
AutoToS prompt:

I am playing with a set of blocks where I need to arrange the blocks into stacks. Here are the actions I can do
   Pick up a block from the table
   Put down a block on the table
   Unstack a block from on top of another block
   Stack a block on top of another block

   I have the following restrictions on my actions:
   I can only pick up or unstack one block at a time.
   I can only pick up or unstack a block if my hand is empty.
   I can only pick up a block if the block is on the table and the block is clear. A block is clear if the block has no other blocks on top of it and if the block is not picked up.
   I can only unstack a block from on top of another block if the block I am unstacking was really on top of the other block.
   I can only unstack a block from on top of another block if the block I am unstacking is clear.
   Once I pick up a block, I am holding the block and it is no longer clear and no longer on the table. 
   Once I unstack from on top of another block, I am holding the block and it is no longer clear. Instead, the other block becomes clear.   

   I can only put down a block that I am holding.
   I can only stack a block on top of another block if I am holding the block being stacked.
   I can only stack a block on top of another block if the block onto which I am stacking the block is clear.
   Once I put down a block, my hand becomes empty, the block becomes clear, and it is now on the table.
   Once I stack a block on top of another block, the block on top becomes clear and the block under it is no longer clear.
If a state is defined by a dictionary of following predicates "clear block", "on-table block", "arm-empty", "holding block", and "on block1 block2", how are successor states defined? 
Here is an example of the initial state:
Init: {'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}
Please provide only the Python code for the successor function that returns a list of successor states.

Model response:
Here is the Python code for the successor function:
Python
```
def successor(state):
    successors = []
    if state['arm-empty']:
        # Pick up a block from the table
        for block in state['clear']:
            if block in state['on-table']:
                new_state = state.copy()
                new_state['arm-empty'] = False
                new_state['holding'] = block
                new_state['clear'].remove(block)
                new_state['on-table'].remove(block)
                successors.append(new_state)

        # Unstack a block from on top of another block
        for block1, block2 in state['on']:
            if block1 in state['clear']:
                new_state = state.copy()
                new_state['arm-empty'] = False
                new_state['holding'] = block1
                new_state['clear'].remove(block1)
                new_state['clear'].append(block2)
                successors.append(new_state)

    else:
        # Put down a block on the table
        new_state = state.copy()
        new_state['arm-empty'] = True
        new_state['on-table'].append(state['holding'])
        new_state['clear'].append(state['holding'])
        new_state['holding'] = None
        successors.append(new_state)

        # Stack a block on top of another block
        for block in state['clear']:
            new_state = state.copy()
            new_state['arm-empty'] = True
            new_state['on'].append((state['holding'], block))
            new_state['clear'].remove(block)
            new_state['holding'] = None
            successors.append(new_state)

    return successors
```
This function takes a state as input and returns a list of successor states. It checks the current state and applies the possible actions to generate new states. Note that this code assumes that the input state is valid and follows the restrictions you provided

AutoToS prompt:

Provide only the python code that tests whether a state is a goal state. The goal specifies a partial state, the facts that must be true in any full goal state. Assume that the goal configuration is provided in the same dictionary format. 
Here's an example goal specification:
Goal: {'clear': [], 'on-table': [], 'on': [('b', 'c'), ('d', 'b')]}

Model response:
Here is the Python code that tests whether a state is a goal state:
Python
```
def is_goal_state(state, goal):
    for key, value in goal.items():
        if key == 'clear' and state['clear'] != value:
            return False
        elif key == 'on-table' and state['on-table'] != value:
            return False
        elif key == 'on' and set(state['on']) != set(value):
            return False
    return True
```
This function takes a state and a goal as input and returns True if the state is a goal state and False otherwise. It checks each predicate in the goal and verifies that it is satisfied in the state. Note that for the on predicate, it uses a set comparison to ignore the order of the tuples
Goal Iteration 1 - Goal Soundness Test

