CSE 428: Quizzes

Spring 2001, CSE 428: Quiz 9.2 - 29 March 2001

Please write your Name and Student ID,at the top of the page.
By default, this quiz will be returned in Section 2 (morning section).

[Pts 4] Consider the following definition of the function "member"
```
   fun memb(x, []) = false
     | memb(x, y::L) = if x = y then true else memb(x,L);
```
For each of the following expressions, say what is the result (true, false, or error). Remember that the two arguments of "=" must have the same type, and that it must be an equality type.
- memb(1.0, [1,2,3]); error
- memb(1, [2,3,4]); false
- memb([1], [1,2,3]); error
- memb(fn x => 1, [ fn x => 1 , fn x => 2 ]); error
[Pts 2] Consider the following datatype representing binary trees with integer labels, and the definition of a function f on that datatype
```
   datatype tree = Leaf of int | Node of (tree * int * tree);
 
   fun f (Leaf n) = Leaf n
     | f (Node(t1,n,t2)) = Node(f t1, 0, f t2);
```
Say what is the semantics of f (only one answer, please)
- f takes a tree t and returns n if t is a leaf labeled by n, 0 otherwise
- f takes a tree t and produces the list of integers on the frontier of t
- error, because the fisrt case returns a Leaf and the second case returns a Node
- f takes a tree t and returns the tree obtained by replacing all the labels of the internal nodes of t by 0
[Pts 2] Consider the following function map:
```
    fun map(f, []) = []
      | map(f, x::L) = (f x) :: (map(f,L));
```
Say what is the result of the following expression (only one answer, please)
```
 
   map( fn x => tl x , [[2,1],[3,4],[5,6]])
```
- error
- [5,6]
- [[1],[4],[6]]
- [[3,4],[5,6]]
[Pts 2] A higher order function is: (only one answer, please)
- an anonymous function
- a function whose arguments or results are functions
- a function which is written in a high level langauge
- a function which is greater than another function in the pointwise functional ordering