Problem Sheet 1
                   ---------------

This problem  sheet is to get  you started on  Haskell programming and
for familiarity with the Haskell  interpreter Hugs.  The TAs will help
you  in solving  these  problems.   Though your  answers  will not  be
graded, you will have to submit the assignment.


1. Consider a representation of matrices as lists where the matrix

            | a  b  c |
            | d  e  f |

is represented as 

    [[a,b,c],[d,e,f]]

Call   this  matrix  m.   Now  define   the  following   functions  on
matrices. Use higher order functions as much as possible.

   1. A function firstcol, such that (firstcol m) will return [[a],[d]].
   2. A function lastcols, such that (lastcols m) will return [[b,c],[e,f]].
   5. A function dot-product with the obvious meaning.
   4. A function transpose which will transpose a matrix.
   3. A function matmult which will return the multiplication of two matrices.


2.  (a) Using foldr  write a function called inits which finds all the initial
    segments of a list.

    Examples:  (inits []) = [[]]
               (inits [1,2,3,4]) =  [[],[1],[1,2],[1,2,3],[1,2,3,4]]

    (b) Once again  using foldr  write a function tails which will find all
    the tail segments of a list.

    Examples:  (tails []) = [[]]
               (tails [1,2,3,4] = [[],[4],[3,4],[2,3,4],[1,2,3,4]]

    (c) Now  using inits  tails  and map  define a function called sublists
    which will find all the sublists of a list.

    Example:   (sublist []) = [[]]
               (sublist [1,2,3,4]) = [[],[1] [1,2] [1,2,3],[1,2,3,4],[2],[2,3],
                                      [2,3,4],[3] [3,4],[4]]


3. A general tree is defined by the datatype declaration:

      data Gtree a = Gnode a [Gtree a]

   Define functions  

      dft :: Gtree a -> [a],  and 
      bft :: Gtree a -> [a] 

   which will do depth-first traversals and breadth-first traversals
   over general trees.