Exercise 4      Name       ____________________   Points __/18

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1. (5) Give the anonymous functions equivalent to:

   1. fun dubal x = 2 * x;                           
   2. fun sub x y = x - y;                            
   3. fun gt x y = x > y;                             
   4. fun max x y = if x > y then x else y;    
   5. fun pre x y z = if (x y z) then y else z; 

2. (4) Duplicate using anonymous functions.

   1. map dubal [1,2,3,4];                    
   2. foldr sub 1 [1,2,3,4];                 
   3. map2 sub [1,2,3] [4,5,6]              
   4. map2 max [3,2,1] [1,2,3];            

3. (2) Give the staged version of the member function.
   
   fun member (_,[]) = false                              
   |    member (a,(h::t)) =                                  
                       if a=h then true                          
                       else member (a, t);                     
    
4. (7) Evaluate the following:

   1. foldr (op *) 1 [1,2,3,4];                            
   2. foldr (op -) 0 [1,2,3,4];                             
   3. map (gt 2) [1,2,3,4];                                
   4. foldl (op -) 0 [1,2,3,4];                             
   5. map (max 2) [1,2,3,4];                             
   6. map ((fn x => fn y => x > y) 2) [1,2,3,4]; 
   7. [dubal 4, sub 5 4];