On the static and dynamic extents of delimited continuations

We show that breadth-first traversal exploits the difference between the static delimited-control operator shift (alias image) and the dynamic delimited-control operator control (alias image). For the last 15 years, this difference has been repeatedly mentioned in the literature but it has only been illustrated with one-line toy examples. Breadth-first traversal fills this vacuum. We also point out where static delimited continuations naturally give rise to the notion of control stack whereas dynamic delimited continuations can be made to account for a notion of ‘control queue’.