week4 tweaks

Signed-off-by: Jim Pryor <profjim@jimpryor.net>

diff --git a/week4.mdwn b/week4.mdwn
index daa1898..fca995e 100644 (file)
--- a/week4.mdwn
+++ b/week4.mdwn
@@ -589,14 +589,29 @@ detail](http://okmij.org/ftp/Streams.html#enumerator-stream).
 >      that `5` is the outer/leftmost head of the list. That's not an efficient way
 >      to get the leftmost head.
 >      
 >      that `5` is the outer/leftmost head of the list. That's not an efficient way
 >      to get the leftmost head.
 >      

->      We could improve this by building lists as left folds when implementing them
->      as continuation-passing style folds. We'd just replace above:
+>      We could improve this by building lists as **left folds**. What's that?
+>      
+>      Well, the right fold of `f` over a list `[a;b;c;d;e]`, using starting value z, is:
+>      
+>              f a (f b (f c (f d (f e z))))
+>      
+>      The left fold on the other hand starts combining `z` with elements from the left. `f z z` is then combined with `b`, and so on:
+>      
+>              f (f (f (f (f z a) b) c) d) e
+>      
+>      or, if we preferred the arguments to each `f` flipped:
+>      
+>              f e (f d (f c (f b (f a z))))
+>      
+>      Recall we implemented v3 lists as their own right-fold functions. We could
+>      instead implement lists as their own left-fold functions. To do that with our
+>      v5 lists, we'd replace above:

 >      
 >                      let make_list = \h t. \f2 z continue_handler abort_handler.
 >                              f2 h z (\z. t f2 z continue_handler abort_handler) abort_handler
 >      
 >      
 >                      let make_list = \h t. \f2 z continue_handler abort_handler.
 >                              f2 h z (\z. t f2 z continue_handler abort_handler) abort_handler
 >      

->      now `extract_head` should return the leftmost head directly, using its
->      `abort_handler`:
+>      Having done that, now `extract_head` can return the leftmost head
+>      directly, using its `abort_handler`:

 >      
 >                      let extract_head = \lst larger_computation. lst
 >                                      (\hd sofar continue_handler abort_handler. abort_handler hd)
 >      
 >                      let extract_head = \lst larger_computation. lst
 >                                      (\hd sofar continue_handler abort_handler. abort_handler hd)