parse.py 118 KB
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# parse.py - parser combinators for DHParser
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#
# Copyright 2016  by Eckhart Arnold (arnold@badw.de)
#                 Bavarian Academy of Sciences an Humanities (badw.de)
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
# implied.  See the License for the specific language governing
# permissions and limitations under the License.
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"""
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Module ``parse`` contains the python classes and functions for
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DHParser's packrat-parser. It's central class is the
``Grammar``-class, which is the base class for any concrete
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Grammar. Grammar-objects are callable and parsing is done by
calling a Grammar-object with a source text as argument.

The different parsing functions are callable descendants of class
``Parser``. Usually, they are organized in a tree and defined
within the namespace of a grammar-class. See ``ebnf.EBNFGrammar``
for an example.
"""

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from collections import defaultdict
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import copy
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from typing import Callable, cast, List, Tuple, Set, Dict, \
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    DefaultDict, Sequence, Union, Optional, Any
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from DHParser.configuration import get_config_value
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from DHParser.error import Error
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from DHParser.log import CallItem, HistoryRecord
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from DHParser.preprocess import BEGIN_TOKEN, END_TOKEN, RX_TOKEN_NAME
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from DHParser.stringview import StringView, EMPTY_STRING_VIEW
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from DHParser.syntaxtree import ChildrenType, Node, RootNode, WHITESPACE_PTYPE, \
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    TOKEN_PTYPE, ZOMBIE_TAG, EMPTY_NODE, ResultType
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from DHParser.toolkit import sane_parser_name, escape_control_characters, re, cython, \
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    abbreviate_middle, RX_NEVER_MATCH, RxPatternType, linebreaks, line_col
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__all__ = ('ParserError',
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           'ApplyFunc',
           'FlagFunc',
           'ParseFunc',
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           'Parser',
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           'UnknownParserError',
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           'GrammarErrorType',
           'GrammarError',
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           'Grammar',
           'PreprocessorToken',
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           'Token',
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           'DropToken',
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           'RegExp',
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           'RE',
           'TKN',
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           'Whitespace',
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           'DropRegExp',
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           'mixin_comment',
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           'mixin_noempty',
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           'MetaParser',
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           'UnaryParser',
           'NaryParser',
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           'Drop',
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           'Synonym',
           'Option',
           'ZeroOrMore',
           'OneOrMore',
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           'MandatoryNary',
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           'Series',
           'Alternative',
           'AllOf',
           'SomeOf',
           'Unordered',
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           'Interleave',
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           'Required',
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           'Lookahead',
           'NegativeLookahead',
           'Lookbehind',
           'NegativeLookbehind',
           'last_value',
           'counterpart',
           'accumulate',
           'Capture',
           'Retrieve',
           'Pop',
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           'Forward')
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########################################################################
#
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# ParserError class
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#
########################################################################


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class ParserError(Exception):
    """
    A `ParserError` is thrown for those parser errors that allow the
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    controlled re-entrance of the parsing process after the error occurred.
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    If a reentry-rule has been configured for the parser where the error
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    occurred, the parser guard can resume the parsing process.
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    Currently, the only case when a `ParserError` is thrown (and not some
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    different kind of error like `UnknownParserError`) is when a `Series`-
    or `AllOf`-parser detects a missing mandatory element.
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    """
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    def __init__(self, node: Node, rest: StringView, error: Error, first_throw: bool):
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        assert node is not None
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        self.node = node    # type: Node
        self.rest = rest    # type: StringView
        self.error = error  # type: Error
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        self.first_throw = first_throw  # type: bool
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        self.frozen_callstack = tuple()  # type: Tuple[CallItem, ...]  # tag_name, location
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    def __str__(self):
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        return "%i: %s    %s" % (self.node.pos, str(self.rest[:25]), repr(self.node))
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ResumeList = List[RxPatternType]  # list of regular expressiones
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@cython.locals(upper_limit=cython.int, closest_match=cython.int, pos=cython.int)
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def reentry_point(rest: StringView,
                  rules: ResumeList,
                  comment_regex,
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                  search_window: int = -1) -> int:
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    """
    Finds the point where parsing should resume after a ParserError has been caught.
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    The algorithm makes sure that this reentry-point does not lie inside a comment.
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    The re-entry point is always the point after the end of the match of the regular
    expression defining the re-entry point. (Use look ahead, if you wand to define
    the re-entry point by what follows rather than by what text precedes the point.)
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    Args:
        rest:  The rest of the parsed text or, in other words, the point where
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            a ParserError was thrown.
        rules: A list of regular expressions. The rest of the text is searched for
            each of these. The closest match is the point where parsing will be
            resumed.
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        comment_regex: A regular expression object that matches comments.
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        search_window: The maximum size of the search window for finding the
            reentry-point. A value smaller or equal zero means that
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    Returns:
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        The integer index of the closest reentry point or -1 if no reentry-point
        was found.
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    """
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    upper_limit = len(rest) + 1
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    closest_match = upper_limit
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    comments = None  # typ: Optional[Iterator]

