X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment4.mdwn;h=12c1ef2a213e195cd9f88066baf9e8e53e9d5c46;hp=8b8a19dc78c1b71ec20e64e6df79d8599f245755;hb=4c15241dde4586a70e36948d3a9cb035c33c8e5e;hpb=2dad468862d6fff48c8f499386dc571bd899bc28 diff --git a/assignment4.mdwn b/assignment4.mdwn index 8b8a19dc..12c1ef2a 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: . / \ @@ -61,15 +68,13 @@ 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# -
    +
    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 +132,7 @@ 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.)