parser.py 60.8 KB
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"""parsers.py - parser combinators for for DHParser
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Copyright 2016  by Eckhart Arnold (arnold@badw.de)
                Bavarian Academy of Sciences an Humanities (badw.de)

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
implied.  See the License for the specific language governing
permissions and limitations under the License.
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Module ``parsers.py`` contains a number of classes that together
make up parser combinators for left-recursive grammers. For each
element of the extended Backus-Naur-Form as well as for a regular
expression token a class is defined. The set of classes can be used to
define a parser for (ambiguous) left-recursive grammers.


References and Acknowledgements:

Dominikus Herzberg: Objekt-orientierte Parser-Kombinatoren in Python,
Blog-Post, September, 18th 2008 on denkspuren. gedanken, ideen,
anregungen und links rund um informatik-themen, URL:
http://denkspuren.blogspot.de/2008/09/objekt-orientierte-parser-kombinatoren.html

Dominikus Herzberg: Eine einfache Grammatik für LaTeX, Blog-Post,
September, 18th 2008 on denkspuren. gedanken, ideen, anregungen und
links rund um informatik-themen, URL:
http://denkspuren.blogspot.de/2008/09/eine-einfache-grammatik-fr-latex.html

Dominikus Herzberg: Uniform Syntax, Blog-Post, February, 27th 2007 on
denkspuren. gedanken, ideen, anregungen und links rund um
informatik-themen, URL:
http://denkspuren.blogspot.de/2007/02/uniform-syntax.html

Richard A. Frost, Rahmatullah Hafiz and Paul Callaghan: Parser
Combinators for Ambiguous Left-Recursive Grammars, in: P. Hudak and
D.S. Warren (Eds.): PADL 2008, LNCS 4902, pp. 167–181, Springer-Verlag
Berlin Heidelberg 2008.

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Elizabeth Scott and Adrian Johnstone, GLL Parsing,
in: Electronic Notes in Theoretical Computer Science 253 (2010) 177–189,
http://dotat.at/tmp/gll.pdf

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Juancarlo Añez: grako, a PEG parser generator in Python,
https://bitbucket.org/apalala/grako
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Vegard Øye: General Parser Combinators in Racket, 2012,
https://epsil.github.io/gll/
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"""

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import abc
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import copy
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import os
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from functools import partial

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try:
    import regex as re
except ImportError:
    import re
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try:
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    from typing import Any, Callable, cast, Dict, Iterator, List, Set, Tuple, Union
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    # try:
    #     from typing import Collection
    # except ImportError:
    #     pass
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except ImportError:
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    from .typing34 import Any, Callable, cast, Dict, Iterator, List, Set, Tuple, Union
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from DHParser.toolkit import is_logging, log_dir, logfile_basename, escape_re, sane_parser_name
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from DHParser.syntaxtree import WHITESPACE_PTYPE, TOKEN_PTYPE, ZOMBIE_PARSER, ParserBase, \
    Node, TransformationFunc
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from DHParser.toolkit import load_if_file, error_messages
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__all__ = ('PreprocessorFunc',
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           'HistoryRecord',
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           'Parser',
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           'Grammar',
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           'RX_PREPROCESSOR_TOKEN',
           'BEGIN_TOKEN',
           'END_TOKEN',
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           'make_token',
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           'nil_preprocessor',
           'PreprocessorToken',
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           'RegExp',
           'RE',
           'Token',
           'mixin_comment',
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           # 'UnaryOperator',
           # 'NaryOperator',
           'Synonym',
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           'Optional',
           'ZeroOrMore',
           'OneOrMore',
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           'Series',
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           'Alternative',
           'FlowOperator',
           'Required',
           'Lookahead',
           'NegativeLookahead',
           'Lookbehind',
           'NegativeLookbehind',
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           'last_value',
           'counterpart',
           'accumulate',
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           'Capture',
           'Retrieve',
           'Pop',
           'Forward',
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           'Compiler',
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           'compile_source')
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########################################################################
#
# Grammar and parsing infrastructure
#
########################################################################


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PreprocessorFunc = Union[Callable[[str], str], partial]
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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 = 5  # type: int
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# stop trying to recover parsing after so many errors
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class HistoryRecord:
    """
    Stores debugging information about one completed step in the
    parsing history. 

