Teach Yourself Scheme: 13.1 call-with-current-continuation

The operator call-with-current-continuation calls its argument, which must be a unary procedure, with a value called the ``current continuation''. If nothing else, this explains the name of the operator. But it is a long name, and is often abbreviated call/cc.⁴

The current continuation at any point in the execution of a program is an abstraction of the rest of the program. Thus in the program

(+ 1 (call/cc
       (lambda (k)
         (+ 2 (k 3)))))

the rest of the program, from the point of view of the call/cc-application, is the following program-with-a-hole (with representing the hole):

(+ 1 )

In other words, this continuation is a program that will add 1 to whatever is used to fill its hole.

This is what the argument of call/cc is called with. Remember that the argument of call/cc is the procedure

(lambda (k)
  (+ 2 (k 3)))

This procedure's body applies the continuation (bound now to the parameter k) to the argument 3. This is when the unusual aspect of the continuation springs to the fore. The continuation call abruptly abandons its own computation and replaces it with the rest of the program saved in k! In other words, the part of the procedure involving the addition of 2 is jettisoned, and k's argument 3 is sent directly to the program-with-the-hole:

(+ 1 )

The program now running is simply

(+ 1 3)

which returns 4. In sum,

(+ 1 (call/cc
       (lambda (k)
         (+ 2 (k 3)))))
=> 4

The above illustrates what is called an escaping continuation, one used to exit out of a computation (here: the (+ 2 ) computation). This is a useful property, but Scheme's continuations can also be used to return to previously abandoned contexts, and indeed to invoke them many times. The ``rest of the program'' enshrined in a continuation is available whenever and how many ever times we choose to recall it, and this is what contributes to the great and sometimes confusing versatility of call/cc. As a quick example, type the following at the listener:

(define r #f)

(+ 1 (call/cc
       (lambda (k)
         (set! r k)
         (+ 2 (k 3)))))
=> 4

The latter expression returns 4 as before. The difference between this use of call/cc and the previous example is that here we also store the continuation k in a global variable r.

Now we have a permanent record of the continuation in r. If we call it on a number, it will return that number incremented by 1:

(r 5)
=> 6

Note that r will abandon its own continuation, which is better illustrated by embedding the call to r inside some context:

(+ 3 (r 5))
=> 6

The continuations provided by call/cc are thus abortive continuations.

⁴ If your Scheme does not already have this abbreviation, include (define call/cc call-with-current-continuation) in your initialization code and protect yourself from RSI.

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