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    @cython.locals(a=cython.int, b=cython.int)
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    def next_comment() -> Tuple[int, int]:
        nonlocal rest, comments
        if comments:
            try:
                m = next(comments)
                a, b = m.span()
                return rest.index(a), rest.index(b)
            except StopIteration:
                comments = None
        return -1, -2

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    # def str_search(s, start: int = 0) -> Tuple[int, int]:
    #     nonlocal rest
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    #     return rest.find(s, start, start + search_window), len(s)
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    @cython.locals(start=cython.int, end=cython.int)
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    def rx_search(rx, start: int = 0) -> Tuple[int, int]:
        nonlocal rest
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        m = rest.search(rx, start, start + search_window)
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        if m:
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            begin, end = m.span()
            return rest.index(begin), end - begin
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        return -1, 0

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    @cython.locals(a=cython.int, b=cython.int, k=cython.int, length=cython.int)
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    def entry_point(search_func, search_rule) -> int:
        a, b = next_comment()
        k, length = search_func(search_rule)
        while a < b <= k:
            a, b = next_comment()
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        # find next as long as start or end point of resume regex are inside a comment
        while (a < k < b) or (a < k + length < b):
            k, length = search_func(search_rule, b)
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            while a < b <= k:
                a, b = next_comment()
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        return k + length if k >= 0 else upper_limit
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    # find closest match
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    for rule in rules:
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        comments = rest.finditer(comment_regex)
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        assert not isinstance(rule, str), \
            'Strings not allowed as search rules, use a regular expression instead.'
        pos = entry_point(rx_search, rule)
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        closest_match = min(pos, closest_match)
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    # in case no rule matched return -1
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    if closest_match == upper_limit:
        closest_match = -1
    return closest_match
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########################################################################
#
# Parser base class
#
########################################################################


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ApplyFunc = Callable[['Parser'], None]
FlagFunc = Callable[[ApplyFunc, Set[ApplyFunc]], bool]
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ParseFunc = Callable[[StringView], Tuple[Optional[Node], StringView]]
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class Parser:
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    """
    (Abstract) Base class for Parser combinator parsers. Any parser
    object that is actually used for parsing (i.e. no mock parsers)
    should should be derived from this class.

    Since parsers can contain other parsers (see classes UnaryOperator
    and NaryOperator) they form a cyclical directed graph. A root
    parser is a parser from which all other parsers can be reached.
    Usually, there is one root parser which serves as the starting
    point of the parsing process. When speaking of "the root parser"
    it is this root parser object that is meant.

    There are two different types of parsers:

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    1. *Named parsers* for which a name is set in field `parser.pname`.
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       The results produced by these parsers can later be retrieved in
       the AST by the parser name.

    2. *Anonymous parsers* where the name-field just contains the empty
       string. AST-transformation of Anonymous parsers can be hooked
       only to their class name, and not to the individual parser.

    Parser objects are callable and parsing is done by calling a parser
    object with the text to parse.

    If the parser matches it returns a tuple consisting of a node
    representing the root of the concrete syntax tree resulting from the
    match as well as the substring `text[i:]` where i is the length of
    matched text (which can be zero in the case of parsers like
    `ZeroOrMore` or `Option`). If `i > 0` then the parser has "moved
    forward".

    If the parser does not match it returns `(None, text). **Note** that
    this is not the same as an empty match `("", text)`. Any empty match
    can for example be returned by the `ZeroOrMore`-parser in case the
    contained parser is repeated zero times.

    Attributes and Properties:
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        pname:  The parser's name or a (possibly empty) alias name in case
                of an anonymous parser.
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        anonymous: A property indicating that the parser remains anynomous
                anonymous with respect to the nodes it returns. For performance
                reasons this is implemented as an object variable rather
                than a property. This property must always be equal to
                `self.tag_name[0] == ":"`.
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        drop_content: A property (for performance reasons implemented as
                simple field) that, if set, induces the parser not to return
                the parsed content or sub-tree if it has matched but the
                dummy `EMPTY_NODE`. In effect the parsed content will be
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                dropped from the concrete syntax tree already. Only
                anonymous (or pseudo-anonymous) parsers are allowed to
                drop content.
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        tag_name: The tag_name for the nodes that are created by
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                the parser. If the parser is named, this is the same as
                `pname`, otherwise it is the name of the parser's type.
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        visited:  Mapping of places this parser has already been to
                during the current parsing process onto the results the
                parser returned at the respective place. This dictionary
                is used to implement memoizing.

        recursion_counter:  Mapping of places to how often the parser
                has already been called recursively at this place. This
                is needed to implement left recursion. The number of
                calls becomes irrelevant once a resault has been memoized.

        cycle_detection:  The apply()-method uses this variable to make
                sure that one and the same function will not be applied
                (recursively) a second time, if it has already been
                applied to this parser.

