GEB – The MU Puzzle

mu.py

import unittest

def rule1(string):
    """Adds "U" to the end of a string if it ends with "I".

    Args:
        string: The input string.

    Returns:
        The modified string with "U" added if applicable.
    """
    if string.endswith("I"):
        #print("Returning %s" % string + "U")
        yield string + "U"
    
def rule2(string):
    """Returns "Mxx" for theorems in "Mx".

    Args:
        string: The input string.

    Returns:
        The modified string "Mxx" if applicable.
    """
    if string.startswith("M"):
        yield "M" + string[1:] + string[1:]
    
def rule3(string):
    """Replaces "III" with "U".

    Args:
        string: The input string.

    Returns:
        The modified strings if applicable.
    """
    index = 0
    while True:
        index = string.find("III", index)
        if index == -1:
            break
        yield string[0:index] + "U" + string[index+len("III"):]
        index += 1

def rule4(string):
    """Replaces "UU" with "".

    Args:
        string: The input string.

    Returns:
        The modified strings if applicable.
    """
    index = 0
    while True:
        index = string.find("UU", index)
        if index == -1:
            break
        yield string[0:index] + string[index+len("UU"):]
        index += 1

def gen_rules():
    axioms = set(("MI",))
    theorems = axioms
    found_new_theorems = True
    depth = 0
    while found_new_theorems and depth < 6:
        print("Depth = %s" % depth)
        depth += 1
        found_new_theorems = False
        for theorem in theorems.copy():
            for rule in (rule1, rule2, rule3, ):
                for string in rule(theorem):
                    #print("Looking at %s" % string)
                    if string not in theorems:
                        theorems.add(string)
                        found_new_theorems = True
                        print("Found %s" % string)


class TestAddU(unittest.TestCase):
    def test_ends_with_i(self):
        result = rule1("MI")
        self.assertEqual(next(result), "MIU")

    def test_does_not_end_with_i(self):
        result = rule1("MU")
        with self.assertRaises(StopIteration):
            next(result)

    def test_empty_string(self):
        result = rule1("")
        with self.assertRaises(StopIteration):
            next(result)

if __name__ == '__main__':
    gen_rules()
    unittest.main()