What are Scala continuations and why use them?

Question

I just finished Programming in Scala, and I've been looking into the changes between Scala 2.7 and 2.8. The one that seems to be the most important is the continuations plugin, but I don't understand what it's useful for or how it works. I've seen that it's good for asynchronous I/O, but I haven't been able to find out why. Some of the more popular resources on the subject are these:

• Delimited continuations and Scala
• Goto in Scala
• A Taste of 2.8: Continuations
• Delimited Continuations Explained (in Scala)

And this question on Stack Overflow:

• What are the biggest differences between Scala 2.8 and Scala 2.7?

Unfortunately, none of these references try to define what continuations are for or what the shift/reset functions are supposed to do, and I haven't found any references that do. I haven't been able to guess how any of the examples in the linked articles work (or what they do), so one way to help me out could be to go line-by-line through one of those samples. Even this simple one from the third article:

reset {
    ...
    shift { k: (Int=>Int) =>  // The continuation k will be the '_ + 1' below.
        k(7)
    } + 1
}
// Result: 8

Why is the result 8? That would probably help me to get started.

Answer 1

My blog does explain what reset and shift do, so you may want to read that again.

Another good source, which I also point in my blog, is the Wikipedia entry on continuation passing style. That one is, by far, the most clear on the subject, though it does not use Scala syntax, and the continuation is explicitly passed.

The paper on delimited continuations, which I link to in my blog but seems to have become broken, gives many examples of usage.

But I think the best example of the concept of delimited continuations is Scala Swarm. In it, the library stops the execution of your code at one point, and the remaining computation becomes the continuation. The library then does something -- in this case, transferring the computation to another host, and returns the result (the value of the variable which was accessed) to the computation that was stopped.

Now, you don't understand even the simple example on the Scala page, so do read my blog. In it I'm only concerned with explaining these basics, of why the result is 8.