
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):
    def is_clear(position):
        x, y = position
        return grid[x][y] in (0, 2)

    def move_player(from_pos, to_pos):
        return {
            'at-player': to_pos,
            'at-stone': state['at-stone']
        }

    def push_stone(player_pos, stone_pos, target_pos):
        return {
            'at-player': stone_pos,
            'at-stone': [target_pos if stone == stone_pos else stone for stone in state['at-stone']]
        }

    x, y = state['at-player']
    stones = state['at-stone']
    directions = {
        'up': (-1, 0),
        'down': (1, 0),
        'left': (0, -1),
        'right': (0, 1)
    }
    
    successor_states = []

    for direction, (dx, dy) in directions.items():
        new_player_pos = (x + dx, y + dy)

        if 0 <= new_player_pos[0] < len(grid) and 0 <= new_player_pos[1] < len(grid[0]):
            if is_clear(new_player_pos):
                successor_states.append(move_player((x, y), new_player_pos))
                
            for i, stone_pos in enumerate(stones):
                if stone_pos == new_player_pos:
                    target_pos = (stone_pos[0] + dx, stone_pos[1] + dy)
                    if 0 <= target_pos[0] < len(grid) and 0 <= target_pos[1] < len(grid[0]):
                        if is_clear(target_pos):
                            successor_states.append(push_stone((x, y), stone_pos, target_pos))
    
    return successor_states
```

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, goal_grid):
    def is_at_goal(stone_pos):
        x, y = stone_pos
        return goal_grid[x][y] == 2

    return all(is_at_goal(stone) for stone in state['at-stone'])
```

System message:
Goal Soundness Test Passed
Soundness test
Successor Iteration 1

AutoToS prompt:
Error occurred for grid configuration: [[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]]
Invalid transition: a stone and the player are at the same location.
Let's think step by step. First think through in words why the successor function produced a successor that has a stone and the player at the same location. Then provide the complete Python code for the revised successor function that ensures that in all successors the player and the stones are at different locations.
Remember how you fixed the previous mistakes, if any. Keep the same function signature.

Input state: {'at-player': (4, 3), 'at-stone': [(2, 2), (3, 3)]}
Example wrong successor state: {'at-player': (3, 3), 'at-stone': [(2, 2), (3, 3)]}

Model response:
The issue arises when the successor function allows for the player to move directly onto a position occupied by a stone without checking whether the stone is already there. This results in invalid successor states where both the player and stone occupy the same location. 

To resolve this, we need to ensure that when processing movements and pushes, we do not create any states where the player's position coincides with the position of any stone. We can achieve this by adding a condition to check if the new player position is not already occupied by a stone before adding it to the list of successor states.

Here is the revised successor function:

```python
def successor_states(state, grid):
    def is_clear(position):
        x, y = position
        return grid[x][y] in (0, 2)

    def move_player(from_pos, to_pos):
        return {
            'at-player': to_pos,
            'at-stone': state['at-stone']
        }

    def push_stone(player_pos, stone_pos, target_pos):
        return {
            'at-player': stone_pos,
            'at-stone': [target_pos if stone == stone_pos else stone for stone in state['at-stone']]
        }

    x, y = state['at-player']
    stones = state['at-stone']
    directions = {
        'up': (-1, 0),
        'down': (1, 0),
        'left': (0, -1),
        'right': (0, 1)
    }
    
    successor_states = []

    for direction, (dx, dy) in directions.items():
        new_player_pos = (x + dx, y + dy)

        if 0 <= new_player_pos[0] < len(grid) and 0 <= new_player_pos[1] < len(grid[0]):
            if is_clear(new_player_pos) and new_player_pos not in stones:
                successor_states.append(move_player((x, y), new_player_pos))
                
            for i, stone_pos in enumerate(stones):
                if stone_pos == new_player_pos:
                    target_pos = (stone_pos[0] + dx, stone_pos[1] + dy)
                    if 0 <= target_pos[0] < len(grid) and 0 <= target_pos[1] < len(grid[0]):
                        if is_clear(target_pos):
                            successor_states.append(push_stone((x, y), stone_pos, target_pos))
    
    return successor_states
```
Successor Iteration 2

AutoToS prompt:
Error occurred for grid configuration: [[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]]
Invalid transition: multiple stones at the same location.
Let's think step by step. First think through in words why the successor function produced a successor that has two stones at the same location. Then provide the complete Python code for the revised successor function that ensures that in all successors all stones are at different locations.
Remember how you fixed the previous mistakes, if any. Keep the same function signature.

Input state: {'at-player': (2, 1), 'at-stone': [(2, 2), (2, 3)]}
Example wrong successor state: {'at-player': (2, 2), 'at-stone': [(2, 3), (2, 3)]}

Model response:
The issue arises when we allow the same stone to be pushed to a target location that is already occupied by another stone. This can occur especially if the new position of the stone after the push coincides with an existing stone's position in the successor state. 

To avoid this situation, we need to ensure that when we push a stone, the target position is clear of all other stones. We can do this by adding a check to see if the target position already contains a stone in the successor state before proceeding with any push.

Here is the revised successor function with the necessary checks:

```python
def successor_states(state, grid):
    def is_clear(position):
        x, y = position
        return grid[x][y] in (0, 2)

    def move_player(from_pos, to_pos):
        return {
            'at-player': to_pos,
            'at-stone': state['at-stone']
        }

    def push_stone(player_pos, stone_pos, target_pos):
        return {
            'at-player': stone_pos,
            'at-stone': [target_pos if stone == stone_pos else stone for stone in state['at-stone']]
        }

    x, y = state['at-player']
    stones = state['at-stone']
    directions = {
        'up': (-1, 0),
        'down': (1, 0),
        'left': (0, -1),
        'right': (0, 1)
    }
    
    successor_states = []

    for direction, (dx, dy) in directions.items():
        new_player_pos = (x + dx, y + dy)

        if 0 <= new_player_pos[0] < len(grid) and 0 <= new_player_pos[1] < len(grid[0]):
            if is_clear(new_player_pos) and new_player_pos not in stones:
                successor_states.append(move_player((x, y), new_player_pos))
                
            for stone_pos in stones:
                if stone_pos == new_player_pos:
                    target_pos = (stone_pos[0] + dx, stone_pos[1] + dy)
                    if 0 <= target_pos[0] < len(grid) and 0 <= target_pos[1] < len(grid[0]):
                        if is_clear(target_pos) and target_pos not in stones:
                            successor_states.append(push_stone((x, y), stone_pos, target_pos))
    
    return successor_states
```

System message:
Successor States Soundness Test Passed
Completeness test
Successor Completeness Test Passed
Total success: 11, failure: 0, total expansions 764128, total generated 1956111
