First, read this: [[Implementing trees]]
<OL start=3>
-<LI>blah
-
-(See [[hints/Assignment 4 hint 3]] if you need some hints.)
+<LI>Write an implementation of leaf-labeled trees. You can do something v3-like, or use the Y combinator, as you prefer.
+
+You'll need an operation `make_leaf` that turns a label into a new leaf. You'll
+need an operation `make_node` that takes two subtrees (perhaps leaves, perhaps
+other nodes) and joins them into a new tree. You'll need an operation `isleaf`
+that tells you whether a given tree is a leaf. And an operation `extract_label`
+that tells you what value is associated with a given leaf. And an operation
+`extract_left` that tells you what the left subtree is of a tree that isn't a
+leaf. (Presumably, `extract_right` will work similarly.)
+
+<LI>The **fringe** of a leaf-labeled tree is the list of values at its leaves,
+ordered from left to right. For example, the fringe of this tree:
+
+ .
+ / \
+ . 3
+ / \
+ 1 2
+
+is `[1;2;3]`. And that is also the fringe of this tree:
+
+ .
+ / \
+ 1 .
+ / \
+ 2 3
+
+The two trees are different, but they have the same fringe. We're going to
+return later in the term to the problem of determining when two trees have the
+same fringe. For now, one straightforward way to determine this would be:
+enumerate the fringe of the first tree. That gives you a list. Enumerate the
+fringe of the second tree. That also gives you a list. Then compare the two
+lists to see if they're equal.
+
+Write the fringe-enumeration function. It should work on the
+implementation of trees you designed in the previous step.
+
+Then combine this with the list comparison function you wrote for question 2,
+to yield a same-fringe detector. (To use your list comparison function, you'll
+have to make sure you only use Church numerals as the labels of your leaves,
+though nothing enforces this self-discipline.)
</OL>
+
#Mutually-recursive functions#
-<OL start=4>
+<OL start=5>
<LI>(Challenging.) One way to define the function `even` is to have it hand off
part of the work to another function `odd`:
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.)
+(See [[hints/Assignment 4 hint 3]] if you need some hints.)
</OL>