parse.py

# parse.py - parser combinators for DHParser
#
# 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.


"""
Module ``parse`` contains the python classes and functions for
DHParser's packrat-parser. It's central class is the
``Grammar``-class, which is the base class for any concrete
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.
"""


from collections import defaultdict
import copy
from typing import Callable, cast, List, Tuple, Set, AbstractSet, Dict, \
    DefaultDict, Sequence, Union, Optional, Iterator

from DHParser.configuration import get_config_value
from DHParser.error import Error, ErrorCode, MANDATORY_CONTINUATION, \
    UNDEFINED_RETRIEVE, PARSER_LOOKAHEAD_FAILURE_ONLY, \
    PARSER_LOOKAHEAD_MATCH_ONLY, PARSER_STOPPED_BEFORE_END, PARSER_NEVER_TOUCHES_DOCUMENT, \
    MALFORMED_ERROR_STRING, MANDATORY_CONTINUATION_AT_EOF, DUPLICATE_PARSERS_IN_ALTERNATIVE, \
    CAPTURE_WITHOUT_PARSERNAME, CAPTURE_DROPPED_CONTENT_WARNING, LOOKAHEAD_WITH_OPTIONAL_PARSER, \
    BADLY_NESTED_OPTIONAL_PARSER, BAD_ORDER_OF_ALTERNATIVES, BAD_MANDATORY_SETUP, \
    OPTIONAL_REDUNDANTLY_NESTED_WARNING, CAPTURE_STACK_NOT_EMPTY, BAD_REPETITION_COUNT, \
    AUTORETRIEVED_SYMBOL_NOT_CLEARED, RECURSION_DEPTH_LIMIT_HIT
from DHParser.log import CallItem, HistoryRecord
from DHParser.preprocess import BEGIN_TOKEN, END_TOKEN, RX_TOKEN_NAME
from DHParser.stringview import StringView, EMPTY_STRING_VIEW
from DHParser.syntaxtree import ChildrenType, Node, RootNode, WHITESPACE_PTYPE, \
    TOKEN_PTYPE, ZOMBIE_TAG, EMPTY_NODE, ResultType
from DHParser.toolkit import sane_parser_name, escape_ctrl_chars, re, cython, \
    abbreviate_middle, RX_NEVER_MATCH, RxPatternType, linebreaks, line_col, identity


__all__ = ('ParserError',
           'ApplyFunc',
           'FlagFunc',
           'ParseFunc',
           'Parser',
           'AnalysisError',
           'GrammarError',
           'Grammar',
           'Always',
           'Never',
           'AnyChar',
           'PreprocessorToken',
           'Text',
           'DropText',
           'RegExp',
           'update_scanner',
           'RE',
           'TKN',
           'Whitespace',
           'DropRegExp',
           'mixin_comment',
           'mixin_nonempty',
           'CombinedParser',
           'UnaryParser',
           'NaryParser',
           'Drop',
           'Synonym',
           'Option',
           'ZeroOrMore',
           'OneOrMore',
           'NO_MANDATORY',
           'MandatoryNary',
           'Series',
           'Alternative',
           'INFINITE',
           'Counted',
           'Interleave',
           'Required',
           'Lookahead',
           'NegativeLookahead',
           'Lookbehind',
           'NegativeLookbehind',
           'last_value',
           'optional_last_value',
           'matching_bracket',
           'Capture',
           'Retrieve',
           'Pop',
           'Forward')


########################################################################
#
# ParserError class
#
########################################################################


class ParserError(Exception):
    """
    A `ParserError` is thrown for those parser errors that allow the
    controlled re-entrance of the parsing process after the error occurred.
    If a reentry-rule has been configured for the parser where the error
    occurred, the parser guard can resume the parsing process.