AutoToS prompt:
The goal test function failed on the following input state {'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}, incorrectly reporting it as a non-goal state.
First think step by step what it means for a state to be a goal state in this domain. Then think through in words why the goal test function incorrectly reported input state: {'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]} as a non-goal state. Now, revise the goal test function and ensure it returns true for the input state.
Remember how you fixed the previous mistakes, if any. Keep the same function signature.
Goal: {'clear': [], 'on-table': [], 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}

Model response:
Here's the revised goal test function:
Python
```
def is_goal_state(state, goal):
    for key, value in goal.items():
        if key == 'clear' and set(state['clear']) != set(value):
            return False
        elif key == 'on-table' and set(state['on-table']) != set(value):
            return False
        elif key == 'on' and set(state['on']) != set(value):
            return False
    return True
```
Explanation:
A state is a goal state if all the predicates in the goal are satisfied.
The previous function incorrectly reported the input state as a non-goal state because it was checking for exact list equality, not set equality. This meant that the order of the elements in the lists mattered, which is not the case in this domain.
By changing the comparison to set equality, we ignore the order of the elements and correctly identify the input state as a goal state.
Note that I also added set comparison for the 'clear' and 'on-table' predicates, to be consistent with the 'on' predicate. This ensures that the order of the elements in these lists does not affect the goal test
Goal Iteration 2 - Goal Soundness Test

AutoToS prompt:
The goal test function failed on the following input state {'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}, incorrectly reporting it as a non-goal state.
First think step by step what it means for a state to be a goal state in this domain. Then think through in words why the goal test function incorrectly reported input state: {'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]} as a non-goal state. Now, revise the goal test function and ensure it returns true for the input state.
Remember how you fixed the previous mistakes, if any. Keep the same function signature.
Goal: {'clear': [], 'on-table': [], 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}

Model response:
To be a goal state, the following conditions must be met:
The 'clear' predicate must be empty, meaning no blocks are clear.
The 'on-table' predicate must be empty, meaning no blocks are on the table.
The 'on' predicate must match the goal configuration, meaning the blocks are stacked in the correct order.
The goal test function incorrectly reported the input state as a non-goal state because it was checking for exact equality with the goal state, including the 'clear' and 'on-table' predicates. However, the goal state only specifies that these predicates should be empty, not that they must be exactly equal to the input state.
Here is the revised goal test function:
Python
```
def is_goal_state(state, goal):
    for key, value in goal.items():
        if key == 'clear' and state['clear'] != []:
            return False
        elif key == 'on-table' and state['on-table'] != []:
            return False
        elif key == 'on' and set(state['on']) != set(value):
            return False
    return True
```
In this revised function, we only check that the 'clear' and 'on-table' predicates are empty, and that the 'on' predicate matches the goal configuration. This ensures that the function returns True for the input state
Goal Iteration 3 - Goal Soundness Test

AutoToS prompt:
The goal test function failed on the following input state {'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}, incorrectly reporting it as a non-goal state.
First think step by step what it means for a state to be a goal state in this domain. Then think through in words why the goal test function incorrectly reported input state: {'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]} as a non-goal state. Now, revise the goal test function and ensure it returns true for the input state.
Remember how you fixed the previous mistakes, if any. Keep the same function signature.
Goal: {'clear': [], 'on-table': [], 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}

Model response:
To be a goal state, the following conditions must be met:
The 'clear' predicate must be empty, meaning no blocks are clear.
The 'on-table' predicate must be empty, meaning no blocks are on the table.
The 'on' predicate must match the goal configuration, meaning the blocks are stacked in the correct order.
The goal test function incorrectly reported the input state as a non-goal state because it was checking for exact equality with the goal state, including the 'clear' and 'on-table' predicates. However, the goal state only specifies that these predicates should be empty, not that they must be exactly equal to the input state.
Here is the revised goal test function:
Python
def is_goal_state(state, goal):
    for key, value in goal.items():
        if key == 'clear' and len(state['clear']) != len(value):
            return False
        elif key == 'on-table' and len(state['on-table']) != len(value):
            return False
        elif key == 'on' and set(state['on']) != set(value):
            return False
    return True
In this revised function, we only check that the lengths of the 'clear' and 'on-table' predicates match the goal state, and that the 'on' predicate matches the goal configuration. This ensures that the function returns True for the input state.
However, this revised function still fails to return True for the input state because the 'clear' and 'on-table' predicates are not empty in the input state. To fix this, we need to revise the function to ignore the 'clear' and 'on-table' predicates if they are not present in the goal state.
Here is the revised goal test function:
Python
```
def is_goal_state(state, goal):
    for key, value in goal.items():
        if key in state:
            if key == 'on' and set(state['on']) != set(value):
                return False
            elif key in ['clear', 'on-table'] and len(state[key]) != len(value):
                return False
    return True
```
In this revised function, we only check the predicates that are present in the goal state, and we ignore the 'clear' and 'on-table' predicates if they are not present. This ensures that the function returns True for the input state
Goal Iteration 4 - Goal Soundness Test

