# Copyright 2004-2005 Elemental Security, Inc. All Rights Reserved. # Licensed to PSF under a Contributor Agreement. # Modifications: # Copyright David Halter and Contributors # Modifications are dual-licensed: MIT and PSF. """ This module defines the data structures used to represent a grammar. Specifying grammars in pgen is possible with this grammar:: grammar: (NEWLINE | rule)* ENDMARKER rule: NAME ':' rhs NEWLINE rhs: items ('|' items)* items: item+ item: '[' rhs ']' | atom ['+' | '*'] atom: '(' rhs ')' | NAME | STRING This grammar is self-referencing. This parser generator (pgen2) was created by Guido Rossum and used for lib2to3. Most of the code has been refactored to make it more Pythonic. Since this was a "copy" of the CPython Parser parser "pgen", there was some work needed to make it more readable. It should also be slightly faster than the original pgen2, because we made some optimizations. """ from ast import literal_eval from parso.pgen2.grammar_parser import GrammarParser, NFAState class Grammar(object): """ Once initialized, this class supplies the grammar tables for the parsing engine implemented by parse.py. The parsing engine accesses the instance variables directly. The only important part in this parsers are dfas and transitions between dfas. """ def __init__(self, start_nonterminal, rule_to_dfas, reserved_syntax_strings): self.nonterminal_to_dfas = rule_to_dfas # Dict[str, List[DFAState]] self.reserved_syntax_strings = reserved_syntax_strings self.start_nonterminal = start_nonterminal class DFAPlan(object): """ Plans are used for the parser to create stack nodes and do the proper DFA state transitions. """ def __init__(self, next_dfa, dfa_pushes=[]): self.next_dfa = next_dfa self.dfa_pushes = dfa_pushes def __repr__(self): return '%s(%s, %s)' % (self.__class__.__name__, self.next_dfa, self.dfa_pushes) class DFAState(object): """ The DFAState object is the core class for pretty much anything. DFAState are the vertices of an ordered graph while arcs and transitions are the edges. Arcs are the initial edges, where most DFAStates are not connected and transitions are then calculated to connect the DFA state machines that have different nonterminals. """ def __init__(self, from_rule, nfa_set, final): assert isinstance(nfa_set, set) assert isinstance(next(iter(nfa_set)), NFAState) assert isinstance(final, NFAState) self.from_rule = from_rule self.nfa_set = nfa_set self.arcs = {} # map from terminals/nonterminals to DFAState # In an intermediary step we set these nonterminal arcs (which has the # same structure as arcs). These don't contain terminals anymore. self.nonterminal_arcs = {} # Transitions are basically the only thing that the parser is using # with is_final. Everyting else is purely here to create a parser. self.transitions = {} #: Dict[Union[TokenType, ReservedString], DFAPlan] self.is_final = final in nfa_set def add_arc(self, next_, label): assert isinstance(label, str) assert label not in self.arcs assert isinstance(next_, DFAState) self.arcs[label] = next_ def unifystate(self, old, new): for label, next_ in self.arcs.items(): if next_ is old: self.arcs[label] = new def __eq__(self, other): # Equality test -- ignore the nfa_set instance variable assert isinstance(other, DFAState) if self.is_final != other.is_final: return False # Can't just return self.arcs == other.arcs, because that # would invoke this method recursively, with cycles... if len(self.arcs) != len(other.arcs): return False for label, next_ in self.arcs.items(): if next_ is not other.arcs.get(label): return False return True __hash__ = None # For Py3 compatibility. def __repr__(self): return '<%s: %s is_final=%s>' % ( self.__class__.__name__, self.from_rule, self.is_final ) class ReservedString(object): """ Most grammars will have certain keywords and operators that are mentioned in the grammar as strings (e.g. "if") and not token types (e.g. NUMBER). This class basically is the former. """ def __init__(self, value): self.value = value def __repr__(self): return '%s(%s)' % (self.__class__.__name__, self.value) def _simplify_dfas(dfas): """ This is not theoretically optimal, but works well enough. Algorithm: repeatedly look for two states that have the same set of arcs (same labels pointing to the same nodes) and unify them, until things stop changing. dfas is a list of DFAState instances """ changes = True while changes: changes = False for i, state_i in enumerate(dfas): for j in range(i + 1, len(dfas)): state_j = dfas[j] if state_i == state_j: #print " unify", i, j del dfas[j] for state in dfas: state.unifystate(state_j, state_i) changes = True break def _make_dfas(start, finish): """ Uses the powerset construction algorithm to create DFA states from sets of NFA states. Also does state reduction if some states are not needed. """ # To turn an NFA into a DFA, we define the states of the DFA # to correspond to *sets* of states of the NFA. Then do some # state reduction. assert isinstance(start, NFAState) assert isinstance(finish, NFAState) def addclosure(nfa_state, base_nfa_set): assert isinstance(nfa_state, NFAState) if nfa_state in base_nfa_set: return base_nfa_set.add(nfa_state) for nfa_arc in nfa_state.arcs: if nfa_arc.nonterminal_or_string is None: addclosure(nfa_arc.next, base_nfa_set) base_nfa_set = set() addclosure(start, base_nfa_set) states = [DFAState(start.from_rule, base_nfa_set, finish)] for state in states: # NB states grows while we're iterating arcs = {} # Find state transitions and store them in arcs. for nfa_state in state.nfa_set: for nfa_arc in nfa_state.arcs: if nfa_arc.nonterminal_or_string is not None: nfa_set = arcs.setdefault(nfa_arc.nonterminal_or_string, set()) addclosure(nfa_arc.next, nfa_set) # Now create the dfa's with no None's in arcs anymore. All Nones have # been eliminated and state transitions (arcs) are properly defined, we # just need to create the dfa's. for nonterminal_or_string, nfa_set in arcs.items(): for nested_state in states: if nested_state.nfa_set == nfa_set: # The DFA state already exists for this rule. break else: nested_state = DFAState(start.from_rule, nfa_set, finish) states.append(nested_state) state.add_arc(nested_state, nonterminal_or_string) return states # List of DFAState instances; first one is start def _dump_nfa(start, finish): print("Dump of NFA for", start.from_rule) todo = [start] for i, state in enumerate(todo): print(" State", i, state is finish and "(final)" or "") for arc in state.arcs: label, next_ = arc.nonterminal_or_string, arc.next if next_ in todo: j = todo.index(next_) else: j = len(todo) todo.append(next_) if label is None: print(" -> %d" % j) else: print(" %s -> %d" % (label, j)) def _dump_dfas(dfas): print("Dump of DFA for", dfas[0].from_rule) for i, state in enumerate(dfas): print(" State", i, state.is_final and "(final)" or "") for nonterminal, next_ in state.arcs.items(): print(" %s -> %d" % (nonterminal, dfas.index(next_))) def generate_grammar(bnf_grammar, token_namespace): """ ``bnf_text`` is a grammar in extended BNF (using * for repetition, + for at-least-once repetition, [] for optional parts, | for alternatives and () for grouping). It's not EBNF according to ISO/IEC 14977. It's a dialect Python uses in its own parser. """ rule_to_dfas = {} start_nonterminal = None for nfa_a, nfa_z in GrammarParser(bnf_grammar).parse(): #_dump_nfa(nfa_a, nfa_z) dfas = _make_dfas(nfa_a, nfa_z) #_dump_dfas(dfas) # oldlen = len(dfas) _simplify_dfas(dfas) # newlen = len(dfas) rule_to_dfas[nfa_a.from_rule] = dfas #print(nfa_a.from_rule, oldlen, newlen) if start_nonterminal is None: start_nonterminal = nfa_a.from_rule reserved_strings = {} for nonterminal, dfas in rule_to_dfas.items(): for dfa_state in dfas: for terminal_or_nonterminal, next_dfa in dfa_state.arcs.items(): if terminal_or_nonterminal in rule_to_dfas: dfa_state.nonterminal_arcs[terminal_or_nonterminal] = next_dfa else: transition = _make_transition( token_namespace, reserved_strings, terminal_or_nonterminal ) dfa_state.transitions[transition] = DFAPlan(next_dfa) _calculate_tree_traversal(rule_to_dfas) return Grammar(start_nonterminal, rule_to_dfas, reserved_strings) def _make_transition(token_namespace, reserved_syntax_strings, label): """ Creates a reserved string ("if", "for", "*", ...) or returns the token type (NUMBER, STRING, ...) for a given grammar terminal. """ if label[0].isalpha(): # A named token (e.g. NAME, NUMBER, STRING) return getattr(token_namespace, label) else: # Either a keyword or an operator assert label[0] in ('"', "'"), label assert not label.startswith('"""') and not label.startswith("'''") value = literal_eval(label) try: return reserved_syntax_strings[value] except KeyError: r = reserved_syntax_strings[value] = ReservedString(value) return r def _calculate_tree_traversal(nonterminal_to_dfas): """ By this point we know how dfas can move around within a stack node, but we don't know how we can add a new stack node (nonterminal transitions). """ # Map from grammar rule (nonterminal) name to a set of tokens. first_plans = {} nonterminals = list(nonterminal_to_dfas.keys()) nonterminals.sort() for nonterminal in nonterminals: if nonterminal not in first_plans: _calculate_first_plans(nonterminal_to_dfas, first_plans, nonterminal) # Now that we have calculated the first terminals, we are sure that # there is no left recursion. for dfas in nonterminal_to_dfas.values(): for dfa_state in dfas: transitions = dfa_state.transitions for nonterminal, next_dfa in dfa_state.nonterminal_arcs.items(): for transition, pushes in first_plans[nonterminal].items(): if transition in transitions: prev_plan = transitions[transition] # Make sure these are sorted so that error messages are # at least deterministic choices = sorted([ ( prev_plan.dfa_pushes[0].from_rule if prev_plan.dfa_pushes else prev_plan.next_dfa.from_rule ), ( pushes[0].from_rule if pushes else next_dfa.from_rule ), ]) raise ValueError( "Rule %s is ambiguous; given a %s token, we " "can't determine if we should evaluate %s or %s." % ( ( dfa_state.from_rule, transition, ) + tuple(choices) ) ) transitions[transition] = DFAPlan(next_dfa, pushes) def _calculate_first_plans(nonterminal_to_dfas, first_plans, nonterminal): """ Calculates the first plan in the first_plans dictionary for every given nonterminal. This is going to be used to know when to create stack nodes. """ dfas = nonterminal_to_dfas[nonterminal] new_first_plans = {} first_plans[nonterminal] = None # dummy to detect left recursion # We only need to check the first dfa. All the following ones are not # interesting to find first terminals. state = dfas[0] for transition, next_ in state.transitions.items(): # It's a string. We have finally found a possible first token. new_first_plans[transition] = [next_.next_dfa] for nonterminal2, next_ in state.nonterminal_arcs.items(): # It's a nonterminal and we have either a left recursion issue # in the grammar or we have to recurse. try: first_plans2 = first_plans[nonterminal2] except KeyError: first_plans2 = _calculate_first_plans(nonterminal_to_dfas, first_plans, nonterminal2) else: if first_plans2 is None: raise ValueError("left recursion for rule %r" % nonterminal) for t, pushes in first_plans2.items(): new_first_plans[t] = [next_] + pushes first_plans[nonterminal] = new_first_plans return new_first_plans