parse.py

# parse.py - parser combinators for DHParser
#
# Copyright 2016  by Eckhart Arnold (arnold@badw.de)
#                 Bavarian Academy of Sciences an Humanities (badw.de)
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
# implied.  See the License for the specific language governing
# permissions and limitations under the License.


"""
Module ``parse`` contains the python classes and functions for
DHParser's packrat-parser. It's central class is the
``Grammar``-class, which is the base class for any concrete
Grammar. Grammar-objects are callable and parsing is done by
calling a Grammar-object with a source text as argument.

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


from collections import defaultdict
import copy

from 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, \
    PLAINTEXT_PTYPE, TOKEN_PTYPE, ZOMBIE_PARSER
from DHParser.toolkit import sane_parser_name, escape_control_characters, re, typing
from typing import Callable, cast, Dict, DefaultDict, List, Set, Tuple, Union, Optional


__all__ = ('Parser',
           'UnknownParserError',
           'Grammar',
           'PreprocessorToken',
           'RegExp',
           'Whitespace',
           'RE',
           'Token',
           '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


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 and, optionally, tracing
    (aka "history tracking") of parser calls. Returns the wrapped call.
    """
    def guarded_call(parser: 'Parser', text: StringView) -> Tuple[Optional[Node], StringView]:
        try:
            grammar = parser.grammar
            location = grammar.document_length__ - len(text)

            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 meomized results
                return parser.visited[location]

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

            # 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

            # run original __call__ method
            node, rest = parser_func(parser, text)

            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
                    parser.visited[location] = (node, rest)

            # Mind that meomized parser calls will not appear in the history record!
            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


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.
    """

    ApplyFunc = Callable[['Parser'], None]

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

        # add "aspect oriented" wrapper around parser calls
        # for memoizing, left recursion and tracing
        if not isinstance(self, Forward):  # should Forward-Parser no 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.
        """
        return self.__class__(self.name)

    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[Callable]

    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':
        return self._grammar

    @grammar.setter
    def grammar(self, grammar: 'Grammar'):
        if self._grammar is None:
            self._grammar = grammar
            self._grammar_assigned_notifier()
        else:
            assert self._grammar == grammar, \
                "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) -> bool:
        """
        Applies function `func(parser)` recursively to this parser and all
        descendant parsers if any exist. The same function can never
        be applied twice between calls of the ``reset()``-method!
        Returns `True`, if function has been applied, `False` if function
        had been applied earlier already and thus has not been applied again.
        """
        if func in self.cycle_detection:
            return False
        else:
            assert not self.visited, "No calls to Parser.apply() during or " \
                                     "after ongoing parsing process. (Call Parser.reset() first.)"
            self.cycle_detection.add(func)
            func(self)
            return True


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 | Token("(") + expression + Token(")")
            term = factor + ZeroOrMore((Token("*") | Token("/")) + factor)
            expression.set(term + ZeroOrMore((Token("+") | Token("-")) + 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:
        COMMENT__:  regular expression string for matching comments

        WSP__:   regular expression for whitespace and comments

        wspL__:  regular expression string for left aligned whitespace,
                 which either equals WSP__ or is empty.

        wspR__:  regular expression string for right aligned whitespace,
                 which either equals WSP__ or is empty.

        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.

        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

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

        whitespace__: A parser for the implicit optional whitespace (or the
                :class:zombie-parser if the default is empty). The default
                whitespace will be used by parsers :class:`Token` and, if no
                other parsers are passed to its constructor, by parser
                :class:`RE`. It can also be place explicitly in the
                EBNF-Grammar via the "~"-sign.

        wsp_left_parser__: The same as ``whitespace`` for
               left-adjacent-whitespace.

        wsp_right_parser__: The same as ``whitespace`` for
               right-adjacent-whitespace.

