Separating stages in the continuation-passing style transformation

Abstract

The continuation-passing style (CPS) transformation is powerful but complex. Our thesis is that this transformation is in fact compound, and we set out to stage it. We factor the CPS transformation into several steps, separating aspects in each step: (1) Intermediate values are named; (2) Continuations are introduced; (3) Sequencing order is decided and administrative reductions are performed.Step 1 determines the evaluation order (e.g., call-by-name or call-by-value). Step 2 isolates the introduction of continuations and is expressed with local, structure-preserving rewrite rules — a novel aspect standing in sharp contrast with the usual CPS transformations. Step 3 determines the ordering of continuations (e.g., left-to-right or right-to-left evaluation) and leads to the familiar-looking continuation-passing terms.Step 2 is completely reversible and Steps 1 and 3 form Galois connections. Together they lead to the direct style (DS) transformation of our earlier work (including first-class continuations): (1) Intermediate continuations are named and sequencing order is abstracted; (2) Second-class continuations are eliminated; (3) Administrative reductions are performed.A subset of these transformations can leverage program manipulation systems: CPS-based compilers can modify sequencing to improve e.g., register allocation; static program analyzers can yield more precise results; and overspecified CPS programs can be rescheduled. Separating aspects of the CPS transformation also enables a new programming style, with applications to nondeterministic programming. As a byproduct, our work also suggests a new continuation semantics for unspecified sequencing orders in programming languages (e.g., Scheme).