[kmill]

Just to clarify, continuations don't have a snapshot of the whole heap, and they can be thought of as being a snapshot of just the interpreter state for a particular execution thread (roughly the call stack and source position). If heap objects are modified between creating a continuation and calling it, then the continuation will see the modified versions of all those objects. When it comes to garbage collection, continuations keep any objects referred to in their saved call stack alive. This is similar to any other closure, but instead of keeping things alive according to lexical scope, this is more of a dynamic scope thing (it's based on whatever functions happened to call this one).

Persisting a continuation seems like it's similarly as challenging as persisting an arbitrary closure. Like usual there are things you can't really persist, for example in your call stack you might have some unwind handlers for closing files -- how do you persist file handles?