    Currently, the only case when a `ParserError` is thrown (and not some
    different kind of error like `UnknownParserError`) is when a `Series`-
    or `Interleave`-parser detects a missing mandatory element.
    """
    def __init__(self,
                 parser: 'Parser',
                 node: Node,
                 rest: StringView,
                 error: Error, *,
                 first_throw: bool):
        assert node is not None
        self.parser = parser  # type: 'Parser'
        self.node = node      # type: Node
        self.rest = rest      # type: StringView
        self.error = error    # type: Error
        self.first_throw = first_throw   # type:
        self.attributes_locked = frozenset({'parser', 'node', 'rest', 'error', 'first_throw'})
        self.frozen_callstack = tuple()  # type: Tuple[CallItem, ...]  # tag_name, location

    def __setattr__(self, name, value):
        if name == "attributes_locked":
            self.__dict__[name] = value
        elif "attributes_locked" not in self.__dict__ \
                or name not in self.__dict__['attributes_locked']:
            self.__dict__[name] = value
        else:
            raise TypeError('Attribute %s of ParserError-object must not be reassigned!' % name)

    def __str__(self):
        return "%i: %s    %s (%s)" \
               % (self.node.pos, str(self.rest[:25]), repr(self.node), str(self.error))


    def new_PE(self, **kwargs):
        """Returns a new ParserError object with the same attribute values
        as `self`, except those that are reassigned in `**kwargs`.

        >>> pe = ParserError(Parser(), Node('test', ""), StringView(""), Error("", 0), first_throw=True)
        >>> pe_derived = pe.new_PE(first_throw = False)
        >>> pe.first_throw
        True
        >>> pe_derived.first_throw
        False
        """
        args = { "parser": self.parser,
                 "node": self.node,
                 "rest": self.rest,
                 "error": self.error,
                 "first_throw": self.first_throw }
        assert len(kwargs.keys() - args.keys()) == 0, str(kwargs.keys() - args.keys())
        args.update(kwargs)
        pe = ParserError(**args)
        pe.frozen_callstack = self.frozen_callstack
        return pe


PatternMatchType = Union[RxPatternType, str, Callable]
ErrorMessagesType = List[Tuple[PatternMatchType, str]]
ResumeList = List[PatternMatchType]  # list of strings or regular expressions
ReentryPointAlgorithm = Callable[[StringView, int, int], Tuple[int, int]]
# (text, start point, end point) => (reentry point, match length)
# A return value of (-1, x) means that no reentry point before the end of the document was found


@cython.returns(cython.int)
@cython.locals(upper_limit=cython.int, closest_match=cython.int, pos=cython.int)
def reentry_point(rest: StringView,
                  rules: ResumeList,
                  comment_regex,
                  search_window: int = -1) -> int:
    """
    Finds the point where parsing should resume after a ParserError has been caught.
    The algorithm makes sure that this reentry-point does not lie inside a comment.
    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.)

    REMARK: The algorithm assumes that any stretch of the document that matches
    `comment_regex` is actually a comment. It is possible to define grammars,
    where the use of comments is restricted to certain areas and that allow to
    use constructs that look like comments (i.e. will be matched by `comment_regex`)
    but are none in other areas. For example::

            my_string = "# This is not a comment"; foo()  # This is a comment
            bar()

    Here the reentry-algorithm would overlook `foo()` and jump directly to `bar()`.
    However, since the reentry-algorithm only needs to be good enough to do its
    work, this seems acceptable.

    :param rest:  The rest of the parsed text or, in other words, the point where
        a ParserError was thrown.
    :param rules: A list of strings, regular expressions or search functions.
        The rest of the text is searched for each of these. The closest match
        is the point where parsing will be resumed.
    :param comment_regex: A regular expression object that matches comments.
    :param search_window: The maximum size of the search window for finding the
        reentry-point. A value smaller than zero means that the complete remaining
        text will be searched. A value of zero effectively turns of resuming after
        error.
    :return: The integer index of the closest reentry point or -1 if no
        reentry-point was found.
    """
    upper_limit = len(rest) + 1
    closest_match = upper_limit
    comments = None  # type: Optional[Iterator]
    if search_window < 0:
        search_window = len(rest)

    @cython.locals(a=cython.int, b=cython.int)
    def next_comment() -> Tuple[int, int]:
        """Returns the [start, end[ intervall of the next comment in the text.
        The comment-iterator start at the beginning of the `rest` of the
        document and is reset for each search rule.
        """
        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

    @cython.locals(start=cython.int)
    def str_search(s, start: int = 0) -> Tuple[int, int]:
        """Returns the starting position of the next occurrence of `s` in
        the `rest` of the document beginning with `start` and the length
        of the match, which in this case is always the length of `s` itself.
        If their is no match, the returned starting position will be -1.
        """
        nonlocal rest
        return rest.find(s, start, start + search_window), len(s)

