implementation Strategies for First-Class Continuations

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    Abstract

    We present the first formalization of implementation strategies for first-class continuations. The formalization hinges on abstract machines for continuation-passing style (CPS) programs with a special treatment for the current continuation, accounting for the essence of first-class continuations. These abstract machines are proven equivalent to a standard, substitution-based abstract machine. The proof techniques work uniformly for various representations of continuations. As a byproduct, we also present a formal proof of the two folklore theorems that one continuation identifier is enough for second-class continuations and that second-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 provides a uniform setting for specifying and formalizing their representation.
    Original languageEnglish
    Book seriesB R I C S Report Series
    IssueRS-99-51
    Number of pages16
    ISSN0909-0878
    Publication statusPublished - 1999

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