✎ fp:lab10 [books]

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===== 9.3. Trees =====

9.3.1. Implement a datatype for trees of integers. Write a function which checks if a tree is complete:
<code haskell>
isComplete :: IntTree -> Bool
</code>

9.3.2. Write a function which flattens a tree to a list:
<code haskell>
flatten :: IntTree -> [Integer]
</code>

9.3.3. The game Tic-Tac-Toe (or X and 0) is played on a three-by-three board of **positions**. Each position may be: free, with an X or with a 0.
  * write a ADT ''Position'' which encodes the value of each position.
  * write an ADT ''Board'' which encodes (using matrices) a 3-by-3 board of positions.
  * write a function which checks if either '''X''' or '''0''' have won (''won :: Char -> Board -> Bool'')

Starting from a given (initial) board, we want to build **a tree** of all possible outcomes of the game.  Example:

<code>
Parent node:

X 0 0
0   X
  0

Children (It is X-s turn to move):

X 0 0    X 0 0     X 0 0
0 X X    0   X     0   X
  0      X 0         0 X
</code>


9.3.4.