        _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
    # some default values
    COMMENT__ = r''  # type: str  # r'#.*(?:\n|$)'
    WSP__ = mixin_comment(whitespace=r'[\t ]*', comment=COMMENT__)  # type: str
    wspL__ = ''     # type: str
    wspR__ = WSP__  # 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. Names assigned via the ``name``-parameter of the
        constructor will not be overwritten. 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 not parser.name:
                        parser._name = entry
                    if isinstance(parser, Forward) and (not cast(Forward, parser).parser.name):
                        cast(Forward, parser).parser._name = entry
            cls.parser_initialization__ = "done"


    def __init__(self, root: Parser = None) -> None:
        # if not hasattr(self.__class__, 'parser_initialization__'):
        #     self.__class__.parser_initialization__ = "pending"
        # if not hasattr(self.__class__, 'wspL__'):
        #     self.wspL__ = ''
        # if not hasattr(self.__class__, 'wspR__'):
        #     self.wspR__ = ''
        self.all_parsers__ = set()             # type: Set[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__)

        if self.WSP__:
            try:
                probe = self.whitespace__  # type: RegExp
                assert self.whitespace__.regexp.pattern == self.WSP__
            except AttributeError:
                self.whitespace__ = Whitespace(self.WSP__)  # type: RegExp
            self.whitespace__.grammar = self
            self.all_parsers__.add(self.whitespace__)   # don't you forget about me...
        else:
            self.whitespace__ = cast(RegExp, ZOMBIE_PARSER)

        assert not self.wspL__ or self.wspL__ == self.WSP__
        assert not self.wspR__ or self.wspR__ == self.WSP__
        self.wsp_left_parser__ = self.whitespace__ if self.wspL__ else ZOMBIE_PARSER
        self.wsp_right_parser__ = self.whitespace__ if self.wspR__ else ZOMBIE_PARSER

        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[Parser]
        # 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__.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!' % parser.name)
            setattr(self, parser.name, parser)
        self.all_parsers__.add(parser)
        parser.grammar = self


    def __call__(self, document: str, start_parser="root__") -> Node:
        """
        Parses a document with with parser-combinators.

        Args:
            document (str): The source text to be parsed.
            start_parser (str): The name of the parser with which to
                start. This is useful for testing particular parsers
                (i.e. particular parts of the EBNF-Grammar.)
        Returns:
            Node: The root node ot the parse tree.
        """

        def tail_pos(predecessors: Union[List[Node], Tuple[Node, ...]]) -> 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__ = is_logging()
        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
        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))
        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:
                    error_msg = 'Parser did not match! Invalid source file?' \
                                '\n    Most advanced: %s\n    Last match:    %s;' % \
                                (str(HistoryRecord.most_advanced_match(self.history__)),
                                 str(HistoryRecord.last_match(self.history__)))
                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.")
                stitches.append(Node(None, skip).init_pos(tail_pos(stitches)))
                self.tree__.new_error(stitches[-1], error_msg)
                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))
            result = Node(None, tuple(stitches)).init_pos(0)
        if any(self.variables__.values()):
            error_str = "Capture-retrieve-stack not empty after end of parsing: " \
                + str(self.variables__)
            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_str)
                    result.result = result.children + (error_node,)
                else:
                    self.tree__.new_error(result, error_str)
        # result.pos = 0  # calculate all positions
        # result.collect_errors(self.document__)
        self.tree__.swallow(result)
        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)


########################################################################
#
# 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__(token)

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

    Example::

        >>> while_token = PlainText("while")
        >>> Grammar(while_token)("while").content
        'while'
    """
    assert PLAINTEXT_PTYPE == ":PlainText"

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

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

    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, name: str = '') -> None:
        super().__init__(name)
        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
        return self.__class__(regexp, self.name)

    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)


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"


#######################################################################
#######################################################################
#
# WARNING: The following code is hard to maintain, because it
# introduces a special case, i.e. a parser with child parsers that is
# not a descendant of the NaryOperator and because it interacts
# With the constructor of the Grammar class (see the instantiations of
# the Whitespace-class, there).
#
# That is all the more regrettable, as class RE basically just
# introduces syntactical sugar for
#
#     Series(whitespace__, RegExp('something'), whitespace__)
#
# What to do? Throw the syntactical sugar out? :-( Or find a more
# robust solution for that kind of syntactical sugar? Or just leave
# it be?
#
######################################################################
######################################################################


class RE(Parser):
    r"""
    Regular Expressions with optional leading or trailing whitespace.

    The RE-parser parses pieces of text that match a given regular
    expression. Other than the ``RegExp``-Parser it can also skip
    "implicit whitespace" before or after the matched text.

    The whitespace is in turn defined by a regular expression. It should
    be made sure that this expression also matches the empty string,
    e.g. use r'\s*' or r'[\t ]+', but not r'\s+'. If the respective
    parameters in the constructor are set to ``None`` the default
    whitespace expression from the Grammar object will be used.

