X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment4.mdwn;h=6a528a23c943a8f0b3a0e909f999092f657f900d;hp=cd927873638b3ffbd724d09b599e2e1f211d5c89;hb=9888d5cbf679f92c7447c7d4eb06ad407e974f94;hpb=f3e44d1a6911bf2bf8376bd3b711adf63cdeee13 diff --git a/assignment4.mdwn b/assignment4.mdwn index cd927873..6a528a23 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 +64,21 @@ 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, and it +should make use of the list comparison function you wrote for question +2. Thus you'll have to make sure you only use Church numerals as the +labels of your leaves, though nothing enforces this self-discipline. -(See [[hints/Assignment 4 hint 3]] if you need some hints.) #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 +136,7 @@ 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.)