edits

[lambda.git] / from_list_zippers_to_continuations.mdwn

diff --git a/from_list_zippers_to_continuations.mdwn b/from_list_zippers_to_continuations.mdwn
index 3890f90..1ef5f9c 100644 (file)
--- a/from_list_zippers_to_continuations.mdwn
+++ b/from_list_zippers_to_continuations.mdwn
@@ -1,5 +1,5 @@
-Refunctionalizing list zippers
-------------------------------
+Refunctionalizing zippers: from lists to continuations
+------------------------------------------------------

 
 If zippers are continuations reified (defuntionalized), then one route
 to continuations is to re-functionalize a zipper.  Then the
 
 If zippers are continuations reified (defuntionalized), then one route
 to continuations is to re-functionalize a zipper.  Then the


@@ -26,7 +26,7 @@ In linguistic terms, this is a kind of anaphora
 resolution, where `'S'` is functioning like an anaphoric element, and
 the preceding string portion is the antecedent.
 
 resolution, where `'S'` is functioning like an anaphoric element, and
 the preceding string portion is the antecedent.
 

-This deceptively simple task gives rise to some mind-bending complexity.
+This task can give rise to considerable complexity.

 Note that it matters which 'S' you target first (the position of the *
 indicates the targeted 'S'):
 
 Note that it matters which 'S' you target first (the position of the *
 indicates the targeted 'S'):
 


@@ -58,7 +58,7 @@ versus
                     *
        ~~> ...
 
                     *
        ~~> ...
 

-Aparently, this task, as simple as it is, is a form of computation,
+Apparently, 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.
 


@@ -75,10 +75,10 @@ entire list has been unzipped (and so the zipped half of the zipper is empty).
        type 'a list_zipper = ('a list) * ('a list);;
        
        let rec tz (z : char list_zipper) =
        type 'a list_zipper = ('a list) * ('a list);;
        
        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 *)
+          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 *)

        
        # tz ([], ['a'; 'b'; 'S'; 'd']);;
        - : char list = ['a'; 'b'; 'a'; 'b'; 'd']
        
        # tz ([], ['a'; 'b'; 'S'; 'd']);;
        - : char list = ['a'; 'b'; 'a'; 'b'; 'd']


@@ -92,7 +92,7 @@ Task completed.
 One way to see exactly what is going on is to watch the zipper in
 action by tracing the execution of `tz`.  By using the `#trace`
 directive in the OCaml interpreter, the system will print out the
 One way to see exactly what is going on is to watch the zipper in
 action by tracing the execution of `tz`.  By using the `#trace`
 directive in the OCaml interpreter, the system will print out the

-arguments to `tz` each time it is (recurcively) called.  Note that the
+arguments to `tz` each time it is (recursively) 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


@@ -117,7 +117,7 @@ The nice thing about computations involving lists is that it's so easy
 to visualize them as a data structure.  Eventually, we want to get to
 a place where we can talk about more abstract computations.  In order
 to get there, we'll first do the exact same thing we just did with
 to visualize them as a data structure.  Eventually, we want to get to
 a place where we can talk about more abstract computations.  In order
 to get there, we'll first do the exact same thing we just did with

-concrete zipper using procedures.
+concrete zipper using procedures instead.

 
 Think of a list as a procedural recipe: `['a'; 'b'; 'S'; 'd']` is the result of
 the computation `'a'::('b'::('S'::('d'::[])))` (or, in our old style,
 
 Think of a list as a procedural recipe: `['a'; 'b'; 'S'; 'd']` is the result of
 the computation `'a'::('b'::('S'::('d'::[])))` (or, in our old style,


@@ -141,7 +141,7 @@ the recipe below the horizontal line is the function `fun (tail : char
 list) -> 'a'::('b'::tail)`.
 
 This means that we can now represent the unzipped part of our
 list) -> 'a'::('b'::tail)`.
 
 This means that we can now represent the unzipped part of our

-zipper---the part we've already unzipped---as a continuation: a function
+zipper as a continuation: a function

 describing how to finish building a list.  We'll write a new
 function, `tc` (for task with continuations), that will take an input
 list (not a zipper!) and a continuation `k` (it's conventional to use `k` for continuation variables) and return a processed list.
 describing how to finish building a list.  We'll write a new
 function, `tc` (for task with continuations), that will take an input
 list (not a zipper!) and a continuation `k` (it's conventional to use `k` for continuation variables) and return a processed list.


@@ -167,7 +167,7 @@ some small but interesting differences.  We've included the orginal
        # tc ['a'; 'S'; 'b'; 'S'] (fun tail -> tail);;
        - : char list = ['a'; 'a'; 'b'; 'a'; 'a'; 'b']
 
        # tc ['a'; 'S'; 'b'; 'S'] (fun tail -> tail);;
        - : char list = ['a'; 'a'; 'b'; 'a'; 'a'; 'b']
 

-To emphasize the parallel, I've re-used the names `zipped` and
+To emphasize the parallel, we've re-used the names `zipped` and

 `target`.  The trace of the procedure will show that these variables
 take on the same values in the same series of steps as they did during
 the execution of `tz` above.  There will once again be one initial and
 `target`.  The trace of the procedure will show that these variables
 take on the same values in the same series of steps as they did during
 the execution of `tz` above.  There will once again be one initial and


@@ -176,13 +176,13 @@ four recursive calls to `tc`, and `zipped` will take on the values
 the first `match` clause will fire, so the the variable `zipped` will
 not be instantiated).
 
 the first `match` clause will fire, so the the variable `zipped` will
 not be instantiated).
 

-I have not called the functional argument `unzipped`, although that is
+We have not called the functional argument `unzipped`, although that is

 what the parallel would suggest.  The reason is that `unzipped` is a
 list, but `k` is a function.  That's the most crucial difference, the
 point of the excercise, and it should be emphasized.  For instance,
 you can see this difference in the fact that in `tz`, we have to glue
 what the parallel would suggest.  The reason is that `unzipped` is a
 list, but `k` is a function.  That's the most crucial difference, the
 point of the excercise, and it should be emphasized.  For instance,
 you can see this difference in the fact that in `tz`, we have to glue

-together the two instances of `unzipped` with an explicit (and
-relatively inefficient) `List.append`.
+together the two instances of `unzipped` with an explicit (and,
+computationally speaking, relatively inefficient) `List.append`.

 In the `tc` version of the task, we simply compose `k` with itself:
 `k o k = fun tail -> k (k tail)`.
 
 In the `tc` version of the task, we simply compose `k` with itself:
 `k o k = fun tail -> k (k tail)`.