    Example (allowing whitespace on the right hand side, but not on
    the left hand side of a regular expression)::

        >>> word = RE(r'\w+', wR=r'\s*')
        >>> parser = Grammar(word)
        >>> result = parser('Haus ')
        >>> result.content
        'Haus '
        >>> result.structure
        '(:RE (:RegExp "Haus") (:Whitespace " "))'
        >>> str(parser(' Haus'))
        ' <<< Error on " Haus" | Parser did not match! Invalid source file?\n    Most advanced: None\n    Last match:    None; >>> '

    EBNF-Notation:  ``/ ... /~`  or  `~/ ... /`  or  `~/ ... /~``

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

    def __init__(self, regexp, wL=None, wR=None, name: str='') -> None:
        r"""Constructor for class RE.

        Args:
            regexp (str or regex object):  The regular expression to be
                used for parsing.
            wL (str or regexp):  Left whitespace regular expression,
                i.e. either ``None``, the empty string or a regular
                expression (e.g. "\s*") that defines whitespace. An
                empty string means no whitespace will be skipped; ``None``
                means that the default whitespace will be used.
            wR (str or regexp):  Right whitespace regular expression.
                See above.
            name:  The optional name of the parser.
        """
        super().__init__(name)
        self.rx_wsl = wL
        self.rx_wsr = wR
        self.wsp_left = Whitespace(wL) if wL else ZOMBIE_PARSER
        self.wsp_right = Whitespace(wR) if wR else ZOMBIE_PARSER
        self.main = self.create_main_parser(regexp)

    def __deepcopy__(self, memo={}):
        try:
            regexp = copy.deepcopy(self.main.regexp, memo)
        except TypeError:
            regexp = self.main.regexp.pattern
        return self.__class__(regexp, self.rx_wsl, self.rx_wsr, self.name)

    def __call__(self, text: StringView) -> Tuple[Optional[Node], StringView]:
        # assert self.main.regexp.pattern != "@"
        txt = text    # type: StringView
        wsl, txt = self.wsp_left(txt)
        main, txt = self.main(txt)
        if main:
            wsr, txt = self.wsp_right(txt)
            result = tuple(nd for nd in (wsl, main, wsr) if nd)
            return Node(self, result), txt
        return None, text

    def __repr__(self):
        wsl = '~' if self.wsp_left != ZOMBIE_PARSER else ''
        wsr = '~' if self.wsp_right != ZOMBIE_PARSER else ''
        return wsl + '/%s/' % self.main.regexp.pattern + wsr

    def _grammar_assigned_notifier(self):
        if self.grammar:
            # use default whitespace parsers if not otherwise specified
            if self.rx_wsl is None:
                self.wsp_left = self.grammar.wsp_left_parser__
            if self.rx_wsr is None:
                self.wsp_right = self.grammar.wsp_right_parser__

    def apply(self, func: Parser.ApplyFunc) -> bool:
        if super().apply(func):
            if self.rx_wsl:
                self.wsp_left.apply(func)
            if self.rx_wsr:
                self.wsp_right.apply(func)
            self.main.apply(func)
            return True
        return False

    def create_main_parser(self, arg) -> Parser:
        """Creates the main parser of this compound parser. Can be overridden."""
        return RegExp(arg)


class Token(RE):
    """
    Class Token parses simple strings. Any regular regular expression
    commands will be interpreted as simple sequence of characters.

    Other than that class Token is essentially a renamed version of
    class RE. Because tokens often have a particular semantic different
    from other REs, parsing them with a separate parser class allows to
    distinguish them by their parser type.
    """
    assert TOKEN_PTYPE == ":Token"

    def __init__(self, token: str, wL=None, wR=None, name: str = '') -> None:
        self.token = token
        super().__init__(token, wL, wR, name)

    def __deepcopy__(self, memo={}):
        return self.__class__(self.token, self.rx_wsl, self.rx_wsr, self.name)

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

    def create_main_parser(self, arg) -> Parser:
        return PlainText(arg)


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

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

    def apply(self, func: Parser.ApplyFunc) -> bool:
        if super().apply(func):
            self.parser.apply(func)
            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, name: str = '') -> None:
        super().__init__(name)
        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)
        return self.__class__(*parsers, name=self.name)

    def apply(self, func: Parser.ApplyFunc) -> bool:
        if super().apply(func):
            for parser in self.parsers:
                parser.apply(func)
            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(Token('-')) + 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, name: str = '') -> None:
        super().__init__(parser, name)
        # assert isinstance(parser, Parser)
        assert not isinstance(parser, Option), \
            "Redundant nesting of options: %s(%s)" % (str(name), str(parser.name))
        # assert not isinstance(parser, Required), \
        #     "Nesting options with required elements is contradictory: " \
        #     "%s(%s)" % (str(name), str(parser.name))

    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.

