Introduction to Programming
		      Assignment 2, 27 Aug, 2004
                         Due Fri 3 Sep, 2004

1. Define the function "majority" that takes as input a list of
   values of type Bool and returns True if half or more of them
   are True.  For instance:
  
          majority [True,True,False,False] = True
          majority [False,True,False] = False

2. Define the function "remdup" that takes as input a list of Int
   and removes all duplicate values from the list.  The function
   should retain the first copy of each duplicate value.  For
   instance:

          remdup [3,1,3,2,1] = [3,1,2]
          remdup [3,4,1] = [3,4,1]

3. A subsequence of a list is a sublist of elements of the
   original list in the same order, but not necessarily
   contiguous.  For instance, [3,1,2] is a subsequence of
   [3,1,7,2,3] but [3,1,2] is not a subsequence of
   [1,3,2,3,7]. Define the function "subseqs" that takes as input
   a list of Int and returns the list of all subsequences of that
   list.  The subsequences may be listed out in any order, but
   there should be no duplicates. For instance:

          subseqs [1,2] = [[],[1],[1,2],[2]]
          subseqs [1,2,3] = [[],[1],[1,2],[1,3],[1,2,3],[2],[2,3],[3]]

4. One String is a substring of another if the first String
   appears as a contiguous part of the second String.  For
   instance "abra" is a substring of "abracadabra" but "brad" is
   not a substring of "abracadbra".  The first example shows that
   a substring may match more than one portion of the second
   string.  Write the function "strpos" that takes as input two
   Strings and returns the earliest position in the second String
   where the first String occurs as a substring.  "strpos" should
   return -1 if the first String is not a substring of the second
   String.  The positions of a String of length n are defined to
   run from 0 to n-1.  For instance:

          strpos "abra" "abracadabra" = 0
          strpos "cad" "abracadabra" = 4
          strpos "brad" "abracadabra" = -1

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