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, OrderedDict
import copy

from DHParser.error import Error, linebreaks
from DHParser.log import is_logging, HistoryRecord
from DHParser.preprocess import BEGIN_TOKEN, END_TOKEN, RX_TOKEN_NAME
from DHParser.stringview import StringView, EMPTY_STRING_VIEW
from DHParser.syntaxtree import Node, RootNode, ParserBase, WHITESPACE_PTYPE, \
    TOKEN_PTYPE, ZOMBIE_PARSER, ResultType
from DHParser.toolkit import sane_parser_name, escape_control_characters, re, typing
from typing import Callable, cast, List, Tuple, Set, Dict, DefaultDict, Union, Optional, Any


__all__ = ('Parser',
           'UnknownParserError',
           'Grammar',
           'PreprocessorToken',
           'Token',
           'RegExp',
           'RE',
           'TKN',
           'Whitespace',
           'mixin_comment',
           'UnaryOperator',
           'NaryOperator',
           'Synonym',
           'Option',
           'ZeroOrMore',
           'OneOrMore',
           'Series',
           'Alternative',
           'AllOf',
           'SomeOf',
           'Unordered',
           'Required',
           'Lookahead',
           'NegativeLookahead',
           'Lookbehind',
           'NegativeLookbehind',
           'last_value',
           'counterpart',
           'accumulate',
           'Capture',
           'Retrieve',
           'Pop',
           'Forward')


########################################################################
#
# Grammar and parsing infrastructure
#
########################################################################


LEFT_RECURSION_DEPTH = 8  # type: int
# because of python's recursion depth limit, this value ought not to be
# set too high. PyPy allows higher values than CPython
MAX_DROPOUTS = 3  # type: int
# stop trying to recover parsing after so many errors


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`-
    detects a missing mandatory element.
    """
    def __init__(self, node: Node, rest: StringView, first_throw: bool):
        self.node = node  # type: Node
        self.rest = rest  # type: StringView
        self.first_throw = first_throw  # type: bool


ResumeList = List[Union[str, Any]]  # list of strings or regular expressiones


def reentry_point(rest: StringView, rules: ResumeList) -> int:
    """
    Finds the point where parsing should resume after a ParserError has been caught.
    Args:
        rest:  The rest of the parsed text or, in other words, the point where
                a ParserError was thrown.
        rules: A list of strings or regular expressions. The rest of the text is
                searched for each of these. The closest match is the point where
                parsing will be resumed.
    Returns:
        The integer index of the closest reentry point or -1 if no reentry-point
        was found.
    """
    upper_limit = len(rest) + 1
    i = upper_limit
    #find closest match
    for rule in rules:
        if isinstance(rule, str):
            k = rest.find(rule)
            i = min(k if k >= 0 else upper_limit, i)
        else:
            m = rest.search(rule)
            if m:
                i = min(rest.index(m.start()), i)
    # in case no rule matched return -1
    if i == upper_limit:
        i = -1
    return i
    # return Node(None, rest[:i]), rest[i:]


def add_parser_guard(parser_func):
    """
    Add a wrapper function to a parser functions (i.e. Parser.__call__ method)
    that takes care of memoizing, left recursion, error catching and,
    optionally, tracing (aka "history tracking") of parser calls.
    Returns the wrapped call.
    """
    def guarded_call(parser: 'Parser', text: StringView) -> Tuple[Optional[Node], StringView]:
        """Wrapper method for Parser.__call__. This is used to add in an aspect-oriented
        fashion the business intelligence that is common to all parsers."""
        grammar = parser._grammar  # read protected member instead property to avoid function call
        location = grammar.document_length__ - len(text)

        try:
            if grammar.last_rb__loc__ >= location:
                grammar.rollback_to__(location)

            # if location has already been visited by the current parser,
            # return saved result
            if location in parser.visited:
                # no history recording in case of memoized results
                return parser.visited[location]