    Examples::

        >>> sentence = ZeroOrMore(RE(r'\w+,?')) + Token('.')
        >>> Grammar(sentence)('Wo viel der Weisheit, da auch viel des Grämens.').content
        'Wo viel der Weisheit, da auch viel des Grämens.'
        >>> Grammar(sentence)('.').content  # an empty sentence also matches
        '.'

    EBNF-Notation: ``{ ... }``

    EBNF-Example:  ``sentence = { /\w+,?/ } "."``
    """

    def __call__(self, text: StringView) -> Tuple[Optional[Node], StringView]:
        results = ()  # type: Tuple[Node, ...]
        n = len(text) + 1  # type: int
        infinite_loop_error = None  # type: Optional[Error]
        while text and len(text) < n:
            n = len(text)
            node, text = self.parser(text)
            if not node:
                break
            if len(text) == n:
                node.errors.append(Error("Infinite loop!", node.pos, Error.MESSAGE))
                infinite_loop_error = Error(dsl_error_msg(self, 'Infinite Loop encountered.'),
                                            node.pos)
            results += (node,)
        node = Node(self, results)
        if infinite_loop_error:
            self.grammar.tree__.add_error(node, infinite_loop_error)
        return node, 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 OneOrMore(UnaryOperator):
    r"""
    `OneOrMore` applies a parser repeatedly as long as this parser
    matches. Other than `ZeroOrMore` which always matches, at least
    one match is required by `OneOrMore`.

    Examples::

        >>> sentence = OneOrMore(RE(r'\w+,?')) + Token('.')
        >>> Grammar(sentence)('Wo viel der Weisheit, da auch viel des Grämens.').content
        'Wo viel der Weisheit, da auch viel des Grämens.'
        >>> str(Grammar(sentence)('.'))  # an empty sentence also matches
        ' <<< Error on "." | Parser did not match! Invalid source file?\n    Most advanced: None\n    Last match:    None; >>> '

    EBNF-Notation: ``{ ... }+``

    EBNF-Example:  ``sentence = { /\w+,?/ }+``
    """

    def __init__(self, parser: Parser, name: str = '') -> None:
        super().__init__(parser, name)
        assert not isinstance(parser, Option), \
            "Use ZeroOrMore instead of nesting OneOrMore and Option: " \
            "%s(%s)" % (str(name), str(parser.name))

    def __call__(self, text: StringView) -> Tuple[Optional[Node], StringView]:
        results = ()  # type: Tuple[Node, ...]
        text_ = text  # type: StringView
        n = len(text) + 1  # type: int
        infinite_loop_error = None  # type: Optional[Error]
        while text_ and len(text_) < n:
            n = len(text_)
            node, text_ = self.parser(text_)
            if not node:
                break
            if len(text_) == n:
                node.errors.append(Error("Infinite loop!", node.pos, Error.MESSAGE))
                infinite_loop_error = Error(dsl_error_msg(self, 'Infinite Loop encountered.'),
                                            node.pos)
            results += (node,)
        if results == ():
            return None, text
        node = Node(self, results)
        if infinite_loop_error:
            self.grammar.tree__.add_error(node, infinite_loop_error)
        return node, 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 Series(NaryOperator):
    r"""
    Matches if each of a series of parsers matches exactly in the order of
    the series.

    Example::

        >>> variable_name = RegExp('(?!\d)\w') + RE('\w*')
        >>> Grammar(variable_name)('variable_1').content
        'variable_1'
        >>> str(Grammar(variable_name)('1_variable'))
        ' <<< Error on "1_variable" | Parser did not match! Invalid source file?\n    Most advanced: None\n    Last match:    None; >>> '

    EBNF-Notation: ``... ...``    (sequence of parsers separated by a blank or new line)

    EBNF-Example:  ``series = letter letter_or_digit``
    """
    RX_ARGUMENT = re.compile(r'\s(\S)')
    NOPE = 1000

    def __init__(self, *parsers: Parser, mandatory: int = NOPE, name: str = '') -> None:
        super().__init__(*parsers, name=name)
        length = len(self.parsers)
        assert 1 <= length < Series.NOPE, \
            'Length %i of series exceeds maximum length of %i' % (length, Series.NOPE)
        if mandatory < 0:
            mandatory += length
        assert 0 <= mandatory < length or mandatory == Series.NOPE
        self.mandatory = mandatory