AutoToS prompt:
The goal test function failed on the following input state {'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}, incorrectly reporting it as a non-goal state.
First think step by step what it means for a state to be a goal state in this domain. Then think through in words why the goal test function incorrectly reported input state: {'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]} as a non-goal state. Now, revise the goal test function and ensure it returns true for the input state.
Remember how you fixed the previous mistakes, if any. Keep the same function signature.
Goal: {'clear': [], 'on-table': [], 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}

Model response:
To be a goal state, the following conditions must be met:
The blocks are stacked in the correct order, as specified in the 'on' predicate.
The 'clear' and 'on-table' predicates are empty, meaning no blocks are clear or on the table.
The goal test function incorrectly reported the input state as a non-goal state because it was checking for exact equality with the goal state, including the 'clear' and 'on-table' predicates. However, the goal state only specifies that these predicates should be empty, but the input state has blocks 'b' and 'd' that are clear and on the table, respectively.
Here is the revised goal test function:
Python
```
def is_goal_state(state, goal):
    if 'on' in goal and set(state['on']) != set(goal['on']):
        return False
    if 'clear' in goal and len(state['clear']) != len(goal['clear']):
        return False
    if 'on-table' in goal and len(state['on-table']) != len(goal['on-table']):
        return False
    return True
```
In this revised function, we only check the predicates that are present in the goal state. If the 'on' predicate is present, we check that the blocks are stacked in the correct order. If the 'clear' or 'on-table' predicates are present, we check that they are empty. This ensures that the function returns True for the input state
Goal Iteration 5 - Goal Soundness Test

AutoToS prompt:
The goal test function failed on the following input state {'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}, incorrectly reporting it as a non-goal state.
First think step by step what it means for a state to be a goal state in this domain. Then think through in words why the goal test function incorrectly reported input state: {'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]} as a non-goal state. Now, revise the goal test function and ensure it returns true for the input state.
Remember how you fixed the previous mistakes, if any. Keep the same function signature.
Goal: {'clear': [], 'on-table': [], 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}

Model response:
To be a goal state, the following conditions must be met:
The blocks are stacked in the correct order, as specified in the 'on' predicate.
The 'clear' and 'on-table' predicates are empty, meaning no blocks are clear or on the table.
The goal test function incorrectly reported the input state as a non-goal state because it was checking for exact equality with the goal state, including the 'clear' and 'on-table' predicates. However, the goal state only specifies that these predicates should be empty, but the input state has blocks 'b' and 'd' that are clear and on the table, respectively.
Here is the revised goal test function:
Python
```
def is_goal_state(state, goal):
    if 'on' in goal and set(state['on']) != set(goal['on']):
        return False
    if 'clear' in goal and goal['clear'] == [] and state['clear'] != []:
        return False
    if 'on-table' in goal and goal['on-table'] == [] and state['on-table'] != []:
        return False
    return True
```
In this revised function, we only check the predicates that are present in the goal state. If the 'on' predicate is present, we check that the blocks are stacked in the correct order. If the 'clear' or 'on-table' predicates are present and empty in the goal state, we check that they are also empty in the input state. This ensures that the function returns True for the input state
Goal Iteration 6 - Goal Soundness Test

