
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['clear'].remove(block)
                new_state['on-table'].remove(block)
                new_state['arm-empty'] = False
                new_state['holding'] = 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['clear'].remove(block1)
                new_state['clear'].append(block2)
                new_state['arm-empty'] = False
                new_state['holding'] = block1
                new_state['on'].remove((block1, block2))
                successors.append(new_state)
    
    else:
        # Put down a block on the table
        new_state = state.copy()
        new_state['clear'].append(state['holding'])
        new_state['on-table'].append(state['holding'])
        new_state['arm-empty'] = True
        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['clear'].remove(block)
            new_state['clear'].append(state['holding'])
            new_state['on'].append((state['holding'], block))
            new_state['arm-empty'] = True
            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 the successor states. Note that this function assumes that the input state is a dictionary with the same structure as the initial state 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':
            if len(state[key]) != len(value) or any(block not in state[key] for block in value):
                return False
        elif key == 'on-table':
            if len(state[key]) != len(value) or any(block not in state[key] for block in value):
                return False
        elif key == 'on':
            if len(state[key]) != len(value) or any((block1, block2) not in state[key] for block1, block2 in value):
                return False
        elif key == 'arm-empty':
            if state[key] != value:
                return False
        elif key == 'holding':
            if state[key] != 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 true in the state
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:
A state is a goal state if it satisfies all the conditions specified in the goal. In this domain, the goal specifies the desired relationships between blocks (on top of which other blocks) and does not care about the 'clear' and 'on-table' predicates.
The goal test function incorrectly reported the input state as a non-goal state because it checked if the 'clear' and 'on-table' predicates in the state matched the goal, which is not necessary. The goal only cares about the 'on' predicate.
Here is the revised goal test function:
Python
```
def is_goal_state(state, goal):
    for key, value in goal.items():
        if key == 'on':
            if len(state[key]) != len(value) or any((block1, block2) not in state[key] for block1, block2 in value):
                return False
        elif key == 'arm-empty':
            if state[key] != value:
                return False
        elif key == 'holding':
            if state[key] != value:
                return False
    return True
```
This revised function only checks the 'on', 'arm-empty', and 'holding' predicates, which are the only ones that matter for the goal in this domain. It will correctly return True for the input state
Goal Iteration 2 - 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:
A state is a goal state if it satisfies all the conditions specified in the goal. In this domain, the goal specifies the desired relationships between blocks (on top of which other blocks) and does not care about the 'clear' and 'on-table' predicates unless they are specified in the goal.
The goal test function incorrectly reported the input state as a non-goal state because it checked if the 'arm-empty' and 'holding' predicates in the state matched the goal, which is not necessary. The goal only cares about the 'on' predicate and the 'clear' and 'on-table' predicates if they are specified.
Here is the revised goal test function:
Python
```
def is_goal_state(state, goal):
    for key, value in goal.items():
        if key == 'on':
            if not all((block1, block2) in state[key] for block1, block2 in value):
                return False
        elif key in ['clear', 'on-table']:
            if value and not all(block in state[key] for block in value):
                return False
    return True
```
This revised function only checks the predicates that are specified in the goal and ignores the others. It will correctly return True for the input state. Note that it also checks if all the desired 'on' relationships are present in the state, not just if the state's 'on' relationships are a subset of the goal's

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'), ('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 because the function is modifying the state directly instead of creating a new copy of the state. This is likely due to the use of shallow copy (e.g., new_state = state.copy()) which only creates a new reference to the original state's mutable objects, such as lists.
Here is the revised successor function that returns a list of successor states without modifying the input state:
Python
```
import copy

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 = copy.deepcopy(state)
                new_state['clear'].remove(block)
                new_state['on-table'].remove(block)
                new_state['arm-empty'] = False
                new_state['holding'] = 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 = copy.deepcopy(state)
                new_state['clear'].remove(block1)
                new_state['clear'].append(block2)
                new_state['arm-empty'] = False
                new_state['holding'] = block1
                new_state['on'].remove((block1, block2))
                successors.append(new_state)
    
    else:
        # Put down a block on the table
        new_state = copy.deepcopy(state)
        new_state['clear'].append(state['holding'])
        new_state['on-table'].append(state['holding'])
        new_state['arm-empty'] = True
        new_state['holding'] = None
        successors.append(new_state)
        
        # Stack a block on top of another block
        for block in state['clear']:
            new_state = copy.deepcopy(state)
            new_state['clear'].remove(block)
            new_state['clear'].append(state['holding'])
            new_state['on'].append((state['holding'], block))
            new_state['arm-empty'] = True
            new_state['holding'] = None
            successors.append(new_state)
    
    return successors
```
In this revised function, I used copy.deepcopy(state) to create a deep copy of the state, which ensures that any modifications made to the new state do not affect the original state

System message:
Successor States Soundness Test Passed
Completeness test
Successor Completeness Test Passed
Evaluating the final outcome
Success: 502, failure: 0, total expansions 50484, total generated 130127