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

    def __call__(self, text: StringView) -> Tuple[Optional[Node], StringView]:
        results = ()  # type: Tuple[Node, ...]
        text_ = text  # type: StringView
        pos = 0
        mandatory_violation = None
        for parser in self.parsers:
            node, text_ = parser(text_)
            if not node:
                if pos < self.mandatory:
                    return None, text
                else:
                    # Provide useful error messages
                    match = text.search(Series.RX_ARGUMENT)
                    i = max(1, text.index(match.regs[1][0])) if match else 1
                    location = self.grammar.document_length__ - len(text_)
                    node = Node(self, text_[:i]).init_pos(location)
                    node.errors.append(Error("§ %s violation" % parser.repr,
                                             location, Error.MESSAGE))
                    if not mandatory_violation:
                        msg = '%s expected, "%s" found!' \
                              % (parser.repr, text_[:10].replace('\n', '\\n '))
                        mandatory_violation = Error(msg, location, Error.MANDATORY_CONTINUATION)
                    text_ = text_[i:]
            results += (node,)
            # if node.error_flag:  # break on first error
            #    break
            pos += 1
        assert len(results) <= len(self.parsers)
        node = Node(self, results)
        if mandatory_violation:
            self.grammar.tree__.add_error(node, mandatory_violation)
        return node, text_

    def __repr__(self):
        return " ".join([parser.repr for parser in self.parsers[:self.mandatory]]
                        + (['§'] if self.mandatory != Series.NOPE else [])
                        + [parser.repr for parser in self.parsers[self.mandatory:]])

    # The following operator definitions add syntactical sugar, so one can write:
    # `RE('\d+') + Optional(RE('\.\d+)` instead of `Series(RE('\d+'), Optional(RE('\.\d+))`

    @staticmethod
    def combined_mandatory(left: Parser, right: Parser):
        """
        Returns the position of the first mandatory element (if any) when
        parsers `left` and `right` are joined to a sequence.
        """
        left_mandatory, left_length = (left.mandatory, len(left.parsers)) \
            if isinstance(left, Series) else (Series.NOPE, 1)
        if left_mandatory != Series.NOPE:
            return left_mandatory
        right_mandatory = right.mandatory if isinstance(right, Series) else Series.NOPE
        if right_mandatory != Series.NOPE:
            return right_mandatory + left_length
        return Series.NOPE

    def __add__(self, other: Parser) -> 'Series':
        other_parsers = cast('Series', other).parsers if isinstance(other, Series) \
            else cast(Tuple[Parser, ...], (other,))  # type: Tuple[Parser, ...]
        return Series(*(self.parsers + other_parsers),
                      mandatory=self.combined_mandatory(self, other))

    def __radd__(self, other: Parser) -> 'Series':
        other_parsers = cast('Series', other).parsers if isinstance(other, Series) \
            else cast(Tuple[Parser, ...], (other,))  # type: Tuple[Parser, ...]
        return Series(*(other_parsers + self.parsers),
                      mandatory=self.combined_mandatory(other, self))

    def __iadd__(self, other: Parser) -> 'Series':
        other_parsers = cast('Series', other).parsers if isinstance(other, Series) \
            else cast(Tuple[Parser, ...], (other,))  # type: Tuple[Parser, ...]
        self.parsers += other_parsers
        self.mandatory = self.combined_mandatory(self, other)
        return self


class Alternative(NaryOperator):
    r"""
    Matches if one of several alternatives matches. Returns
    the first match.

    This parser represents the EBNF-operator "|" with the qualification
    that both the symmetry and the ambiguity of the EBNF-or-operator
    are broken by selecting the first match.::

        # the order of the sub-expression matters!
        >>> number = RE('\d+') | RE('\d+') + RE('\.') + RE('\d+')
        >>> str(Grammar(number)("3.1416"))
        '3 <<< Error on ".141" | Parser stopped before end! trying to recover... >>> '

        # the most selective expression should be put first:
        >>> number = RE('\d+') + RE('\.') + RE('\d+') | RE('\d+')
        >>> Grammar(number)("3.1416").content
        '3.1416'