            # break left recursion at the maximum allowed depth
            if grammar.left_recursion_handling__:
                if parser.recursion_counter[location] > LEFT_RECURSION_DEPTH:
                    grammar.recursion_locations__.add(location)
                    return None, text
                parser.recursion_counter[location] += 1

            if grammar.history_tracking__:
                grammar.call_stack__.append(parser)
                grammar.moving_forward__ = True

            try:
                # PARSER CALL: run original __call__ method
                node, rest = parser_func(parser, text)
            except ParserError as error:
                # does this play well with variable setting? add rollback clause here? tests needed...
                gap = len(text) - len(error.rest)
                rules = grammar.resume_rules__.get(parser.name, [])
                rest = error.rest[len(error.node):]
                i = reentry_point(rest, rules)
                if i >= 0 or parser == grammar.start_parser__:
                    # apply reentry-rule or catch error at root-parser
                    if i < 0:
                        i = 1
                    nd = Node(None, rest[:i])
                    rest = rest[i:]
                    assert error.node.children
                    if error.first_throw:
                        node = error.node
                        node.result += (nd,)
                    else:
                        node = Node(parser, (Node(None, text[:gap]), error.node, nd))
                elif error.first_throw:
                    raise ParserError(error.node, error.rest, first_throw=False)
                else:
                    result = (Node(None, text[:gap]), error.node) if gap else error.node  # type: ResultType
                    raise ParserError(Node(parser, result), text, first_throw=False)

            if grammar.left_recursion_handling__:
                parser.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__:
                    if location in parser.visited:
                        node, rest = parser.visited[location]
                        # TODO: maybe add a warning about occurrence of left-recursion here?
                    # 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
                    parser.visited[location] = (None, rest)
            else:
                assert node._pos < 0
                node._pos = location
                assert node._pos >= 0, str("%i < %i" % (grammar.document_length__, location))
                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
                    # TODO: need a unit-test concerning interference of variable manipulation and left recursion algorithm?
                    parser.visited[location] = (node, rest)

            # Mind that memoized parser calls will not appear in the history record!
            # Does this make sense? Or should it be changed?
            if grammar.history_tracking__:
                # don't track returning parsers except in case an error has occurred
                # remaining = len(rest)
                if (grammar.moving_forward__ or (node and node.errors)):
                    record = HistoryRecord(grammar.call_stack__, node, text)
                    grammar.history__.append(record)
                    # print(record.stack, record.status, rest[:20].replace('\n', '|'))
                grammar.moving_forward__ = False
                grammar.call_stack__.pop()

        except RecursionError:
            node = Node(None, str(text[:min(10, max(1, text.find("\n")))]) + " ...")
            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

    return guarded_call


ApplyFunc = Callable[['Parser'], None]
FlagFunc = Callable[[ApplyFunc, Set[ApplyFunc]], bool]


class Parser(ParserBase):
    """
    (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.name`.
       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:
        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.

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

    def __init__(self) -> None:
        # assert isinstance(name, str), str(name)
        super().__init__()
        self._grammar = ZOMBIE_GRAMMAR  # type: Grammar
        self.reset()

        # add "aspect oriented" wrapper around parser calls
        # for memoizing, left recursion and tracing
        if not isinstance(self, Forward):  # should Forward-Parser not be guarded? Not sure...
            guarded_parser_call = add_parser_guard(self.__class__.__call__)
            # The following check is necessary for classes that don't override
            # the __call__() method, because in these cases the non-overridden
            # __call__()-method would be substituted a second time!
            if self.__class__.__call__.__code__ != guarded_parser_call.__code__:
                self.__class__.__call__ = guarded_parser_call

    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 constructor,
        `__deepcopy__`-method must be replaced (i.e. overridden without
        calling the same method from the superclass) by the derived class.
        """
        duplicate = self.__class__()
        duplicate.name = self.name
        duplicate.ptype = self.ptype
        return duplicate

    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]]
        self.recursion_counter = defaultdict(lambda: 0)  # type: DefaultDict[int, int]
        self.cycle_detection = set()  # type: Set[ApplyFunc]

    def __call__(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."""
        return None, text  # default behaviour: don't match

    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)

    @property
    def grammar(self) -> 'Grammar':
        if self._grammar != ZOMBIE_GRAMMAR:
            return self._grammar
        else:
            raise AssertionError('Grammar has not yet been set!')