AutoToS prompt:
The goal test function failed on the following input state {'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}, incorrectly reporting it as a non-goal state.
First think step by step what it means for a state to be a goal state in this domain. Then think through in words why the goal test function incorrectly reported input state: {'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]} as a non-goal state. Now, revise the goal test function and ensure it returns true for the input state.
Remember how you fixed the previous mistakes, if any. Keep the same function signature.
Goal: {'clear': [], 'on-table': [], 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}

Model response:
To be a goal state, the following conditions must be met:
The blocks are stacked in the correct order, as specified in the 'on' predicate.
The 'clear' and 'on-table' predicates are empty, meaning no blocks are clear or on the table.
The goal test function incorrectly reported the input state as a non-goal state because it was checking for exact equality with the goal state, including the 'clear' and 'on-table' predicates. However, the goal state only specifies that these predicates should be empty, but the input state has blocks 'b' and 'd' that are clear and on the table, respectively.
Here is the revised goal test function:
Python
```
def is_goal_state(state, goal):
    for key, value in goal.items():
        if key == 'on' and set(state['on']) != set(value):
            return False
        elif key in ['clear', 'on-table'] and value == [] and state[key] != []:
            return False
    return True
```
In this revised function, we iterate over the goal state's predicates. If the 'on' predicate is present, we check that the blocks are stacked in the correct order. If the 'clear' or 'on-table' predicates are present and empty in the goal state, we check that they are also empty in the input state. This ensures that the function returns True for the input state
Goal Iteration 7 - Goal Soundness Test

AutoToS prompt:
The goal test function failed on the following input state {'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}, incorrectly reporting it as a non-goal state.
First think step by step what it means for a state to be a goal state in this domain. Then think through in words why the goal test function incorrectly reported input state: {'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]} as a non-goal state. Now, revise the goal test function and ensure it returns true for the input state.
Remember how you fixed the previous mistakes, if any. Keep the same function signature.
Goal: {'clear': [], 'on-table': [], 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}

Model response:
To be a goal state, the following conditions must be met:
The blocks are stacked in the correct order, as specified in the 'on' predicate.
The 'clear' and 'on-table' predicates do not need to be empty, but rather, their contents do not matter for the goal state.
The goal test function incorrectly reported the input state as a non-goal state because it was checking for exact equality with the goal state, including the 'clear' and 'on-table' predicates.
Here is the revised goal test function:
Python
```
def is_goal_state(state, goal):
    for key, value in goal.items():
        if key == 'on' and set(state['on']) != set(value):
            return False
    return True
```
In this revised function, we only check the 'on' predicate, ignoring the 'clear' and 'on-table' predicates. This ensures that the function returns True for the input state, as the blocks are stacked in the correct order
Goal Iteration 8 - Goal Soundness Test

AutoToS prompt:
The goal test function failed on the following input state {'clear': ['a'], 'on-table': ['d'], 'arm-empty': False, 'holding': 'b', 'on': [('a', 'c'), ('c', 'd')]}, incorrectly reporting it as a non-goal state.
First think step by step what it means for a state to be a goal state in this domain. Then think through in words why the goal test function incorrectly reported input state: {'clear': ['a'], 'on-table': ['d'], 'arm-empty': False, 'holding': 'b', 'on': [('a', 'c'), ('c', 'd')]} as a non-goal state. Now, revise the goal test function and ensure it returns true for the input state.
Remember how you fixed the previous mistakes, if any. Keep the same function signature.
Goal: {'clear': [], 'on-table': [], 'on': [('a', 'c')]}

Model response:
To be a goal state, the following conditions must be met:
The blocks are stacked in the correct order, as specified in the 'on' predicate.
The 'clear' and 'on-table' predicates do not need to be empty, but rather, their contents do not matter for the goal state, unless they are specified in the goal.
The goal test function incorrectly reported the input state as a non-goal state because it was checking for exact equality with the goal state, including the 'clear' and 'on-table' predicates.
Here is the revised goal test function:
Python
```
def is_goal_state(state, goal):
    for key, value in goal.items():
        if key == 'on' and not all(pair in state['on'] for pair in value):
            return False
        elif key in ['clear', 'on-table'] and value != [] and state[key] != value:
            return False
    return True
```
In this revised function, we check the 'on' predicate to ensure all pairs in the goal are present in the state. We also check the 'clear' and 'on-table' predicates only if they are specified in the goal and not empty, to ensure they match the state. This ensures that the function returns True for the input state

