Merge branch 'working'

[lambda.git] / topics / week4_fixed_point_combinators.mdwn

diff --git a/topics/week4_fixed_point_combinators.mdwn b/topics/week4_fixed_point_combinators.mdwn
index 601ad81..ed22cff 100644 (file)
--- a/topics/week4_fixed_point_combinators.mdwn
+++ b/topics/week4_fixed_point_combinators.mdwn
@@ -293,6 +293,7 @@ The strategy we will present will turn out to be a general way of
 finding a fixed point for any lambda term.
 
 
 finding a fixed point for any lambda term.
 
 

+<a id=deriving-y></a>

 ## Deriving Y, a fixed point combinator ##
 
 How shall we begin?  Well, we need to find an argument to supply to
 ## Deriving Y, a fixed point combinator ##
 
 How shall we begin?  Well, we need to find an argument to supply to


@@ -533,7 +534,7 @@ 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 ##
 

-[[tatto|/images/y-combinator-fixed.jpg]]
+[[tatto|/images/y-combinator-fixed.png]]

 
 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.
 


@@ -553,9 +554,9 @@ then this is a fixed-point combinator:
 For those of you who like to watch ultra slow-mo movies of bullets
 piercing apples, here's a stepwise computation of the application of a
 recursive function.  We'll use a function `sink`, which takes one
 For those of you who like to watch ultra slow-mo movies of bullets
 piercing apples, here's a stepwise computation of the application of a
 recursive function.  We'll use a function `sink`, which takes one

-argument.  If the argument is boolean true (i.e., `\x y. x`), it
+argument.  If the argument is boolean true (i.e., `\y n. y`), it

 returns itself (a copy of `sink`); if the argument is boolean false
 returns itself (a copy of `sink`); if the argument is boolean false

-(`\x y. y`), it returns `I`.  That is, we want the following behavior:
+(`\y n. n`), it returns `I`.  That is, we want the following behavior:

 
     sink false <~~> I
     sink true false <~~> I
 
     sink false <~~> I
     sink true false <~~> I