X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment3.mdwn;h=e240b732b1405e176d696bbab3c5974a1d125f35;hp=df06d526a99c58495f34260629d8977bbc1f9e91;hb=7a822d410076318ea12be4e3cdb57e1b91218f42;hpb=6a60dbeb81ccc4949724a6db13a264a0b322a22d diff --git a/assignment3.mdwn b/assignment3.mdwn index df06d526..e240b732 100644 --- 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]]. + +
+ 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.
-
1. Write a function that sums the number of leaves in a tree. +
2. 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