Exercise 4a      Name       ____________________   Points __/26

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Valid answers are in bold.

1. (5) Which are valid for definition:

   datatype intbunch = One of int
   |                             Group of int list;

   1. One 5;                           
   2. [One 5, One 4];                            
   3. Group[1,2,3];                             
   4. [Group[1,2,3], One 5];    
   5. Group[One 5, One 3]; 

    

2. (4) Which are valid for definition: 

   datatype bunch = One of int
   |                         Group of bunch list;

   1. One 5;                    
   2. Group[Group[One 5,One 4],Group[One 2]];
   3. Group[Group[One 5,One 4],One 4];   
   4. Group[Group[One 5.4,One 4.2],One 4.7];   

                         

3. (4) Which are valid for definition: 

   datatype 'ex bunch = One of 'ex
   |                              Group of 'ex bunch list;

   1. One 5;                    
   2. Group[Group[One 5,One 4],Group[One 2]];
   3. Group[Group[One 5,One 4],One 4];   
   4. Group[Group[One 5.4,One 4.2],One 4.7];   

4. (5) Which are valid for definition: 

datatype 'ex bunch = NIL
|                              One of 'ex
|                              Group of 'ex * 'ex bunch;

1. NIL;
2. One 5;                    
3. Group(4,Group(5, One 6));
4. Group(4,Group(5, NIL));
5. Group(true,Group(false, One false));

5. (4) Define a function to return the sum of the elements of a bunch as defined in Question 4.

   sum (Group( 3, Group( 2, One 1) )); returns 6

   fun sum NIL = 0
   |    sum (One x) = x
   |    sum (Group(h,t)) = h+sum t;