    A parsing step is "completed" when the last one of a nested
    sequence of parser-calls returns. The call stack including
    the last parser call will be frozen in the ``HistoryRecord``-
    object. In addition a reference to the generated leaf node
    (if any) will be stored and the result status of the last
    parser call, which ist either MATCH, FAIL (i.e. no match)
    or ERROR.
    """
    __slots__ = ('call_stack', 'node', 'remaining')

    MATCH = "MATCH"
    ERROR = "ERROR"
    FAIL = "FAIL"

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    def __init__(self, call_stack: List['Parser'], node: Node, remaining: int) -> None:
        self.call_stack = call_stack    # type: List['Parser']
        self.node = node                # type: Node
        self.remaining = remaining      # type: int
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    def err_msg(self) -> str:
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        return self.ERROR + ": " + "; ".join(self.node._errors).replace('\n', '\\')

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    @property
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    def stack(self) -> str:
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        return "->".join((repr(p) if p.ptype == ':RegExp' else p.name or p.ptype)
                         for p in self.call_stack)
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    @property
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    def status(self) -> str:
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        return self.FAIL if self.node is None else \
            self.err_msg() if self.node._errors else self.MATCH
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    @property
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    def extent(self) -> slice:
        return (slice(-self.remaining - self.node.len, -self.remaining) if self.node
                else slice(-self.remaining, None))
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def add_parser_guard(parser_func):
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    """
    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.
    """
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    def guarded_call(parser: 'Parser', text: str) -> Tuple[Node, str]:
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        try:
            location = len(text)
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            grammar = parser.grammar  # grammar may be 'None' for unconnected parsers!

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            if not grammar.moving_forward__:
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                # rollback variable changes from discarded parser passes
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                if grammar.last_rb__loc__ <= location:
                    grammar.rollback_to__(location)
                grammar.moving_forward__ = True
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                grammar.left_recursion_encountered__ = False
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            if grammar.history_tracking__:
                grammar.call_stack__.append(parser)
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            # if location has already been visited by the current parser,
            # return saved result
            if location in parser.visited:
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                return parser.visited[location]
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            # break left recursion at the maximum allowed depth
            if parser.recursion_counter.setdefault(location, 0) > LEFT_RECURSION_DEPTH:
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                grammar.left_recursion_encountered__ = True
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                return None, text

            parser.recursion_counter[location] += 1

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

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            if node is None:
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                # retrieve an earlier match result (from left recursion)
                # if it exists
                node, rest = parser.visited.get(location, (None, rest))
                # 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!
                if node is None and not grammar.left_recursion_encountered__:
                    # ortherwise also cache None-results
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                    parser.visited[location] = None, rest
            else:
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                # variable manipulating parsers will be excluded, though,
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                # because caching would interfere with changes of variable state
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                if grammar.last_rb__loc__ > location:
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                    # in case of left recursion, the first recursive step that
                    # matches will store its result in the cache
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                    parser.visited[location] = (node, rest)
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                grammar.last_node__ = node   # store last node for Lookbehind parser
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            parser.recursion_counter[location] -= 1

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            if grammar.history_tracking__:
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                # don't track returning parsers except in case an error has occurred
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                if grammar.moving_forward__ or (node and node._errors):
                    record = HistoryRecord(grammar.call_stack__.copy(), node, len(rest))
                    grammar.history__.append(record)
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                    # print(record.stack, record.status, rest[:20].replace('\n', '|'))
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                grammar.call_stack__.pop()
            grammar.moving_forward__ = False
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        except RecursionError:
            node = Node(None, text[:min(10, max(1, text.find("\n")))] + " ...")
            node.add_error("maximum recursion depth of parser reached; "
                           "potentially due to too many errors!")
            rest = ''

        return node, rest

    return guarded_call


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class ParserMetaClass(abc.ABCMeta):
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    """
    ParserMetaClass adds a wrapper to the __call__ method of parser
    objects during initialization that takes care of memoizing,
    left recursion and tracing.
    """
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    def __init__(cls, name, bases, attrs):
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        guarded_parser_call = add_parser_guard(cls.__call__)
        # The following check is necessary for classes that don't override
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        # the __call__() method, because in these cases the non-overridden
        # __call__()-method would be substituted a second time!
        if cls.__call__.__code__ != guarded_parser_call.__code__:
            cls.__call__ = guarded_parser_call
        super(ParserMetaClass, cls).__init__(name, bases, attrs)


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class Parser(ParserBase, metaclass=ParserMetaClass):
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    """
    (Abstract) Base class for Parser combinator parsers. Any parser
    object that is actually used for parsing (i.e. no mock parsers)
    should should be derived from this class.
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    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.
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    """

