From: jim <jim@web>
Date: Fri, 20 Feb 2015 17:48:40 +0000 (-0500)
Subject: update some functions
X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=71f5a9d7f646424ae3c8e543f889f952ed6ea9d3;hp=4398d51300777f367c01ef6b88a664b8dfe733b2;ds=inline

update some functions
---

diff --git a/exercises/_assignment4.mdwn b/exercises/_assignment4.mdwn
index 4dfd5dbf..3eec4e6a 100644
--- a/exercises/_assignment4.mdwn
+++ b/exercises/_assignment4.mdwn
@@ -27,9 +27,13 @@ For instance, `fact 0 ~~> 1`, `fact 1 ~~> 1`, `fact 2 ~~> 2`, `fact 3 ~~>
 
         let true = \y n. y in
         let false = \y n. n in
-        let zero? = \n. n (\p. false) true in
-        let pred = \n f z. n (\u v. v (u f)) (K z) I in
+        let pair = \a b. \v. v a b in
+        let fst = \a b. a in   ; aka true
+        let snd = \a b. b in   ; aka false
+        let zero = \s z. z in
         let succ = \n s z. s (n s z) in
+        let zero? = \n. n (\p. false) true in
+        let pred = \n. n (\p. p (\a b. pair (succ a) a)) (pair zero zero) snd in
         let add = \l r. r succ l in
         let mult = \l r. r (add l) 0 in
         let Y = \h. (\u. h (u u)) (\u. h (u u)) in
@@ -46,7 +50,15 @@ For instance, `fact 0 ~~> 1`, `fact 1 ~~> 1`, `fact 2 ~~> 2`, `fact 3 ~~>
     -->
 
         ; all functions from the previous question, plus
-        let num_equal? = ??? in
+        ; `num_cmp x y lt eq gt` returns lt when x<y, eq when x==y, gt when x>y
+        let num_cmp = (\base build consume. \l r. r consume (l build base) fst)
+                ; where base is
+                (pair (\a b c. b) (K (\a b c. a)))
+                ; and build is
+                (\p. pair (\a b c. c) p)
+                ; and consume is
+                (\p. p fst p (p snd) (p snd)) in
+        let num_equal? = \x y. num_cmp x y false true false in
         let neg = \b y n. b n y in
         let empty = \f n. n in
         let cons = \x xs. \f n. f x xs in