    @grammar.setter
    def grammar(self, grammar: 'Grammar'):
        if self._grammar == ZOMBIE_GRAMMAR:
            self._grammar = grammar
            self._grammar_assigned_notifier()
        elif self._grammar != grammar:
              raise AssertionError("Parser has already been assigned"
                                   "to a different Grammar object!")

    def _grammar_assigned_notifier(self):
        """A function that notifies the parser object that it has been
        assigned to a grammar."""
        pass

    def _apply(self, func: ApplyFunc, flip: FlagFunc) -> bool:
        """
        Applies function `func(parser)` recursively to this parser and all
        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!
        """
        if flip(func, self.cycle_detection):
            return False
        else:
            func(self)
            return True

    def apply(self, func: ApplyFunc):
        """
        Applies function `func(parser)` recursively to this parser and all
        descendant parsers, if any exist. Traversal is pre-order.
        """
        def positive_flip(f: ApplyFunc, flagged: Set[Callable]) -> 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: Set[Callable]) -> 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:
            self._apply(func, negative_flip)
        else:
            self._apply(func, positive_flip)


def mixin_comment(whitespace: str, comment: str) -> str:
    """
    Returns a regular expression that merges comment and whitespace
    regexps. Thus comments cann occur whereever 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).
    """
    wspc = '(?:' + whitespace + '(?:' + comment + whitespace + ')*)'
    return wspc


class UnknownParserError(KeyError):
    """UnknownParserError is raised if a Grammar object is called with a
    parser that does not exist or if in the course of parsing a parser
    is referred to that does not exist."""


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('\d+') + RE('\.') + RE('\d+') | RE('\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.

    3. The parsers in the class do not necessarily need to be connected
       to one single root parser, which is helpful for testing and
       building up a parser successively of 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.
    Any parser that is directly assigned to a class variable is a
    'named' parser and its field `parser.name` contains the variable
    name after instantiation of the Grammar class. All other parsers,
    i.e. parsers that are defined within a `named` parser, remain
    "anonymous parsers" where `parser.name` is the empty string, unless
    a name has been passed explicitly upon instantiation.
    If one and the same parser is assigned to several class variables
    such as, for example the parser `expression` in the example above,
    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:

    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 or search
                strings that act as rules to find the the reentry point if a ParserError
                was thrown during the execution of the parser with the respective name.

        parser_initializiation__:  Before the parser 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.

        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`).

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

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

        history_tracking__:  A flag indicating that the parsing history shall
                be tracked

        _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__:  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.

        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.

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

        variables__:  A mapping for variable names to a stack of their respective
                string values - needed by the :class:`Capture`-, :class:`Retrieve`-
                and :class:`Pop`-parsers.

        rollback__:  A list of tuples (location, rollback-function) that are
                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.

        last_rb__loc__:  The last, i.e. most advanced location in the text
                where a variable changing operation occurred. If the parser
                backtracks to a location at or before last_rb__loc__ (i.e.
                location <= last_rb__loc__) then a rollback of all variable
                changing operations is necessary that occurred after the
                location to which the parser backtracks. This is done by
                calling method :func:`rollback_to__(location)`.

        call_stack__:  A stack of all parsers that have been called. This
                is required for recording the parser history (for debugging)
                and, eventually, i.e. one day in the future, for tracing through
                the parsing process.

        history__:  A list of parser-call-stacks. A parser-call-stack is
                appended to the list each time a parser either matches, fails
                or if a parser-error occurs.

        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
                recording is turned off! (See :func:`add_parser_guard` and its local
                function :func:`guarded_call`)

        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:`add_parser_guard` and its
                local function :func:`guarded_call`)

        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)

        left_recursion_handling__:  Turns left recursion handling on or off.
                If turned off, a recursion error will result in case of left
                recursion.
    """
    python_src__ = ''  # type: str
    root__ = ZOMBIE_PARSER  # type: ParserBase
    # root__ must be overwritten with the root-parser by grammar subclass
    parser_initialization__ = "pending"  # type: str
    resume_rules__ = dict()  # type: Dict[str, ResumeList]
    # some default values
    # COMMENT__ = r''  # type: str  # r'#.*(?:\n|$)'
    # WSP_RE__ = mixin_comment(whitespace=r'[\t ]*', comment=COMMENT__)  # type: str


    @classmethod
    def _assign_parser_names__(cls):
        """
        Initializes the `parser.name` fields of those
        Parser objects that are directly assigned to a class field with
        the field's name, e.g.::

            class Grammar(Grammar):
                ...
                symbol = RE('(?!\\d)\\w+')

