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60df8ae3 · Giammarco, Kristin M · 0cfeb35b · 60df8ae3
Commit 60df8ae3 authored 3 years ago by Giammarco, Kristin M
--- a/models/Application_examples/Tic_tac_toe.mp
+++ b/models/Application_examples/Tic_tac_toe.mp
+/*┬────────────────────────────────────────────────────────┐
+│*│ ┌─[ Title and Authors ]──────────────────────────────┐ │
+│*│ │ Model of Tic Tac Toe                               │ │
+│*│ │  Created by Michael Collins in December, 2021.     │ │
+│*│ │  Modified by Michael Collins and Pamela Dyer       │ │
+│*│ │     in January through May, 2022.                  │ │
+│*│ │                                                    | |
+│*│ │  Thanks to Emma Werking for her contributions.     │ │
+│*│ └────────────────────────────────────────────────────┘ │
+│*│                                                        │
+│*│ ┌─[ Purpose ]────────────────────────────────────────┐ │
+│*│ │ To demonstrate using MP to model simple strategies │ │
+│*│ │ in the context of a game of Tic-tac-toe.           │ │
+│*│ └────────────────────────────────────────────────────┘ │
+│*│                                                        │
+│*│ ┌─[ Description ]────────────────────────────────────┐ │
+│*│ │ How to play Tic-tac-toe:                           | |
+│*│ │ The game board is a 3 by 3 grid of cells.          | |
+│*│ │ The player who goes first is known as 'X'.         | |
+│*│ │ The player who goes second is known as 'O'.        | |
+│*│ │ The players alternate placing Xs and Os on the     | |
+│*│ │  board until either one of the players has three in| |
+│*│ │  a line or until all cells on the grid are filled. | |
+│*│ │                                                    | |
+│*│ │ The goal is to never lose a game of Tic-Tac-Toe.   | |
+|*| |                                                    | |
+│*│ │ The following rules simplify the strategy:         | |
+│*│ │     1) X never makes any mistakes.                 │ │
+|*| |     2) O makes at most one mistake.                | |
+│*│ │     3) X always chooses a corner on the first move | |
+|*| |        of the game.                                | |
+|*| |                                                    | |
+│*│ │ Strategy: List all possible 2nd moves of the       | |
+|*| |           game. Show how X can win or play to a    | |
+|*| |           draw in each case by listing every move. | |
+|*| |           When playing the game as X, use these    | |
+|*| |           predetermined games as your directions   | |
+|*| |           for how to play.                         | |
+│*│ └────────────────────────────────────────────────────┘ │
+│*│                                                        │
+│*│ ┌─[ References ]─────────────────────────────────────┐ │
+│*│ │ Yates, James. "Tic Tac Toe Strategy Guide."        │ │
+│*│ │ Chess and Poker Dot Com. Accessed April 6, 2022.   │ │
+│*│ │https://www.chessandpoker.com/tic_tac_toe_strategy.html
+│*│ └────────────────────────────────────────────────────┘ │
+│*│                                                        │
+│*│ ┌─[ Search Terms ]───────────────────────────────────┐ │
+│*│ │ tic-tac-toe, behavior; strategy; assertion checking│ │
+│*│ └────────────────────────────────────────────────────┘ │
+│*│                                                        │
+│*│ ┌─[ Instructions ]───────────────────────────────────┐ │
+│*│ │ Run for Scope 1.                                   │ │
+│*│ ├─[ Run Statistics ]─────────────────────────────────┤ │
+│*│ │ Scope 1: 5 traces in less than 1 sec.              │ │
+│*│ └────────────────────────────────────────────────────┘ │
+└*┴───────────────────────────────────────────────────────*/
+
+SCHEMA Tic_tac_toe;
+/*
+Explanation:
+
+  The 3x3 board with definitions for all cells:
+
+     Corner | Remnant | Corner
+    ----------------------------
+     Remnant| Center  | Remnant
+    ----------------------------
+     Corner	| Remnant | Corner
+
+    The center  cell has 0-outer edges.
+    A   remnant cell has 1-outer edge.  ( corners are also edge cells )
+    A   corner  cell has 2-outer edges.
