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 continuationpassing terms. Step 2 is completely reversible and Steps 1 and 3 form Galois connections. Together they leading to the direct style (DS) transformation of our earlier work (including first...

Citations