edits

[lambda.git] / week3.mdwn

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index c646e8c..39e472b 100644 (file)
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@@ -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:
 ##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##
 
 
 ##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.
 
 
 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.
 
 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,
 <code>&Omega;</code> is *a* fixed point for `I`, and perhaps it has
 some a privileged status among all the fixed points for `I`, being the
 these results.  Thinking again of the truth-teller paradox, yes,
 <code>&Omega;</code> 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
 
 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
 pronouns denote (you guessed it!) identity functions...
 
 Ultimately, in the context of this course, these paradoxes are more