X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week3.mdwn;h=39e472bf9a644c1bdac774790ed134f26ab7cf31;hp=c646e8ccd1fea4eb3ec20893f83cdb47e19fadce;hb=eb8ac48a126c26a8195d19dfc0e1f60009198746;hpb=0f35e8d18e58f334d8c147d161c18c4df81acc17
diff --git a/week3.mdwn b/week3.mdwn
index c646e8cc..39e472bf 100644
--- a/week3.mdwn
+++ b/week3.mdwn
@@ -1,3 +1,12 @@
+[[!toc]]
+
+##More on evaluation strategies##
+
+Here are notes on [[evaluation order]] that make the choice of which
+lambda to reduce next the selection of a route through a network of
+links.
+
+
##Computing the length of a list##
How could we compute the length of a list? Without worrying yet about what lambda-calculus implementation we're using for the list, the basic idea would be to define this recursively:
@@ -415,7 +424,7 @@ to *the tail* of the list we were evaluating its application to at the previous
##Fixed-point Combinators Are a Bit Intoxicating##
-![tatoo](/y-combinator.jpg)
+![tatoo](/y-combinator-fixed.jpg)
There's a tendency for people to say "Y-combinator" to refer to fixed-point combinators generally. We'll probably fall into that usage ourselves. Speaking correctly, though, the Y-combinator is only one of many fixed-point combinators.
@@ -583,7 +592,9 @@ truth and circularity](http://tinyurl.com/2db62bk) for an approach
that is similar, but expressed in terms of non-well-founded sets
rather than recursive functions.
-HOWEVER, you should be cautious about feeling too comfortable with
+##However...##
+
+You should be cautious about feeling too comfortable with
these results. Thinking again of the truth-teller paradox, yes,
`Ω`

is *a* fixed point for `I`, and perhaps it has
some a privileged status among all the fixed points for `I`, being the
@@ -620,7 +631,8 @@ for any object.
The chameleon nature of (3), by the way (a description that is equally
good at describing any object), makes it particularly well suited as a
-gloss on pronouns such as *it*. In the system of [Jacobson 1999](http://www.zas.gwz-berlin.de/mitarb/homepage/sauerland/jacobson99.pdf)
+gloss on pronouns such as *it*. In the system of
+[Jacobson 1999](http://www.springerlink.com/content/j706674r4w217jj5/),
pronouns denote (you guessed it!) identity functions...
Ultimately, in the context of this course, these paradoxes are more