        After the call of this method symbol.name == "symbol" holds.
        Parser names starting or ending with a double underscore like
        ``root__`` will be ignored. See :func:`sane_parser_name()`

        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.
        """
        if cls.parser_initialization__ != "done":
            cdict = cls.__dict__
            for entry, parser in cdict.items():
                if isinstance(parser, Parser) and sane_parser_name(entry):
                    if isinstance(parser, Forward):
                        if not cast(Forward, parser).parser.name:
                            cast(Forward, parser).parser.name = entry
                    else:   # if not parser.name:
                        parser.name = entry
            cls.parser_initialization__ = "done"


    def __init__(self, root: Parser = None) -> None:
        self.all_parsers__ = set()             # type: Set[ParserBase]
        self.start_parser__ = None             # type: Optional[ParserBase]
        self._dirty_flag__ = False             # type: bool
        self.history_tracking__ = False        # type: bool
        self.memoization__ = True              # type: bool
        self.left_recursion_handling__ = True  # type: bool
        self._reset__()

        # prepare parsers in the class, first
        self._assign_parser_names__()

        # then deep-copy the parser tree from class to instance;
        # parsers not connected to the root object will be copied later
        # on demand (see Grammar.__getitem__()). Usually, the need to
        # do so only arises during testing.
        self.root__ = copy.deepcopy(root) if root else copy.deepcopy(self.__class__.root__)
        self.root__.apply(self._add_parser__)


    def __getitem__(self, key):
        try:
            return self.__dict__[key]
        except KeyError:
            parser_template = getattr(self, key, None)
            if parser_template:
                # add parser to grammar object on the fly...
                parser = copy.deepcopy(parser_template)
                parser.apply(self._add_parser__)
                # assert self[key] == parser
                return self[key]
            raise UnknownParserError('Unknown parser "%s" !' % key)


    def _reset__(self):
        self.tree__ = RootNode()              # type: RootNode
        self.document__ = EMPTY_STRING_VIEW   # type: StringView
        self._reversed__ = EMPTY_STRING_VIEW  # type: StringView
        self.document_length__ = 0            # type: int
        self.document_lbreaks__ = []          # type: List[int]
        # variables stored and recalled by Capture and Retrieve parsers
        self.variables__ = defaultdict(lambda: [])  # type: DefaultDict[str, List[str]]
        self.rollback__ = []                  # type: List[Tuple[int, Callable]]
        self.last_rb__loc__ = -1              # type: int
        # support for call stack tracing
        self.call_stack__ = []                # type: List[ParserBase]
        # snapshots of call stacks
        self.history__ = []                   # type: List[HistoryRecord]
        # also needed for call stack tracing
        self.moving_forward__ = False         # type: bool
        self.recursion_locations__ = set()    # type: Set[int]


    @property
    def reversed__(self) -> StringView:
        """
        Returns a reversed version of the currently parsed document. As
        about the only case where this is needed is the Lookbehind-parser,
        this is done lazily.
        """
        if not self._reversed__:
            self._reversed__ = StringView(self.document__.get_text()[::-1])
        return self._reversed__


    def _add_parser__(self, parser: Parser) -> None:
        """
        Adds the particular copy of the parser object to this
        particular instance of Grammar.
        """
        if parser.name:
            # prevent overwriting instance variables or parsers of a different class
            assert parser.name not in self.__dict__ or \
                isinstance(self.__dict__[parser.name], parser.__class__), \
                ('Cannot add parser "%s" because a field with the same name '
                 'already exists in grammar object: %s!'
                 % (parser.name, str(self.__dict__[parser.name])))
            setattr(self, parser.name, parser)
        self.all_parsers__.add(parser)
        parser.grammar = self


    def __call__(self,
                 document: str,
                 start_parser: Union[str, Parser] = "root__",
                 track_history: bool = False) -> RootNode:
        """
        Parses a document with with parser-combinators.

        Args:
            document (str): The source text to be parsed.
            start_parser (str or Parser): The name of the parser with which
                to start. This is useful for testing particular parsers
                (i.e. particular parts of the EBNF-Grammar.)
            track_history (bool): If true, the parsing history will be
                recorded in self.history__. If logging is turned on (i.e.
                DHParser.log.is_logging() returns true), the parsing history
                will always be recorded, even if `False` is passed to
                the `track_history` parameter.
        Returns:
            Node: The root node to the parse tree.
        """

        def tail_pos(predecessors: Union[List[Node], Tuple[Node, ...], None]) -> int:
            """Adds the position after the last node in the list of
            predecessors to the node."""
            return predecessors[-1].pos + len(predecessors[-1]) if predecessors else 0

        # assert isinstance(document, str), type(document)
        if self.root__ is None:
            raise NotImplementedError()
        if self._dirty_flag__:
            self._reset__()
            for parser in self.all_parsers__:
                parser.reset()
        else:
            self._dirty_flag__ = True
        self.history_tracking__ = track_history or is_logging()
        # safe tracking state, because history_tracking__ might be set to false, later,
        # but original tracking state is needed for additional error information.
        track_history = self.history_tracking__
        self.document__ = StringView(document)
        self.document_length__ = len(self.document__)
        self.document_lbreaks__ = linebreaks(document) if self.history_tracking__ else []
        self.last_rb__loc__ = -1  # rollback location
        parser = self[start_parser] if isinstance(start_parser, str) else start_parser
        self.start_parser__ = parser
        assert parser.grammar == self, "Cannot run parsers from a different grammar object!" \
                                       " %s vs. %s" % (str(self), str(parser.grammar))
        result = None  # type: Optional[Node]
        stitches = []  # type: List[Node]
        rest = self.document__
        if not rest:
            result, _ = parser(rest)
            if result is None:
                result = Node(None, '').init_pos(0)
                self.tree__.new_error(result,
                                      'Parser "%s" did not match empty document.' % str(parser),
                                      Error.PARSER_DID_NOT_MATCH)
        while rest and len(stitches) < MAX_DROPOUTS:
            result, rest = parser(rest)
            if rest:
                fwd = rest.find("\n") + 1 or len(rest)
                skip, rest = rest[:fwd], rest[fwd:]
                if result is None:
                    err_info = '' if not track_history else \
                               '\n    Most advanced: %s\n    Last match:    %s;' % \
                               (str(HistoryRecord.most_advanced_match(self.history__)),
                                str(HistoryRecord.last_match(self.history__)))
                    # Check if a Lookahead-Parser did match. Needed for testing, because
                    # in a test case this is not necessarily an error.
                    last_record = self.history__[-2] if len(self.history__) > 1 else None  # type: Optional[HistoryRecord]
                    if last_record and parser != self.root__ \
                            and last_record.status == HistoryRecord.MATCH \
                            and last_record.node.pos \
                            + len(last_record.node) >= len(self.document__) \
                            and any(isinstance(parser, Lookahead)
                                    for parser in last_record.call_stack):
                        error_msg = 'Parser did not match except for lookahead! ' + err_info
                        error_code = Error.PARSER_LOOKAHEAD_MATCH_ONLY
                    else:
                        error_msg = 'Parser did not match!' + err_info
                        error_code = Error.PARSER_DID_NOT_MATCH
                else:
                    stitches.append(result)
                    error_msg = "Parser stopped before end" \
                        + (("! trying to recover"
                            + (" but stopping history recording at this point."
                               if self.history_tracking__ else "..."))
                            if len(stitches) < MAX_DROPOUTS
                            else " too often! Terminating parser.")
                    error_code = Error.PARSER_STOPPED_BEFORE_END
                stitches.append(Node(None, skip).init_pos(tail_pos(stitches)))
                self.tree__.new_error(stitches[-1], error_msg, error_code)
                if self.history_tracking__:
                    # # some parsers may have matched and left history records with nodes != None.
                    # # Because these are not connected to the stitched root node, their pos-
                    # # properties will not be initialized by setting the root node's pos property
                    # # to zero. Therefore, their pos properties need to be initialized here
                    # for record in self.history__:
                    #     if record.node and record.node._pos < 0:
                    #         record.node.init_pos(0)
                    record = HistoryRecord(self.call_stack__.copy(), stitches[-1], rest)
                    self.history__.append(record)
                    # stop history tracking when parser returned too early
                    self.history_tracking__ = False
        if stitches:
            if rest:
                stitches.append(Node(None, rest))
            #try:
            result = Node(None, tuple(stitches)).init_pos(0)
            # except AssertionError as error:
            #     # some debugging output
            #     print(Node(None, tuple(stitches)).as_sxpr())
            #     raise error
        if any(self.variables__.values()):
            error_msg = "Capture-retrieve-stack not empty after end of parsing: " \
                + str(self.variables__)
            error_code = Error.CAPTURE_STACK_NOT_EMPTY
            if result:
                if result.children:
                    # add another child node at the end to ensure that the position
                    # of the error will be the end of the text. Otherwise, the error
                    # message above ("...after end of parsing") would appear illogical.
                    error_node = Node(ZOMBIE_PARSER, '').init_pos(tail_pos(result.children))
                    self.tree__.new_error(error_node, error_msg, error_code)
                    result.result = result.children + (error_node,)
                else:
                    self.tree__.new_error(result, error_msg, error_code)
        # result.pos = 0  # calculate all positions
        # result.collect_errors(self.document__)
        if result:
            self.tree__.swallow(result)
        self.start_parser__ = None
        return self.tree__


