
AutoToS prompt:

Logical deduction is performed by applying rules of the form if X then Y to our current knowledge about a world, extending our knowledge with each single rule application. 
A rule if X then Y is applicable if we know X. If a state is defined as our current knowledge of the world, how are successor states defined, given a collection of rules? Please think step by step. Then, provide only the Python implementation for the successor function that receives a state and rules and returns a list of successor states.

Example initial state: {"integer"}
Example rules: [("integer", "real number"), ("integer", "float")]

Model response:
Successor States Definition
Given a state and a collection of rules, we define successor states as follows:
Initialize an empty list to store the successor states.
For each rule of the form "if X then Y":
Check if X is present in the current state.
If X is present, create a new state by adding Y to the current state.
Add the new state to the list of successor states.
Return the list of successor states.
Python Implementation
Python
```
def successor_states(state, rules):
    """
    Generate successor states by applying rules to the current state.

    Args:
        state (set): Current knowledge of the world.
        rules (list): List of rules of the form (X, Y), meaning "if X then Y".

    Returns:
        list: List of successor states.
    """
    successor_states = []
    for rule in rules:
        X, Y = rule
        if X in state:
            new_state = state.copy()
            new_state.add(Y)
            successor_states.append(new_state)
    return successor_states

# Example usage
initial_state = {"integer"}
rules = [("integer", "real number"), ("integer", "float")]
successors = successor_states(initial_state, rules)
print(successors)
```
This implementation assumes that the state is represented as a set of strings, and the rules are represented as a list of tuples, where each tuple contains two strings representing the condition and the conclusion of the rule. The successor_states function returns a list of sets, where each set represents a successor state.
Generated by Meta Llama 3.1-405

AutoToS prompt:

Provide only the Python function for the goal test function that tests, given a target fact, whether a state is a goal state. 

Model response:
Goal Test Function
Python
```
def is_goal_state(state, target_fact):
    """
    Check if a state is a goal state by verifying if it contains the target fact.

    Args:
        state (set): Current knowledge of the world.
        target_fact: The fact that must be present in the state to consider it a goal state.

    Returns:
        bool: True if the state is a goal state, False otherwise.
    """
    return target_fact in state
```
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
Success: 4000, failure: 0, total expansions 87519, total evaluations 523818