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        proxied: The original `_parse()`-method is stored here, if a
                proxy (e.g. a tracing debugger) is installed via the
                `set_proxy()`-method.

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        _grammar:  A reference to the Grammar object to which the parser
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                is attached.
    """

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    def __init__(self) -> None:
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        # assert isinstance(name, str), str(name)
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        self.pname = ''               # type: str
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        self.anonymous = True         # type: bool
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        self.drop_content = False     # type: bool
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        self.tag_name = self.ptype    # type: str
        self.cycle_detection = set()  # type: Set[ApplyFunc]
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        # this indirection is required for Cython-compatibility
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        self._parse_proxy = self._parse    # type: ParseFunc
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        # self.proxied = None           # type: Optional[ParseFunc]
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        try:
            self._grammar = GRAMMAR_PLACEHOLDER  # type: Grammar
        except NameError:
            pass
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        self.reset()

    def __deepcopy__(self, memo):
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        """Deepcopy method of the parser. Upon instantiation of a Grammar-
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        object, parsers will be deep-copied to the Grammar object. If a
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        derived parser-class changes the signature of the `__init__`-constructor,
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        `__deepcopy__`-method must be replaced (i.e. overridden without
        calling the same method from the superclass) by the derived class.
        """
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        duplicate = self.__class__()
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        copy_parser_attrs(self, duplicate)
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        return duplicate
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    def __repr__(self):
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        return self.pname + self.ptype
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    def __str__(self):
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        return self.pname + (' = ' if self.pname else '') + repr(self)
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    @property
    def ptype(self) -> str:
        """Returns a type name for the parser. By default this is the name of
        the parser class with an added leading colon ':'. """
        return ':' + self.__class__.__name__

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    @property
    def repr(self) -> str:
        """Returns the parser's name if it has a name and self.__repr___() otherwise."""
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        return self.pname if self.pname else self.__repr__()
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    def reset(self):
        """Initializes or resets any parser variables. If overwritten,
        the `reset()`-method of the parent class must be called from the
        `reset()`-method of the derived class."""
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        self.visited = dict()  # type: Dict[int, Tuple[Optional[Node], StringView]]
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        self.recursion_counter = defaultdict(int)  # type: DefaultDict[int, int]
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    @cython.locals(location=cython.int, gap=cython.int, i=cython.int)
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    def __call__(self: 'Parser', text: StringView) -> Tuple[Optional[Node], StringView]:
        """Applies the parser to the given text. This is a wrapper method that adds
        the business intelligence that is common to all parsers. The actual parsing is
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        done in the overridden method `_parse()`. This wrapper-method can be thought of
        as a "parser guard", because it guards the parsing process.
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        """
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        # def get_error_node_id(error_node: Node, root_node: RootNode) -> int:
        #     if error_node:
        #         error_node_id = id(error_node)
        #         while error_node_id not in grammar.tree__.error_nodes and error_node.children:
        #             error_node = error_node.result[-1]
        #             error_node_id = id(error_node)
        #     else:
        #         error_node_id = 0
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        grammar = self._grammar
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        location = grammar.document_length__ - text._len  # faster then len(text)?
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        try:
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            # rollback variable changing operation if parser backtracks
            # to a position before the variable changing operation occurred
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            if grammar.last_rb__loc__ >= location:
                grammar.rollback_to__(location)

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            # if location has already been visited by the current parser, return saved result
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            visited = self.visited  # using local variable for better performance
            if location in visited:
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                # no history recording in case of memoized results
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                return visited[location]
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            # break left recursion at the maximum allowed depth
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            left_recursion_depth__ = grammar.left_recursion_depth__
            if left_recursion_depth__:
                if self.recursion_counter[location] > left_recursion_depth__:
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                    grammar.recursion_locations__.add(location)
                    return None, text
                self.recursion_counter[location] += 1

