edits

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

diff --git a/zipper-lists-continuations.mdwn b/zipper-lists-continuations.mdwn
index a14ed50..a2603db 100644 (file)
--- a/zipper-lists-continuations.mdwn
+++ b/zipper-lists-continuations.mdwn
@@ -243,16 +243,9 @@ lists, so that they will print out.
 
 Ta da!
 
-Just for mnemonic purposes (sneaking in an instance of eta reduction
-to the definition of unit), we can summarize the result as follows:
-
-    type ('a, 'b) list' = ('a -> 'b -> 'b) -> 'b -> 'b
-    l'_unit x = fun f -> f x
-    l'_bind u f = fun k -> u (fun x -> f x k)
-
 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
 ----------------------------------------------------------
@@ -278,10 +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: