Merge branch 'pryor'

[lambda.git] / week11.mdwn

diff --git a/week11.mdwn b/week11.mdwn
index 8eae2cc..b48dd5f 100644 (file)
--- a/week11.mdwn
+++ b/week11.mdwn
@@ -648,8 +648,40 @@ Okay, so that's our second execution pattern.
 
 ##What do these have in common?##
 
 
 ##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
+-->

 
 
 
 
 
 


@@ -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.
 
 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
 
 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).

 
 <pre>
 type 'a list_zipper = ('a list) * ('a list);;
 
 <pre>
 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
 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
 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
 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.  

 
 <pre>
 # #trace tz;;
 
 <pre>
 # #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)
 -----------------------------------------
 (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)

-<pre>
+</pre>

 
 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
 
 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


@@ -885,9 +919,15 @@ describing how to finish building the list.  We'll write a new
 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
 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>
 
 <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))
 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))


@@ -925,18 +965,23 @@ the recipe to produce the desired result (which is the same list,
 
 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
 
 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
 
 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
 
 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