Formulate the following problems in terms of a map(), a fold(), or a 
combination of map() and fold(). You do not need to specify the full 
definition of your map() or fold(); just give a few sentences on what 
would be performed by each function.

   1. Given a list of vectors [(x1, y1, z1), (x2, y2, z2), ... ], add 
them to determine the resultant vector. Note that by "vector" we are 
referring to a physics vector, e.g., a displacement vector.



fun AddVectors lst = 
  foldl (fn ((x,y,z),(a,b,c)) => (x+a, y+b, z+c)) (0,0,0) lst






   2. Given a company's monthly paystubs for all employees for an entire 
year, calculate how much income tax is owed per-person. Your input will 
be an unordered list of the form [ (empID1, monthID1, monthlyWage1), 
(empID1, monthID2, monthlyWage2), (empID5, monthID5, monthlyWage5), ... ], 
and your output should be of the form [ (empID1, taxOwed1), ... ].



Fold over the input list to create a new list containing all 
the employee ids along with the sum of their wages. This will
involve an inner map over the list being passed along as the
accumulator, which must find the employee id that is the same, 
and update it with the monthly salary total. Then do a final 
map to compute tax from wages

fun calculateTaxes lst =
  let allIds = foldl (fn ((emp,_,_), ids) => 
                  if (List.exists (fn id => id = emp) ids) 
                   then ids else emp::ids) lst in
  let ids_with_zeros = map (fn x => (x,0)) allIds in
  let ids_with_wages = foldl 
      ((fn (emp,_,wage),ids) => 
         map (fn (id,sum) => if id=emp 
             then (id,sum+wage) else (id,sum)) ids) ids_with_zeros lst
  in 
    map computeTaxFromWages ids_with_wages


(List.exists f lst returns true if (f x) is true for some x in lst,
 and false otherwise.)


   3. Find the smallest element in an array.



fun ListMin lst =
  foldl (fn (x,a) => if (x < a) then x else a) INT_MAX lst






   4. Bonus question: Run-length encoding
      Run-length encoding takes a possibly-repetitive string and rewrites 
it as a (substring, frequency) pair, eg "aaabccccdd" becomes "a3bc5d2"

    (an exercise for the adventurous.)