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

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

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

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    def reset(self):
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        self.visited = dict()            # type: Dict[int, Tuple[Node, str]]
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        self.recursion_counter = dict()  # type: Dict[int, int]
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        self.cycle_detection = set()     # type: Set[Callable]
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        return self
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    def __call__(self, text: str) -> Tuple[Node, str]:
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        return None, text  # default behaviour: don't match

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    def __add__(self, other: 'Parser') -> 'Series':
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        """The + operator generates a series-parser that applies two
        parsers in sequence."""
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        return Series(self, other)
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    def __or__(self, other: 'Parser') -> 'Alternative':
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        """The | operator generates an alternative parser that applies
        the first parser and, if that does not match, the second parser.
        """
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        return Alternative(self, other)

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    @property
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    def grammar(self) -> 'Grammar':
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        return self._grammar

    @grammar.setter
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    def grammar(self, grammar: 'Grammar'):
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        assert self._grammar is None or self._grammar == grammar, \
            "Parser has already been assigned to a Grammar object!"
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        self._grammar = grammar
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        self._grammar_assigned_notifier()

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

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    def apply(self, func: ApplyFunc):
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        """
        Applies function `func(parser)` recursively to this parser and all
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        descendants of the tree of parsers. The same function can never
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        be applied twice between calls of the ``reset()``-method!
        """
        if func in self.cycle_detection:
            return False
        else:
            self.cycle_detection.add(func)
            func(self)
            return True


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def mixin_comment(whitespace: str, comment: str) -> str:
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    """
    Returns a regular expression that merges comment and whitespace
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    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


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class Grammar:
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    """
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    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 instantian of a grammar:

        >>> number = RE('\d+') + RE('\.') + RE('\d+') | RE('\d+')
        >>> number_parser = Grammar(number)
        >>> number_parser("3.1416").show()
        '3.1416'

    Collecting the parsers that define a grammar in a descentand 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.

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

            # parsers
            expression = Forward()
            INTEGER = RE('\\d+')
            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,
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    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.
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    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 objects contain a few special fields for implicit
    whitespace and comments that should be overwritten, if the defaults
    (no comments, horizontal right aligned whitespace) don't fit:
    COMMENT__   - regular expression string for matching comments
    wspL__      - regular expression string for left aligned whitespace
    wspR__      - regular expression string for right aligned whitespace
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    root__      - the root parser of the grammar
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    """

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    root__ = None  # type: Union[Parser, None]
    # root__ must be overwritten with the root-parser by grammar subclass
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    parser_initialization__ = "pending"  # type: str
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    # some default values
    COMMENT__ = r''  # r'#.*(?:\n|$)'
    WSP__ = mixin_comment(whitespace=r'[\t ]*', comment=COMMENT__)
    wspL__ = ''
    wspR__ = WSP__
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    @classmethod
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    def _assign_parser_names__(cls):
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        """
        Initializes the `parser.name` fields of those
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        Parser objects that are directly assigned to a class field with
        the field's name, e.g.
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            class Grammar(Grammar):
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                ...
                symbol = RE('(?!\\d)\\w+')
        After the call of this method symbol.name == "symbol"
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        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 ``toolkit.sane_parser_name()``
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        This is done only once, upon the first instantiation of the
        grammar class!