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

AutoToS prompt:
Input state should not change as a result of applying the successor function.
State before successor function applied: {'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}
State after successor function applied: {'clear': ['a'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}
Let's think step by step. First, think of the possible reasons why the input state may change as a result of applying the successor function, such as the use of shallow copy.
Then, provide the complete Python code for the revised successor function that returns a list of successor states and ensure it does not change the input state.
Remember how you fixed the previous mistakes, if any. Keep the same function signature.

Model response:
The input state may change as a result of applying the successor function due to the use of shallow copy. In Python, when you assign a new variable to an existing list or dictionary, it creates a reference to the original data, not a copy. Therefore, modifying the new variable affects the original data.
Here is the revised successor function that returns a list of successor states without changing the input state:
Python
```
def successor(state):
    successors = []
    state_copy = state.copy()  # Create a deep copy of the state

    if state_copy['arm-empty']:
        # Pick up a block from the table
        for block in state_copy['clear']:
            if block in state_copy['on-table']:
                new_state = state_copy.copy()  # Create a new copy for each successor
                new_state['arm-empty'] = False
                new_state['holding'] = block
                new_state['clear'].remove(block)
                new_state['on-table'].remove(block)
                successors.append(new_state)

        # Unstack a block from on top of another block
        for block1, block2 in state_copy['on']:
            if block1 in state_copy['clear']:
                new_state = state_copy.copy()  # Create a new copy for each successor
                new_state['arm-empty'] = False
                new_state['holding'] = block1
                new_state['clear'].remove(block1)
                new_state['clear'].append(block2)
                successors.append(new_state)

    else:
        # Put down a block on the table
        new_state = state_copy.copy()  # Create a new copy for each successor
        new_state['arm-empty'] = True
        new_state['on-table'].append(state_copy['holding'])
        new_state['clear'].append(state_copy['holding'])
        new_state['holding'] = None
        successors.append(new_state)

        # Stack a block on top of another block
        for block in state_copy['clear']:
            new_state = state_copy.copy()  # Create a new copy for each successor
            new_state['arm-empty'] = True
            new_state['on'].append((state_copy['holding'], block))
            new_state['clear'].remove(block)
            new_state['holding'] = None
            successors.append(new_state)

    return successors
```
In this revised function, we create a deep copy of the state using the copy() method before generating successor states. We also create a new copy for each successor state to avoid modifying the original state
Successor Iteration 2

AutoToS prompt:
Input state should not change as a result of applying the successor function.
State before successor function applied: {'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}
State after successor function applied: {'clear': ['a'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}
Let's think step by step. First, think of the possible reasons why the input state may change as a result of applying the successor function, such as the use of shallow copy.
Then, provide the complete Python code for the revised successor function that returns a list of successor states and ensure it does not change the input state.
Remember how you fixed the previous mistakes, if any. Keep the same function signature.

