
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, a successor state is defined as the state extended with the application of one rule. In other words, if we have a state S and a rule if X then Y, a successor state S' is created by adding Y to S if X is already in S.
Formally, given a state S and a rule if X then Y, a successor state S' is defined as:
$S' = S \cup {Y} if X \in S$
In simpler terms, we create a new state by adding the conclusion of the rule (Y) to the current state (S) if the premise of the rule (X) is already known in the current state.
Python Implementation
Here is the Python implementation of the successor function:
Python
```
def successor_states(state, rules):
    """
    Returns a list of successor states given a state and a collection of rules.

    Args:
        state (set): The current state of knowledge.
        rules (list of tuples): A list of rules, where each rule is a tuple (X, Y) meaning "if X then Y".

    Returns:
        list of sets: A list of successor states.
    """
    successor_states = []
    for rule in rules:
        premise, conclusion = rule
        if premise in state:
            new_state = state.copy()
            new_state.add(conclusion)
            successor_states.append(new_state)
    return successor_states
```
You can use this function like this:
Python
initial_state = {"integer"}
rules = [("integer", "real number"), ("integer", "float")]
successors = successor_states(initial_state, rules)
print(successors)  # Output: [{"integer", "real number"}, {"integer", "float"}]
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:
Python
```
def is_goal_state(state, target_fact):
    """
    Tests whether a state is a goal state given a target fact.

    Args:
        state (set): The current state of knowledge.
        target_fact: The target fact to be checked.

    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 88259, total evaluations 528408