    def push_rollback__(self, location, func):
        """
        Adds a rollback function that either removes or re-adds
        values on the variable stack (`self.variables`) that have been
        added (or removed) by Capture or Pop Parsers, the results of
        which have been dismissed.
        """
        self.rollback__.append((location, func))
        self.last_rb__loc__ = location


    def rollback_to__(self, location):
        """
        Rolls back the variable stacks (`self.variables`) to its
        state at an earlier location in the parsed document.
        """
        while self.rollback__ and self.rollback__[-1][0] >= location:
            _, rollback_func = self.rollback__.pop()
            # assert not loc > self.last_rb__loc__, \
            #     "Rollback confusion: line %i, col %i < line %i, col %i" % \
            #     (*line_col(self.document__, len(self.document__) - loc),
            #      *line_col(self.document__, len(self.document__) - self.last_rb__loc__))
            rollback_func()
        self.last_rb__loc__ == self.rollback__[-1][0] if self.rollback__ \
            else (len(self.document__) + 1)


def dsl_error_msg(parser: Parser, error_str: str) -> str:
    """
    Returns an error message for errors in the parser configuration,
    e.g. errors that result in infinite loops.

    Args:
        parser (Parser):  The parser where the error was noticed. Note
            that this is not necessarily the parser that caused the
            error but only where the error became apparent.
        error_str (str):  A short string describing the error.
    Returns:
        str: An error message including the call stack if history
        tacking has been turned in the grammar object.
    """
    msg = ["DSL parser specification error:", error_str, 'Caught by parser "%s".' % str(parser)]
    if parser.grammar.history__:
        msg.extend(["\nCall stack:", parser.grammar.history__[-1].stack])
    else:
        msg.extend(["\nEnable history tracking in Grammar object to display call stack."])
    return " ".join(msg)


ZOMBIE_GRAMMAR = Grammar()


########################################################################
#
# _Token and Regular Expression parser classes (i.e. leaf classes)
#
########################################################################


class PreprocessorToken(Parser):
    """
    Parses tokens that have been inserted by a preprocessor.

    Preprocessors can generate Tokens with the ``make_token``-function.
    These tokens start and end with magic characters that can only be
    matched by the PreprocessorToken Parser. Such tokens can be used to
    insert BEGIN - END delimiters at the beginning or ending of a
    quoted block, for example.
    """

    def __init__(self, token: str) -> None:
        assert token and token.isupper()
        assert RX_TOKEN_NAME.match(token)
        super().__init__()
        self.name = token

    def __deepcopy__(self, memo):
        duplicate = self.__class__(self.name)
        duplicate.name = self.name
        duplicate.ptype = self.ptype
        return duplicate

