X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week3.mdwn;h=a1e79f5c0538e4d913d8e3e6360f908c8590cdfc;hp=0129f2a957e3ef073760d70804d42afc8c7a33d4;hb=4de03f98830a8404cfdcf256c719661d5ab85787;hpb=4d04ec1d56a71cce8cfce3aef6e39ef824ee63d8 diff --git a/week3.mdwn b/week3.mdwn index 0129f2a9..a1e79f5c 100644 --- a/week3.mdwn +++ b/week3.mdwn @@ -134,8 +134,8 @@ Some computable functions are just not definable in this way. The simplest funct | else -> A(m-1, A(m,n-1)) A(0,y) = y+1 - A(1,y) = y+2 - A(2,y) = 2y + 3 + A(1,y) = 2+(y+3) - 3 + A(2,y) = 2(y+3) - 3 A(3,y) = 2^(y+3) - 3 A(4,y) = 2^(2^(2^...2)) [where there are y+3 2s] - 3 ... @@ -340,7 +340,7 @@ Two of the simplest:
Θ′ ≡ (\u f. f (\n. u u f n)) (\u f. f (\n. u u f n))
 Y′ ≡ \f. (\u. f (\n. u u n)) (\u. f (\n. u u n))
-Θ′ has the advantage that f (Θ′ f) really *reduces to* Θ′ f. +Θ′ has the advantage that f (Θ′ f) really *reduces to* Θ′ f. f (Y′ f) is only convertible with Y′ f; that is, there's a common formula they both reduce to. For most purposes, though, either will do.