+++ /dev/null
-#Reversing a list#
-
-<OL>
-<LI>How would you define an operation to reverse a list? (Don't peek at the
-[[lambda_library]]! Try to figure it out on your own.) Choose whichever
-implementation of list you like. Even then, there are various strategies you
-can use.
-
-(See [[hints/Assignment 4 hint 1]] if you need some hints.)
-</OL>
-
-
-#Comparing lists for equality#
-
-
-<OL start=2>
-<LI>Suppose you have two lists of integers, `left` and `right`. You want to determine whether those lists are equal: that is, whether they have all the same members in the same order. (Equality for the lists we're working with is *extensional*, or parasitic on the equality of their members, and the list structure. Later in the course we'll see lists which aren't extensional in this way.)
-
-How would you implement such a list comparison?
-
-(See [[hints/Assignment 4 hint 2]] if you need some hints.)
-</OL>
-
-
-#Enumerating the fringe of a leaf-labeled tree#
-
-First, read this: [[Implementing trees]]
-
-<OL start=3>
-<LI>blah
-
-(See [[hints/Assignment 4 hint 3]] if you need some hints.)
-</OL>
-
-
-#Mutually-recursive functions#
-
-<OL start=4>
-<LI>(Challenging.) One way to define the function `even` is to have it hand off part of the work to another function `odd`:
-
- let even = \x. iszero x
- ; if x == 0 then result is
- true
- ; else result turns on whether x's pred is odd
- (odd (pred x))
-
-At the same tme, though, it's natural to define `odd` in such a way that it hands off part of the work to `even`:
-
- let odd = \x. iszero x
- ; if x == 0 then result is
- false
- ; else result turns on whether x's pred is even
- (even (pred x))
-
-Such a definition of `even` and `odd` is called **mutually recursive**. If you trace through the evaluation of some sample numerical arguments, you can see that eventually we'll always reach a base step. So the recursion should be perfectly well-grounded:
-
- even 3
- ~~> iszero 3 true (odd (pred 3))
- ~~> odd 2
- ~~> iszero 2 false (even (pred 2))
- ~~> even 1
- ~~> iszero 1 true (odd (pred 1))
- ~~> odd 0
- ~~> iszero 0 false (even (pred 0))
- ~~> false
-
-But we don't yet know how to implement this kind of recursion in the lambda calculus.
-
-The fixed point operators we've been working with so far worked like this:
-
- let X = Y T in
- X <~~> T X
-
-Suppose we had a pair of fixed point operators, `Y1` and `Y2`, that operated on a *pair* of functions `T1` and `T2`, as follows:
-
- let X1 = Y1 T1 T2 in
- let X2 = Y2 T1 T2 in
- X1 <~~> T1 X1 X2 and
- X2 <~~> T2 X1 X2
-
-If we gave you such a `Y1` and `Y2`, how would you implement the above definitions of `even` and `odd`?
-
-
-<LI>(More challenging.) Using our derivation of Y from the [Week3 notes](/week3/#index4h2) as a model, construct a pair `Y1` and `Y2` that behave in the way described.
-
-(See [[hints/Assignment 4 hint 4]] if you need some hints.)
-
-</OL>
-