Vwwxrf

A few months back, I posted a state machine for review. Thanks to the feedback, I was able to greatly simplify the implementation. I am posting the revised version, together with the Regex class which calls it.

I think I'm mainly looking for feedback on structure. The relationship between my Node class and StateMachine class feels a little tangled; I'm not always sure which method ought to belong to which class. I think the way I communicate the next token of my lexer is also cumbersome.

state_machine.py

class Node:
 def __init__(self, value):
 self.value = value
 self.children = set()

 def empty(self):
 return self.value == ''

 def add_child(self, other):
 self.children.add(other)

 def find_parent_of_terminal(self, terminal):
 """
 We assume that there shall only be one node leading to the terminal
 and that there is only one terminal
 """
 visited = set()
 to_explore = self
 while to_explore:
 current = to_explore.pop()
 visited.add(current)
 if terminal in current.children:
 # If this fails, then there is a bug in union, concat, or kleene
 assert len(current.children) == 1
 return current
 to_explore.update(node for node in current.children 
 if node not in visited)
 return None

 def leads_to(self, value):
 """
 Return True iff argument can be reached by traversing empty nodes
 """
 return bool(self._get_node_if_reachable(value))

 def _get_node_if_reachable(self, value):
 for node in self.children:
 while node and node.empty():
 if node == value:
 return node
 node = node._get_node_if_reachable(value)
 return None

 def __repr__(self):
 result = ' : ['.format(self.value)
 for node in self.children:
 result += str(node.value) + ', '
 result += ']n'

 return result


def EmptyNode():
 return Node('')


class StateMachine:

 def __init__(self):
 self.initial = EmptyNode()
 self.terminal = EmptyNode()

 def __repr__(self):
 return str(self.initial)

 @staticmethod
 def from_string(source):
 dfa = StateMachine()
 nodes = [Node(char) for char in source]

 dfa.initial.add_child(nodes[0])
 for i in range(len(source) - 1):
 nodes[i].add_child(nodes[i + 1])
 nodes[-1].add_child(dfa.terminal)
 return dfa

 @staticmethod
 def from_set(chars):
 dfa = StateMachine()
 first = EmptyNode()
 penultimate = EmptyNode()
 dfa.initial.children = first

 for char in chars:
 char_node = Node(char)
 first.add_child(char_node)
 char_node.add_child(penultimate)

 penultimate.add_child(dfa.terminal)
 return dfa

 def concat(self, other):
 other.initial.find_parent_of_terminal(other.terminal).children = self.terminal
 self.initial.find_parent_of_terminal(self.terminal).children = other.initial.children

 return self

 def union(self, other):
 self.initial.children.update(other.initial.children)

 this_last = self.initial.find_parent_of_terminal(self.terminal)
 other_last = other.initial.find_parent_of_terminal(other.terminal)
 empty_node = EmptyNode()
 empty_node.add_child(self.terminal)
 this_last.children = empty_node
 other_last.children = empty_node
 return self

 def kleene(self):
 penultimate_node = self.initial.find_parent_of_terminal(self.terminal)
 dummy = EmptyNode()
 penultimate_node.children = dummy
 dummy.add_child(self.terminal)
 penultimate_node.add_child(self.initial)
 self.initial.add_child(dummy)
 return self

 def _get_next_state(self, nodes, value, visited=None):
 if visited is None:
 visited = set()
 result = set()
 for node in nodes:
 visited.add(node)
 for child in node.children:
 if child.empty() and child not in visited:
 result.update(self._get_next_state([child], value, visited))
 elif child.value == value:
 result.add(child)
 return result

 def is_match(self, nodes):
 for node in nodes:
 if node .leads_to(self.terminal):
 return True
 return False

 def match(self, source):
 """
 Match a target string by simulating a NFA
 :param source: string to match
 :return: Matched part of string, or None if no match is found
 """
 result = ''
 last_match = None
 current = self.initial
 for char in source:
 next_nodes = self._get_next_state(current, char)
 if next_nodes:
 current = next_nodes
 result += char

 if self.is_match(current):
 last_match = result
 else:
 break

 if self.is_match(current):
 last_match = result
 return last_match

regex.py

import collections
import enum
import string


from state_machine import StateMachine


class Token(enum.Enum):
 METACHAR = 0
 CHAR = 1
 ERROR = 2


class LexResult(collections.namedtuple('LexResult', ['token', 'lexeme'])):
 def __bool__(self):
 return self.token != Token.ERROR


class RegexLexer(object):
 metachars = '-|[]^().*'

 def __init__(self, pattern: str):
 self._pattern = pattern
 self._pos = 0
 self._stack = []

