X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week3.mdwn;h=5d05c700b44cd86f8c6d3b541ee2dc58ab78cfad;hp=3fa20f6180b312361b6bd72e0bf5edf15fa7a35e;hb=20da31063b4f8c95e219e7364512054e72b6db44;hpb=5d6405438fee2a81634a9d53bef64629621c1411 diff --git a/week3.mdwn b/week3.mdwn index 3fa20f61..5d05c700 100644 --- a/week3.mdwn +++ b/week3.mdwn @@ -333,14 +333,14 @@ Isn't that cool? ##Okay, then give me a fixed-point combinator, already!## -Many fixed-point combinators have been discovered. (And given a fixed-point combinator, there are ways to use it as a model to build infinitely many more, non-equivalent fixed-point combinators.) +Many fixed-point combinators have been discovered. (And some fixed-point combinators give us models for building infinitely many more, non-equivalent fixed-point combinators.) 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.