- This evaluates to `101`; `(+ 100 (let/cc k (+ 10 (k 1))))` is the same as `(reset (+ 100 (shift k (k 1))))`. + This evaluates to `101`. See also example 11, below. 3.100 +let/cc k (10 + k 1)

- In the second line, we extract the continuation function (the bold part of the previous code) from the pair `p` and apply it to the argument `(2, ident)`. That results in the following code being run: + In the first line, we bind the continuation function (the bold code) to `k` and then bind the pair of `1` and that function to the variable `p`. + In the second line, we extract the continuation function from the pair `p` and apply it to the argument `(2, ident)`. That results in the following code being run:let p =let/cc k (1,k)in let y = snd p (2, ident) in (fst p, y)

which in turn results in the nested pair `(2, (2, ident))`. + Notice how the first time through, when `p`'s second element is a continuation, applying it to an argument is a bit like time-travel? The metaphysically impossible kind of time-travel, where you can change what happened. The second time through, `p` gets bound to a different pair, whose second element is the ordinary `ident` function. 4.let p =(2, ident)in let y = snd p (2, ident) in (fst p, y)

Here the box is implicit, understood to be the rest of the code. The result is just the abort value `11`, because the bold code is skipped. @@ -156,17 +161,25 @@ Here are some examples of using these different continuation operators. The cont Here the box or delimiter is explicitly specified. The bold code is skipped, but the outside code `1000 + < >` is still executed, so we get `1011`. 6.1000 + (100 +abort 11)

1000 + reset- Equivalent to preceding; results in `1011`. + Equivalent to preceding. We bind the bold code to `k` but then never apply `k`, so the value `10 + 1` is supplied directly to the outside code `1000 + < >`, resulting in `1011`. 7.(100 +shift k (10 + 1))

1000 + resetHere we do invoke the captured continuation, so what gets passed to the outside code `1000 + < >` is `k (10 + 1)`, that is, `(100 + (10 + 1))`. Result is `1111`. + In general, if the last thing that happens inside a `shift k ( ... )` body is that `k` is applied to an argument, then we do continue running the bold code between `shift k ( ... )` and the edge of the `reset` box. 8.(100 +shift k (k (10 + 1)))

1000 + reset- This also results in `1111`, but via a different path than the preceding. First, note that `k` is bound to `100 + < >`. So `k 1` is `101`. Then `10 + k 1` is `10 + 101`. Then we exit the body of `shift k ( ... )`, without invoking `k` again, so we don't anymore add `100`. Thus we pass `10 + 101` to the outside code `1000 + < >`. So the result is `1000 + (10 + 101)` or `1111`. (Whereas in the preceding example, the result was `1000 + (100 + 11)`. The order in which the operations are performed is different. If we used a non-commutative operation instead of `+`, the results of these two examples would be different from each other.) + This also results in `1111`, but via a different path than the preceding. First, note that `k` is bound to `100 + < >`. So `k 1` is `101`. Then `10 + k 1` is `10 + 101`. Then we exit the body of `shift k ( ... )`, without invoking `k` again, so we don't add `100` any more times. Thus we pass `10 + 101` to the outside code `1000 + < >`. So the result is `1000 + (10 + 101)` or `1111`. (Whereas in the preceding example, the result was `1000 + (100 + 11)`. The order in which the operations are performed is different. If we used a non-commutative operation instead of `+`, the results of these two examples would be different from each other.) 9.(100 +shift k (10 + k 1))

1000 + reset- Here `k` is bound to `100 + < >`. That's what's returned by the `shift k ( ... )` block, and since `k` isn't invoked (applied) when doing so, the rest of the bold `reset` block is skipped (for now). So we resume the outside code `1000 + < > 1`, with what fills the gap `< >` being the function that was bound to `k`. Thus this is equivalent to `1000 + (fun x -> 100 + x) 1` or `1000 + 101` or `1101`. + Here `k` is bound to `100 + < >`. That function `k` is what's returned by the `shift k ( ... )` block, and since `k` isn't invoked (applied) when doing so, the rest of the bold `reset` block is skipped (for now). So we resume the outside code `1000 + < > 1`, with what fills the gap `< >` being the function that was bound to `k`. Thus this is equivalent to `1000 + (fun x -> 100 + x) 1` or `1000 + 101` or `1101`. 10.(100 +shift k (k))1

1000 + reset- Here `k` is bound to `100 + < >`. Thus `k 1` is `101`. Now there are two ways to think about what happens next. (Both are valid.) One way to think is that since the `shift` block ends with an additional outermost application of `k`, we continue through the bold code with the value `k 1` or `101`. Thus we get `100 + 101`, and then we continue with the outermost code `1000 + < >`, getting `1000 + (100 + 101)`, or `1201`. The other way to think is that since `k` is `100 + < >`, and `k 1` is `101`, then `k (k 1)` is `201`. Now we leave the `shift` block *without* executing the bold code a third time (we've already taken account of the two applications of `k`), resuming with the outside code `1000 + < >`, thereby getting `1000 + 201` as before. + Here `k` is bound to `100 + < >`. Thus `k 1` is `101`. Now there are two ways to think about what happens next. (Both are valid.) One way to think is that since the `shift` block ends with an additional outermost application of `k`, then as described in example 7 above, we continue through the bold code with the value `k 1` or `101`. Thus we get `100 + 101`, and then we continue with the outermost code `1000 + < >`, getting `1000 + (100 + 101)`, or `1201`. The other way to think is that since `k` is `100 + < >`, and `k 1` is `101`, then `k (k 1)` is `201`. Now we leave the `shift` block *without* executing the bold code a third time (we've already taken account of the two applications of `k`), resuming with the outside code `1000 + < >`, thereby getting `1000 + 201` as before. + +11. Here's a comparison of `let/cc` to `shift`. Recall example 2 above was: +(100 +shift k (k (k 1)))

+ which evaluated to `101`. The parallel code where we instead capture the continuation using `shift k ( ... )` would look like this: +100 +let/cc k (10 + k 1)

reset+ But this evaluates differently. In the `let/cc` example, `k` is bound to the rest of the computation *including its termination*, so after executing `k 1` we never come back and finish with `10 + < >`. A `let/cc`-bound `k` never returns to the context where it was invoked. Whereas the `shift`-bound `k` only includes up to the edge of the `reset` box --- here, the rest of the computation, but *not including* its termination. So after `k 1`, if there is still code inside the body of `shift`, as there is here, we continue executing it. Thus the `shift` code evaluates to `111` not to `101`. + Thus code using `let/cc` can't be *straightforwardly* translated into code using `shift`. It can be translated, but the algorithm will be more complex. -- 2.11.0(100 +shift k (10 + k 1))