[edit, I wrote this before you changed your comment so say "one-shot". In short my continuations are not one shot, they are delimited though, by necessity because I don't rewrite ALL functions into continuation passing style, and you can't recast what lua calls metafunctions.]

Continuations are not coroutines.

Continuations let you save the current position, like setjump/longjump. But unlike setjump/longjump you can continue inside a function that already returned, ie as long as there is a continuation remembering that position then the activation record can't be deleted.

That means that activation records (ie local variables) can't be just the top of the stack - it changes things deep.

Also note that continuations only save the position, they don't restore the values of variables to what they were at that position, so re-evaluating continuation more than once will break any code that wasn't expecting to re-run.

Something that snapshots some local variables as well as the position will be more useful than raw continuations for things like search, backtracking, and logical programming languages.

[edit 2, I am ALSO adding snapshot continuations for these purposes]

Running an OUTER continuation rather than an inner one looks like an exception.