+*/
+
+ROOT Strategy_based_on_2nd_move_of_the_game:
+(
+  choosing_remnant_next_to_X_on_2nd_move                 |/* Mistake, X wins  */
+  choosing_remnant_NOT_beside_an_X_on_2nd_move           |/* Mistake, X wins  */
+  choosing_a_corner_on_2nd_move                          |/* Mistake, X wins  */
+  choosing_center_on_2nd_Move_and_any_corner_on_4th_move |/* Mistake, X wins  */
+  choosing_center_on_2nd_Move_and_any_remnant_on_4th_move /* No mistakes,Draw */
+);
+
+/* Player going second makes mistake on second move of the game */
+choosing_remnant_next_to_X_on_2nd_move :
+ /* first   move */           X_chooses_corner
+ /* second  move - mistake */ O_chooses_remnant_next_to_X_on_first_turn
+ /* third   move */           X_chooses_center
+ /* fourth  move */           O_blocks_
+ /* fifth   move */           X_chooses_corner_NOT_beside_any_O
+ /* sixth   move */           O_blocks
+ /* seventh move */           X_wins;
+
+/* Player going second makes mistake on second move of the game */
+choosing_remnant_NOT_beside_an_X_on_2nd_move :
+ /* first   move */           X_chooses_corner
+ /* second  move - mistake */ O_chooses_remnant_NOT_beside_an_X_on_first_turn
+ /* third   move */           X_chooses_center
+ /* fourth  move */           O_blocks_
+ /* fifth   move */           X_blocks
+ /* sixth   move */           O_blocks
+ /* seventh move */           X_wins;
+
+
+/* Player going second makes mistake on second move of the game */
+choosing_a_corner_on_2nd_move :
+ /* first   move */		      X_chooses_corner
+ /* second  move - mistake */ O_chooses_corner
+ /* third   move */		      X_chooses_any_corner
+ /* fourth  move */		      O_blocks_
+ /* fifth   move */		      X_chooses_last_corner
+ /* sixth   move */		      O_blocks_one_path
+ /* seventh move */		      X_wins;
+
+
+/* Player going second makes mistake on fourth move of the game */
+choosing_center_on_2nd_Move_and_any_corner_on_4th_move :
+ /* first   move */           X_chooses_corner
+ /* second  move */           O_chooses_center
+ /* third   move */           X_chooses_corner_opposite_previous_X
+ /* fourth  move - mistake */ O_chooses_any_corner
+ /* fifth   move */           X_blocks
+ /* sixth   move */           O_blocks
+ /* seventh move */	          X_wins;
+
+
+/* No mistakes made by either player */
+choosing_center_on_2nd_Move_and_any_remnant_on_4th_move :
+ /* first   move */           X_chooses_corner
+ /* second  move */           O_chooses_center
+ /* third   move */           X_chooses_corner_opposite_previous_X
+ /* fourth  move */           O_chooses_any_remnant
+ /* fifth   move */           X_blocks
+ /* sixth   move */           O_blocks
+ /* seventh move */           X_blocks
+ /* eighth  move */           O_blocks
+ /* ninth   move */           STALEMATE;
+
+CHECK #X_wins == 1 OR #STALEMATE == 1
+ONFAIL SAY ("X LOST!");
+
+
+
+
+
+
+
+
+
+
+
+/*----------------COORDINATION SOLELY FOR VISUAL AID ___ */
+/*NONE OF THIS COORDINATION CONSTRAINS OR INFLUENCES THE STRATEGY */
+/* JUST VISUAL COMMENTARY FOR THE VIEWER */
+COORDINATE $XEE_XEO: ( choosing_remnant_next_to_X_on_2nd_move |
+                       choosing_remnant_NOT_beside_an_X_on_2nd_move )
+DO
+	ADD SAY("O chooses a remnant on second move.") PRECEDES $XEE_XEO;
+OD;
+COORDINATE $XEE_XEO: choosing_a_corner_on_2nd_move
+DO
+	ADD SAY("O chooses any corner on second move. ") PRECEDES $XEE_XEO;
+OD;
+COORDINATE $XOE: (
+                   choosing_center_on_2nd_Move_and_any_corner_on_4th_move |
+                   choosing_center_on_2nd_Move_and_any_remnant_on_4th_move
+                 )
+DO
+	ADD SAY("O chooses center on second move.") PRECEDES $XOE;
+OD;
+COORDINATE $first_move: X_chooses_corner
+DO
+	ADD SAY("FIRST MOVE OF THE GAME.") PRECEDES $first_move;
+OD;
+COORDINATE $second_move:
+ (
+     	O_chooses_remnant_next_to_X_on_first_turn           |
+        O_chooses_remnant_NOT_beside_an_X_on_first_turn       |
+     	O_chooses_corner	                                    |
+     	O_chooses_center
+ )
+DO
+	ADD SAY("SECOND MOVE OF THE GAME.") PRECEDES $second_move;
+OD;
+COORDINATE $third_move:
+ (
+     	X_chooses_center                         |
+        X_chooses_any_corner                       |
+     	X_chooses_corner_opposite_previous_X
+ )
+DO
+	ADD SAY("THIRD MOVE OF THE GAME.") PRECEDES $third_move;
+OD;
+COORDINATE $fourth_move:
+        ( O_blocks_ | O_chooses_any_corner )
+DO
+	ADD SAY("FOURTH MOVE OF THE GAME."  ) PRECEDES $fourth_move;
+	ADD SAY("X is now guaranteed to win") PRECEDES $fourth_move;
+OD;
+COORDINATE $fourth_move:  O_chooses_any_remnant
+DO
+	ADD SAY("FOURTH MOVE OF THE GAME."    ) PRECEDES $fourth_move;
+	ADD SAY("STALEMATE IS NOW GUARANTEED ") PRECEDES $fourth_move;
+OD;
+/******************************************************************/