##What do these have in common?##
+ In both of these patterns, we need to have some way to take a snapshot of where we are in the evaluation of a complex piece of code, so that we might later resume execution at that point. In the coroutine example, the two threads need to have a snapshot of where they were in the enumeration of their tree's leaves. In the abort example, we need to have a snapshot of where to pick up again if some embedded piece of code aborts. Sometimes we might distill that snapshot into a datastructure like a zipper. But we might not always know how to do so; and learning how to think about these snapshots without the help of zippers will help us see patterns and similarities we might otherwise miss.
+ A more general way to think about these snapshots is to think of the code we're taking a snapshot of as a *function.* For example, in this code:
+ let foo x =
+ try
+ (if x = 1 then 10
+ else abort 20) + 1
+ end
+ in (foo 2) + 1;;
+
+ we can imagine a box:
+
+ let foo x =
+ +---------------------------+
+ | try |
+ | (if x = 1 then 10 |
+ | else abort 20) + 1 |
+ | end |
+ +---------------------------+
+ in (foo 2) + 1;;
+
+ and as we're about to enter the box, we want to take a snapshot of the code *outside* the box. If we decide to abort, we'd be aborting to that snapshotted code.
+
+ <!--
+ # #require "delimcc";;
+ # open Delimcc;;
+ # let reset body = let p = new_prompt () in push_prompt p (body p);;
+ val reset : ('a Delimcc.prompt -> unit -> 'a) -> 'a = <fun>
+ # let foo x = reset(fun p () -> (shift p (fun k -> if x = 1 then k 10 else 20)) + 1) in (foo 1) + 100;;
+ - : int = 111
+ # let foo x = reset(fun p () -> (shift p (fun k -> if x = 1 then k 10 else 20)) + 1) in (foo 2) + 100;;
+ - : int = 120
+ -->
function, `tc` (for task with continuations), that will take an input
list (not a zipper!) and a continuation and return a processed list.
The structure and the behavior will follow that of `tz` above, with
-some small but interesting differences:
+some small but interesting differences. We've included the orginal
+`tz` to facilitate detailed comparison:
<pre>
+let rec tz (z:char list_zipper) =
+ match z with (unzipped, []) -> List.rev(unzipped) (* Done! *)
+ | (unzipped, 'S'::zipped) -> tz ((List.append unzipped unzipped), zipped)
+ | (unzipped, target::zipped) -> tz (target::unzipped, zipped);; (* Pull zipper *)
+
let rec tc (l: char list) (c: (char list) -> (char list)) =
match l with [] -> List.rev (c [])
| 'S'::zipped -> tc zipped (fun x -> c (c x))
A good way to test your understanding is to figure out what the
continuation function `c` must be at the point in the computation when
-`tc` is called with
+`tc` is called with the first argument `"Sd"`. Two choices: is it
+`fun x -> a::b::x`, or it is `fun x -> b::a::x`?
+The way to see if you're right is to execute the following
+command and see what happens:
+
+ tc ['S'; 'd'] (fun x -> 'a'::'b'::x);;
There are a number of interesting directions we can go with this task.
The task was chosen because the computation can be viewed as a
simplified picture of a computation using continuations, where `'S'`
plays the role of a control operator with some similarities to what is
-often called `shift`. &sset; &integral; In the analogy, the list
-portrays a string of functional applications, where `[f1; f2; f3; x]`
-represents `f1(f2(f3 x))`. The limitation of the analogy is that it
-is only possible to represent computations in which the applications
-are always right-branching, i.e., the computation `((f1 f2) f3) x`
-cannot be directly represented.
+often called `shift`. In the analogy, the list portrays a string of
+functional applications, where `[f1; f2; f3; x]` represents `f1(f2(f3
+x))`. The limitation of the analogy is that it is only possible to
+represent computations in which the applications are always
+right-branching, i.e., the computation `((f1 f2) f3) x` cannot be
+directly represented.
One possibile development is that we could add a special symbol `'#'`,
and then the task would be to copy from the target `'S'` only back to