edits

[lambda.git] / assignment3.mdwn

diff --git a/assignment3.mdwn b/assignment3.mdwn
index 50495f5..289f818 100644 (file)
--- a/assignment3.mdwn
+++ b/assignment3.mdwn
@@ -14,32 +14,30 @@ Recall that version 1 style lists are constructed like this (see
        let false = \x y. y in
        let and = \l r. l (r true false) false in
 
-       ; version 1 lists
        let make_pair = \f s g. g f s in
-       let fst = true in
-       let snd = false in
+       let get_fst = true in
+       let get_snd = false in
        let empty = make_pair true junk in
-       let isempty = \x. x fst in
+       let isempty = \x. x get_fst in
        let make_list = \h t. make_pair false (make_pair h t) in
-       let head = \l. isempty l err (l snd fst) in
-       let tail = \l. isempty l err (l snd snd) in
-
+       let head = \l. isempty l err (l get_snd get_fst) in
+       let tail = \l. isempty l err (l get_snd get_snd) in
+       
        ; a list of numbers to experiment on
        let mylist = make_list 1 (make_list 2 (make_list 3 empty)) in
-
-       ; a fixed-point combinator for defining recursive functions
-       let Y = \f. (\h. f (h h)) (\h. f (h h)) in
-
+       
        ; church numerals
        let iszero = \n. n (\x. false) true in
        let succ = \n s z. s (n s z) in
-       let mult = \m n s. m (n s) in
-       let length = Y (\length l. isempty l 0 (succ (length (tail l)))) in
-       let pred = \n. iszero n 0 (length (tail (n (\p. make_list junk p) empty)))
-       in
+       let mul = \m n s. m (n s) 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
+       
        eq 2 2 yes no
 
 
@@ -51,7 +49,7 @@ Then `length mylist` evaluates to 3.
 function, write a function that computes factorials.  (Recall that n!,
 the factorial of n, is n times the factorial of n-1.)
 
-Warning: it takes a long time for my browser to compute factorials larger than 4!
+       Warning: it takes a long time for my browser to compute factorials larger than 4!
 
 3. (Easy) Write a function `equal_length` that returns true just in case
 two lists have the same length.  That is,
@@ -108,7 +106,8 @@ whether the length of the list is less than or equal to 1.  This will
 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.
+<OL start=6>
+<LI>Write a function that sums the values at the leaves in a tree.
 
 Expected behavior:
 
@@ -131,5 +130,7 @@ Expected behavior:
        sum-leaves tc ~~> 6
 
 
-2.   Write a function that counts the number of leaves.
+<LI>Write a function that counts the number of leaves.
+
+</OL>