Exercise 3      Name       ____________________   Points __/17

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1. Below is the gt4 function that returns true for tuples where value of first element is greater than 4.
   
       fun gt4 (x, _) = x > 4;
   
   Use gt4 and the filter functional to return only tuples where the first element is greater than 4. Filtering [(7,"CSCI"),(3,"CHEM"), (6,"PHY")] returns [(7, "CSCI"), (6, "PHY")].
   
   
           filter (gt4, [(7,"CSCI"),(3,"CHEM"), (6,"PHY")] );
    
2. What is the Cartesian product of:
   
   A = {1, 2, 3};
   B = {"a", "b", "c"}
   
   A x B = { (1, "a"), (1, "b"), (1, "c"), (2, "a"), (2, "b"), (2, "c"), (3, "a"), (3, "b"), (3, "c")}
    
3. Write a function named dist to construct a list of tuples from one element paired with every element of a list. For example:
   
   dist (3, ["a","b","c"]) returns [(3, "a"), (3, "b"), (3, "c")]
   
   
   fun dist _ []     = []
   |   dist a (h::t) = (a,h)::(dist a t);
   
    
4. Write a function named pairs that constructs all possible tuples of two lists. For example:
   
   pairs [1,2,3,4] ["a","b","c","d"]; returns
       [(1, "a"), (1, "b"), (1, "c"), (1, "d"),
        (2, "a"), (2, "b"), (2, "c"), (2, "d"),
        (3, "a"), (3, "b"), (3, "c"), (3, "d"),
        (4, "a"), (4, "b"), (4, "c"), (4, "d")]
   
   Hint: Use dist.
   
       fun pairs [] _     = []
     |   pairs (h::t) L = (dist h L)@(pairs t L);
    
5. Given member and union functions what is:

   union ( [(1, "a"), (1, "b"), (1, "c")], [(1, "a"), (1, "x"), (2, "c")]);

           [(1, "b"), (1, "c"), (1, "a"), (1, "x"), (2, "c")]

   fun member (_,[]) = false
   |    member (a,(h::t)) =
                       if a=h then true
                       else member (a, t);
   
   fun union ([],L) = L
   |    union ((h::t),L) =
                   if member(h,L) then union(t,L)
                   else h::union(t,L);

    

6. (3) Give appropriate ML datatype definitions for the following:
    
   1. Enumerate the set coin using the names of US coins worth $1.00 or less.
      
      datatype coin = dollar | half | quarter | dime | nickel | penny;
       
   2. The union SIR of a string, int or real.
      
      datatype SIR = S of string
      |              I of int
      |              R of real;
       
   3. Add coin to the union SIR to define the union SIRC.
      
      datatype SIR = S of string
      |              I of int
      |              R of real
      |              C of coin;
       
7. (3) Define function amount that totals the decimal amount of a list of coin. For example:
   
       amount [dollar, dollar, dime, nickel]; returns 215
   
      
       fun amount []           = 0
       |   amount (dollar::t)  = 100+amount t
       |   amount (half::t)    = 50 +amount t
       |   amount (quarter::t) = 25 +amount t
       |   amount (dime::t)    = 10 +amount t
       |   amount (nickel::t)  = 5 +amount t
       |   amount (penny::t)   = 1 +amount t;
    
8. (2) Complete function amount that totals the decimal amount of a list of SIRC. For example:
      
       amount [I 43, C dollar, R 52.0, S "nickel" ]; returns 200
    

   fun amount []                 = 0
   |   amount ((R h)::t)         = (trunc h) + amount t
   |   amount ((I h)::t)         = h + amount t
   |   amount ((S "dollar")::t)  = 100+amount t
   |   amount ((S "nickel")::t)  = 5 +amount t
   |   amount ((C dollar)::t)    = 100 +amount t
   |   amount ((C half)::t)      = 50 +amount t
   |   amount ((C quarter)::t)   = 25 +amount t
   |   amount ((C dime)::t)      = 10 +amount t
   |   amount ((C nickel)::t)    = 5 +amount t
   |   amount ((C penny)::t)     = 1 +amount t;