
AutoToS prompt:

This domain models the classic Sokoban game, where the robot needs to move around and push stones to specific locations while adhering to the constraints defined by the walls in the maze. 
The maze is defined by a grid of values 0,1, and 2, where 2 means it is a goal location for a stone, 1 means the cell is blocked, and either 0 or 2 means that the cell can be occupied. A cell is clear if it can be occupied, but is not occupied by either the player or any stone.

The actions are:

move: This action moves the player in a specified direction. To perform this action, the target location must be clear and adjacent to player's location. Performing this action will result in the player being at the target location and no longer at the starting location, meaning the starting location is now clear, while the target location is now not clear.

push: This action allows the player to push a stone in a specified direction. To perform this action, the player's location, the stone location, and the target location must line up in the same direction, and the target location must be clear. Performing the action results in player being at the stone's initial location and the stone is at the target location. Further, the player's previous location is clear, while the target location is not clear.

Assume that states are defined by a dictionary with keys at-player and at-stone. 
Here is an example of a state
{'at-player': (4, 4), 'at-stone': [(2, 2), (3, 3)]}
Here is an example of the grid:
[[1, 1, 1, 1, 0, 0, 0, 0], [1, 0, 0, 1, 1, 0, 0, 0], [1, 0, 0, 0, 1, 1, 1, 1], [1, 0, 0, 0, 1, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 1], [0, 1, 1, 1, 2, 2, 0, 1], [0, 0, 0, 1, 0, 1, 0, 1], [0, 0, 0, 1, 0, 0, 0, 1], [0, 0, 0, 1, 1, 1, 1, 1]]

Provide a Python implementation of successor states function, receiving a state and a grid and returning a list of immediate successor states.

Model response:
Python
```
def successor_states(state, grid):
    """
    This function generates all possible successor states given a state and a grid.
    
    Parameters:
    state (dict): A dictionary containing the current state of the game. It has two keys: 'at-player' and 'at-stone'.
                  'at-player' is a tuple representing the current position of the player.
                  'at-stone' is a list of tuples representing the current positions of the stones.
    grid (list): A 2D list representing the game grid. It contains 0s, 1s, and 2s where 0 represents an empty cell,
                 1 represents a blocked cell, and 2 represents a goal location.
    
    Returns:
    list: A list of dictionaries representing all possible successor states.
    """

    # Define all possible movements (up, down, left, right)
    movements = [(0, 1), (0, -1), (1, 0), (-1, 0)]

    # Function to check if a cell is clear
    def is_clear(cell):
        return grid[cell[0]][cell[1]] != 1 and cell not in state['at-stone'] and cell != state['at-player']

    # Function to check if a cell is a valid position for a stone
    def is_valid_stone_position(cell):
        return grid[cell[0]][cell[1]] in [0, 2]

    # Initialize the list of successor states
    successor_states = []

    # Check all possible movements for the player
    for movement in movements:
        new_player_position = (state['at-player'][0] + movement[0], state['at-player'][1] + movement[1])

        # Check if the new position is clear and within the grid boundaries
        if (0 <= new_player_position[0] < len(grid)) and (0 <= new_player_position[1] < len(grid[0])) and is_clear(new_player_position):
            # Create a new state with the updated player position
            new_state = {'at-player': new_player_position, 'at-stone': state['at-stone'].copy()}

            # Add the new state to the list of successor states
            successor_states.append(new_state)

        # Check if the player can push a stone
        for stone in state['at-stone']:
            # Calculate the position of the stone after pushing
            new_stone_position = (stone[0] + movement[0], stone[1] + movement[1])

            # Check if the stone is adjacent to the player and the new position is clear and within the grid boundaries
            if (stone[0] == state['at-player'][0] + movement[0] and stone[1] == state['at-player'][1] + movement[1] and
                (0 <= new_stone_position[0] < len(grid)) and (0 <= new_stone_position[1] < len(grid[0])) and
                is_clear(new_stone_position) and is_valid_stone_position(new_stone_position)):
                # Create a new state with the updated player and stone positions
                new_state = {'at-player': stone, 'at-stone': state['at-stone'].copy()}
                new_state['at-stone'].remove(stone)
                new_state['at-stone'].append(new_stone_position)

                # Add the new state to the list of successor states
                successor_states.append(new_state)

    return successor_states
```
Generated by Meta Llama 3.1-405

AutoToS prompt:

Provide only the python code that tests whether a state is a goal state for a given goal configuration. Assume that the goal configuration is provided by the 2-dimensional array as before. The function should receive a state and the 2-dimensional array and return True if the state is a goal state and False otherwise.

Model response:
Python
```
def is_goal_state(state, grid):
    """
    This function checks if a given state is a goal state.
    
    Parameters:
    state (dict): A dictionary containing the current state of the game. It has two keys: 'at-player' and 'at-stone'.
                  'at-player' is a tuple representing the current position of the player.
                  'at-stone' is a list of tuples representing the current positions of the stones.
    grid (list): A 2D list representing the game grid. It contains 0s, 1s, and 2s where 0 represents an empty cell,
                 1 represents a blocked cell, and 2 represents a goal location.
    
    Returns:
    bool: True if the state is a goal state, False otherwise.
    """
    # Check if all stones are at goal locations
    for stone in state['at-stone']:
        if grid[stone[0]][stone[1]] != 2:
            return False

    # If all stones are at goal locations, the state is a goal state
    return True
```
Generated by Meta Llama 3.1-405

System message:
Goal Soundness Test Passed
Soundness test

System message:
Successor States Soundness Test Passed
Completeness test
Successor Completeness Test Passed
Total success: 11, failure: 0, total expansions 763750, total generated 1955669
