edits

[lambda.git] / zipper-lists-continuations.mdwn

diff --git a/zipper-lists-continuations.mdwn b/zipper-lists-continuations.mdwn
index f0a252e..ed822f8 100644 (file)
--- a/zipper-lists-continuations.mdwn
+++ b/zipper-lists-continuations.mdwn
@@ -245,7 +245,7 @@ Ta da!
 
 To bad this digression, though it ties together various
 elements of the course, has *no relevance whatsoever* to the topic of
-continuations.
+continuations...
 
 Montague's PTQ treatment of DPs as generalized quantifiers
 ----------------------------------------------------------
@@ -271,10 +271,12 @@ the bind follow naturally.  We've done this enough times that we won't
 belabor the construction of the bind function, the derivation is
 similar to the List monad just given:
 
-   type 'a continuation = ('a -> 'b) -> 'b
-   c_unit (x:'a) = fun (p:'a -> 'b) -> p x
-   c_bind (u:('a -> 'b) -> 'b) (f: 'a -> ('c -> 'd) -> 'd): ('c -> 'd) -> 'd =
-     fun (k:'a -> 'b) -> u (fun (x:'a) -> f x k)
+<pre>
+type 'a continuation = ('a -> 'b) -> 'b
+c_unit (x:'a) = fun (p:'a -> 'b) -> p x
+c_bind (u:('a -> 'b) -> 'b) (f: 'a -> ('c -> 'd) -> 'd): ('c -> 'd) -> 'd =
+  fun (k:'a -> 'b) -> u (fun (x:'a) -> f x k)
+</pre>
 
 How similar is it to the List monad?  Let's examine the type
 constructor and the terms from the list monad derived above:
@@ -292,8 +294,6 @@ parallel in a deep sense.  To emphasize the parallel, we can
 instantiate the type of the list' monad using the Ocaml list type:
 
     type 'a c_list = ('a -> 'a list) -> 'a list
-    let c_list_unit x = fun f -> f x;;
-    let c_list_bind u f = fun k -> u (fun x -> f x k);;
 
 Have we really discovered that lists are secretly continuations?
 Or have we merely found a way of simulating lists using list