post week9

[lambda.git] / assignment3.mdwn

diff --git a/assignment3.mdwn b/assignment3.mdwn
index df06d52..e240b73 100644 (file)
--- a/assignment3.mdwn
+++ b/assignment3.mdwn
@@ -1,6 +1,19 @@
 Assignment 3
 ------------
 
+Erratum corrected 11PM Sun 3 Oct: the following line
+
+       let tb = (make_list t12 (make_list t3 empty)) in
+
+originally read 
+
+       let tb = (make_list t12 t3) in
+
+This has been corrected below, and in the preloaded evaluator for 
+working on assignment 3, available here: [[assignment 3 evaluator]].
+
+<hr>
+
 Once again, the lambda evaluator will make working through this
 assignment much faster and more secure.
 
@@ -29,14 +42,16 @@ Recall that version 1 style lists are constructed like this (see
        ; church numerals
        let iszero = \n. n (\x. false) true in
        let succ = \n s z. s (n s z) in
+       let add = \l r. l succ r in
        let mul = \m n s. m (n s) in
-       let pred = \n. iszero n 0 (length (tail (n (\p. make_list junk p) empty))) in
+       let pred = (\shift n. n shift (make\_pair 0 0) get\_snd) (\p. p (\x y. make\_pair (succ x) x)) in
        let leq = \m n. iszero(n pred m) in
        let eq = \m n. and (leq m n)(leq n m) in
        
        ; a fixed-point combinator for defining recursive functions
        let Y = \f. (\h. f (h h)) (\h. f (h h)) in
        let length = Y (\length l. isempty l 0 (succ (length (tail l)))) in
+       let fold = Y (\f l g z. isempty l z (g (head l)(f (tail l) g z))) in
        
        eq 2 2 yes no
 
@@ -107,7 +122,7 @@ be your base case for your recursive functions that operate on these
 trees.
 
 <OL start=6>
-<LI>Write a function that sums the number of leaves in a tree.
+<LI>Write a function that sums the values at the leaves in a tree.
 
 Expected behavior:
 
@@ -117,7 +132,7 @@ Expected behavior:
        let t12 = (make_list t1 (make_list t2 empty)) in
        let t23 = (make_list t2 (make_list t3 empty)) in
        let ta = (make_list t1 t23) in
-       let tb = (make_list t12 t3) in
+       let tb = (make_list t12 (make_list t3 empty)) in
        let tc = (make_list t1 (make_list t23 empty)) in
 
        sum-leaves t1 ~~> 1