CSE 428: Quizzes

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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, [1,2,3]); true
- memb(1, [1.0,2.0,3.0]); error
- memb([1], [[1,2],[3]]); false
- memb(fn x => x+1, [ fn x => x+1 , fn x => 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 (remember that @ is the pre-defined append function):
```
   datatype tree = Leaf of int | Node of (tree * int * tree);
 
   fun f (Leaf n) = [n]
     | f (Node(t1,n,t2)) = (f t1) @ (n::(f t2));
```
Say what is the semantics of f (only one answer, please)
- f takes a tree t and returns the maximum element of t
- f takes a tree t and produces the list of integers according to the in-order traversal of t
- error, because @ is an operator on lists
- f takes two trees t1 and t2 , and an integer n, and produces a new tree which has n as root and t1 and t2 as the left and right subtrees.

[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,y) => if x < y then y else x , [(2,1),(3,4),(5,6)] )

[Pts 2] An anonymous function is: (only one answer, please)
- a function which returns a private name (namely, a name local to another function)
- a function which is represented by an expression, without being associated to a name
- a higher order function
- a function which is declared within the scope of another function