Expected behavior:
-<pre>
-t "abSd" ~~> "ababd"
-</pre>
+ t "abSd" ~~> "ababd"
In linguistic terms, this is a kind of anaphora
Note that it matters which 'S' you target first (the position of the *
indicates the targeted 'S'):
-<pre>
- t "aSbS"
- *
-~~> t "aabS"
- *
-~~> "aabaab"
-</pre>
+ t "aSbS"
+ *
+ ~~> t "aabS"
+ *
+ ~~> "aabaab"
versus
-<pre>
- t "aSbS"
- *
-~~> t "aSbaSb"
- *
-~~> t "aabaSb"
- *
-~~> "aabaaabab"
-</pre>
+ t "aSbS"
+ *
+ ~~> t "aSbaSb"
+ *
+ ~~> t "aabaSb"
+ *
+ ~~> "aabaaabab"
versus
-<pre>
- t "aSbS"
- *
-~~> t "aSbaSb"
- *
-~~> t "aSbaaSbab"
- *
-~~> t "aSbaaaSbaabab"
- *
-~~> ...
-</pre>
+ t "aSbS"
+ *
+ ~~> t "aSbaSb"
+ *
+ ~~> t "aSbaaSbab"
+ *
+ ~~> t "aSbaaaSbaabab"
+ *
+ ~~> ...
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
move elements to the zipped part by pulling the zipper 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);;
-
-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 *)
-
-# tz ([], ['a'; 'b'; 'S'; 'd']);;
-- : char list = ['a'; 'b'; 'a'; 'b'; 'd']
-
-# tz ([], ['a'; 'S'; 'b'; 'S']);;
-- : char list = ['a'; 'a'; 'b'; 'a'; 'a'; 'b']
-</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 *)
+
+ # tz ([], ['a'; 'b'; 'S'; 'd']);;
+ - : char list = ['a'; 'b'; 'a'; 'b'; 'd']
+
+ # tz ([], ['a'; 'S'; 'b'; 'S']);;
+ - : char list = ['a'; 'a'; 'b'; 'a'; 'a'; 'b']
Note that this implementation enforces the evaluate-leftmost rule.
Task completed.
concrete zipper using procedures.
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)))`).
+is the result of the computation `'a'::('b'::('S'::('d'::[])))` (or, in our old
+style, `make_list 'a' (make_list 'b' (make_list 'S' (make_list 'd' empty)))`).
The recipe for constructing the list goes like this:
<pre>
(or group of steps) a **continuation** of the recipe. So in this
context, a continuation is a function of type `char list -> char
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
+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.
some small but interesting differences. We've included the orginal
`tz` to facilitate detailed comparison:
-<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))
- | target::zipped -> tc zipped (fun x -> target::(c x));;
-
-# tc ['a'; 'b'; 'S'; 'd'] (fun x -> x);;
-- : char list = ['a'; 'b'; 'a'; 'b']
-
-# tc ['a'; 'S'; 'b'; 'S'] (fun x -> x);;
-- : char list = ['a'; 'a'; 'b'; 'a'; 'a'; 'b']
-</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))
+ | target::zipped -> tc zipped (fun x -> target::(c x));;
+
+ # tc ['a'; 'b'; 'S'; 'd'] (fun x -> x);;
+ - : char list = ['a'; 'b'; 'a'; 'b']
+
+ # 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
`target`. The trace of the procedure will show that these variables