+1. What does `head (tail (tail mylist))` evaluate to?
+
+2. Using the `length` function as a model, and using the predecessor
+function, write a function that computes factorials. (Recall that n!,
+the factorial of n, is n times the factorial of n-1.)
+
+Warning: my browser isn't able to compute factorials of numbers
+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
+same length. That is,
+
+ 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.
+
+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,
+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.
+
+#Computing with trees#
+
+Linguists analyze natural language expressions into trees.
+We'll need trees in future weeks, and tree structures provide good
+opportunities for learning how to write recursive functions.
+Making use of the resources we have at the moment, we can approximate
+trees as follows: instead of words, we'll use Church numerals.
+Then a tree will be a (version 1 type) list in which each element is
+itself a tree. For simplicity, we'll adopt the convention that
+a tree of length 1 must contain a number as its only element.
+Then we have the following representations:
+
+<pre>
+ (a) (b) (c)
+ .
+ /|\ /\ /\
+ / | \ /\ 3 1 /\
+ 1 2 3 1 2 2 3
+
+[[1];[2];[3]] [[[1];[2]];[3]] [[1];[[2];[3]]]
+</pre>
+
+Limitations of this scheme include the following: there is no easy way
+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 these
+trees.
+
+1. Write a function that sums the number of leaves in a tree.
+
+Expected behavior:
+
+<pre>
+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
+
+sum-leaves t1 ~~> 1
+sum-leaves t2 ~~> 2
+sum-leaves t3 ~~> 3
+sum-leaves t12 ~~> 3
+sum-leaves t23 ~~> 5
+sum-leaves ta ~~> 6
+sum-leaves tb ~~> 6
+sum-leaves tc ~~> 6
+</pre>
+
+2. Write a function that counts the number of leaves.
+