X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment4.mdwn;h=9b7ec2c028622dc92e17dced54403aa6043b8896;hp=8b8a19dc78c1b71ec20e64e6df79d8599f245755;hb=27ce0d45d4ab28840605ec2130f6ba4ecd9d6213;hpb=2dad468862d6fff48c8f499386dc571bd899bc28 diff --git a/assignment4.mdwn b/assignment4.mdwn index 8b8a19dc..9b7ec2c0 100644 --- a/assignment4.mdwn +++ b/assignment4.mdwn @@ -34,9 +34,16 @@ First, read this: [[Implementing trees]]
1. 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. +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.) -
2. 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. 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: . / \ @@ -44,7 +51,7 @@ First, read this: [[Implementing trees]] / \ 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: . / \ @@ -57,19 +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`: @@ -127,7 +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.)