X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week11.mdwn;h=f1d9b28d95867179dc26b9bc74b221a6f86671e7;hp=8eae2ccd4202bf0d4f55a3cf276989a39d3c5d81;hb=338ce074e719b92e2dbae562d75f96f5b1a67987;hpb=767dc2f1f56176d59b16840613d6c0b170a229f3;ds=sidebyside diff --git a/week11.mdwn b/week11.mdwn index 8eae2ccd..f1d9b28d 100644 --- a/week11.mdwn +++ b/week11.mdwn @@ -648,8 +648,40 @@ Okay, so that's our second execution pattern. ##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. + + @@ -799,13 +831,15 @@ Aparently, this task, as simple as it is, is a form of computation, and the order in which the `'S'`s get evaluated can lead to divergent behavior. -For now, we'll agree to always evaluate the leftmost `'S'`. +For now, we'll agree to always evaluate the leftmost `'S'`, which +guarantees termination, and a final string without any `'S'` in it. This is a task well-suited to using a zipper. We'll define a function -`tz`, which accomplished the task by mapping a char list zipper to a -char list. We'll call the two parts of the zipper `unzipped` and -`zipped`; we start with a fully zipped list, and move elements to the -zipped part by pulling the zipped down until the zipped part is empty. +`tz` (for task with zippers), which accomplishes the task by mapping a +char list zipper to a char list. We'll call the two parts of the +zipper `unzipped` and `zipped`; we start with a fully zipped list, and +move elements to the zipped part by pulling the zipped down until the +entire list has been unzipped (and so the zipped half of the zipper is empty).
 type 'a list_zipper = ('a list) * ('a list);;
@@ -826,13 +860,13 @@ Note that this implementation enforces the evaluate-leftmost rule.
 Task completed.
 
 One way to see exactly what is going on is to watch the zipper in
-action by tracing the execution of `t1`.  By using the `#trace`
+action by tracing the execution of `tz`.  By using the `#trace`
 directive in the Ocaml interpreter, the system will print out the
-arguments to `t1` each time it is (recurcively) called.  Note that the
+arguments to `tz` each time it is (recurcively) called.  Note that the
 lines with left-facing arrows (`<--`) show (recursive) calls to `tz`,
 giving the value of its argument (a zipper), and the lines with
 right-facing arrows (`-->`) show the output of each recursive call, a
-list.  
+simple list.  
 
 
 # #trace tz;;
@@ -869,7 +903,7 @@ The recipe for constructing the list goes like this:
 -----------------------------------------
 (3)  make a new list whose first element is 'b' and whose tail is the list constructed in step (2)
 (4)  make a new list whose first element is 'a' and whose tail is the list constructed in step (3)
-
+
What is the type of each of these steps? Well, it will be a function from the result of the previous step (a list) to a new list: it will