X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=zipper-lists-continuations.mdwn;h=142a2ba88d63ba3d4b31816c80af7c36a490284d;hp=fef92b735ab4224691dfa13c69b6151bde0f9fbb;hb=adfec786a8d1caa0ae42c1d392c76e99d305a975;hpb=ef15f2c1e2c9c82e41b64d9d11a3301e225ea331

diff --git a/zipper-lists-continuations.mdwn b/zipper-lists-continuations.mdwn
index fef92b73..142a2ba8 100644
--- a/zipper-lists-continuations.mdwn
+++ b/zipper-lists-continuations.mdwn
@@ -26,10 +26,10 @@ constructor is
 
 then we can deduce the unit and the bind:
 
-    runit x:'a -> 'a reader = fun (e:env) -> x
+    r_unit x:'a -> 'a reader = fun (e:env) -> x
 
 Since the type of an `'a reader` is `fun e:env -> 'a` (by definition),
-the type of the `runit` function is `'a -> e:env -> 'a`, which is a
+the type of the `r_unit` function is `'a -> e:env -> 'a`, which is a
 specific case of the type of the *K* combinator.  So it makes sense
 that *K* is the unit for the reader monad.
 
@@ -43,24 +43,30 @@ We can deduce the correct `bind` function as follows:
 
 We have to open up the `u` box and get out the `'a` object in order to
 feed it to `f`.  Since `u` is a function from environments to
-objects of type `'a`, we'll have
+objects of type `'a`, the way we open a box in this monad is
+by applying it to an environment:
 
          .... f (u e) ...
 
 This subexpression types to `'b reader`, which is good.  The only
-problem is that we don't have an `e`, so we have to abstract over that
-variable:
+problem is that we invented an environment `e` that we didn't already have ,
+so we have to abstract over that variable to balance the books:
 
          fun e -> f (u e) ...
 
 This types to `env -> 'b reader`, but we want to end up with `env ->
-'b`.  The easiest way to turn a 'b reader into a 'b is to apply it to
+'b`.  Once again, the easiest way to turn a `'b reader` into a `'b` is to apply it to
 an environment.  So we end up as follows:
 
     r_bind (u:'a reader) (f:'a -> 'b reader):('b reader) = f (u e) e         
 
 And we're done.
 
+[This bind is a simplified version of the careful `let a = u e in ...`
+constructions we provided in earlier lectures.  We use the simplified
+versions here in order to emphasize similarities of structure across
+monads; the official bind is still the one with the plethora of `let`'s.]
+
 The **State Monad** is similar.  We somehow intuit that we want to use
 the following type constructor:
 
@@ -115,14 +121,14 @@ And sure enough,
 But where is the reasoning that led us to this unit and bind?
 And what is the type `['a]`?  Magic.
 
-So let's take a *completely useless digressing* and see if we can
-gain some insight into the details of the List monad.  Let's choose
-type constructor that we can peer into, using some of the technology
-we built up so laboriously during the first half of the course.  I'm
-going to use type 3 lists, partly because I know they'll give the
-result I want, but also because they're my favorite.  These were the
-lists that made lists look like Church numerals with extra bits
-embdded in them:
+So let's indulge ourselves in a completely useless digression and see
+if we can gain some insight into the details of the List monad.  Let's
+choose type constructor that we can peer into, using some of the
+technology we built up so laboriously during the first half of the
+course.  I'm going to use type 3 lists, partly because I know they'll
+give the result I want, but also because they're my favorite.  These
+were the lists that made lists look like Church numerals with extra
+bits embdded in them:
 
     empty list:                fun f z -> z
     list with one element:     fun f z -> f 1 z
@@ -228,10 +234,12 @@ Sigh.  Ocaml won't show us our own list.  So we have to choose an `f`
 and a `z` that will turn our hand-crafted lists into standard Ocaml
 lists, so that they will print out.
 
+<pre>
 # let cons h t = h :: t;;  (* Ocaml is stupid about :: *)
 # l'_bind (fun f z -> f 1 (f 2 z)) 
           (fun i -> fun f z -> f i (f (i+1) z)) cons [];;
 - : int list = [1; 2; 2; 3]
+</pre>
 
 Ta da!
 
@@ -302,3 +310,6 @@ versa.  The connections will be expecially relevant when we consider
 indefinites and Hamblin semantics on the linguistic side, and
 non-determinism on the list monad side.
 
+Refunctionalizing zippers
+-------------------------
+