X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=from_lists_to_continuations.mdwn;h=3dc6dde76734c777f1258799d4d581bc87a8b299;hp=f2e6989d14e362e2f9b10e2c5d5d07b08da49ae7;hb=56b4312b90432a6655b94558ebfb5dca78209ac3;hpb=9c7ca26e6dd0c1ce1b6cd653e27a083b7379a5dd diff --git a/from_lists_to_continuations.mdwn b/from_lists_to_continuations.mdwn index f2e6989d..3dc6dde7 100644 --- 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. -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'): @@ -66,7 +66,7 @@ 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. @@ -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 -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).
``` 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']
@@ -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
-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
@@ -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
-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
-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:

@@ -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)`.

-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:

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 [])
@@ -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);;
-- : 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']

-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
@@ -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
-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
-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
```