I'm thinking a less formally than that. Protocol in a very layman-y "perform is supposed to do this, resume is supposed to do this".

For example, Koka compiles handlers differently depending if they do multi-shot continuations or not. It can do this because all that matters is "perform is supposed to do this, resume is supposed to do this", not what they turn into (same as "if" turning into "cmov" in certain cases). I think it uses a continuation-passing style sort of implementation, but I can't quite remember.

Daan's libhandler implements effects for C in an entirely different manner. It captures the stack much like my example or a stackful coroutine library would.

I'm sure there a formal definitions in both the koka papers and the libhandler paper, but I just skim that stuff ;)