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""" |
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This module defines the data structures used to represent a grammar. |
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|
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Specifying grammars in pgen is possible with this grammar:: |
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grammar: (NEWLINE | rule)* ENDMARKER |
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rule: NAME ':' rhs NEWLINE |
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rhs: items ('|' items)* |
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items: item+ |
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item: '[' rhs ']' | atom ['+' | '*'] |
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atom: '(' rhs ')' | NAME | STRING |
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This grammar is self-referencing. |
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This parser generator (pgen2) was created by Guido Rossum and used for lib2to3. |
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Most of the code has been refactored to make it more Pythonic. Since this was a |
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"copy" of the CPython Parser parser "pgen", there was some work needed to make |
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it more readable. It should also be slightly faster than the original pgen2, |
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because we made some optimizations. |
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""" |
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from ast import literal_eval |
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from typing import TypeVar, Generic, Mapping, Sequence, Set, Union |
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from parso.pgen2.grammar_parser import GrammarParser, NFAState |
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_TokenTypeT = TypeVar("_TokenTypeT") |
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class Grammar(Generic[_TokenTypeT]): |
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""" |
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Once initialized, this class supplies the grammar tables for the |
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parsing engine implemented by parse.py. The parsing engine |
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accesses the instance variables directly. |
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The only important part in this parsers are dfas and transitions between |
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dfas. |
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""" |
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def __init__(self, |
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start_nonterminal: str, |
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rule_to_dfas: Mapping[str, Sequence['DFAState[_TokenTypeT]']], |
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reserved_syntax_strings: Mapping[str, 'ReservedString']): |
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self.nonterminal_to_dfas = rule_to_dfas |
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self.reserved_syntax_strings = reserved_syntax_strings |
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self.start_nonterminal = start_nonterminal |
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class DFAPlan: |
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""" |
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Plans are used for the parser to create stack nodes and do the proper |
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DFA state transitions. |
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""" |
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def __init__(self, next_dfa: 'DFAState', dfa_pushes: Sequence['DFAState'] = []): |
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self.next_dfa = next_dfa |
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self.dfa_pushes = dfa_pushes |
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def __repr__(self): |
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return '%s(%s, %s)' % (self.__class__.__name__, self.next_dfa, self.dfa_pushes) |
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class DFAState(Generic[_TokenTypeT]): |
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""" |
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The DFAState object is the core class for pretty much anything. DFAState |
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are the vertices of an ordered graph while arcs and transitions are the |
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edges. |
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Arcs are the initial edges, where most DFAStates are not connected and |
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transitions are then calculated to connect the DFA state machines that have |
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different nonterminals. |
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""" |
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def __init__(self, from_rule: str, nfa_set: Set[NFAState], final: NFAState): |
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assert isinstance(nfa_set, set) |
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assert isinstance(next(iter(nfa_set)), NFAState) |
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assert isinstance(final, NFAState) |
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self.from_rule = from_rule |
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self.nfa_set = nfa_set |
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self.arcs: Mapping[str, DFAState] = {} |
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self.nonterminal_arcs: Mapping[str, DFAState] = {} |
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self.transitions: Mapping[Union[_TokenTypeT, ReservedString], DFAPlan] = {} |
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self.is_final = final in nfa_set |
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def add_arc(self, next_, label): |
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assert isinstance(label, str) |
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assert label not in self.arcs |
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assert isinstance(next_, DFAState) |
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self.arcs[label] = next_ |
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def unifystate(self, old, new): |
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for label, next_ in self.arcs.items(): |
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if next_ is old: |
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self.arcs[label] = new |
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def __eq__(self, other): |
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assert isinstance(other, DFAState) |
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if self.is_final != other.is_final: |
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return False |
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if len(self.arcs) != len(other.arcs): |
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return False |
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for label, next_ in self.arcs.items(): |
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if next_ is not other.arcs.get(label): |
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return False |
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return True |
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def __repr__(self): |
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return '<%s: %s is_final=%s>' % ( |
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self.__class__.__name__, self.from_rule, self.is_final |
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) |
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class ReservedString: |
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""" |
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Most grammars will have certain keywords and operators that are mentioned |
