X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment3.mdwn;h=f669cb1e6488906d7d2baf66d27927d91abf1ab0;hp=342896c2c429ee51d798d943352d415d682aa7a5;hb=c0674bbb2f8587d3fd625277628140a99b52a9d6;hpb=825c122aac6dd19e421ea72049b608615c00f46a

diff --git a/assignment3.mdwn b/assignment3.mdwn
index 342896c2..f669cb1e 100644
--- a/assignment3.mdwn
+++ b/assignment3.mdwn
@@ -36,12 +36,11 @@ 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 predecessor = \n. length (tail (n (\p. makeList meh p) nil)) in
-let leq = ; (leq m n) will be true iff m is less than or equal to n
-  Y (\leq m n. isZero m true (isZero n false (leq (predecessor m)(predecessor n)))) 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
 
-eq 3 3
+eq 2 2 yes no
 </pre>
 
 
@@ -66,13 +65,13 @@ same length.  That is,
      listLenEq mylist (makeList meh (makeList meh nil))) ~~> false
 
 
-4. (Still easy) Now write the same function, but don't use the length function (hint: use `leq` as a model).
+4. (Still easy) Now write the same function, but don't use the length function.
 
 5. In assignment 2, we discovered that version 3-type 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 3 lists are within our
-reach.  Give definitions for such a map and a filter.
+reach.  Give definitions for `map` and a `filter` for verson 1 type lists.
 
 6. Linguists analyze natural language expressions into trees.  
 We'll need trees in future weeks, and tree structures provide good
@@ -95,20 +94,20 @@ Then we have the following representations:
 </pre>
 
 Limitations of this scheme include the following: there is no easy way
-to label a constituent (typically a syntactic category, S or NP or VP,
+to label a constituent with a syntactic category (S or NP or VP,
 etc.), and there is no way to represent a tree in which a mother has a
 single daughter.
 
 When processing a tree, you can test for whether the tree contains
 only a numeral (in which case the tree is leaf node) by testing for
 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 trees.
+be your base case for your recursive functions that operate on these
+trees.
 
-Write a function that sums the number of leaves in a tree.
+#Write a function that sums the number of leaves in a tree.#
 Expected behavior:
 
 <pre>
-
 let t1 = (make-list 1 nil) in
 let t2 = (make-list 2 nil) in
 let t3 = (make-list 3 nil) in
@@ -126,37 +125,7 @@ count-leaves t23 ~~> 5
 count-leaves ta ~~> 6
 count-leaves tb ~~> 6
 count-leaves tc ~~> 6
-<pre>
-
-Write a function that counts the number of leaves.
-
-
-
-
-[The following should be correct, but won't run in my browser:
-
-<pre>
-let factorial = Y (\fac n. isZero n 1 (mult n (fac (predecessor n)))) in
-
-let reverse = 
-  Y (\rev l. isNil l nil 
-                   (isNil (tail l) l 
-                          (makeList (head (rev (tail l))) 
-                                    (rev (makeList (head l) 
-                                                   (rev (tail (rev (tail l))))))))) in
-
-reverse (makeList 1 (makeList 2 (makeList 3 nil)))
 </pre>
 
-It may require more resources than my browser is willing to devote to
-JavaScript.]
-
-; trees
-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
+#Write a function that counts the number of leaves.#
+