Primer 2

• type Posn = (Int, Int)

• occupied :: Posn -> [Posn] -> Bool. True if the first argument appears somewhere in the list which is the second argument.

• allOccupied:: [Posn] -> [Posn] -> Bool. True if every one of the posns in the first list appear somewhere in the second list.

    True == allOccupied [(1,5),(2,7)] [(2,7),(1,5),(3,7)]
    False == allOccupied [(1,5),(2,7)] [(2,7),(3,7)]
    False == allOccupied [(1,5),(2,7)] [(2,6),(2,8),(1,5)]
  

• occupiedPosn :: Board -> [Posn]: Just extract the occupied positions, regardless of player.

• dropDown :: Int -> [Posn] -> Int. The function dropDown x occupied gives a number that is one more than the largest y coordinate in the board with the same x coordinate. If there are no pieces in the given column, return 1 as the answer.

  In the example below, the column with x=4 has points with y=1 and y=2, so one more than largest y coordinate is y=3.

    dropDown 4 [(4,2),(1,1),(2,1),(2,2),(4,1),(2,3)] == 3
    dropDown 6 [(4,2),(1,1),(2,1),(2,2),(4,1),(2,3)] == 1