From: Jim Pryor Date: Mon, 4 Oct 2010 01:04:52 +0000 (-0400) Subject: continuing assignment4 X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=2dad468862d6fff48c8f499386dc571bd899bc28 continuing assignment4 Signed-off-by: Jim Pryor --- diff --git a/assignment4.mdwn b/assignment4.mdwn index 1eec95e1..8b8a19dc 100644 --- a/assignment4.mdwn +++ b/assignment4.mdwn @@ -32,12 +32,41 @@ How would you implement such a list comparison? First, read this: [[Implementing trees]]
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  1. blah +
  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. + +
  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. (You just programmed this above.) + +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.)
+ #Mutually-recursive functions#