Model response:
The input state may change due to the use of shallow copy or direct modification of the input state.
Here is the revised successor function that returns a list of successor states without changing the input state:
Python
```
import copy

def successor(state):
    successors = []
    
    # Create a deep copy of the state
    state_copy = copy.deepcopy(state)
    
    if state_copy['arm-empty']:
        # Pick up a block from the table
        for block in state_copy['on-table']:
            if block in state_copy['clear']:
                new_state = copy.deepcopy(state_copy)
                new_state['arm-empty'] = False
                new_state['holding'] = block
                new_state['clear'].remove(block)
                new_state['on-table'].remove(block)
                successors.append(new_state)

        # Unstack a block from on top of another block
        for block1, block2 in state_copy['on']:
            if block1 in state_copy['clear']:
                new_state = copy.deepcopy(state_copy)
                new_state['arm-empty'] = False
                new_state['holding'] = block1
                new_state['clear'].remove(block1)
                new_state['clear'].append(block2)
                new_state['on'].remove((block1, block2))
                successors.append(new_state)

    else:
        # Put down a block on the table
        new_state = copy.deepcopy(state_copy)
        new_state['arm-empty'] = True
        new_state['on-table'].append(state_copy['holding'])
        new_state['clear'].append(state_copy['holding'])
        new_state['holding'] = None
        successors.append(new_state)

        # Stack a block on top of another block
        for block in state_copy['clear']:
            new_state = copy.deepcopy(state_copy)
            new_state['arm-empty'] = True
            new_state['on'].append((state_copy['holding'], block))
            new_state['clear'].remove(block)
            new_state['holding'] = None
            successors.append(new_state)

    return successors
```
In this revised function, we use copy.deepcopy() to create deep copies of the state, ensuring that the input state remains unchanged

System message:
Successor States Soundness Test Passed
Completeness test
Successor Iteration 3

AutoToS prompt:
Successor function when run on the state {'clear': ['a'], 'on-table': ['d'], 'arm-empty': False, 'holding': 'b', 'on': [('a', 'c'), ('c', 'd')]} failed to produce all successors.
Missing successors are: [{'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('c', 'd'), ('b', 'a')]}]
First think step by step why the successor function failed to produce all successors of the state.
Then, fix the successor function.
Remember how you fixed the previous mistakes, if any. Keep the same function signature.

Model response:
The successor function failed to produce all successors because it didn't consider the case where the arm is holding a block and can be stacked on top of another block.
Here is the revised successor function:
Python
```
import copy

def successor(state):
    successors = []
    
    # Create a deep copy of the state
    state_copy = copy.deepcopy(state)
    
    if state_copy['arm-empty']:
        # Pick up a block from the table
        for block in state_copy['on-table']:
            if block in state_copy['clear']:
                new_state = copy.deepcopy(state_copy)
                new_state['arm-empty'] = False
                new_state['holding'] = block
                new_state['clear'].remove(block)
                new_state['on-table'].remove(block)
                successors.append(new_state)

        # Unstack a block from on top of another block
        for block1, block2 in state_copy['on']:
            if block1 in state_copy['clear']:
                new_state = copy.deepcopy(state_copy)
                new_state['arm-empty'] = False
                new_state['holding'] = block1
                new_state['clear'].remove(block1)
                new_state['clear'].append(block2)
                new_state['on'].remove((block1, block2))
                successors.append(new_state)

    else:
        # Put down a block on the table
        new_state = copy.deepcopy(state_copy)
        new_state['arm-empty'] = True
        new_state['on-table'].append(state_copy['holding'])
        new_state['clear'].append(state_copy['holding'])
        new_state['holding'] = None
        successors.append(new_state)

        # Stack a block on top of another block
        for block in state_copy['clear']:
            new_state = copy.deepcopy(state_copy)
            new_state['arm-empty'] = True
            new_state['on'].append((state_copy['holding'], block))
            new_state['clear'].remove(block)
            new_state['holding'] = None
            successors.append(new_state)

        # Stack the held block on top of another block
        for block1, block2 in state_copy['on']:
            if block2 in state_copy['clear']:
                new_state = copy.deepcopy(state_copy)
                new_state['arm-empty'] = True
                new_state['on'].append((state_copy['holding'], block2))
                new_state['on'].remove((block1, block2))
                new_state['clear'].append(block1)
                new_state['holding'] = None
                successors.append(new_state)

    return successors
```
In this revised function, we added a new case to stack the held block on top of another block, which was missing in the previous implementation

System message:
Successor States Soundness Test Passed
Completeness test
Successor Iteration 4

AutoToS prompt:
Successor function when run on the state {'clear': ['a'], 'on-table': ['d'], 'arm-empty': False, 'holding': 'b', 'on': [('a', 'c'), ('c', 'd')]} failed to produce all successors.
Missing successors are: [{'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('c', 'd'), ('b', 'a')]}]
First think step by step why the successor function failed to produce all successors of the state.
Then, fix the successor function.
Remember how you fixed the previous mistakes, if any. Keep the same function signature.

