Revisiting the CPS Transformation and its Implementation

We give a machine-checked definition and proof of semantic correctness for Danvy and Filinski’s properly tail-recursive, one-pass, call-by-value CPS transformation. We do so in the setting of the pure λ -calculus extended with a let construct. We propose a new first-order, one-pass, compositional formulation of the transformation. We point out that Danvy and Filinski’s simulation diagram does not hold in the presence of let, and prove a slightly more complex diagram, which involves parallel reduction. We represent variables as de Bruijn indices and show that, given the current state of the art, this does not represent a significant impediment to formalization. Finally, we note that, given this representation of terms, it is not obvious how to efficiently implement the transformation. To address this issue, we propose a novel higher-order formulation of the transformation. We prove that it is correct and informally argue that it runs in time O(n logn).