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in the grammar as strings (e.g. "if") and not token types (e.g. NUMBER). |
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This class basically is the former. |
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""" |
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def __init__(self, value: str): |
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self.value = value |
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def __repr__(self): |
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return '%s(%s)' % (self.__class__.__name__, self.value) |
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def _simplify_dfas(dfas): |
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""" |
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This is not theoretically optimal, but works well enough. |
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Algorithm: repeatedly look for two states that have the same |
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set of arcs (same labels pointing to the same nodes) and |
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unify them, until things stop changing. |
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dfas is a list of DFAState instances |
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""" |
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changes = True |
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while changes: |
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changes = False |
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for i, state_i in enumerate(dfas): |
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for j in range(i + 1, len(dfas)): |
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state_j = dfas[j] |
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if state_i == state_j: |
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del dfas[j] |
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for state in dfas: |
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state.unifystate(state_j, state_i) |
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changes = True |
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break |
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def _make_dfas(start, finish): |
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""" |
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Uses the powerset construction algorithm to create DFA states from sets of |
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NFA states. |
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Also does state reduction if some states are not needed. |
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""" |
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assert isinstance(start, NFAState) |
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assert isinstance(finish, NFAState) |
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def addclosure(nfa_state, base_nfa_set): |
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assert isinstance(nfa_state, NFAState) |
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if nfa_state in base_nfa_set: |
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return |
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base_nfa_set.add(nfa_state) |
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for nfa_arc in nfa_state.arcs: |
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if nfa_arc.nonterminal_or_string is None: |
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addclosure(nfa_arc.next, base_nfa_set) |
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base_nfa_set = set() |
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addclosure(start, base_nfa_set) |
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states = [DFAState(start.from_rule, base_nfa_set, finish)] |
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for state in states: |
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arcs = {} |
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for nfa_state in state.nfa_set: |
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for nfa_arc in nfa_state.arcs: |
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if nfa_arc.nonterminal_or_string is not None: |
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nfa_set = arcs.setdefault(nfa_arc.nonterminal_or_string, set()) |
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addclosure(nfa_arc.next, nfa_set) |
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for nonterminal_or_string, nfa_set in arcs.items(): |
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for nested_state in states: |
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if nested_state.nfa_set == nfa_set: |
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break |
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else: |
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nested_state = DFAState(start.from_rule, nfa_set, finish) |
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states.append(nested_state) |
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state.add_arc(nested_state, nonterminal_or_string) |
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return states |
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def _dump_nfa(start, finish): |
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print("Dump of NFA for", start.from_rule) |
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todo = [start] |
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for i, state in enumerate(todo): |
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print(" State", i, state is finish and "(final)" or "") |
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for arc in state.arcs: |
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label, next_ = arc.nonterminal_or_string, arc.next |
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if next_ in todo: |
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j = todo.index(next_) |
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else: |
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j = len(todo) |
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todo.append(next_) |
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if label is None: |
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print(" -> %d" % j) |
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else: |
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print(" %s -> %d" % (label, j)) |
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def _dump_dfas(dfas): |
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print("Dump of DFA for", dfas[0].from_rule) |
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for i, state in enumerate(dfas): |
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print(" State", i, state.is_final and "(final)" or "") |
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for nonterminal, next_ in state.arcs.items(): |
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print(" %s -> %d" % (nonterminal, dfas.index(next_))) |
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def generate_grammar(bnf_grammar: str, token_namespace) -> Grammar: |
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""" |
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``bnf_text`` is a grammar in extended BNF (using * for repetition, + for |
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at-least-once repetition, [] for optional parts, | for alternatives and () |
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for grouping). |
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It's not EBNF according to ISO/IEC 14977. It's a dialect Python uses in its |
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own parser. |
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""" |
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rule_to_dfas = {} |
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start_nonterminal = None |
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for nfa_a, nfa_z in GrammarParser(bnf_grammar).parse(): |
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dfas = _make_dfas(nfa_a, nfa_z) |
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_simplify_dfas(dfas) |
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rule_to_dfas[nfa_a.from_rule] = dfas |
