X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week4.mdwn;h=2fa501c6bf204324cf38fbe5f9d5fd0c2ad3f69f;hp=c002a4713d83200ced68f2bd7914d3a1520767ab;hb=8eb66bfd3d6eec21e1a4d31a244200e80e73e888;hpb=99d1d57f9a1cf2447938744849531a5c68aee7b1

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+++ b/week4.mdwn
@@ -1,9 +1,6 @@
 [[!toc]]
 
-#These notes return to the topic of fixed point combiantors for one more return to the topic of fixed point combinators#
-
-#Q: How do you know that every term in the untyped lambda calculus has
-a fixed point?#
+#Q: How do you know that every term in the untyped lambda calculus has a fixed point?#
 
 A: That's easy: let `T` be an arbitrary term in the lambda calculus.  If
 `T` has a fixed point, then there exists some `X` such that `X <~~>
@@ -161,3 +158,16 @@ A 2 x is to A 1 x as multiplication is to addition;
 A 3 x is to A 2 x as exponentiation is to multiplication---
 so A 4 x is to A 3 x as hyper-exponentiation is to exponentiation...
 
+#Q. What other questions should I be asking?#
+
+*    What is it about the variant fixed-point combinators that makes
+     them compatible with a call-by-value evaluation strategy?
+
+*    How do you know that the Ackerman function can't be computed
+     using primitive recursion techniques?
+
+*    What *exactly* is primitive recursion?
+
+*    I hear that `Y` delivers the *least* fixed point.  Least
+     according to what ordering?  How do you know it's least?
+     Is leastness important?