COSC 341/342  HW 1012   FALL 2017     Haskell Exercises

Distributed 10/12/2017    Due 10/19/2017

All code should be place in a single file.  You will write a function for each 
of the problems below.

Use list comprehension and pattern matching when possible.

You should not use a Haskell function that immediately solves the problem.
  
All functions should be given type declarations.  For function names, you
 should use the names I have supplied in the following problems.
 

(1) Given a list, return the tail of the list (note: do not use Haskell's tail)

    tail' [2, 3, 4]  returns [3, 4]


(2) Given a list of numbers, return product of the elements in the list 
    (do not use Haskell's product)

    product' [2, 3, 4]  returns 24  


(3) Given two tuples (x1, y1) and (x2, y2), return the city block distance
between them:
distance = abs (x1 - x2) + abs (y1 - y2)    -- abs is the mathematical absolute value
    
    cityBlock (1, 3) (4, 4) returns 4
    

(4) Given two tuples (x1 y1) and (x2, y2), that are each (Number, Number), 
    return the distance between the two points:  
    distance = sqrt ( (x1 - x2) ^ 2 + (y1 - y2) ^2 )
    You can use Haskell's sqrt

    euclid (1, 1) (2, 2)  returns 1.414213, approximately
    
    
(5) Given two lists of numbers, return a list that is the sum of corresponding
    elements.  If the lists are different lengths, stop the summing at the
    end of the shorter list.
    
    sum'' [] [1, 2, 3]  returns []
    
    sum'' [1, 2, 3] [4, 5, 6]  returns [5, 7, 9]

     
(6) Given two lists, they can be of any type, return the zipped list.
    Do not use Haskell's zip.
    
    zip' [] [1, 2, 3]   returns []
    zip' ['a', 'b'] [1, 2, 3] returns [('a', 1), ('b', 2) ] 

  
(7) Given two lists, the first has a list of values of any type, the
    second has a list of Bool values.
    Return the list containing only values in the first list where the
    corresponding value in the second list is True.
    
    pickIt [1, 2, 3] [True, False, True]  returns [1, 3]
    pickIt ['a', 'b', 'c'] [False, False, True] returns ['c']
    
         
(8) Given a list of 2-tuples, the first element of each tuple is a String,
    the second element of each tuple is a Bool.
    The function pack will return the list of tuples that contains only the tuples 
    that have the Bool value set to True. That is, the Bool value of each 
    tuple can be thought of as a 'delete' bit.
    
    Example: pack  [ ("a", True), ("b", False), ("c", False), ("d", True) ]
           returns [ ("a", True), ("d", True)  ]

    
(9) Implement ackermann's function.
See: https://en.wikipedia.org/wiki/Ackermann_function


Turn in:
  - Demo and walk-thru of at least two (instructor's choice)
  - hard copy of source code
  - screen shot showing each function's execution on all legal inputs.