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if start_nonterminal is None: |
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start_nonterminal = nfa_a.from_rule |
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reserved_strings: Mapping[str, ReservedString] = {} |
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for nonterminal, dfas in rule_to_dfas.items(): |
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for dfa_state in dfas: |
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for terminal_or_nonterminal, next_dfa in dfa_state.arcs.items(): |
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if terminal_or_nonterminal in rule_to_dfas: |
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dfa_state.nonterminal_arcs[terminal_or_nonterminal] = next_dfa |
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else: |
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transition = _make_transition( |
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token_namespace, |
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reserved_strings, |
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terminal_or_nonterminal |
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) |
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dfa_state.transitions[transition] = DFAPlan(next_dfa) |
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_calculate_tree_traversal(rule_to_dfas) |
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return Grammar(start_nonterminal, rule_to_dfas, reserved_strings) |
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def _make_transition(token_namespace, reserved_syntax_strings, label): |
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""" |
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Creates a reserved string ("if", "for", "*", ...) or returns the token type |
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(NUMBER, STRING, ...) for a given grammar terminal. |
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""" |
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if label[0].isalpha(): |
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return getattr(token_namespace, label) |
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else: |
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assert label[0] in ('"', "'"), label |
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assert not label.startswith('"""') and not label.startswith("'''") |
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value = literal_eval(label) |
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try: |
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return reserved_syntax_strings[value] |
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except KeyError: |
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r = reserved_syntax_strings[value] = ReservedString(value) |
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return r |
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def _calculate_tree_traversal(nonterminal_to_dfas): |
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""" |
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By this point we know how dfas can move around within a stack node, but we |
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don't know how we can add a new stack node (nonterminal transitions). |
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""" |
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first_plans = {} |
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nonterminals = list(nonterminal_to_dfas.keys()) |
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nonterminals.sort() |
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for nonterminal in nonterminals: |
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if nonterminal not in first_plans: |
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_calculate_first_plans(nonterminal_to_dfas, first_plans, nonterminal) |
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for dfas in nonterminal_to_dfas.values(): |
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for dfa_state in dfas: |
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transitions = dfa_state.transitions |
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for nonterminal, next_dfa in dfa_state.nonterminal_arcs.items(): |
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for transition, pushes in first_plans[nonterminal].items(): |
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if transition in transitions: |
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prev_plan = transitions[transition] |
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choices = sorted([ |
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( |
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prev_plan.dfa_pushes[0].from_rule |
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if prev_plan.dfa_pushes |
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else prev_plan.next_dfa.from_rule |
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), |
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( |
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pushes[0].from_rule |
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if pushes else next_dfa.from_rule |
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), |
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]) |
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raise ValueError( |
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"Rule %s is ambiguous; given a %s token, we " |
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"can't determine if we should evaluate %s or %s." |
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% ( |
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( |
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dfa_state.from_rule, |
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transition, |
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) + tuple(choices) |
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) |
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) |
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transitions[transition] = DFAPlan(next_dfa, pushes) |
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def _calculate_first_plans(nonterminal_to_dfas, first_plans, nonterminal): |
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""" |
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Calculates the first plan in the first_plans dictionary for every given |
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nonterminal. This is going to be used to know when to create stack nodes. |
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""" |
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dfas = nonterminal_to_dfas[nonterminal] |
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new_first_plans = {} |
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first_plans[nonterminal] = None |
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state = dfas[0] |
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for transition, next_ in state.transitions.items(): |
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new_first_plans[transition] = [next_.next_dfa] |
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for nonterminal2, next_ in state.nonterminal_arcs.items(): |
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try: |
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first_plans2 = first_plans[nonterminal2] |
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except KeyError: |
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first_plans2 = _calculate_first_plans(nonterminal_to_dfas, first_plans, nonterminal2) |
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else: |
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if first_plans2 is None: |
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raise ValueError("left recursion for rule %r" % nonterminal) |
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for t, pushes in first_plans2.items(): |
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new_first_plans[t] = [next_] + pushes |
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first_plans[nonterminal] = new_first_plans |
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return new_first_plans |
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