    @cython.locals(start=cython.int, end=cython.int)
    def rx_search(rx, start: int = 0) -> Tuple[int, int]:
        """Returns the staring position and the length of the next match of
        the regular expression `rx` in the `rest` of the document, starting
        with `start`.
        If their is no match, the returned starting position will be -1.
        """
        nonlocal rest
        m = rest.search(rx, start, start + search_window)
        if m:
            begin, end = m.span()
            return rest.index(begin), end - begin
        return -1, 0

    def algorithm_search(func: ReentryPointAlgorithm, start: int = 0):
        """Returns the next match as a tuple of position and length that
        the reentry-point-search-function `func` yields.
        """
        nonlocal rest
        return func(rest, start, start + search_window)

    @cython.returns(cython.int)
    @cython.locals(a=cython.int, b=cython.int, k=cython.int, length=cython.int)
    def entry_point(search_func, search_rule) -> int:
        """Returns the next reentry-point outside a comment that `search_func`
        yields. If no reentry point is found, the first position after the
        end of the text ("upper limit") is returned."""
        a, b = next_comment()
        k, length = search_func(search_rule)
        while a < b <= k + length:
            a, b = next_comment()
        # 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)
            while a < b <= k:
                a, b = next_comment()
        return k + length if k >= 0 else upper_limit

    # find closest match
    for rule in rules:
        comments = rest.finditer(comment_regex)
        if callable(rule):
            search_func = algorithm_search
        elif isinstance(rule, str):
            search_func = str_search
        else:
            search_func = rx_search
        pos = entry_point(search_func, rule)
        closest_match = min(pos, closest_match)

    # in case no rule matched return -1
    if closest_match == upper_limit:
        closest_match = -1
    return closest_match


########################################################################
#
# Parser base class
#
########################################################################


ApplyFunc = Callable[[List['Parser']], Optional[bool]]
# The return value of `True` stops any further application
FlagFunc = Callable[[ApplyFunc, Set[ApplyFunc]], bool]
ParseFunc = Callable[[StringView], Tuple[Optional[Node], StringView]]


class Parser:
    """
    (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:

    1. *Named parsers* for which a name is set in field `parser.pname`.
       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:

        pname:  The parser's name or a (possibly empty) alias name in case
                of an anonymous parser.

        anonymous: A property indicating that the parser remains anonymous
                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] == ":"`.

        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
                dropped from the concrete syntax tree already. Only
                anonymous (or pseudo-anonymous) parsers are allowed to
                drop content.

        tag_name: The tag_name for the nodes that are created by
                the parser. If the parser is named, this is the same as
                `pname`, otherwise it is the name of the parser's type
                prefixed with a colon ":".

        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.

        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.

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

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

        _symbol:  The name of the closest named parser to which this
                parser is connected in a grammar. If pname is not the
                empty string, this will become the same as pname, when
                the property `symbol` is read for the first time.
    """

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

    def __deepcopy__(self, memo):
        """Deepcopy method of the parser. Upon instantiation of a Grammar-
        object, parsers will be deep-copied to the Grammar object. If a
        derived parser-class changes the signature of the `__init__`-constructor,
        `__deepcopy__`-method must be replaced (i.e. overridden without
        calling the same method from the superclass) by the derived class.
        """
        duplicate = self.__class__()
        copy_parser_base_attrs(self, duplicate)
        return duplicate

    def __repr__(self):
        return self.pname + self.ptype

    def __str__(self):
        return self.pname + (' = ' if self.pname else '') + repr(self)

    @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__

    @property
    def symbol(self) -> str:
        """Returns the symbol with which the parser is associated in a grammar.
        This is the closest parser with a pname that contains this parser."""
        if not self._symbol:
            try:
                self._symbol = self.grammar.associated_symbol__(self).pname
            except AttributeError:
                # return an empty string, if parser is not connected to grammar,
                # but be sure not to save the empty string in self._symbol
                return ''
        return self._symbol

    @property
    def repr(self) -> str:
        """Returns the parser's name if it has a name and self.__repr___() otherwise."""
        return self.pname if self.pname else self.__repr__()

    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."""
        self.visited = dict()  # type: Dict[int, Tuple[Optional[Node], StringView]]

