X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week3.mdwn;h=39e472bf9a644c1bdac774790ed134f26ab7cf31;hp=88b1c4f9e5b0f33a886c075b2071db5b54122845;hb=9a815152fb9ad1fa4ee5778376dc59007cc687f3;hpb=2e064948c0cb722be400441476fd13b2add6d636 diff --git a/week3.mdwn b/week3.mdwn index 88b1c4f9..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 @@ -620,8 +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