X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?a=blobdiff_plain;f=week3.mdwn;h=f83d377c90296d304bacae0175c8459391bf8fdd;hb=7ee83a5cebdf94623bfce3edc2dfad4f93c79c9a;hp=b29d095a1f8157725ec1febe67ccfa3abf9663b7;hpb=1d29453465d5f709699abd2adeb2b75ad6695a7f;p=lambda.git diff --git a/week3.mdwn b/week3.mdwn index b29d095a..f83d377c 100644 --- a/week3.mdwn +++ b/week3.mdwn @@ -214,7 +214,6 @@ and the initial `(\x. x x)` is just what we earlier called the ωω (\h \lst. (isempty lst) zero (add one ((h h) (extract-tail lst)))) - and this will indeed implement the recursive function we couldn't earlier figure out how to define. In broad brush-strokes, `H` is half of the `get_length` function we're seeking, and `H` has the form: @@ -546,18 +545,17 @@ sentence in which it occurs, the sentence denotes a fixed point for the identity function. Here's a fixed point for the identity function: -
-    Y I
-    (\f. (\h. f (h h)) (\h. f (h h))) I
-    (\h. I (h h)) (\h. I (h h)))
-    (\h. (h h)) (\h. (h h)))
-    ω ω
-    &Omega
-
+
Y I
+(\f. (\h. f (h h)) (\h. f (h h))) I
+(\h. I (h h)) (\h. I (h h)))
+(\h. (h h)) (\h. (h h)))
+ω ω
+&Omega
+
Oh. Well! That feels right. The meaning of *This sentence is true* in a context in which *this sentence* refers to the sentence in which -it occurs is Ω, our prototypical infinite loop... +it occurs is Ω, our prototypical infinite loop... What about the liar paradox?