Merge branch 'master' of ssh://server.philosophy.fas.nyu.edu/Users/lambda/lambda

[lambda.git] / assignment4.mdwn

diff --git a/assignment4.mdwn b/assignment4.mdwn
index 8b8a19d..9b7ec2c 100644 (file)
--- a/assignment4.mdwn
+++ b/assignment4.mdwn
@@ -34,9 +34,16 @@ First, read this: [[Implementing trees]]
 <OL start=3>
 <LI>Write an implementation of leaf-labeled trees. You can do something v3-like, or use the Y combinator, as you prefer.
 
 <OL start=3>
 <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.
+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:
+<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:

 
                .
           / \
 
                .
           / \


@@ -44,7 +51,7 @@ First, read this: [[Implementing trees]]
         / \
        1   2
 
         / \
        1   2
 

-is [1;2;3]. And that is also the fringe of this tree:
+is `[1;2;3]`. And that is also the fringe of this tree:

 
                .
           / \
 
                .
           / \


@@ -57,19 +64,22 @@ 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
 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. (You just programmed this above.)
+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.
+Write the fringe-enumeration function. It should work on the
+implementation of trees you designed in the previous step.

 
 

-(See [[hints/Assignment 4 hint 3]] if you need some hints.)
+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>
 
 
 
 #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`:
 
 <LI>(Challenging.) One way to define the function `even` is to have it hand off
 part of the work to another function `odd`:
 


@@ -127,7 +137,7 @@ definitions of `even` and `odd`?
 notes](/week3/#index4h2) as a model, construct a pair `Y1` and `Y2` that behave
 in the way described.
 
 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>
 
 
 </OL>