X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment4.mdwn;h=9b7ec2c028622dc92e17dced54403aa6043b8896;hp=cd927873638b3ffbd724d09b599e2e1f211d5c89;hb=e5f582330945c265a211cbebb30bc06a94f3ed91;hpb=50a9ebe3ecc8c1b392c8118546ded369fe39d1d4 diff --git a/assignment4.mdwn b/assignment4.mdwn index cd927873..9b7ec2c0 100644 --- a/assignment4.mdwn +++ b/assignment4.mdwn @@ -38,7 +38,9 @@ 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. +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.)
• 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: @@ -49,7 +51,7 @@ ordered from left to right. For example, the fringe of this tree: / \ 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: . / \ @@ -62,19 +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 -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.) #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`: @@ -132,7 +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.)