X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment4.mdwn;h=3e3b71841c6fa51e546c65c4c527cf798836de40;hp=1eec95e1422d65266ef5349ae41484029db52ee7;hb=95dad38cb4aa443a3dde5bad742d53f023b0ca33;hpb=a0f99722a5a10cb939258a6c7eba32a28f2944e8 diff --git a/assignment4.mdwn b/assignment4.mdwn index 1eec95e1..3e3b7184 100644 --- a/assignment4.mdwn +++ b/assignment4.mdwn @@ -32,12 +32,48 @@ 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. 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. (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#