currently, when I am experimenting the continuation in functional languages, my understanding is that a continuation records the current program counter and register files, and when a continuation is returned, then the PC and the registered files will be restored to the values it has recorded.
So in the following dumb example from Might's blog post,
; right-now : -> moment
(define (right-now)
(call-with-current-continuation
(lambda (cc)
(cc cc))))
; go-when : moment -> ...
(define (go-when then)
(then then))
; An infinite loop:
(let ((the-beginning (right-now)))
(display "Hello, world!")
(newline)
(go-when the-beginning)) ; here the-beginning continuation passed to go-when, which ultimately will have an continuation applied to an continuation, that returns a continuation, which will cause the the program point resumed to the PC and registers states recorded in it.
I am not sure my understanding right.. Please correct me if you think it is not.....
Program counter and register files are not what the continuation records.
The best way to describe the meaning of call-with-current-continuation is that it records the program context. For instance, suppose you're evaluating the program
(+ 3 (f (call-with-current-continuation g)))
In this case, the context of the call-with-current-continuation expression would be
(+ 3 (f [hole]))
That is, the stuff surrounding the current expression.
Call-with-current-continuation captures one of these contexts. Invoking a continuation causes the replacement of the current context with the one stored in the continuation.
The idea of a context is a lot like that of a stack, except that there's nothing special about function calls in contexts.
This is a very brief treatment. I strongly urge you to take a look at Shriram Krishnamurthi's (free, online) book PLAI, in particular Part VII, for a more detailed and careful look at this topic.