In the expression (call/cc (lambda (k) (k 12))), there are three continuations: (k 12), (lambda (k) (k 12)), and (call/cc (lambda (k) (k 12))). Which one is the "current continuation"?
And continuations in some books are viewed as a procedure which is waiting for a value and it will return immediately when it's applied to a value. Is that right?
Can anyone explain what current continuations are in detail?
Things like (k 12) are not continuations. There is a continuation associated with each subexpression in some larger program. So for example, the continuation of x in (* 3 (+ x 42)) is (lambda (_) (* 3 (+ _ 42))).
In your example, the "current continuation" of (call/cc (lambda (k) (k 12))) would be whatever is surrounding that expression. If you just typed it into a scheme prompt, there is nothing surrounding it, so the "current continuation" is simply (lambda (_) _). If you typed something like (* 3 (+ (call/cc (lambda (k) (k 12))) 42)), then the continuation is (lambda (_) (* 3 (+ _ 42))).
Note that the lambdas I used to represent the "current continuation" are not the same as what call/cc passes in (named k in your example). k has a special control effect of aborting the rest of the computation after evaluating the current continuation.