    def __call__(self, text: StringView) -> Tuple[Optional[Node], StringView]:
        if text[0:1] == BEGIN_TOKEN:
            end = text.find(END_TOKEN, 1)
            if end < 0:
                node = Node(self, '')
                self.grammar.tree__.new_error(
                    node,
                    'END_TOKEN delimiter missing from preprocessor token. '
                    '(Most likely due to a preprocessor bug!)')  # type: Node
                return node, text[1:]
            elif end == 0:
                node = Node(self, '')
                self.grammar.tree__.new_error(
                    node,
                    'Preprocessor-token cannot have zero length. '
                    '(Most likely due to a preprocessor bug!)')
                return node, text[2:]
            elif text.find(BEGIN_TOKEN, 1, end) >= 0:
                node = Node(self, text[len(self.name) + 1:end])
                self.grammar.tree__.new_error(
                    node,
                    'Preprocessor-tokens must not be nested or contain '
                    'BEGIN_TOKEN delimiter as part of their argument. '
                    '(Most likely due to a preprocessor bug!)')
                return node, text[end:]
            if text[1:len(self.name) + 1] == self.name:
                return Node(self, text[len(self.name) + 2:end]), text[end + 1:]
        return None, text


class Token(Parser):
    """
    Parses plain text strings. (Could be done by RegExp as well, but is faster.)

    Example::

        >>> while_token = Token("while")
        >>> Grammar(while_token)("while").content
        'while'
    """
    assert TOKEN_PTYPE == ":Token"

    def __init__(self, text: str) -> None:
        super().__init__()
        self.text = text
        self.len = len(text)

    def __deepcopy__(self, memo):
        duplicate = self.__class__(self.text)
        duplicate.name = self.name
        duplicate.ptype = self.ptype
        return duplicate

    def __call__(self, text: StringView) -> Tuple[Optional[Node], StringView]:
        if text.startswith(self.text):
            return Node(self, self.text, True), text[self.len:]
        return None, text

    def __repr__(self):
        return ("'%s'" if self.text.find("'") <= 0 else '"%s"') % self.text


class RegExp(Parser):
    r"""
    Regular expression parser.

    The RegExp-parser parses text that matches a regular expression.
    RegExp can also be considered as the "atomic parser", because all
    other parsers delegate part of the parsing job to other parsers,
    but do not match text directly.

    Example::

        >>> word = RegExp(r'\w+')
        >>> Grammar(word)("Haus").content
        'Haus'

    EBNF-Notation:  ``/ ... /``

    EBNF-Example:   ``word = /\w+/``
    """

    def __init__(self, regexp) -> None:
        super().__init__()
        self.regexp = re.compile(regexp) if isinstance(regexp, str) else regexp

    def __deepcopy__(self, memo):
        # `regex` supports deep copies, but not `re`
        try:
            regexp = copy.deepcopy(self.regexp, memo)
        except TypeError:
            regexp = self.regexp.pattern
        duplicate = self.__class__(regexp)
        duplicate.name = self.name
        duplicate.ptype = self.ptype
        return duplicate

    def __call__(self, text: StringView) -> Tuple[Optional[Node], StringView]:
        match = text.match(self.regexp)
        if match:
            capture = match.group(0)
            end = text.index(match.end())
            # regular expression must never match preprocessor-tokens!
            # TODO: Find a better solution here? e.g. static checking/re-mangling at compile time
            i = capture.find(BEGIN_TOKEN)
            if i >= 0:
                capture = capture[:i]
                end = i
            return Node(self, capture, True), text[end:]
        return None, text

    def __repr__(self):
        return escape_control_characters('/%s/' % self.regexp.pattern)


def withWS(parser_factory, wsL='', wsR=r'\s*'):
    """Syntactic Sugar for 'Series(Whitespace(wsL), parser_factory(), Whitespace(wsR))'.
    """
    if wsL and isinstance(wsL, str):
        wsL = Whitespace(wsL)
    if wsR and isinstance(wsR, str):
        wsR = Whitespace(wsR)
    if wsL and wsR:
        return Series(wsL, parser_factory(), wsR)
    elif wsL:
        return Series(wsL, parser_factory())
    elif wsR:
        return Series(parser_factory(), wsR)
    else:
        return parser_factory()


def RE(regexp, wsL='', wsR=r'\s*'):
    """Syntactic Sugar for 'Series(Whitespace(wsL), RegExp(regexp), Whitespace(wsR))'"""
    return withWS(lambda: RegExp(regexp), wsL, wsR)


def TKN(token, wsL='', wsR=r'\s*'):
    """Syntactic Sugar for 'Series(Whitespace(wsL), Token(token), Whitespace(wsR))'"""
    return withWS(lambda: Token(token), wsL, wsR)


class Whitespace(RegExp):
    """An variant of RegExp that signifies through its class name that it
    is a RegExp-parser for whitespace."""
    assert WHITESPACE_PTYPE == ":Whitespace"

    def __repr__(self):
        return '~'


########################################################################
#
# Containing parser classes, i.e. parsers that contain other parsers
# to which they delegate parsing
#
########################################################################


class UnaryOperator(Parser):
    """
    Base class of all unary parser operators, i.e. parser that contains
    one and only one other parser, like the optional parser for example.