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            # finally, the actual parser call!
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            try:
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                node, rest = self._parse_proxy(text)
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            except ParserError as pe:
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                # catching up with parsing after an error occurred
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                gap = len(text) - len(pe.rest)
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                rules = grammar.resume_rules__.get(self.pname, [])
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                rest = pe.rest[len(pe.node):]
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                i = reentry_point(rest, rules, grammar.comment_rx__,
                                  grammar.reentry_search_window__)
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                if i >= 0 or self == grammar.start_parser__:
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                    assert pe.node.children or (not pe.node.result)
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                    # apply reentry-rule or catch error at root-parser
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                    if i < 0:  i = 0
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                    try:
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                        zombie = pe.node[ZOMBIE_TAG]  # type: Optional[Node]
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                    except (KeyError, ValueError):
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                        zombie = None
                    if zombie and not zombie.result:
                        zombie.result = rest[:i]
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                        tail = tuple()  # type: ChildrenType
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                    else:
                        nd = Node(ZOMBIE_TAG, rest[:i]).with_pos(location)
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                        # nd.attr['err'] = pe.error.message
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                        tail = (nd,)
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                    rest = rest[i:]
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                    if pe.first_throw:
                        node = pe.node
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                        node.result = node.children + tail
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                    else:
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                        node = Node(
                            self.tag_name,
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                            (Node(ZOMBIE_TAG, text[:gap]).with_pos(location), pe.node) + tail) \
                            .with_pos(location)
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                elif pe.first_throw:
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                    # TODO: Is this case still needed with module "trace"?
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                    raise ParserError(pe.node, pe.rest, pe.error, first_throw=False)
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                elif grammar.tree__.errors[-1].code == Error.MANDATORY_CONTINUATION_AT_EOF:
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                    # try to create tree as faithful as possible
                    node = Node(self.tag_name, pe.node).with_pos(location)
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                else:
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                    result = (Node(ZOMBIE_TAG, text[:gap]).with_pos(location), pe.node) if gap \
                        else pe.node  # type: ResultType
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                    raise ParserError(Node(self.tag_name, result).with_pos(location),
                                      text, pe.error, first_throw=False)
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            if left_recursion_depth__:
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                self.recursion_counter[location] -= 1
                # don't clear recursion_locations__ !!!

            if node is None:
                # retrieve an earlier match result (from left recursion) if it exists
                if location in grammar.recursion_locations__:
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                    if location in visited:
                        node, rest = visited[location]
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                        if location != grammar.last_recursion_location__:
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                            grammar.tree__.add_error(
                                node, Error("Left recursion encountered. "
                                            "Refactor grammar to avoid slow parsing.",
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                                            node.pos if node else location,
                                            Error.LEFT_RECURSION_WARNING))
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                            # error_id = id(node)
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                            grammar.last_recursion_location__ = location
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                    # don't overwrite any positive match (i.e. node not None) in the cache
                    # and don't add empty entries for parsers returning from left recursive calls!
                elif grammar.memoization__:
                    # otherwise also cache None-results
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                    visited[location] = (None, rest)
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            else:
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                # assert node._pos < 0 or node == EMPTY_NODE
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                # if node._pos != EMPTY_NODE:
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                node._pos = location
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                # assert node._pos >= 0 or node == EMPTY_NODE, \
                #     str("%i < %i" % (grammar.document_length__, location))
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                if (grammar.last_rb__loc__ < location
                        and (grammar.memoization__ or location in grammar.recursion_locations__)):
                    # - variable manipulating parsers will not be entered into the cache,
                    #   because caching would interfere with changes of variable state
                    # - in case of left recursion, the first recursive step that
                    #   matches will store its result in the cache
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                    # TODO: need a unit-test concerning interference of variable manipulation
                    #       and left recursion algorithm?
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                    visited[location] = (node, rest)
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        except RecursionError:
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            node = Node(ZOMBIE_TAG, str(text[:min(10, max(1, text.find("\n")))]) + " ...")
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            node._pos = location
            grammar.tree__.new_error(node, "maximum recursion depth of parser reached; "
                                           "potentially due to too many errors!")
            rest = EMPTY_STRING_VIEW

        return node, rest
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    def __add__(self, other: 'Parser') -> 'Series':
        """The + operator generates a series-parser that applies two
        parsers in sequence."""
        return Series(self, other)

    def __or__(self, other: 'Parser') -> 'Alternative':
        """The | operator generates an alternative parser that applies
        the first parser and, if that does not match, the second parser.
        """
        return Alternative(self, other)

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    def _parse(self, text: StringView) -> Tuple[Optional[Node], StringView]:
        """Applies the parser to the given `text` and returns a node with
        the results or None as well as the text at the position right behind
        the matching string."""
        raise NotImplementedError

