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__pycache__
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*.pyc
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*.swp
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import enum
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from collections import namedtuple
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from regex import lit, concat, bar, star
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NFA = namedtuple('NFA', ['start', 'accept', 'transitions'])
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def copy_nfa(nfa):
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transitions_copy = {}
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for from_state in nfa.transitions:
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transitions_copy[from_state] = nfa.transitions[from_state].copy()
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return NFA(nfa.start, nfa.accept, transitions_copy)
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def remove_states(nfa):
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start, accept, transitions = nfa
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states = transitions.keys()
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states_to_remove = [i for i in states if i != start and i not in accept]
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while len(states_to_remove) > 0:
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# Select a state to remove this round
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removed_state = states_to_remove.pop()
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print('\nRemoving state:', removed_state)#debg
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# Remove loops from this state back into itself
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if removed_state in transitions[removed_state]:
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loop_condition = transitions[removed_state][removed_state]
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del transitions[removed_state][removed_state]
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# Prepend (condition)* to all transitions leading out
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# of this state
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for to_state in transitions[removed_state]:
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condition = transitions[removed_state][to_state]
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transitions[removed_state][to_state] = concat(star(loop_condition), condition)
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print(); prettyprint(nfa)#debg
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# Rewrite all transitions A→this→B as A→B transitions
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#
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# If the condition A→this is foo and this→B is bar, the
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# condition for A→B becomes simply foobar
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#
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# Since we've removed all loops back into this state, this
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# results in there being no transitions into this state
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for from_state in transitions:
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if removed_state in transitions[from_state]:
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# Create a list of new transitions to add to the
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# transition table for from_state
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new_transitions = {}
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condition_to_here = transitions[from_state][removed_state]
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for to_state in transitions[removed_state]:
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condition_from_here = transitions[removed_state][to_state]
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new_transitions[to_state] = concat(condition_to_here, condition_from_here)
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# Remove the transition to the state being deleted
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del transitions[from_state][removed_state]
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# Add the new transitions
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# Since they may lead to the same place as
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# already-existing transitions, we may need to
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# combine the conditions with pre-existing ones
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for to_state in new_transitions:
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if to_state in transitions[from_state]:
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# Already a transition leading
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# to the same state
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# If its condition is foo and
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# ours is bar, then the new
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# condition will be foo|bar
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other_condition = transitions[from_state][to_state]
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our_condition = new_transitions[to_state]
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transitions[from_state][to_state] = bar(other_condition, our_condition)
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else:
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# No pre-existing transition
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transitions[from_state][to_state] = new_transitions[to_state]
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# Finally, remove the state we no longer need
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del transitions[removed_state]
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print(); prettyprint(nfa)#debg
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return NFA(start, accept, transitions)
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def to_regex(nfa):
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# Rewrite the NFA so that there are no transitions leading in to the
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# start state or any leading out of an accept state. The easy way to
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# do this is by creating a new start state that leads to the old one
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# with empty condition (i.e. it consumes no input), and creating a new
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# accept state that has similar empty condition transitions from all
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# the old ones. Since we have an NFA and not a DFA, that operation is
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# safe
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#
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# As a bonus, this rewrite gives us two useful properties:
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# a) There is exactly one start state and one accept state
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# b) After running remove_state() there will be only one transition,
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# that of start to accept
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#
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# S
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class _(enum.Enum): start, end = range(2)
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start, accept, transitions = copy_nfa(nfa)
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# Add new start state
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transitions[_.start] = {start: lit('')}
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# Add new accept state and transitions to it
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transitions[_.end] = {}
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for state in accept:
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transitions[state][_.end] = lit('')
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# Package everything into a new NFA
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nfa = NFA(_.start, [_.end], transitions)
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print();prettyprint(nfa)#debg
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processed = remove_states(nfa)
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return processed.transitions[_.start][_.end]
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def prettyprint(nfa):
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def process_state(state):
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nonlocal start, accept
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t = ''
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if state == start:
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# Bold
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t += '\x1b[1m'
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if state in accept:
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# Green
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t += '\x1b[32m'
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if t != '':
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return t + str(state) + '\x1b[0m'
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else:
