From: Jim Pryor Date: Sat, 16 Oct 2010 18:48:29 +0000 (-0400) Subject: alternate Y1,Y2 tweak X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=8c28339b991f2d4f0940d295bf4d265a00751b05 alternate Y1,Y2 tweak Signed-off-by: Jim Pryor --- diff --git a/hints/assignment_4_hint_3_alternate_1.mdwn b/hints/assignment_4_hint_3_alternate_1.mdwn index 900c6cb1..99a4202b 100644 --- a/hints/assignment_4_hint_3_alternate_1.mdwn +++ b/hints/assignment_4_hint_3_alternate_1.mdwn @@ -11,15 +11,23 @@ Alternate strategy for Y1, Y2 is implemented using regular, non-mutual recursion, like this (`u` is a variable not occurring free in `A`, `B`, or `C`): - let rec u g x = (let f = u g in A) + let rec u g x = (let f = u g in A) in let rec g y = (let f = u g in B) - in let f = u g in + in let f = u g in C or, expanded into the form we've been working with: let u = Y (\u g x. (\f. A) (u g)) in - let g = Y (\g y. (\f. B) (u g)) in - let f = u g in + let g = Y ( \g y. (\f. B) (u g)) in + let f = u g in C +* Here's the same strategy extended to three mutually-recursive functions. `f`, `g` and `h`: + + let u = Y (\u g h x. (\f. A) (u g h)) in + let w = Y ( \w h x. (\g. (\f. B) (u g h)) (w h)) in + let h = Y ( \h x. (\g. (\f. C) (u g h)) (w h)) in + let g = w h in + let f = u g h in + D