    The UnaryOperator base class supplies __deepcopy__ and apply
    methods for unary parser operators. The __deepcopy__ method needs
    to be overwritten, however, if the constructor of a derived class
    has additional parameters.
    """

    def __init__(self, parser: Parser) -> None:
        super(UnaryOperator, self).__init__()
        assert isinstance(parser, Parser), str(parser)
        self.parser = parser  # type: Parser

    def __deepcopy__(self, memo):
        parser = copy.deepcopy(self.parser, memo)
        duplicate = self.__class__(parser)
        duplicate.name = self.name
        duplicate.ptype = self.ptype
        return duplicate

    def _apply(self, func: ApplyFunc, flip: FlagFunc) -> bool:
        if super()._apply(func, flip):
            self.parser._apply(func, flip)
            return True
        return False


class NaryOperator(Parser):
    """
    Base class of all Nnary parser operators, i.e. parser that
    contains one or more other parsers, like the alternative
    parser for example.

    The NnaryOperator base class supplies __deepcopy__ and apply methods
    for unary parser operators. The __deepcopy__ method needs to be
    overwritten, however, if the constructor of a derived class has
    additional parameters.
    """

    def __init__(self, *parsers: Parser) -> None:
        super().__init__()
        assert all([isinstance(parser, Parser) for parser in parsers]), str(parsers)
        self.parsers = parsers  # type: Tuple[Parser, ...]

    def __deepcopy__(self, memo):
        parsers = copy.deepcopy(self.parsers, memo)
        duplicate = self.__class__(*parsers)
        duplicate.name = self.name
        duplicate.ptype = self.ptype
        return duplicate

    def _apply(self, func: ApplyFunc, flip: FlagFunc) -> bool:
        if super()._apply(func, flip):
            for parser in self.parsers:
                parser._apply(func, flip)
            return True
        return False


class Option(UnaryOperator):
    r"""
    Parser ``Option`` always matches, even if its child-parser
    did not match.

    If the child-parser did not match ``Option`` returns a node
    with no content and does not move forward in the text.

    If the child-parser did match, ``Option`` returns the a node
    with the node returned by the child-parser as its single
    child and the text at the position where the child-parser
    left it.

    Examples::

        >>> number = Option(TKN('-')) + RegExp(r'\d+') + Option(RegExp(r'\.\d+'))
        >>> Grammar(number)('3.14159').content
        '3.14159'
        >>> Grammar(number)('3.14159').structure
        '(:Series (:Option) (:RegExp "3") (:Option (:RegExp ".14159")))'
        >>> Grammar(number)('-1').content
        '-1'

    EBNF-Notation: ``[ ... ]``

    EBNF-Example:  ``number = ["-"]  /\d+/  [ /\.\d+/ ]``
    """

    def __init__(self, parser: Parser) -> None:
        super().__init__(parser)
        # assert isinstance(parser, Parser)
        assert not isinstance(parser, Option), \
            "Redundant nesting of options: %s%s" % (str(parser.name), str(self.ptype))

    def __call__(self, text: StringView) -> Tuple[Optional[Node], StringView]:
        node, text = self.parser(text)
        if node:
            return Node(self, node), text
        return Node(self, ()), text

    def __repr__(self):
        return '[' + (self.parser.repr[1:-1] if isinstance(self.parser, Alternative)
                      and not self.parser.name else self.parser.repr) + ']'


class ZeroOrMore(Option):
    r"""
    `ZeroOrMore` applies a parser repeatedly as long as this parser
    matches. Like `Option` the `ZeroOrMore` parser always matches. In
    case of zero repetitions, the empty match `((), text)` is returned.