XGitUrl: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment3.mdwn;h=6f4f3f64f2bdda0ca0a12729271ef413e3a8eeee;hp=c4ea316287a62ceb9de2af825b31d6a53877470f;hb=fcaf8b03257c825dcacad9882a695560273f5812;hpb=e4ea387ecb1a2dcb069060afccbe8ac1e70f7061
diff git a/assignment3.mdwn b/assignment3.mdwn
index c4ea3162..6f4f3f64 100644
 a/assignment3.mdwn
+++ b/assignment3.mdwn
@@ 36,7 +36,8 @@ 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. isNil l 0 (succ (length (tail l)))) in
let pred = \n. isZero n 0 (length (tail (n (\p. makeList meh p) nil))) in
+let pred = \n. isZero n 0 (length (tail (n (\p. makeList meh p) nil)))
+in
let leq = \m n. isZero(n pred m) in
let eq = \m n. and (leq m n)(leq n m) in
@@ 57,21 +58,27 @@ greater than 2 (it does't provide enough resources for the JavaScript
interpreter; web pages are not supposed to be that computationally
intensive).
3. (Easy) Write a function `listLenEq` that returns true just in case two lists have the
+3. (Easy) Write a function `listLenEq` that returns true just in case
+two lists have the
same length. That is,
 listLenEq mylist (makeList meh (makeList meh (makeList meh nil))) ~~> true
+ listLenEq mylist (makeList meh (makeList meh (makeList meh nil)))
+ ~~> true
listLenEq mylist (makeList meh (makeList meh nil))) ~~> false
4. (Still easy) Now write the same function, but don't use the length function.
+4. (Still easy) Now write the same function, but don't use the length
+function.
5. In assignment 2, we discovered that version 3type lists (the ones that
+5. In assignment 2, we discovered that version 3type lists (the ones
+that
work like Church numerals) made it much easier to define operations
like `map` and `filter`. But now that we have recursion in our toolbox,
+like `map` and `filter`. But now that we have recursion in our
+toolbox,
reasonable map and filter functions for version 1 lists are within our
reach. Give definitions for `map` and a `filter` for verson 1 type lists.
+reach. Give definitions for `map` and a `filter` for verson 1 type
+lists.
#Computing with trees#
@@ 111,23 +118,23 @@ trees.
Expected behavior:
let t1 = (makelist 1 nil) in
let t2 = (makelist 2 nil) in
let t3 = (makelist 3 nil) in
let t12 = (makelist t1 (makelist t2 nil)) in
let t23 = (makelist t2 (makelist t3 nil)) in
let ta = (makelist t1 t23) in
let tb = (makelist t12 t3) in
let tc = (makelist t1 (makelist t23 nil)) in

countleaves t1 ~~> 1
countleaves t2 ~~> 2
countleaves t3 ~~> 3
countleaves t12 ~~> 3
countleaves t23 ~~> 5
countleaves ta ~~> 6
countleaves tb ~~> 6
countleaves tc ~~> 6
+let t1 = (makeList 1 nil) in
+let t2 = (makeList 2 nil) in
+let t3 = (makeList 3 nil) in
+let t12 = (makeList t1 (makeList t2 nil)) in
+let t23 = (makeList t2 (makeList t3 nil)) in
+let ta = (makeList t1 t23) in
+let tb = (makeList t12 t3) in
+let tc = (makeList t1 (makeList t23 nil)) in
+
+sumleaves t1 ~~> 1
+sumleaves t2 ~~> 2
+sumleaves t3 ~~> 3
+sumleaves t12 ~~> 3
+sumleaves t23 ~~> 5
+sumleaves ta ~~> 6
+sumleaves tb ~~> 6
+sumleaves tc ~~> 6
2. Write a function that counts the number of leaves.