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diff --git a/assignment3.mdwn b/assignment3.mdwn
index 9f64d808..f669cb1e 100644
--- a/assignment3.mdwn
+++ b/assignment3.mdwn
@@ -6,7 +6,8 @@ assignment much faster and more secure.
 
 *Writing recursive functions on version 1 style lists*
 
-Recall that version 1 style lists are constructed like this:
+Recall that version 1 style lists are constructed like this (see
+[[lists and numbers]]):
 
 <pre>
 ; booleans
@@ -35,12 +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>
 
 
@@ -65,13 +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
@@ -94,26 +94,28 @@ 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:
 
-let t1 = (make-list 1 nil) 
-let t2 = (make-list 2 nil)
-let t3 = (make-list 3 nil)
-let t12 = (make-list t1 (make-list t2 nil))
-let t23 = (make-list t2 (make-list t3 nil))
-let ta = (make-list t1 t23)
-let tb = (make-list t12 t3)
-let tc = (make-list t1 (make-list t23 nil))
+<pre>
+let t1 = (make-list 1 nil) in
+let t2 = (make-list 2 nil) in
+let t3 = (make-list 3 nil) in
+let t12 = (make-list t1 (make-list t2 nil)) in
+let t23 = (make-list t2 (make-list t3 nil)) in
+let ta = (make-list t1 t23) in
+let tb = (make-list t12 t3) in
+let tc = (make-list t1 (make-list t23 nil)) in
 
 count-leaves t1 ~~> 1
 count-leaves t2 ~~> 2
@@ -123,27 +125,7 @@ count-leaves t23 ~~> 5
 count-leaves ta ~~> 6
 count-leaves tb ~~> 6
 count-leaves tc ~~> 6
-
-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.]
+#Write a function that counts the number of leaves.#