    @cython.locals(location=cython.int, gap=cython.int, i=cython.int)
    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
        done in the overridden method `_parse()`. This wrapper-method can be thought of
        as a "parser guard", because it guards the parsing process.
        """
        grammar = self._grammar
        location = grammar.document_length__ - text._len  # faster then len(text)?

        try:
            # rollback variable changing operation if parser backtracks to a position
            # before or at the location where the variable changing operation occurred
            if location <= grammar.last_rb__loc__:
                grammar.rollback_to__(location)

            # if location has already been visited by the current parser, return saved result
            visited = self.visited  # using local variable for better performance
            if location in visited:
                # no history recording in case of memoized results!
                return visited[location]

            memoization_state = grammar.suspend_memoization__
            grammar.suspend_memoization__ = False

            # now, the actual parser call!
            try:
                node, rest = self._parse_proxy(text)
            except ParserError as pe:
                # catching up with parsing after an error occurred
                gap = len(text) - len(pe.rest)
                rules = grammar.resume_rules__.get(
                    self.pname or grammar.associated_symbol__(self).pname, [])
                rest = pe.rest[len(pe.node):]
                i = reentry_point(rest, rules, grammar.comment_rx__,
                                  grammar.reentry_search_window__)
                if i >= 0 or self == grammar.start_parser__:
                    # either a reentry point was found or the
                    # error has fallen through to the first level
                    assert pe.node.children or (not pe.node.result)
                    # apply reentry-rule or catch error at root-parser
                    if i < 0:  i = 0
                    try:
                        zombie = pe.node.pick_child(ZOMBIE_TAG)  # type: Optional[Node]
                    except (KeyError, ValueError):
                        zombie = None
                    if zombie and not zombie.result:
                        zombie.result = rest[:i]
                        tail = tuple()  # type: ChildrenType
                    else:
                        nd = Node(ZOMBIE_TAG, rest[:i]).with_pos(location)
                        # nd.attr['err'] = pe.error.message
                        tail = (nd,)
                    rest = rest[i:]
                    if pe.first_throw:
                        node = pe.node
                        node.result = node.children + tail
                    else:
                        node = Node(
                            self.tag_name,
                            (Node(ZOMBIE_TAG, text[:gap]).with_pos(location), pe.node) + tail) \
                            .with_pos(location)
                # if no re-entry point was found, do any of the following:
                elif pe.first_throw:
                    # just fall through
                    # TODO: Is this case still needed with module "trace"?
                    raise pe.new_PE(first_throw=False)
                elif grammar.tree__.errors[-1].code == MANDATORY_CONTINUATION_AT_EOF:
                    # try to create tree as faithful as possible
                    node = Node(self.tag_name, pe.node).with_pos(location)
                else:
                    # fall through but skip the gap
                    result = (Node(ZOMBIE_TAG, text[:gap]).with_pos(location), pe.node) if gap \
                        else pe.node  # type: ResultType
                    raise pe.new_PE(node=Node(self.tag_name, result).with_pos(location),
                                    rest=text, first_throw=False)

            if node is not None:
                node._pos = location
            if not grammar.suspend_memoization__:
                visited[location] = (node, rest)
                grammar.suspend_memoization__ = memoization_state

        except RecursionError:
            node = Node(ZOMBIE_TAG, str(text[:min(10, max(1, text.find("\n")))]) + " ...")
            node._pos = location
            error = Error("maximum recursion depth of parser reached; potentially due to too many "
                          "errors or left recursion!", location, RECURSION_DEPTH_LIMIT_HIT)
            grammar.tree__.add_error(node, error)
            grammar.most_recent_error__ = ParserError(self, node, text, error, first_throw=False)
            rest = EMPTY_STRING_VIEW

        return node, rest

    def __add__(self, other: 'Parser') -> 'Series':
        """The + operator generates a series-parser that applies two
        parsers in sequence."""
        if isinstance(other, Series):
            return cast('Series', other).__radd__(self)
        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.
        """
        if isinstance(other, Alternative):
            return cast('Alternative', other).__ror__(self)
        return Alternative(self, other)

    def __mul__(self, other: 'Parser') -> 'Interleave':
        """The * operator generates an interleave parser that applies
        the first parser and the second parser in any possible order
        until both match.
        """
        if isinstance(other, Interleave):
            return cast(Interleave, other).__rmul__(self)
        return Interleave(self, other)