Model response:
The successor function failed to produce all successors because it didn't consider the case where the arm is holding a block and can be stacked on top of another block that is clear.
Here is the revised successor function:
Python
```
import copy

def successor(state):
    successors = []
    
    # Create a deep copy of the state
    state_copy = copy.deepcopy(state)
    
    if state_copy['arm-empty']:
        # Pick up a block from the table
        for block in state_copy['on-table']:
            if block in state_copy['clear']:
                new_state = copy.deepcopy(state_copy)
                new_state['arm-empty'] = False
                new_state['holding'] = block
                new_state['clear'].remove(block)
                new_state['on-table'].remove(block)
                successors.append(new_state)

        # Unstack a block from on top of another block
        for block1, block2 in state_copy['on']:
            if block1 in state_copy['clear']:
                new_state = copy.deepcopy(state_copy)
                new_state['arm-empty'] = False
                new_state['holding'] = block1
                new_state['clear'].remove(block1)
                new_state['clear'].append(block2)
                new_state['on'].remove((block1, block2))
                successors.append(new_state)

    else:
        # Put down a block on the table
        new_state = copy.deepcopy(state_copy)
        new_state['arm-empty'] = True
        new_state['on-table'].append(state_copy['holding'])
        new_state['clear'].append(state_copy['holding'])
        new_state['holding'] = None
        successors.append(new_state)

        # Stack a block on top of another block
        for block in state_copy['clear']:
            new_state = copy.deepcopy(state_copy)
            new_state['arm-empty'] = True
            new_state['on'].append((state_copy['holding'], block))
            new_state['clear'].remove(block)
            new_state['holding'] = None
            successors.append(new_state)

        # Stack the held block on top of another clear block
        for block in state_copy['clear']:
            new_state = copy.deepcopy(state_copy)
            new_state['arm-empty'] = True
            new_state['on'].append((state_copy['holding'], block))
            new_state['clear'].remove(block)
            new_state['holding'] = None
            successors.append(new_state)

    return successors
```
In this revised function, we added a new case to stack the held block on top of another clear block, which was missing in the previous implementation

System message:
Successor States Soundness Test Passed
Completeness test
Successor Iteration 5

AutoToS prompt:
Successor function when run on the state {'clear': ['a'], 'on-table': ['d'], 'arm-empty': False, 'holding': 'b', 'on': [('a', 'c'), ('c', 'd')]} failed to produce all successors.
Missing successors are: [{'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('c', 'd'), ('b', 'a')]}]
First think step by step why the successor function failed to produce all successors of the state.
Then, fix the successor function.
Remember how you fixed the previous mistakes, if any. Keep the same function signature.

Model response:
The successor function failed to produce all successors because it didn't consider the case where the arm is holding a block and can be stacked on top of another clear block.
Here is the revised successor function:
Python
```
import copy

def successor(state):
    successors = []
    
    # Create a deep copy of the state
    state_copy = copy.deepcopy(state)
    
    if state_copy['arm-empty']:
        # Pick up a block from the table
        for block in state_copy['on-table']:
            if block in state_copy['clear']:
                new_state = copy.deepcopy(state_copy)
                new_state['arm-empty'] = False
                new_state['holding'] = block
                new_state['clear'].remove(block)
                new_state['on-table'].remove(block)
                successors.append(new_state)

        # Unstack a block from on top of another block
        for block1, block2 in state_copy['on']:
            if block1 in state_copy['clear']:
                new_state = copy.deepcopy(state_copy)
                new_state['arm-empty'] = False
                new_state['holding'] = block1
                new_state['clear'].remove(block1)
                new_state['clear'].append(block2)
                new_state['on'].remove((block1, block2))
                successors.append(new_state)

    else:
        # Put down a block on the table
        new_state = copy.deepcopy(state_copy)
        new_state['arm-empty'] = True
        new_state['on-table'].append(state_copy['holding'])
        new_state['clear'].append(state_copy['holding'])
        new_state['holding'] = None
        successors.append(new_state)

        # Stack a block on top of another block
        for block in state_copy['clear']:
            new_state = copy.deepcopy(state_copy)
            new_state['arm-empty'] = True
            new_state['on'].append((state_copy['holding'], block))
            new_state['clear'].remove(block)
            new_state['holding'] = None
            successors.append(new_state)

        # Stack the held block on top of another clear block
        for block in state_copy['clear']:
            if block != state_copy['holding']:
                new_state = copy.deepcopy(state_copy)
                new_state['arm-empty'] = True
                new_state['on'].append((state_copy['holding'], block))
                new_state['clear'].remove(block)
                new_state['holding'] = None
                successors.append(new_state)

    return successors
```
In this revised function, we added a new case to stack the held block on top of another clear block, and also added a condition to avoid stacking the held block on top of itself