 def peek(self) -> LexResult:
 if self._pos >= len(self._pattern):
 return LexResult(Token.ERROR, '')
 next_char = self._pattern[self._pos]
 if next_char in self.metachars:
 token = Token.METACHAR
 else:
 token = Token.CHAR
 return LexResult(token, next_char)

 def _eat_token_type(self, token: Token) -> LexResult:
 next_match = self.peek()
 if next_match.token != token:
 return LexResult(Token.ERROR, next_match.lexeme)
 self._pos += 1
 return next_match

 def _eat_token(self, match: LexResult) -> LexResult:
 next_match = self.peek()
 if next_match == match:
 self._pos += 1
 return next_match
 return LexResult(Token.ERROR, next_match.lexeme)

 def mark(self):
 self._stack.append(self._pos)

 def clear(self):
 self._stack.pop()

 def backtrack(self):
 self._pos = self._stack.pop()

 def eat_char(self, char=''):
 if char:
 return self._eat_token(LexResult(Token.CHAR, char))
 return self._eat_token_type(Token.CHAR)

 def eat_metachar(self, metachar):
 return self._eat_token(LexResult(Token.METACHAR, metachar))


class Regex(object):
 CHARACTERS = string.printable

 def __init__(self, pattern: str):
 """
 Initialize regex by compiling provided pattern
 """
 self._lexer = RegexLexer(pattern)
 self._state_machine = self.parse()

 def match(self, text: str) -> str:
 """
 Match text according to provided pattern.
 Returns matched substring if a match was found,
 or None otherwise
 """
 assert self._state_machine
 return self._state_machine.match(text)

 def parse(self):
 nfa = self.parse_simple_re()
 if not nfa:
 return None
 while True:
 self._lexer.mark()
 if not self._lexer.eat_metachar('|'):
 self._lexer.backtrack()
 return nfa
 next_nfa = self.parse_simple_re()
 if not next_nfa:
 self._lexer.backtrack()
 return nfa
 nfa = nfa.union(next_nfa)
 self._lexer.clear()

 def parse_simple_re(self):
 """
 <simple-re> = <basic-re>+
 """
 nfa = self.parse_basic_re()
 if not nfa:
 return None

 while True:
 next_nfa = self.parse_basic_re()
 if not next_nfa:
 break
 nfa = nfa.concat(next_nfa)
 return nfa

 def parse_basic_re(self):
 """
 <elementary-re> "*" | <elementary-re> "+" | <elementary-re>
 """
 nfa = self.parse_elementary_re()
 if not nfa:
 return None
 next_match = self._lexer.peek()
 if not next_match or next_match.token != Token.METACHAR:
 return nfa
 if next_match.lexeme == '*':
 self._lexer.eat_metachar('*')
 return nfa.kleene()
 if next_match.lexeme == '+':
 self._lexer.eat_metachar('+')
 return nfa.union(nfa.kleene())
 return nfa

 def parse_elementary_re(self):
 """
 <elementary-RE> = <group> | <any> | <char> | <set>
 :return: DFA
 """
 self._lexer.mark()
 nfa = self.parse_group()
 if nfa:
 self._lexer.clear()
 return nfa

 self._lexer.backtrack()
 if self._lexer.eat_metachar('.'):
 return StateMachine.from_set(x for x in self.CHARACTERS)

 char = self._lexer.eat_char()
 if char:
 return StateMachine.from_string(char.lexeme)

 set_chars = self.parse_set()
 if not set_chars:
 return None
 return StateMachine.from_set(set_chars)

 def parse_group(self):
 """
 <group> = "(" <RE> ")"
 :return: DFA
 """
 if not self._lexer.eat_metachar('('):
 return None
 state_machine = self.parse()
 if not state_machine:
 return None
 if not self._lexer.eat_metachar(')'):
 return None
 return state_machine

 def parse_range(self) -> str:
 """
 <range> = <CHAR> "-" <CHAR>
 """
 first = self._lexer.eat_char()
 if not first:
 return set()

 if not self._lexer.eat_metachar('-'):
 return set()

 last = self._lexer.eat_char()
 if not last:
 return set()

 return chr(x) for x in range(ord(first.lexeme), ord(last.lexeme) + 1)

 def parse_set_item(self) -> str:
 """
 <set item> = <range> | <char>
 """
 self._lexer.mark()
 set_item = self.parse_range()
 if set_item:
 self._lexer.clear()
 return set_item
 self._lexer.backtrack()
 next_item = self._lexer.eat_char()
 return next_item.lexeme if next_item else set()

