
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 that returns a list of successor states based on the given actions and restrictions:

python
```
def successor(state):
    successors = []
    clear_blocks = state['clear']
    on_table_blocks = state['on-table']
    arm_empty = state['arm-empty']
    holding_block = state['holding']
    on_blocks = state['on']

    # Action: Pick up a block from the table
    if arm_empty and holding_block is None:
        for block in clear_blocks:
            if block in on_table_blocks:
                new_state = state.copy()
                new_state['clear'] = [b for b in clear_blocks if b != block]
                new_state['on-table'] = [b for b in on_table_blocks if b != block]
                new_state['arm-empty'] = False
                new_state['holding'] = block
                successors.append(new_state)

    # Action: Put down a block on the table
    if holding_block is not None:
        new_state = state.copy()
        new_state['clear'] = clear_blocks + [holding_block]
        new_state['on-table'] = on_table_blocks + [holding_block]
        new_state['arm-empty'] = True
        new_state['holding'] = None
        successors.append(new_state)

    # Action: Unstack a block from on top of another block
    if arm_empty and holding_block is None:
        for block1, block2 in on_blocks:
            if block1 in clear_blocks:
                new_state = state.copy()
                new_state['clear'] = [b for b in clear_blocks if b != block1] + [block2]
                new_state['on'] = [t for t in on_blocks if t != (block1, block2)]
                new_state['arm-empty'] = False
                new_state['holding'] = block1
                successors.append(new_state)

    # Action: Stack a block on top of another block
    if holding_block is not None:
        for block in clear_blocks:
            new_state = state.copy()
            new_state['clear'] = [b for b in clear_blocks if b != block] + [holding_block]
            new_state['on'] = on_blocks + [(holding_block, block)]
            new_state['arm-empty'] = True
            new_state['holding'] = None
            successors.append(new_state)

    return successors

# Example usage:
init_state = {'clear': ['b'], 'on-table': ['d'], 'arm-empty': True, 'holding': None, 'on': [('a', 'c'), ('b', 'a'), ('c', 'd')]}
successor_states = successor(init_state)
for s in successor_states:
    print(s)
```

This function takes the current state as input and returns a list of possible successor states based on the available actions and restrictions. Each action is implemented as a separate block of code within the function, ensuring that the state transitions adhere to the rules 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:
python
```
def is_goal_state(state, goal):
    for key in goal:
        if key == 'on':
            for block_pair in goal[key]:
                if block_pair not in state[key]:
                    return False
        else:
            for block in goal[key]:
                if block not in state[key]:
                    return False
    return True

# Example usage:
goal_state = {'clear': [], 'on-table': [], 'on': [('b', 'c'), ('d', 'b')]}
current_state = {'clear': ['a'], 'on-table': ['a'], 'arm-empty': True, 'holding': None, 'on': [('b', 'c'), ('d', 'b')]}
print(is_goal_state(current_state, goal_state))  # Output: True or False depending on the current state
``

System message:
Goal Soundness Test Passed
Soundness test

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