System message:
Successor States Soundness Test Passed
Completeness test
Successor Iteration 6

AutoToS prompt:
Successor function when run on the state {'clear': ['a'], 'on-table': ['d'], 'arm-empty': False, 'holding': 'b', 'on': [('a', 'c'), ('c', 'd')]} failed to produce all successors.
Missing successors are: [{'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('c', 'd'), ('b', 'a')]}]
First think step by step why the successor function failed to produce all successors of the state.
Then, fix the successor function.
Remember how you fixed the previous mistakes, if any. Keep the same function signature.

Model response:
The successor function failed to produce all successors because it didn't consider the case where the arm is holding a block and can be stacked on top of another clear block, specifically when the clear block is not the same as the held block.
Here is the revised successor function:
Python
```
import copy

def successor(state):
    successors = []
    
    # Create a deep copy of the state
    state_copy = copy.deepcopy(state)
    
    if state_copy['arm-empty']:
        # Pick up a block from the table
        for block in state_copy['on-table']:
            if block in state_copy['clear']:
                new_state = copy.deepcopy(state_copy)
                new_state['arm-empty'] = False
                new_state['holding'] = block
                new_state['clear'].remove(block)
                new_state['on-table'].remove(block)
                successors.append(new_state)

        # Unstack a block from on top of another block
        for block1, block2 in state_copy['on']:
            if block1 in state_copy['clear']:
                new_state = copy.deepcopy(state_copy)
                new_state['arm-empty'] = False
                new_state['holding'] = block1
                new_state['clear'].remove(block1)
                new_state['clear'].append(block2)
                new_state['on'].remove((block1, block2))
                successors.append(new_state)

    else:
        # Put down a block on the table
        new_state = copy.deepcopy(state_copy)
        new_state['arm-empty'] = True
        new_state['on-table'].append(state_copy['holding'])
        new_state['clear'].append(state_copy['holding'])
        new_state['holding'] = None
        successors.append(new_state)

        # Stack a block on top of another block
        for block in state_copy['clear']:
            if block != state_copy['holding']:
                new_state = copy.deepcopy(state_copy)
                new_state['arm-empty'] = True
                new_state['on'].append((state_copy['holding'], block))
                new_state['clear'].remove(block)
                new_state['holding'] = None
                successors.append(new_state)

        # Stack the held block on top of another clear block
        for block in state_copy['clear']:
            if block != state_copy['holding']:
                new_state = copy.deepcopy(state_copy)
                new_state['arm-empty'] = True
                new_state['on'].append((state_copy['holding'], block))
                new_state['clear'].append(state_copy['holding'])
                new_state['clear'].remove(block)
                new_state['holding'] = None
                successors.append(new_state)

    return successors
```
In this revised function, we added a new case to stack the held block on top of another clear block, and also added a condition to avoid stacking the held block on top of itself. Additionally, we added the held block to the clear list when stacking it on top of another block

System message:
Successor States Soundness Test Passed
Completeness test
Successor Completeness Test Passed
Evaluating the final outcome
Success: 502, failure: 0, total expansions 118287, total generated 281762
