tic-tac-toe.eve

# Tic-Tac-Toe

## Game logic

Tic-Tac-Toe is a classic game played by two players, "X" and "O", who take turns marking their letter on a 3x3 grid. The first player to mark 3 adjacent cells in a line wins. The game can potentially result in a draw, where all grid cells are marked, but neither player has 3 adjacent cells. To build this game in Eve, we need several parts:

- A game board with cells
- A way to mark a cell as "X" or "O"
- A way to recognize that a player has won the game.

### Game settings

To begin, we initialize the board. We commit a `#board` record to hold our global state and create a set of `#cell`s, which will keep track of the moves players have made. Common connect-N games (a generalized tic-tac-toe for any `NxN` grid) are scored along 4 axes (horizontal, vertical, the diagonal, and the anti-diagonal). We group cells together along each axis up front to make scoring easier later.

The game board is square, with a given size. It contains size ^ 2 cells,
each with a row and column index.

~~~
search
  // board constants
  size = 3
  starting-player = "X"

  // generate the cells
  i = range[from: 1, to: size]
  j = range[from: 1, to: size]

commit
  board = [#board size player: starting-player]
  [#cell board row: i column: j]
~~~

A subtlety here is the last line, [#cell board row: i column: j]. Thanks to our relational semantics, this line actually generates all 9 cells. Since the sets of values computed in i and j have no relation to each other, when we use them together we get the cartesian product of their values. This means that if `i = {1, 2, 3}` and `j = {1, 2, 3}`, then `i x j = {(1, 1), (1, 2), ... (3, 2), (3, 3)}`. These are exactly the indices we need for our grid!

Now we tag some special cell groupings: diagonal and anti-diagonal cells. The diagonal cells are `(1, 1)`, `(2, 2)`, and `(3, 3)`. From this we can see that diagonal cells have a row index equal to its column index

~~~
search
  cells = [#cell row column]
  row = column

bind
  cells += #diagonal
~~~

Similarly, the anti-diagonal cells are `(1, 3)`, `(2, 2)`, and `(3, 1)`.

Anti-diagonal cells satisfy the equation `row + col = N + 1`,
where `N` is the size of the board.

~~~
  search
    cells = [#cell row column]
    [#board size: N]
    row + column = N + 1

  bind
    cells += #anti-diagonal
~~~

### Winning condition

A game is won when a player marks N cells in a row, column, or diagonal.
The game can end in a tie, where no player has N in a row.

~~~
search
  board = [#board size: N, not(winner)]

  (winner, cell) = 
    // Check for a winning row
    if cell = [#cell row player] 
       N = count[given: cell, per: (row, player)] 		
    then (player, cell)
    // Check for a winning column
    else if cell = [#cell column player]
            N = count[given: cell, per: (column, player)] 
    then (player, cell)
    // Check for a diagonal win
    else if cell = [#diagonal row column player]
            N = count[given: cell, per: player] 
    then (player, cell)
    // Check for an anti-diagonal win
    else if cell = [#anti-diagonal row column player]
            N = count[given: cell, per: player] 
    then (player, cell)
    // If all cells are filled but there are no winners
    else if cell = [#cell player]
            N * N = count[given: cell] 
    then ("nobody", cell)

commit
  board.winner := winner
  cell += #winner
~~~

We use the count aggregate in the above block. Count returns the number of discrete values (the cardinality) of the variables in given. The optional per attribute allows you to specify groupings, which yield one result for each set of values in the group.

For example, in count[given: cell, per: player] we group by player, which returns two values: the count of cells marked by player X and those marked by O. This can be read "count the cells per player". In the scoring block, we group by column and player. This will return the count of cells marked by a player in a particular column. Like wise with the row case. By equating this with N, we ensure the winning player is only returned when she has marked N cells in the given direction.

This is how Eve works without looping. Rather than writing a nested for loop and iterating over the cells, we can use Eve's semantics to our advantage.

We first search every row, then every column. Finally we check the diagonal and anti-diagonal. To do this, we leverage the `#diagonal` and `#anti-diagonal` tags we created earlier; instead of searching for `#cell`, we can search for these new tags to select only a subset of cells.

## React to Events

Next, we handle user input. Any time a cell is directly clicked, we:

- Ensure the cell hasn't already been played
- Check for a winner
- Switch to the next player

Then update the cell to reflect its new owner, and switch board's player to the next player.

### Marking a cell

Click on a cell to make your move

~~~
search @event @session @browser
  [#click #direct-target element: [#div cell]]
  // Ensures the cell hasn't been played
  not(cell.player)                               
  // Ensures the game has not been won
  board = [#board player: current, not(winner)]  
  // Switches to the next player
  next_player = if current = "X" then "O"
  							else "X"

commit
  board.player := next_player
  cell.player := current
~~~

### Reset the game

Since games of tic-tac-toe are often very short and extremely competitive, it's imperative that it be quick and easy to begin a new match. When the game is over (the board has a winner attribute), a click anywhere on the drawing area will reset the game for another round of play.

A reset consists of:

- Clearing the board of a winner
- Clearing all of the cells
- Removing the #winner tag from the winning cell set

~~~
search @event @browser @session
  [#click element: [#div board]]
  board = [#board winner]
  cell = [#cell player]

commit
  board.winner -= winner
  cell.player -= player
  cell -= #winner
~~~

## Drawing the Game

We've implemented the game logic, but now we need to actually draw the board so players have something to see and interact with. Our general strategy will be that the game board is a #div with one child `#div` for each cell. Each cell will be drawn with an "X", "O", or empty string as text. We also add a `#status` div, which we'll write game state into later. Our cells have the CSS inlined, but you could just as easily link to an external file.

### Draw the board

~~~
search
  board = [#board]
  cell = [#cell board row column]
  contents = if cell.player then cell.player
  					 else ""

bind @browser
	[#div board #container style: [font-family: "sans-serif"], children:
		[#div #status board class: "status", style: [text-align: "center" width: 150 height: 50, padding-bottom: 10]]
		[#div class: "board", style: [color: "black"] children:
			[#div class: "row", sort: row, children:
				[#div #cell cell class: "cell", text: contents, sort: column,
         style: [display: "inline-block", width: 50, height: 50, border: "1px solid black", background: "white", font-size: "2em", line-height: "50px", text-align: "center", vertical-align: "top"]]]]]
~~~

Winning cells are drawn in a different color

~~~
search @session @browser
  winning-cells = [#cell #winner]
  cell-elements = [#div cell: winning-cells style]

bind @browser
  style.color := "blue"
~~~

### Draw status message

Finally, we fill the previously mentioned #status div with our current game state. If no winner has been declared, we remind the competitors of whose turn it is, and once a winner is found we announce her newly-acquired bragging rights.

Display the current player if the game isn't won

~~~
search @session @browser
  status = [#status board]
  not(board.winner)

bind @browser
  status.text += "It's {{board.player}}'s turn!"
~~~

When the game is won, display the winner

~~~
search @session @browser
  status = [#status board]
  winner = board.winner

bind @browser
  status.text += "{{winner}} wins! Click anywhere to restart!"
~~~