edits

[lambda.git] / from_lists_to_continuations.mdwn

diff --git a/from_lists_to_continuations.mdwn b/from_lists_to_continuations.mdwn
index f2e6989..3dc6dde 100644 (file)
--- a/from_lists_to_continuations.mdwn
+++ b/from_lists_to_continuations.mdwn
@@ -28,7 +28,7 @@ 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 simple task gives 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'):
 


@@ -66,7 +66,7 @@ versus
 ~~> ...
 </pre>
 
 ~~> ...
 </pre>
 

-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.
 


@@ -77,16 +77,17 @@ This is a task well-suited to using a zipper.  We'll define a function
 `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
 `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).
+move elements from the zipped part to the unzipped part by pulling the
+zipper down until the entire list has been unzipped (at which point
+the zipped half of the zipper will be empty).

 
 <pre>
 type 'a list_zipper = ('a list) * ('a list);;
 
 let rec tz (z:char list_zipper) = 
 
 <pre>
 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']


@@ -101,7 +102,7 @@ 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


@@ -128,11 +129,11 @@ 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 zippers 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
 
 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, `makelist a (makelist b (makelist S (makelist c empty)))`).
+style, `makelist 'a' (makelist 'b' (makelist 'S' (makelist 'c' empty)))`).

 The recipe for constructing the list goes like this:
 
 <pre>
 The recipe for constructing the list goes like this:
 
 <pre>


@@ -153,20 +154,19 @@ list`.  For instance, the continuation corresponding to the portion of
 the recipe below the horizontal line is the function `fun (tail:char
 list) -> a::(b::tail)`.
 
 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
-zipper--the part we've already unzipped--as a continuation: a function
-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
-some small but interesting differences.  We've included the orginal
-`tz` to facilitate detailed comparison:
+This means that we can now represent the unzipped part of our zipper
+as a continuation: a function 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 some small but interesting differences.
+We've included the orginal `tz` to facilitate detailed comparison:

 
 <pre>
 let rec tz (z:char list_zipper) = 
 
 <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 *)
+  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 [])
 
 let rec tc (l: char list) (c: (char list) -> (char list)) =
   match l with [] -> List.rev (c [])


@@ -174,13 +174,13 @@ let rec tc (l: char list) (c: (char list) -> (char list)) =
              | target::zipped -> tc zipped (fun x -> target::(c x));;
 
 # tc ['a'; 'b'; 'S'; 'd'] (fun x -> x);;
              | target::zipped -> tc zipped (fun x -> target::(c x));;
 
 # tc ['a'; 'b'; 'S'; 'd'] (fun x -> x);;

-- : char list = ['a'; 'b'; 'a'; 'b']
+- : char list = ['a'; 'b'; 'a'; 'b'; 'd']

 
 # tc ['a'; 'S'; 'b'; 'S'] (fun x -> x);;
 - : char list = ['a'; 'a'; 'b'; 'a'; 'a'; 'b']
 </pre>
 
 
 # tc ['a'; 'S'; 'b'; 'S'] (fun x -> x);;
 - : char list = ['a'; 'a'; 'b'; 'a'; 'a'; 'b']
 </pre>
 

-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


@@ -190,14 +190,15 @@ the first `match` clause will fire, so the the variable `zipper` will
 not be instantiated).
 
 I have not called the functional argument `unzipped`, although that is
 not be instantiated).
 
 I have not called the functional argument `unzipped`, although that is

-what the parallel would suggest.  The reason is that `unzipped` is a
-list, but `c` is a function.  That's the most crucial difference, the
+what the parallel would suggest.  The reason is that `unzipped` (in
+`tz`) is a list, but `c` (in `tc`) is a function.  ('c' stands for
+'continuation', of course.)  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
 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`.
-In the `tc` version of the task, we simply compose `c` with itself: 
-`c o c = fun x -> c (c x)`.
+relatively computationally inefficient) `List.append`.  In the `tc`
+version of the task, we simply compose `c` with itself: `c o c = fun x
+-> c (c x)`.

 
 Why use the identity function as the initial continuation?  Well, if
 you have already constructed the initial list `"abSd"`, what's the next
 
 Why use the identity function as the initial continuation?  Well, if
 you have already constructed the initial list `"abSd"`, what's the next