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diff --git a/assignment5.mdwn b/assignment5.mdwn
index cf8d1448..cc714e90 100644
--- a/assignment5.mdwn
+++ b/assignment5.mdwn
@@ -1,10 +1,10 @@
 Assignment 5
 
-Types and OCAML
+Types and OCaml
 ---------------
 
 0. Recall that the S combinator is given by \x y z. x z (y z).
-   Give two different typings for this function in OCAML.
+   Give two different typings for this function in OCaml.
    To get you started, here's one typing for K:
 
     # let k (y:'a) (n:'b) = y;;
@@ -13,7 +13,7 @@ Types and OCAML
     - : int = 1
 
 
-1. Which of the following expressions is well-typed in OCAML?  
+1. Which of the following expressions is well-typed in OCaml?  
    For those that are, give the type of the expression as a whole.
    For those that are not, why not?
 
@@ -68,11 +68,12 @@ Types and OCAML
 
     let _ = omega () in 2;;
 
-3. The following expression is an attempt to make explicit the
+3. This problem is to begin thinking about controlling order of evaluation.
+The following expression is an attempt to make explicit the
 behavior of `if`-`then`-`else` explored in the previous question.
 The idea is to define an `if`-`then`-`else` expression using 
-other expression types.  So assume that "yes" is any OCAML expression,
-and "no" is any other OCAML expression (of the same type as "yes"!),
+other expression types.  So assume that "yes" is any OCaml expression,
+and "no" is any other OCaml expression (of the same type as "yes"!),
 and that "bool" is any boolean.  Then we can try the following:
 "if bool then yes else no" should be equivalent to
 
@@ -122,7 +123,10 @@ you're allowed to adjust what `b`, `y`, and `n` get assigned to.
 
 [[Hint assignment 5 problem 3]]
 
-4. Baby monads.  Read the lecture notes for week 6, then write a
+Baby monads
+-----------
+
+   Read the lecture notes for week 6, then write a
    function `lift` that generalized the correspondence between + and
    `add`: that is, `lift` takes any two-place operation on integers
    and returns a version that takes arguments of type `int option`
@@ -139,68 +143,72 @@ you're allowed to adjust what `b`, `y`, and `n` get assigned to.
       match x with None -> None | Some n -> f n;;
 
 
-Church lists in System F
-------------------------
+Booleans, Church numbers, and Church lists in OCaml
+---------------------------------------------------
 
-These questions adapted from web materials written by some dude named Acar.
+These questions adapted from web materials written by some smart dude named Acar.
+The idea is to get booleans, Church numbers, "Church" lists, and
+binary trees working in OCaml.
 
    Recall from class System F, or the polymorphic λ-calculus.
 
