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 bisect import bisect_left
import functools
from collections import defaultdict, namedtuple
import copy
from typing import Callable, cast, List, Tuple, Set, AbstractSet, Dict, \
    DefaultDict, Sequence, Union, Optional, Iterator, Hashable, NamedTuple

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, SourceMapFunc
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, EMPTY_PTYPE, 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',
           'TreeReduction',
           'UnaryParser',
           'NaryParser',
           'Drop',
           'Synonym',
           'Option',
           'ZeroOrMore',
           'OneOrMore',
           'NO_MANDATORY',
           'MandatoryNary',
           'Series',
           'Alternative',
           'longest_match',
           '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: bool
        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, 'Parser']
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)
@functools.lru_cache()
@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) -> Tuple[int, Node]:
    """
    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: A tuple of integer index of the closest reentry point and a Node
        capturing all text from ``rest`` up to this point or ``(-1, None)`` if no
        reentry-point was found.
    """
    upper_limit = len(rest) + 1
    closest_match = upper_limit
    skip_node = None
    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 isinstance(rule, Parser):
            _node, _text = cast(Parser, rule)(rest)
            if _node:
                pos = len(rest) - len(_text)
                if pos < closest_match:
                    closest_match = pos
                    skip_node = _node
        else:
            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)
            if pos < closest_match:
                skip_node = None
                closest_match = pos

    # in case no rule matched return -1
    if closest_match == upper_limit:
        closest_match = -1
    if skip_node is None:
        skip_node = Node(ZOMBIE_TAG, rest[:max(closest_match,0)])
    return closest_match, skip_node


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


ParsingResult = Tuple[Optional[Node], StringView]
MemoizationDict = Dict[int, ParsingResult]

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


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. *Disposable parsers* where the name-field just contains the empty
       string. AST-transformation of disposable 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.

        disposable: A property indicating that the parser returns
                anonymous nodes. For performance
                reasons this is implemented as an object variable rather
                than a property. This property should 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 ":".

        eq_class: A unique number for the class of functionally
                equivalent parsers that this parser belongs to.
                (This serves the purpose of optimizing memoization,
                by tying memoization dictionaries to the classes
                of functionally equivalent parsers, rather than to
                the individual parsers themselves.)

        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.disposable = True        # type: bool
        self.drop_content = False     # type: bool
        self.tag_name = self.ptype    # type: str
        self.eq_class = id(self)      # type: int
        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 = get_grammar_placeholder()  # type: Grammar
        except NameError:
            pass                      # ensures Cython-compatibility
        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."""
        global _GRAMMAR_PLACEHOLDER
        grammar = self._grammar
        self.visited: MemoizationDict = grammar.get_memoization_dict__(self)

    @cython.locals(location=cython.int, gap=cython.int, i=cython.int)
    def __call__(self: 'Parser', text: StringView) -> ParsingResult:
        """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 = tuple(grammar.resume_rules__.get(
                    self.pname or grammar.associated_symbol__(self).pname, []))
                rest = pe.rest[len(pe.node):]
                i, skip_node = 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.attr['err'] = pe.error.message
                        tail = (skip_node,)
                    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 None:
                if location > grammar.ff_pos__:
                    grammar.ff_pos__ = location
                    grammar.ff_parser__ = self
            else:
                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) -> ParsingResult:
        """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 fail, 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)

    def name(self, pname: str, disposable: bool = False) -> 'Parser':
        """Sets the parser name to `pname` and returns `self`."""
        self.pname = pname
        self.tag_name = pname or self.ptype
        self.disposable = disposable
        return self

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

    @grammar.setter
    def grammar(self, grammar: 'Grammar'):
        try:
            if is_grammar_placeholder(self._grammar):
                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 _signature(self) -> Hashable:
        """This method should be implemented by any non-abstract descendant
        parser class. The implementation must make sure that all instances
        that have the same signature always yield the same parsing result
        for the same piece of text.

        It does not hurt, but only wastes an opportunity for optimization,
        if two functionally equivalent parsers provide different signatures.
        It is a serious mistake, though, if two functionally non-equivalent
        parsers have the same signature.

        By returning `id(self)` this mistake will become impossible, but
        it will turn signature-based memoization-optimization off for
        this parser.
        """
        return id(self)

    def signature(self) -> Hashable:
        """Returns a value that is identical for two different
        parser objects if they are functionally equivalent, i.e.
        yield the same return value for the same call parameters:

        >>> a = Text('[')
        >>> b = Text('[')
        >>> c = Text(']')
        >>> a is b
        False
        >>> a.signature() == b.signature()
        True
        >>> a.signature() == c.signature()
        False

        The purpose of parser-signatures is to optimize better
        memoization in cases of code repetition in the grammar.

        DO NOT OVERRIDE THIS METHOD. In order to implement a
        signature function, the protected method `_signature`
        should be overridden instead.
        """
        return self.pname if self.pname else self._signature()


    def static_error(self, msg: str, code: ErrorCode) -> 'AnalysisError':
        return AnalysisError(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.disposable = src.disposable
    duplicate.drop_content = src.drop_content
    duplicate.tag_name = src.tag_name
    duplicate.eq_class = src.eq_class


def determine_eq_classes(root: Parser):
    """Sorts the parsers originating in root (imperfectly) into equivalence
    classes and assigns respective the class identifier to the `eq_class`-field
    of each parser."""
    eq_classes: Dict[Hashable, int] = {}

    def assign_eq_class(parser_stack: List[Parser]) -> bool:
        nonlocal eq_classes
        p = parser_stack[-1]
        signature = p.signature()
        p.eq_class = eq_classes.setdefault(signature, id(p))
        return False

    root.apply(assign_eq_class)


def Drop(parser: Parser) -> Parser:
    """Returns the parser with the `parser.drop_content`-property set to `True`."""
    assert parser.disposable, "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 = None  # type: Optional[Parser]
# Don't access PARSER_PLACEHOLDER directly, use get_parser_placeholder() instead


def get_parser_placeholder() -> Parser:
    global PARSER_PLACEHOLDER
    if PARSER_PLACEHOLDER is None:
        PARSER_PLACEHOLDER = Parser.__new__(Parser)  # Parser()
        PARSER_PLACEHOLDER.pname = ''
        PARSER_PLACEHOLDER.disposable = False
        PARSER_PLACEHOLDER.drop_content = False
        PARSER_PLACEHOLDER.tag_name = ':PLACEHOLDER__'
        PARSER_PLACEHOLDER.eq_class = id(PARSER_PLACEHOLDER)
    return cast(Parser, PARSER_PLACEHOLDER)


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: `minin_nonempty` does not work for 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 is / / or /   / or /\t/ won't work, but / */ or /\s*/ or /\s+/
    do work. There is no test for this. Fixed-size regular expressions
    run through `mixin_nonempty` 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, your 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
# class AnalysisError(NamedTuple):
#     symbol: str
#     parser: Parser
#     error: Error

# collections.namedtuple needed for Cython compatbility
AnalysisError = namedtuple('AnalysisError',
    ['symbol',  # type: str
     'parser',  # type: Parser
     'error'    # type: Error
    ], module = __name__)


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))


RESERVED_PARSER_NAMES = ('root__', 'dwsp__', 'wsp__', 'comment__', 'root_parser__', 'ff_parser__')


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</