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    def set_proxy(self, proxy: Optional[ParseFunc]):
        """Sets a proxy that replaces the _parse()-method. The original
        parse-method is copied to the `proxied`-filed of the Parser object and
        can be called by the proxy. Call `set_proxy` with `None` to remove
        a previously set proxy. Typical use case is the installation of a
        tracing debugger. See module `trace`.
        """
        if proxy is None:
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            self._parse_proxy = self._parse
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        else:
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            if not isinstance(proxy, type(self._parse)):
                # assume that proxy is a function and bind it to self
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                proxy = proxy.__get__(self, type(self))
            else:
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                # if proxy is a method it must be a method of self
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                assert proxy.__self__ == self
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            self._parse_proxy = cast(ParseFunc, proxy)
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    @property
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    def grammar(self) -> 'Grammar':
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        try:
            if self._grammar != GRAMMAR_PLACEHOLDER:
                return self._grammar
            else:
                raise AssertionError('Grammar has not yet been set!')
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        except (AttributeError, NameError):
            raise AttributeError('Parser placeholder does not have a grammar!')
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    @grammar.setter
    def grammar(self, grammar: 'Grammar'):
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        try:
            if self._grammar == GRAMMAR_PLACEHOLDER:
                self._grammar = grammar
                # self._grammar_assigned_notifier()
            elif self._grammar != grammar:
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                raise AssertionError("Parser has already been assigned"
                                     "to a different Grammar object!")
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        except AttributeError:
            pass  # ignore setting of grammar attribute for placeholder parser
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        except NameError:  # Cython: No access to GRAMMA_PLACEHOLDER, yet :-(
            self._grammar = grammar
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    def sub_parsers(self) -> Tuple['Parser', ...]:
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        """Returns the list of sub-parsers if there are any.
        Overridden by Unary, Nary and Forward.
        """
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        return tuple()
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    def _apply(self, func: Callable[['Parser'], None],
               flip: Callable[[Callable, Set[Callable]], bool]) -> bool:
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        """
        Applies function `func(parser)` recursively to this parser and all
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        descendant parsers, if any exist.

        In order to break cycles, function `flip` is called, which should
        return `True`, if this parser has already been visited. If not, it
        flips the cycle detection flag and returns `False`.

        This is a protected function and should not called from outside
        class Parser or any of its descendants. The entry point for external
        calls is the method `apply()` without underscore!
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        """
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        if flip(func, self.cycle_detection):
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            return False
        else:
            func(self)
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            for parser in self.sub_parsers():
                parser._apply(func, flip)
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            return True

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    def apply(self, func: Callable[['Parser'], None]):
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        """
        Applies function `func(parser)` recursively to this parser and all
        descendant parsers, if any exist. Traversal is pre-order.
        """
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        def positive_flip(f: Callable[['Parser'], None], flagged: Set[Callable]) -> bool:
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            """Returns True, if function `f` has already been applied to this
            parser and sets the flag accordingly. Interprets `f in flagged == True`
            as meaning that `f` has already been applied."""
            if f in flagged:
                return True
            else:
                flagged.add(f)
                return False

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        def negative_flip(f: Callable[['Parser'], None], flagged: Set[Callable]) -> bool:
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            """Returns True, if function `f` has already been applied to this
            parser and sets the flag accordingly. Interprets `f in flagged == False`
            as meaning that `f` has already been applied."""
            if f not in flagged:
                return True
            else:
                flagged.remove(f)
                return False

        if func in self.cycle_detection:
            self._apply(func, negative_flip)
        else:
            self._apply(func, positive_flip)

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def copy_parser_attrs(src: Parser, duplicate: Parser):
    """Duplicates all parser attributes from source to dest."""
    duplicate.pname = src.pname
    duplicate.anonymous = src.anonymous
    duplicate.drop_content = src.drop_content
    duplicate.tag_name = src.tag_name


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def Drop(parser: Parser) -> Parser:
    """Returns the parser with the `parser.drop_content`-property set to `True`."""
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    assert parser.anonymous, "Parser must be anonymous to be allowed to drop ist content."
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    if isinstance(parser, Forward):
        cast(Forward, parser).parser.drop_content = True
    parser.drop_content = True
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    return parser
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PARSER_PLACEHOLDER = Parser()
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def is_parser_placeholder(parser: Optional[Parser]) -> bool:
    """Returns True, if `parser` is `None` or merely a placeholder for a parser."""
    return not parser or parser.ptype == ":Parser"


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########################################################################
#
# Grammar class, central administration of all parser of a grammar
#
########################################################################

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def mixin_comment(whitespace: str, comment: str) -> str:
    """
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    Returns a regular expression pattern that merges comment and whitespace
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    regexps. Thus comments can occur wherever whitespace is allowed
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    and will be skipped just as implicit whitespace.

