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.
; 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
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:
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