X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=hints%2Fassignment_4_hint_3_alternate_1.mdwn;h=900c6cb16327ad8ac03ca0cf4b4ce645e21a154b;hp=12ddbd6bd9a59bf1d4cb53dee2b15f103cf594ff;hb=f4c96076c1abbdf13bfb90d7e5b56ebe80dd7de7;hpb=d1526a5f26872825688dbd957b8f9b296ff3cf71 diff --git a/hints/assignment_4_hint_3_alternate_1.mdwn b/hints/assignment_4_hint_3_alternate_1.mdwn index 12ddbd6b..900c6cb1 100644 --- a/hints/assignment_4_hint_3_alternate_1.mdwn +++ b/hints/assignment_4_hint_3_alternate_1.mdwn @@ -2,22 +2,24 @@ Alternate strategy for Y1, Y2 * This is (in effect) the strategy used by OCaml. The mutually recursive: - let rec - f x = A ; A may refer to f or g - and - g y = B ; B may refer to f or g - in - C + let rec + f x = A ; A may refer to f or g + and + g y = B ; B may refer to f or g + in + C -is implemented using regular, non-mutual recursion, like this (`f'` is a variable not occurring free in `A`, `B`, or `C`): + is implemented using regular, non-mutual recursion, like this (`u` is a variable not occurring free in `A`, `B`, or `C`): - let rec f' g x = (let f = f' g in A) - in let rec g y = (let f = f' g in B) - in let f = f' g in C + 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 + C -or, expanded into the form we've been working with: + or, expanded into the form we've been working with: - let f' = Y (\f' g x. (\f. A) (f' g)) in - let g = Y (\g y. (\f. B) (f' g)) in - let f = f' g + 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 + C