    Note, that because this works on the level of regular expressions,
    nesting comments is not possible. It also makes it much harder to
    use directives inside comments (which isn't recommended, anyway).
    """
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    if comment:
        return '(?:' + whitespace + '(?:' + comment + whitespace + ')*)'
    return whitespace
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def mixin_noempty(whitespace: str) -> str:
    r"""
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    Returns a regular expression pattern that matches only if the regular
    expression pattern `whitespace` matches AND if the match is not empty.

    If `whitespace` already matches the empty string '', then it will be
    returned unaltered.

    WARNING: `non_empty_ws` does not work regular expressions the matched
    strings of which can be followed by a symbol that can also occur at
    the start of the regular expression.

    In particular, it does not work for fixed size regular expressions,
    that ist / / or /   / or /\t/ won't work, but / */ or /\s*/ or /\s+/
    do work. There is no test for this. Fixed sizes regular expressions
    run through `non_empty_ws` will not match at any more if they are applied
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    to the beginning or the middle of a sequence of whitespaces!

    In order to be safe, you whitespace regular expressions should follow
    the rule: "Whitespace cannot be followed by whitespace" or "Either
    grab it all or leave it all".
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    :param whitespace: a regular expression pattern
    :return: new regular expression pattern that does not match the empty
        string '' any more.
    """
    if re.match(whitespace, ''):
        return r'(?:(?=(.|\n))' + whitespace + r'(?!\1))'
    return whitespace


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class UnknownParserError(KeyError):
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    """UnknownParserError is raised if a Grammar object is called with a
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    parser that does not exist or if in the course of parsing a parser
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    is referred to that does not exist."""
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GrammarErrorType = Tuple[str, Parser, Error]      # TODO: replace with a named tuple?
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class GrammarError(Exception):
    """GrammarError will be raised if static analysis reveals errors
    in the grammar.
    """
    def __init__(self, static_analysis_result: List[GrammarErrorType]):
        assert static_analysis_result  # must not be empty
        self.errors = static_analysis_result

    def __str__(self):
        if len(self.errors) == 1:
            return str(self.errors[0][2])
        return '\n' + '\n'.join(("%i. " % (i + 1) + str(err_tuple[2]))
                                for i, err_tuple in enumerate(self.errors))


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class Grammar:
    r"""
    Class Grammar directs the parsing process and stores global state
    information of the parsers, i.e. state information that is shared
    accross parsers.

    Grammars are basically collections of parser objects, which are
    connected to an instance object of class Grammar. There exist two
    ways of connecting parsers to grammar objects: Either by passing
    the root parser object to the constructor of a Grammar object
    ("direct instantiation"), or by assigning the root parser to the
    class variable "root__" of a descendant class of class Grammar.

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    Example for direct instantiation of a grammar::
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        >>> number = RE(r'\d+') + RE(r'\.') + RE(r'\d+') | RE(r'\d+')
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        >>> number_parser = Grammar(number)
        >>> number_parser("3.1416").content
        '3.1416'

    Collecting the parsers that define a grammar in a descendant class of
    class Grammar and assigning the named parsers to class variables
    rather than global variables has several advantages:

    1. It keeps the namespace clean.

    2. The parser names of named parsers do not need to be passed to the
       constructor of the Parser object explicitly, but it suffices to
       assign them to class variables, which results in better
       readability of the Python code.
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       See classmethod `Grammar._assign_parser_names__()`
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    3. The parsers in the class do not necessarily need to be connected
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       to one single root parser, which is helpful for testing and when
       building up a parser gradually from several components.
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    As a consequence, though, it is highly recommended that a Grammar
    class should not define any other variables or methods with names
    that are legal parser names. A name ending with a double
    underscore '__' is *not* a legal parser name and can safely be
    used.

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    Example::
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        class Arithmetic(Grammar):
            # special fields for implicit whitespace and comment configuration
            COMMENT__ = r'#.*(?:\n|$)'  # Python style comments
            wspR__ = mixin_comment(whitespace=r'[\t ]*', comment=COMMENT__)

            # parsers
            expression = Forward()
            INTEGER = RE('\\d+')
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            factor = INTEGER | TKN("(") + expression + TKN(")")
            term = factor + ZeroOrMore((TKN("*") | TKN("/")) + factor)
            expression.set(term + ZeroOrMore((TKN("+") | TKN("-")) + term))
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            root__ = expression

    Upon instantiation the parser objects are deep-copied to the
    Grammar object and assigned to object variables of the same name.
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    For any parser that is directly assigned to a class variable the
    field `parser.pname` contains the variable name after instantiation
    of the Grammar class. The parser will never the less remain anonymous
    with respect to the tag names of the nodes it generates, if its name
    is matched by the `anonymous__` regular expression.
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    If one and the same parser is assigned to several class variables
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    such as, for example, the parser `expression` in the example above,
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    which is also assigned to `root__`, the first name sticks.
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    Grammar objects are callable. Calling a grammar object with a UTF-8
    encoded document, initiates the parsing of the document with the
    root parser. The return value is the concrete syntax tree. Grammar
    objects can be reused (i.e. called again) after parsing. Thus, it
    is not necessary to instantiate more than one Grammar object per
    thread.