 def parse_set_items(self) -> str:
 """
 <set items> = <set item>+
 """
 items = self.parse_set_item()
 if not items:
 return set()
 next_items = self.parse_set_item()
 while next_items:
 items.update(next_items)
 next_items = self.parse_set_item()
 return items

 def parse_positive_set(self) -> str:
 if not self._lexer.eat_metachar('['):
 return set()
 set_items = self.parse_set_items()
 if not set_items:
 return set()
 if not self._lexer.eat_metachar(']'):
 return set()
 return set_items

 def parse_negative_set(self) -> str:
 if not self._lexer.eat_metachar('['):
 return set()
 if not self._lexer.eat_metachar('^'):
 return set()
 set_items = self.parse_set_items()
 if not set_items:
 return set()
 if not self._lexer.eat_metachar(']'):
 return set()
 return set(string.printable).difference(set_items)

 def parse_set(self) -> str:
 """
 Parse something like [a-z9] and return the set of allowed characters
 """
 self._lexer.mark()
 set_items = self.parse_positive_set()
 if set_items:
 self._lexer.clear()
 return set_items
 self._lexer.backtrack()
 return self.parse_negative_set()

Finally, a small set of unit tests to show usage:

import unittest
from state_machine import StateMachine
from regex import Regex


class TestStateMachine(unittest.TestCase):

 def test_union(self):
 state_machine = StateMachine.from_string('abc')
 state_machine = state_machine.union(StateMachine.from_string('def'))

 self.assertEqual(state_machine.match('abc'), 'abc')
 self.assertEqual(state_machine.match('def'), 'def')
 self.assertIsNone(state_machine.match('de'))

 def test_kleene(self):
 state_machine = StateMachine.from_string('abc')
 state_machine = state_machine.kleene()

 self.assertEqual(state_machine.match(''), '')
 self.assertEqual(state_machine.match('abc'), 'abc')
 self.assertEqual(state_machine.match('abcabc'), 'abcabc')
 self.assertEqual(state_machine.match('abcDabc'), 'abc')

 def test_concat(self):
 state_machine = StateMachine.from_string('ab')
 state_machine = state_machine.concat(StateMachine.from_string('cd'))

 self.assertEqual(state_machine.match('abcd'), 'abcd')
 self.assertEqual(state_machine.match('abcde'), 'abcd')
 self.assertIsNone(state_machine.match('abc'))


class TestRegex(unittest.TestCase):

 def test_identifier_regex(self):
 regex = Regex('[a-zA-Z_][a-zA-Z0-9_]*')
 self.assertEqual(regex.match('a'), 'a')
 self.assertFalse(regex.match('0'))
 self.assertTrue(regex.match('a0'))
 self.assertEqual(regex.match('a0_3bd'), 'a0_3bd')
 self.assertEqual(regex.match('abd-43'), 'abd')

 def test_parentheses(self):
 regex = Regex('d(ab)*')
 self.assertEqual(regex.match('d'), 'd')
 self.assertEqual(regex.match('dab'), 'dab')
 self.assertEqual(regex.match('daa'), 'd')
 self.assertEqual(regex.match('dabab'), 'dabab')

 def test_union(self):
 regex = Regex('(ab*d)|(AG)')
 self.assertEqual(regex.match('adG'), 'ad')
 self.assertEqual(regex.match('AGfe'), 'AG')


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

Yay! You ran flake8 and followed PEP-8. Nice clean code.

 self.assertEqual(state_machine.match('abc'), 'abc')

Ummm, this is arguably backwards.
Convention for xUnit in many languages is to assertEqual(expected, computed).
It can affect how the diagnostic output is displayed for a failure.

 state_machine = state_machine.union(StateMachine.from_string('def'))

Choosing the name union for your public API is perhaps slightly confusing.
"Union" is drawn from set theory,
while "alternation" is the term the regex literature tends to use for |.

 state_machine = StateMachine.from_string('abc')

The class name is perfectly clear, it's great.
For a local variable that we'll be using a bunch, sm would have sufficed.
You already have a line that verifies that .from_string() doesn't blow up, so
consider combining two assignments on a single line:

 sm = StateMachine.from_string('abc').kleene()

The Regex class is wonderfully straightforward.
Pat yourself on the back.

The peek method in the lexer is perhaps a little on the tricky side,
and would benefit from comments
about when we consume something or not.
I'm looking for invariants on pos and the stack.
I like the assert in find_parent_of_terminal, and its comment.

 to_explore.update(node for node in current.children 
 if node not in visited)

That's just set difference, yes? children - visited

Overall, looks good. Ship it!