-   τ ::= α | τ1 → τ2 | ∀α. τ
-   e ::= x | λx:τ. e | e1 e2 | Λα. e | e [τ ]
-   Despite its simplicity, System F is quite expressive. As discussed in class, it has sufficient expressive power
-   to be able to encode many datatypes found in other programming languages, including products, sums, and
-   inductive datatypes.
-   For example, recall that bool may be encoded as follows:
-   bool := ∀α. α → α → α
-   true := Λα. λt:α. λf :α. t
-   false := Λα. λt:α. λf :α. f
-   ifτ e then e1 else e2 := e [τ ] e1 e2
+    τ ::= 'α | τ1 → τ2 | ∀'α. τ | c
+    e ::= x | λx:τ. e | e1 e2 | Λ'α. e | e [τ ]
+
+   Recall that bool may be encoded as follows:
+
+    bool := ∀α. α → α → α
+    true := Λα. λt:α. λf :α. t
+    false := Λα. λt:α. λf :α. f
+
    (where τ indicates the type of e1 and e2)
-   Exercise 1. Show how to encode the following terms. Note that each of these terms, when applied to the
+
+   Note that each of the following terms, when applied to the
    appropriate arguments, return a result of type bool.
-   (a) the term not that takes an argument of type bool and computes its negation;
-   (b) the term and that takes two arguments of type bool and computes their conjunction;
-   (c) the term or that takes two arguments of type bool and computes their disjunction.
-   The type nat may be encoded as follows:
-   nat := ∀α. α → (α → α) → α
-   zero := Λα. λz:α. λs:α → α. z
-   succ := λn:nat. Λα. λz:α. λs:α → α. s (n [α] z s)
+
+    (a) the term not that takes an argument of type bool and computes its negation;
+    (b) the term and that takes two arguments of type bool and computes their conjunction;
+    (c) the term or that takes two arguments of type bool and computes their disjunction.
+
+   The type nat (for "natural number") may be encoded as follows:
+
+    nat := ∀α. α → (α → α) → α
+    zero := Λα. λz:α. λs:α → α. z
+    succ := λn:nat. Λα. λz:α. λs:α → α. s (n [α] z s)
+
    A nat n is defined by what it can do, which is to compute a function iterated n times. In the polymorphic
    encoding above, the result of that iteration can be any type α, as long as you have a base element z : α and
    a function s : α → α.
-   Conveniently, this encoding “is” its own elimination form, in a sense:
-   rec(e, e0, x:τ. e1) := e [τ ] e0 (λx:τ. e1)
-   The case analysis is baked into the very definition of the type.
-   Exercise 2. Verify that these encodings (zero, succ , rec) typecheck in System F. Write down the typing
-   derivations for the terms.
-   1
-
-   ══════════════════════════════════════════════════════════════════════════
-
-   As mentioned in class, System F can express any inductive datatype. Consider the following list type:
-   datatype ’a list =
-   Nil
-   | Cons of ’a * ’a list
-   We can encode τ lists, lists of elements of type τ as follows:1
-   τ list := ∀α. α → (τ → α → α) → α
-   nilτ := Λα. λn:α. λc:τ → α → α. n
-   consτ := λh:τ. λt:τ list. Λα. λn:α. λc:τ → α → α. c h (t [α] n c)
-   As with nats, The τ list type’s case analyzing elimination form is just application. We can write functions
-   like map:
-   map : (σ → τ ) → σ list → τ list
-   := λf :σ → τ. λl:σ list. l [τ list] nilτ (λx:σ. λy:τ list. consτ (f x) y
-   Exercise 3. Consider the following simple binary tree type:
-   datatype ’a tree =
-   Leaf
-   | Node of ’a tree * ’a * ’a tree
-   (a) Give a System F encoding of binary trees, including a definition of the type τ tree and definitions of
-   the constructors leaf : τ tree and node : τ tree → τ → τ tree → τ tree.
-   (b) Write a function height : τ tree → nat. You may assume the above encoding of nat as well as definitions
-   of the functions plus : nat → nat → nat and max : nat → nat → nat.
-   (c) Write a function in-order : τ tree → τ list that computes the in-order traversal of a binary tree. You
-   may assume the above encoding of lists; define any auxiliary functions you need.
-
--- 
-Jim Pryor
-jim@jimpryor.net
+
+   **Excercise**: get booleans and Church numbers working in OCaml,
+     including OCaml versions of bool, true, false, zero, succ, and pred.
+     It's especially useful to do a version of pred, starting with one
+     of the (untyped) versions available in the lambda library
+     accessible from the main wiki page.  The point of the excercise
+     is to do these things on your own, so avoid using the built-in
+     OCaml booleans and list predicates.
+
+   Consider the following list type:
+
+    type ’a list = Nil | Cons of ’a * ’a list
+
+   We can encode τ lists, lists of elements of type τ as follows:
+
+    τ list := ∀α. α → (τ → α → α) → α
+    nilτ := Λα. λn:α. λc:τ → α → α. n
+    makeListτ := λh:τ. λt:τ list. Λα. λn:α. λc:τ → α → α. c h (t [α] n c)
+
+   As with nats, recursion is built into the datatype.
+
+   We can write functions like head, isNil, and map:
+
+    map : (σ → τ ) → σ list → τ list
+
+   We've given you the type for map, you only need to give the term.
+
+   With regard to `head`, think about what value to give back if the
+   argument is the empty list.  Ultimately, we might want to make use
+   of our `'a option` technique, but for this assignment, just pick a
+   strategy, no matter how clunky. 
+
+   Please provide both the terms and the types for each item.