Merge branch 'pryor'

[lambda.git] / hints / assignment_4_hint_3_alternate_1.mdwn

diff --git a/hints/assignment_4_hint_3_alternate_1.mdwn b/hints/assignment_4_hint_3_alternate_1.mdwn
index b0c0673..f75bad0 100644 (file)
--- a/hints/assignment_4_hint_3_alternate_1.mdwn
+++ b/hints/assignment_4_hint_3_alternate_1.mdwn
@@ -18,12 +18,12 @@ Alternate strategy for Y1, Y2
 
        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 u =    Y (\u g. (\f x. A) (u g))  in
+               let g =    Y (  \g. (\f y. B) (u g))  in
                let f =                        u g    in
                C
 
-       We abstract the Y1 and Y2 combinators from this as follows:
+       We could abstract Y1 and Y2 combinators from this as follows:
 
                let Yu = \ff.    Y (\u g. ff ( u      g        ) g)  in
                let Y2 = \ff gg. Y (  \g. gg (Yu ff   g        ) g)  in
@@ -35,19 +35,24 @@ Alternate strategy for Y1, Y2
 
 *      Here's the same strategy extended to three mutually-recursive functions. `f`, `g` and `h`:
 
-               let v = Y (\v g h x.      (\f. A) (v g h)) in
-               let w = Y (  \w h x. (\g. (\f. B) (v g h)) (w h)) in
-               let h = Y (    \h x. (\g. (\f. C) (v g h)) (w h)) in
+               let v = Y (\v g h.      (\f x. A) (v g h)) in
+               let w = Y (  \w h. (\g. (\f y. B) (v g h)) (w h)) in
+               let h = Y (    \h. (\g. (\f z. C) (v g h)) (w h)) in
                let g =                                     w h in
                let f =                            v g h in
                D
 
+       <!--
        Or in Y1of3, Y2of3, Y3of3 form:
 
-               let Yv    = \ff.       Y (\v g h.      ff (    v g h) g h)               in
-               let Yw    = \ff gg.    Y (  \w h. (\g. gg (Yv ff g h) g h) (       w h))  in
+               let Yv    = \ff.       Y (\v g h.      ff ( v    g h) g h)                in
+               let Yw    = \ff gg.    Y (  \w h. (\g. gg (Yv ff g h) g h) ( w       h))  in
                let Y3of3 = \ff gg hh. Y (    \h. (\g. hh (Yv ff g h) g h) (Yw ff gg h))  in
                let Y2of3 = \ff gg hh.                                      Yw ff gg (Y3of3 ff gg hh)  in
-               let Y1of3 = \ff gg hh.                     Yv ff (Y2of3 ff gg hh) (Y3of3 ff gg hh)  in
+               let Y1of3 = \ff gg hh.                     Yv ff (Y2of3 ff gg hh) (Y3of3 ff gg hh)     in
+               let f = Y1of3 (\f g h. A) (\f g h. B) (\f g h. C)  in
+               let g = Y2of3 (\f g h. A) (\f g h. B) (\f g h. C)  in
+               let h = Y3of3 (\f g h. A) (\f g h. B) (\f g h. C)  in
                D
+       -->