X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment4.mdwn;h=9b7ec2c028622dc92e17dced54403aa6043b8896;hp=1eec95e1422d65266ef5349ae41484029db52ee7;hb=e5f582330945c265a211cbebb30bc06a94f3ed91;hpb=a0f99722a5a10cb939258a6c7eba32a28f2944e8 diff --git a/assignment4.mdwn b/assignment4.mdwn index 1eec95e1..9b7ec2c0 100644 --- a/assignment4.mdwn +++ b/assignment4.mdwn @@ -32,15 +32,54 @@ How would you implement such a list comparison? First, read this: [[Implementing trees]]
-
1. blah - -(See [[hints/Assignment 4 hint 3]] if you need some hints.) +
2. 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.) + +
3. 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.)
+ #Mutually-recursive functions# -
+
1. (Challenging.) One way to define the function `even` is to have it hand off part of the work to another function `odd`: @@ -98,7 +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. -(See [[hints/Assignment 4 hint 4]] if you need some hints.) +(See [[hints/Assignment 4 hint 3]] if you need some hints.)