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return str(state)
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start, accept, transitions = nfa
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states = transitions.keys()
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print('\t' + '\t'.join(map(process_state, states)))
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for from_state in states:
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t = []
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for to_state in states:
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if to_state in transitions[from_state]:
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t.append(str(transitions[from_state][to_state]))
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else:
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t.append('\x1b[90m-\x1b[0m')
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print(process_state(from_state) + '\t' + '\t'.join(t))
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def main():
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nfa = NFA('start', ['end'], {
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'start': {'0': lit('s')},
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'0': {'0': lit('0'), '1': lit('1'), 'end': lit('e'), 'start': lit('r')},
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'1': {'0': lit('1'), '1': lit('0'), 'start': lit('r')},
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'end': {'end': lit('e'), 'start': lit('n')}
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})
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prettyprint(nfa)
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print(to_regex(nfa))
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if __name__ == '__main__':
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main()
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class Literal:
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def __init__(self, text):
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self.text = text
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self.single_char = len(text) == 1
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def __repr__(self):
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return 'Literal(%s)' % repr(self.text)
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def __str__(self):
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# ERE-style quotation rules
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# A-Za-z0-9 and space are safe, as are non-ASCII
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# Everything else is safe to quote with backslash
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return ''.join(
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char if ord('A') <= ord(char) <= ord('Z') else
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char if ord('a') <= ord(char) <= ord('z') else
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char if ord('0') <= ord(char) <= ord('9') else
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char if char == ' ' else
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char if ord(char) >= 128 else # Non-ASCII
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'\\' + char # Quote
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for char in self.text
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)
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class Concatenation:
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def __init__(self, *elements):
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self.elements = elements
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def __repr__(self):
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return 'Concatenation(%s)' % ', '.join(map(repr, self.elements))
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def __str__(self):
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return ''.join(
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# Only alternation binds looser than concatenation,
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# so we can pass everything else pass through with
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# no parenthesizing
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str(element) if type(element) != Alternation else
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'(' + str(element) + ')'
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for element in self.elements
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)
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class Alternation:
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def __init__(self, *elements):
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self.elements = elements
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def __repr__(self):
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return 'Alternation(%s)' % ', '.join(map(repr, self.elements))
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def __str__(self):
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if all(type(i) == Literal and i.single_char for i in self.elements):
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# Special case: [abc]
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return '[%s]' % ''.join(map(str, self.elements))
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else:
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# Nothing binds looser than alternation, so just
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# pass everything through as-is
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return '|'.join(map(str, self.elements))
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class Star:
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def __init__(self, element):
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self.element = element
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def __repr__(self):
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return 'Star(%s)' % repr(self.element)
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def __str__(self):
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# * applies to the previous character or a parenthesized
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# group. Therefore, we parentesize unless we havea Literal
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# and it is one-char long
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if type(self.element) == Literal and self.element.single_char:
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return str(self.element) + '*'
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else:
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return '(%s)*' % str(self.element)
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def lit(text):
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return Literal(text)
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def concat(*elements):
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flattened = []
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for element in elements:
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if type(element) == Concatenation:
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flattened.extend(element.elements)
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else:
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flattened.append(element)
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combined = []
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for element in flattened:
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if len(combined) > 0 and type(combined[-1]) == Literal and type(element) == Literal:
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# Combine two literals next to each other
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# into one literal
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previous = combined.pop()
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combined.append(Literal(previous.text + element.text))
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else:
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combined.append(element)
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if len(combined) == 1:
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element, = combined
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return element
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else:
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return Concatenation(*combined)
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def bar(*elements):
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# TODO: rewrite (foo|foo) → foo
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flattened = []
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for element in elements:
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if type(element) == Alternation:
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flattened.extend(element.elements)
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else:
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flattened.append(element)
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if len(flattened) == 1:
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element, = flattened
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return element
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else:
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return Alternation(*flattened)
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def star(element):
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return Star(element)
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