    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

    def is_optional(self) -> Optional[bool]:
        """Returns `True`, if the parser can never fails, i.e. never yields
        `None`, instead of a node. Returns `False`, if the parser can fail.
        Returns `None` if it is not known whether the parser can fail.
        """
        return None

    def set_proxy(self, proxy: Optional[ParseFunc]):
        """Sets a proxy that replaces the _parse()-method. 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:
            self._parse_proxy = self._parse
        else:
            if not isinstance(proxy, type(self._parse)):
                # assume that proxy is a function and bind it to self
                proxy = proxy.__get__(self, type(self))
            else:
                # if proxy is a method it must be a method of self
                assert proxy.__self__ == self
            self._parse_proxy = cast(ParseFunc, proxy)

    @property
    def grammar(self) -> 'Grammar':
        try:
            if self._grammar is not GRAMMAR_PLACEHOLDER:
                return self._grammar
            else:
                raise ValueError('Grammar has not yet been set!')
        except (AttributeError, NameError):
            raise AttributeError('Parser placeholder does not have a grammar!')

    @grammar.setter
    def grammar(self, grammar: 'Grammar'):
        try:
            if self._grammar == GRAMMAR_PLACEHOLDER:
                self._grammar = grammar
                # self._grammar_assigned_notifier()
            elif self._grammar != grammar:
                raise AssertionError("Parser has already been assigned"
                                     "to a different Grammar object!")
        except AttributeError:
            pass  # ignore setting of grammar attribute for placeholder parser
        except NameError:  # Cython: No access to GRAMMAR_PLACEHOLDER, yet :-(
            self._grammar = grammar

    def sub_parsers(self) -> Tuple['Parser', ...]:
        """Returns the list of sub-parsers if there are any.
        Overridden by Unary, Nary and Forward.
        """
        return tuple()

    def _apply(self, func: ApplyFunc, context: List['Parser'], flip: FlagFunc) -> bool:
        """
        Applies function `func(parser)` recursively to this parser and all
        descendant parsers as long as `func()` returns `None` or `False`.
        Otherwise stops the further application of `func` and returns `True`.

        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!
        """
        if not flip(func, self.cycle_detection):
            if func(context + [self]):
                return True
            else:
                for parser in self.sub_parsers():
                    if parser._apply(func, context + [self], flip):
                        return True
                return False
        return False

    def apply(self, func: ApplyFunc) -> Optional[bool]:
        """
        Applies function `func(parser)` recursively to this parser and all
        descendant parsers as long as `func()` returns `None` or `False`.
        Traversal is pre-order. Stops the further application of `func` and
        returns `True` once `func` has returned `True`.

        If `func` has been applied to all descendant parsers without issuing
        a stop signal by returning `True`, `False` is returned.

        This use of the return value allows to use the `apply`-method both
        to issue tests on all descendant parsers (including self) which may be
        decided already after some parsers have been visited without any need
        to visit further parsers. At the same time `apply` can be used to simply
        `apply` a procedure to all descendant parsers (including self) without
        worrying about forgetting the return value of procedure, because a
        return value of `None` means "carry on".
        """
        def positive_flip(f: ApplyFunc, flagged: AbstractSet[ApplyFunc]) -> bool:
            """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

        def negative_flip(f: ApplyFunc, flagged: AbstractSet[ApplyFunc]) -> bool:
            """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:
            return self._apply(func, [], negative_flip)
        else:
            return self._apply(func, [], positive_flip)

    def static_error(self, msg: str, code: ErrorCode) -> 'AnalysisError':
        return self.symbol, self, Error(msg, 0, code)

    def static_analysis(self) -> List['AnalysisError']:
        """Analyses the parser for logical errors after the grammar has been
        instantiated."""
        return []


def copy_parser_base_attrs(src: Parser, duplicate: Parser):
    """Duplicates all attributes of the Parser-class from `src` to `duplicate`."""
    duplicate.pname = src.pname
    duplicate.anonymous = src.anonymous
    duplicate.drop_content = src.drop_content
    duplicate.tag_name = src.tag_name


def Drop(parser: Parser) -> Parser:
    """Returns the parser with the `parser.drop_content`-property set to `True`."""
    assert parser.anonymous, "Parser must be anonymous to be allowed to drop ist content."
    if isinstance(parser, Forward):
        cast(Forward, parser).parser.drop_content = True
    parser.drop_content = True
    return parser


