Equivalence Between the CPS Hierarchy and Monads

Establish whether a definitive equivalence exists between the continuation‑passing style (CPS) hierarchy and monads, and precisely characterize the correspondence if it holds.

Background

The paper systematically exploits iterated CPS (including answer‑type modification and a second continuation for failure) and comonad‑enriched continuations to design invertible format descriptors. This naturally raises the broader theoretical question of how CPS levels relate to monads, especially in light of the need for constructs resembling multiple‑result monads to reconcile context sensitivity with tuple‑trouble‑free composition.

Referring to prior work speculating on such an equivalence, the authors explicitly note that this question remains unresolved decades later, motivating a formal clarification of the relationship.