How to implement continuations?

A good summary is available in Implementation Strategies for First-Class Continuations, an article by Clinger, Hartheimer, and Ost. I recommend looking at Chez Scheme's implementation in particular.

Stack copying isn't that complex and there are a number of well-understood techniques available to improve performance. Using heap-allocated frames is also fairly simple, but you make a tradeoff of creating overhead for "normal" situation where you aren't using explicit continuations.

If you convert input code to continuation passing style (CPS) then you can get away with eliminating the stack altogether. However, while CPS is elegant it adds another processing step in the front end and requires additional optimization to overcome certain performance implications.

I remember reading an article that may be of help to you: Cheney on the M.T.A. :-)

Some implementations of Scheme I know of, such as SISC, allocate their call frames on the heap.

@ollie: You don't need to do the hoisting if all your call frames are on the heap. There's a tradeoff in performance, of course: the time to hoist, versus the overhead required to allocate all frames on the heap. Maybe it should be a tunable runtime parameter in the interpreter. :-P

If you are starting from scratch, you really should look in to Continuation Passing Style (CPS) transformation.

Good sources include "LISP in small pieces" and Marc Feeley's Scheme in 90 minutes presentation.

The traditional way is to use setjmp and longjmp, though there are caveats.

Here's a reasonably good explanation

Examples that you can look at are: Chicken (a Scheme implementation, written in C that support continuations); Paul Graham's On Lisp - where he creates a CPS transformer to implement a subset of continuations in Common Lisp; and Weblocks - a continuation based web framework, which also implements a limited form of continuations in Common Lisp.

Continuations basically consist of the saved state of the stack and CPU registers at the point of context switches. At the very least you don't have to copy the entire stack to the heap when switching, you could only redirect the stack pointer.

Continuations are trivially implemented using fibers. http://en.wikipedia.org/wiki/Fiber_%28computer_science%29 . The only things that need careful encapsulation are parameter passing and return values.

In Windows fibers are done using the CreateFiber/SwitchToFiber family of calls. in Posix-compliant systems it can be done with makecontext/swapcontext.

boost::coroutine has a working implementation of coroutines for C++ that can serve as a reference point for implementation.

As soegaard pointed out, the main reference remains R. Kent Dybvig. "Three Implementation Models for Scheme".

The idea is, a continuation is a closure that keeps its evaluation control stack. The control stack is required in order to continue the evalution from the moment the continuation was created using call/cc.

Oftenly invoking the continuation makes long time of execution and fills the memory with duplicated stacks. I wrote this stupid code to prove that, in mit-scheme it makes the scheme crash,

The code sums the first 1000 numbers 1+2+3+...+1000.

(call-with-current-continuation 
 (lambda (break)
   ((lambda (s) (s s 1000 break))
    (lambda (s n cc)
      (if (= 0 n)
          (cc 0)
          (+ n
             ;; non-tail-recursive,
             ;; the stack grows at each recursive call
             (call-with-current-continuation
              (lambda (__)
                (s s (- n 1) __)))))))))

If you switch from 1000 to 100 000 the code will spend 2 seconds, and if you grow the input number it will crash.

Use an explicit stack instead.

Patrick is correct, the only way you can really do this is to use an explicit stack in your interpreter, and hoist the appropriate segment of stack into the heap when you need to convert to a continuation.

This is basically the same as what is needed to support closures in languages that support them (closures and continuations being somewhat related).