PARSER_PLACEHOLDER = Parser()


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"


# functions for analysing the parser tree/graph ###


def has_non_autocaptured_symbols(context: List[Parser]) -> Optional[bool]:
    """Returns True, if the context contains a Capture-Parser that is not
    shielded by a Retrieve-Parser. This is the case for captured symbols
    that are not "auto-captured" by a Retrieve-Parser.
    """
    for parser in context:
        if parser.ptype == ":Retrieve":
            break
        elif parser.ptype == ":Capture":
            p = cast(UnaryParser, parser).parser
            while p.ptype in (":Synonym", ":Forward"):
                p = cast(UnaryParser, p).parser
            if not isinstance(p, Retrieve):
                return True
    return None


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

def mixin_comment(whitespace: str, comment: str) -> str:
    """
    Returns a regular expression pattern that merges comment and whitespace
    regexps. Thus comments can occur wherever whitespace is allowed
    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).
    """
    if comment:
        whitespace = '(?:' + whitespace + ')'
        comment = '(?:' + comment + ')'
        return '(?:' + whitespace + '(?:' + comment + whitespace + ')*)'
    return whitespace


def mixin_nonempty(whitespace: str) -> str:
    r"""
    Returns a regular expression pattern that matches only if the regular
    expression pattern `whitespace` matches AND if the match is not empty.

    If `whitespace`  does not match the empty string '', anyway,
    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
    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".

    :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


AnalysisError = Tuple[str, Parser, Error]      # pname, parser, error
# TODO: replace with a named tuple?


class GrammarError(Exception):
    """GrammarError will be raised if static analysis reveals errors
    in the grammar.
    """
    def __init__(self, static_analysis_result: List[AnalysisError]):
        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))


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.

    Example for direct instantiation of a grammar::

        >>> number = RE(r'\d+') + RE(r'\.') + RE(r'\d+') | RE(r'\d+')
        >>> 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.
       See classmethod `Grammar._assign_parser_names__()`

    3. The parsers in the class do not necessarily need to be connected
       to one single root parser, which is helpful for testing and when
       building up a parser gradually from several components.

    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.

    Example::

        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+')
            factor = INTEGER | TKN("(") + expression + TKN(")")
            term = factor + ZeroOrMore((TKN("*") | TKN("/")) + factor)
            expression.set(term + ZeroOrMore((TKN("+") | TKN("-")) + term))
            root__ = expression

    Upon instantiation the parser objects are deep-copied to the
    Grammar object and assigned to object variables of the same name.
    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.
    If one and the same parser is assigned to several class variables
    such as, for example, the parser `expression` in the example above,
    which is also assigned to `root__`, the first name sticks.

    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:

    Class Attributes:
        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.

        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.

        skip_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.

        error_messages__: A mapping of parser names to a Tuple of regalar expressions
                and error messages. If a mandatory violation error occurs on a
                specific symbol (i.e. parser name) and any of the regular expressions
                matches the error message of the first matching expression is used
                instead of the generic manadtory violation error messages. This
                allows to answer typical kinds of errors (say putting a colon ","
                where a semi-colon ";" is expected) with more informative error
                messages.

        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
                parsers that are not directly assigned to a class field.

        parser_initialization__:  Before the grammar class (!) has been initialized,
                 which happens upon the first time it is instantiated (see
                 `:func:_assign_parser_names()` for an explanation), this class
                 field contains a value other than "done". A value of "done" indicates
                 that the class has already been initialized.

        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.

        static_analysis_errors__: A list of errors and warnings that were found in the
                static analysis

        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`).

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

        comment_rx__:  The compiled regular expression for comments. If no
                comments have been defined, it defaults to RX_NEVER_MATCH
                This instance-attribute will only be defined if a class-attribute
                with the same name does not already exist!

        start_parser__:  During parsing, the parser with which the parsing process
                was started (see method `__call__`) or `None` if no parsing process
                is running.

        _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.

        document_length__:  the length of the document.

        document_lbreaks__ (property):  list of linebreaks within the document,
                starting with -1 and ending with EOF. This helps generating line
                and column number for history recording and will only be
                initialized if :attr:`history_tracking__` is true.