X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week4.mdwn;h=58d6bc38204bd3bcbf4afabe6d9c4306b82735de;hp=daa18981c30b55931f40807f90b24ec0c766c789;hb=72cca371a48d35b0177427b35f23ae8cc704fdf2;hpb=c25c54424a8631097313817b7ce58191e15f7192

diff --git a/week4.mdwn b/week4.mdwn
index daa18981..58d6bc38 100644
--- a/week4.mdwn
+++ b/week4.mdwn
@@ -520,12 +520,11 @@ but really all we're in a position to mean by that are claims about the result
 of the complex expression semantically depending only on this, not on that. A
 demon evaluator who custom-picked the evaluation order to make things maximally
 bad for you could ensure that all the semantically unnecessary computations got
-evaluated anyway. We don't have any way to prevent that. Later,
-we'll see ways to *semantically guarantee* one evaluation order rather than
-another. Though even then the demonic evaluation-order-chooser could make it
-take unnecessarily long to compute the semantically guaranteed result. Of
-course, in any real computing environment you'll know you're dealing with a
-fixed evaluation order and you'll be able to program efficiently around that.
+evaluated anyway. We don't yet know any way to prevent that. Later, we'll see
+ways to *guarantee* one evaluation order rather than another. Of
+course, in any real computing environment you'll know in advance that you're
+dealing with a fixed evaluation order and you'll be able to program efficiently
+around that.
 
 In detail, then, here's what our v5 lists will look like:
 
@@ -589,14 +588,29 @@ 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.
 >	
->	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 a` 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
 >	
->	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)