From 880952bd8862bde3c8e71238097fc2726c244e57 Mon Sep 17 00:00:00 2001 From: Jim Pryor Date: Sun, 3 Oct 2010 20:23:07 -0400 Subject: [PATCH] continuing assignment4 Signed-off-by: Jim Pryor --- hints/assignment_4_answer_4.mdwn | 27 +++++++++++++++++++++++++++ hints/assignment_4_hint_4.mdwn | 24 ++++++++++++++++++++++++ 2 files changed, 51 insertions(+) create mode 100644 hints/assignment_4_answer_4.mdwn diff --git a/hints/assignment_4_answer_4.mdwn b/hints/assignment_4_answer_4.mdwn new file mode 100644 index 00000000..17c8490f --- /dev/null +++ b/hints/assignment_4_answer_4.mdwn @@ -0,0 +1,27 @@ + + + let Y1 = \t1 t2. + (\elem1 elem2. t1 (elem1 elem1 elem2) (elem2 elem1 elem2)) ; elem1 + (\elem1 elem2. t1 (elem1 elem1 elem2) (elem2 elem1 elem2)) ; elem1 + (\elem1 elem2. t2 (elem1 elem1 elem2) (elem2 elem1 elem2)) ; elem2 + in + + let Y2 = \t1 t2. + (\elem1 elem2. t2 (elem1 elem1 elem2) (elem2 elem1 elem2)) ; elem2 + (\elem1 elem2. t1 (elem1 elem1 elem2) (elem2 elem1 elem2)) ; elem1 + (\elem1 elem2. t2 (elem1 elem1 elem2) (elem2 elem1 elem2)) ; elem2 + in + + + Y1 t1 t2 ~~> elem1 elem1 elem2 + === (\elem1 elem2. t1 (elem1 elem1 elem2) (elem2 elem1 elems2)) elem1 elem2 + ~~> t1 (elem1 elem1 elem2) (elem2 elem1 elem2) + <~~> t1 (Y1 t1 t2) (Y2 t1 t2) + + and + + Y2 t1 t2 ~~> elem2 elem1 elem2 + === (\elem1 elem2. t2 (elem1 elem1 elem2) (elem2 elem1 elems2)) elem1 elem2 + ~~> t2 (elem1 elem1 elem2) (elem2 elem1 elem2) + <~~> t2 (Y1 t1 t2) (Y2 t1 t2) + diff --git a/hints/assignment_4_hint_4.mdwn b/hints/assignment_4_hint_4.mdwn index a30b4861..9cfef8ad 100644 --- a/hints/assignment_4_hint_4.mdwn +++ b/hints/assignment_4_hint_4.mdwn @@ -1,2 +1,26 @@ Hints for Y1,Y2. +* Begin by trying to define `X1` and `X2` directly, then once they're working, you can abstract back to a pair of combinators `Y1` and `Y2` that generate `X1` and `X2` for a given pair of arguments `T1` and `T2`. + + You want: + + X1 <~~> T1 X1 X2 and + X2 <~~> T2 X1 X2 + +* X1 is presumably going to have some form like: + + (\elem1 elem2 ... (T1 + (do-something-with-the-elems-to-make-X1) + (do-something-with-the-elems-to-make-X2) + )) + some-elem1 some-elem2 ... + + Right? What will the form of X2 be? + +* Can you see how to go on? + +* Call the displayed abstract above `(\elem1 elem2 ... (...))` "elem0". What's the relation between `X1`, `elem0`, `elem1`, `elem2`...? + +* Go on, now you can do it. + + -- 2.11.0