    Grammar classes contain a few special class fields for implicit
    whitespace and comments that should be overwritten, if the defaults
    (no comments, horizontal right aligned whitespace) don't fit:

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    Class Attributes:
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        root__:  The root parser of the grammar. Theoretically, all parsers of the
                 grammar should be reachable by the root parser. However, for testing
                 of yet incomplete grammars class Grammar does not assume that this
                 is the case.
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        resume_rules__: A mapping of parser names to a list of regular expressions
                that act as rules to find the reentry point if a ParserError was
                thrown during the execution of the parser with the respective name.
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        anonymous__: A regular expression to identify names of parsers that are
                assigned to class fields but shall never the less yield anonymous
                nodes (i.e. nodes the tag name of which starts with a colon ":"
                followed by the parser's class name). The default is to treat all
                parsers starting with an underscore as anonymous in addition to those
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                parsers that are not directly assigned to a class field.

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        parser_initialization__:  Before the grammar class (!) has been initialized,
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                 which happens upon the first time it is instantiated (see
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                 `:func:_assign_parser_names()` for an explanation), this class
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                 field contains a value other than "done". A value of "done" indicates
                 that the class has already been initialized.
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        static_analysis_pending__: True as long as no static analysis (see the method
                with the same name for more information) has been done to check
                parser tree for correctness. Static analysis
                is done at instantiation and the flag is then set to false, but it
                can also be carried out once the class has been generated
                (by DHParser.ebnf.EBNFCompiler) and then be set to false in the
                definition of the grammar class already.
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        python__src__:  For the purpose of debugging and inspection, this field can
                 take the python src of the concrete grammar class
                 (see `dsl.grammar_provider`).

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    Instance Attributes:
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        all_parsers__:  A set of all parsers connected to this grammar object

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        comment_rx__:  The compiled regular expression for comments. If no
                comments have been defined, it defaults to RX_NEVER_MATCH
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                This instance-attribute will only be defined if a class-attribute
                with the same name does not already exist!
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        start_parser__:  During parsing, the parser with which the parsing process
                was started (see method `__call__`) or `None` if no parsing process
                is running.

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        _dirty_flag__:  A flag indicating that the Grammar has been called at
                least once so that the parsing-variables need to be reset
                when it is called again.

        document__:  the text that has most recently been parsed or that is
                currently being parsed.

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        document_length__:  the length of the document.

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        document_lbreaks__ (property):  list of linebreaks within the document,
                starting with -1 and ending with EOF. This helps generating line
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                and column number for history recording and will only be
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                initialized if :attr:`history_tracking__` is true.
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        tree__: The root-node of the parsing tree. This variable is available
               for error-reporting already during parsing  via
               ``self.grammar.tree__.add_error``, but it references the full
               parsing tree only after parsing has been finished.

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        _reversed__:  the same text in reverse order - needed by the `Lookbehind`-
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                parsers.

        variables__:  A mapping for variable names to a stack of their respective
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                string values - needed by the :class:`Capture`-, :class:`Retrieve`-
                and :class:`Pop`-parsers.
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        rollback__:  A list of tuples (location, rollback-function) that are
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                deposited by the :class:`Capture`- and :class:`Pop`-parsers.
                If the parsing process reaches a dead end then all
                rollback-functions up to the point to which it retreats will be
                called and the state of the variable stack restored accordingly.
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        last_rb__loc__:  The last, i.e. most advanced location in the text
                where a variable changing operation occurred. If the parser
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                backtracks to a location at or before last_rb__loc__ (i.e.
                location <= last_rb__loc__) then a rollback of all variable
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                changing operations is necessary that occurred after the
                location to which the parser backtracks. This is done by
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                calling method :func:`rollback_to__(location)`.
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        recursion_locations__:  Stores the locations where left recursion was
                detected. Needed to provide minimal memoization for the left
                recursion detection algorithm, but, strictly speaking, superfluous
                if full memoization is enabled. (See :func:`Parser.__call__()`)

        last_recursion_location__:  Last location where left recursion was
                detected. This is used to avoid reduplicating warning messages
                about left recursion.

        memoization__:  Turns full memoization on or off. Turning memoization off
                results in less memory usage and sometimes reduced parsing time.
                In some situations it may drastically increase parsing time, so
                it is safer to leave it on. (Default: on)


        # tracing and debugging support

        # These parameters are needed by the debugging functions in module
        # `trace.py`. They should not be manipulated by the users of class
        #  Grammar directly.

        history_tracking__:  A flag indicating that the parsing history is
                being tracked. This flag should not be manipulated by the
                user. Use `trace.set_tracer(grammar, trace.trace_history)` to
                turn (full) history tracking on and
                `trace.set_tracer(grammar, None)` to turn it off. Default is off.

        resume_notices__: A flag indicating that resume messages are generated
                in addition to the error messages, in case the parser was able
                to resume after an error. Use `trace.resume_notices(grammar)` to
                turn resume messages on and `trace.set_tracer(grammar, None)`
                to turn resume messages (as well as history recording) off.
                Default is off.

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        call_stack__:  A stack of the tag names and locations of all parsers
                in the call chain to the currently processed parser during
                parsing. The call stack can be thought of as a breadcrumb trail.
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                This is required for recording the parser history (for debugging)
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                and, eventually, i.e. one day in the future, for tracing through
                the parsing process.

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        history__:  A list of history records. A history record is appended to
                the list each time a parser either matches, fails or if a
                parser-error occurs. See class `log.HistoryRecord`. History
                records store copies of the current call stack.
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        moving_forward__: This flag indicates that the parsing process is currently
                moving forward . It is needed to reduce noise in history recording
                and should not be considered as having a valid value if history
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                recording is turned off! (See :func:`Parser.__call__`)
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        most_recent_error__: The most recent parser error that has occurred
                or `None`. This can be read by tracers. See module `trace`

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        # Configuration parameters.

        # These values of theses parameters are copied from the global configuration
        # in the constructor of the Grammar object. (see mpodule `configuration.py`)
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        flatten_tree__:  If True (default), anonymous nodes will be flattened
                during parsing already. This greatly reduces the concrete syntax
                tree and simplifies and speeds up abstract syntax tree generation.
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                Default is on.
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        left_recursion_depth__: the maximum allowed depth for left-recursion.
                A depth of zero means that no left recursion handling will
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                take place. Default is 5.
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        max_parser_dropouts__: Maximum allowed number of retries after errors
                where the parser would exit before the complete document has
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                been parsed. Default is 1, as usually the retry-attemts lead
                to a proliferation of senseless error messages.
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        reentry_search_window__: The number of following characters that the
                parser considers when searching a reentry point when a syntax error
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                has been encountered. Default is 10.000 characters.
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    """
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    python_src__ = ''  # type: str
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    root__ = PARSER_PLACEHOLDER  # type: Parser
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    # root__ must be overwritten with the root-parser by grammar subclass
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    parser_initialization__ = ["pending"]  # type: List[str]
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    resume_rules__ = dict()  # type: Dict[str, ResumeList]
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    anonymous__ = RX_NEVER_MATCH  # type: RxPatternType
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    # some default values
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    COMMENT__ = r''  # type: str  # r'#.*(?:\n|$)'
    WSP_RE__ = mixin_comment(whitespace=r'[\t ]*', comment=COMMENT__)  # type: str
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    static_analysis_pending__ = [True]  # type: List[bool]
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    @classmethod
    def _assign_parser_names__(cls):
        """
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        Initializes the `parser.pname` fields of those
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        Parser objects that are directly assigned to a class field with
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        the field's name, e.g.::
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            class Grammar(Grammar):
                ...
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                symbol = RE(r'(?!\\d)\\w+')
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        After the call of this method symbol.pname == "symbol" holds.
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        Parser names starting or ending with a double underscore like
        ``root__`` will be ignored. See :func:`sane_parser_name()`
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        This is done only once, upon the first instantiation of the
        grammar class!

        Attention: If there exists more than one reference to the same
        parser, only the first one will be chosen for python versions
        greater or equal 3.6.  For python version <= 3.5 an arbitrarily
        selected reference will be chosen. See PEP 520
        (www.python.org/dev/peps/pep-0520/) for an explanation of why.
        """
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        if cls.parser_initialization__[0] != "done":
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            cdict = cls.__dict__
            for entry, parser in cdict.items():
                if isinstance(parser, Parser) and sane_parser_name(entry):
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                    anonymous = True if cls.anonymous__.match(entry) else False
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                    assert anonymous or not parser.drop_content, entry
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                    if isinstance(parser, Forward):
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                        if not cast(Forward, parser).parser.pname:
                            cast(Forward, parser).parser.pname = entry
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                            cast(Forward, parser).parser.anonymous = anonymous
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                    else:
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                        parser.pname = entry
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                        parser.anonymous = anonymous
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            cls.parser_initialization__[0] = "done"