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

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    def __init__(self, root: Parser=None) -> None:
        # if not hasattr(self.__class__, 'parser_initialization__'):
        #     self.__class__.parser_initialization__ = "pending"
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        # if not hasattr(self.__class__, 'wspL__'):
        #     self.wspL__ = ''
        # if not hasattr(self.__class__, 'wspR__'):
        #     self.wspR__ = ''
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        self.all_parsers__ = set()  # type: Set[Parser]
        self.dirty_flag__ = False
        self.history_tracking__ = False
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        self._reset__()
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        # prepare parsers in the class, first
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        self._assign_parser_names__()
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        # 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.
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        self.root__ = root if root else copy.deepcopy(self.__class__.root__)
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        if self.wspL__:
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            self.wsp_left_parser__ = Whitespace(self.wspL__)  # type: ParserBase
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            self.wsp_left_parser__.grammar = self
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            self.all_parsers__.add(self.wsp_left_parser__)  # don't you forget about me...
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        else:
            self.wsp_left_parser__ = ZOMBIE_PARSER
        if self.wspR__:
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            self.wsp_right_parser__ = Whitespace(self.wspR__)  # type: ParserBase
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            self.wsp_right_parser__.grammar = self
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            self.all_parsers__.add(self.wsp_right_parser__)  # don't you forget about me...
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        else:
            self.wsp_right_parser__ = ZOMBIE_PARSER
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        self.root__.apply(self._add_parser__)
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    def __getitem__(self, key):
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        try:
            return self.__dict__[key]
        except KeyError:
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            parser_template = getattr(self, key, None)
            if parser_template:
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                # add parser to grammar object on the fly...
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                parser = copy.deepcopy(parser_template)
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                parser.apply(self._add_parser__)
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                # assert self[key] == parser
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                return self[key]
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            raise KeyError('Unknown parser "%s" !' % key)
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    def _reset__(self):
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        self.document__ = ""          # type: str
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        # variables stored and recalled by Capture and Retrieve parsers
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        self.variables__ = dict()     # type: Dict[str, List[str]]
        self.rollback__ = []          # type: List[Tuple[int, Callable]]
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        self.last_rb__loc__ = -1  # type: int
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        # previously parsed node, needed by Lookbehind parser
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        self.last_node__ = None       # type: Node
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        # support for call stack tracing
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        self.call_stack__ = []        # type: List[Parser]
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        # snapshots of call stacks
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        self.history__ = []           # type: List[HistoryRecord]
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        # also needed for call stack tracing
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        self.moving_forward__ = True  # type: bool
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        self.left_recursion_encountered__ = False  # type: bool
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    def _add_parser__(self, parser: Parser) -> None:
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        """
        Adds the particular copy of the parser object to this
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        particular instance of Grammar.
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        """
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        if parser.name:
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            # 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__), \
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                ('Cannot add parser "%s" because a field with the same name '
                 'already exists in grammar object!' % parser.name)
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            setattr(self, parser.name, parser)
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        self.all_parsers__.add(parser)
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        parser.grammar = self

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    def __call__(self, document: str, start_parser="root__") -> Node:
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        """
        Parses a document with with parser-combinators.
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        Args:
            document (str): The source text to be parsed.
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            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.)
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        Returns:
            Node: The root node ot the parse tree.
        """
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        # assert isinstance(document, str), type(document)
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        if self.root__ is None:
            raise NotImplementedError()
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        if self.dirty_flag__:
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            self._reset__()
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            for parser in self.all_parsers__:
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                parser.reset()
        else:
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            self.dirty_flag__ = True
        self.history_tracking__ = is_logging()
        self.document__ = document
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        self.last_rb__loc__ = len(document) + 1  # rollback location
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        parser = self[start_parser] if isinstance(start_parser, str) else start_parser
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        assert parser.grammar == self, "Cannot run parsers from a different grammar object!" \
                                       " %s vs. %s" % (str(self), str(parser.grammar))
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        stitches = []  # type: List[Node]
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        rest = document
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        if not rest:
            result, ignore = parser(rest)
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        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?"
                else:
                    stitches.append(result)
                    error_msg = "Parser stopped before end" + \
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                                (("! trying to recover" +
                                  (" but stopping history recording at this point."
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                                   if self.history_tracking__ else "..."))
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                                 if len(stitches) < MAX_DROPOUTS
                                 else " too often! Terminating parser.")
                stitches.append(Node(None, skip))
                stitches[-1].add_error(error_msg)
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                if self.history_tracking__:
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                    # some parsers may have matched and left history records with nodes != None.
                    # Because these are not connected to the stiched 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
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                    for record in self.history__:
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                        if record.node and record.node._pos < 0:
                            record.node.pos = 0
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                    record = HistoryRecord(self.call_stack__.copy(), stitches[-1], len(rest))
                    self.history__.append(record)
                    self.history_tracking__ = False
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        if stitches:
            if rest:
                stitches.append(Node(None, rest))
            result = Node(None, tuple(stitches))
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        if any(self.variables__.values()):
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            result.add_error("Capture-retrieve-stack not empty after end of parsing: "
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                             + str(self.variables__))
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        result.pos = 0  # calculate all positions
        return result

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    def push_rollback__(self, location, func):
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        """
        Adds a rollback function that either removes or re-adds
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        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.
        """
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        self.rollback__.append((location, func))
        self.last_rb__loc__ = location

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

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    def log_parsing_history__(self, log_file_name: str = '') -> None:
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        """
        Writes a log of the parsing history of the most recently parsed
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        document. 
        """
        def prepare_line(record):
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            excerpt = self.document__.__getitem__(record.extent)[:25].replace('\n', '\\n')
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            excerpt = "'%s'" % excerpt if len(excerpt) < 25 else "'%s...'" % excerpt
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            return record.stack, record.status, excerpt
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        def write_log(history, log_name):
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            path = os.path.join(log_dir(), log_name + "_parser.log")
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            if history:
                with open(path, "w", encoding="utf-8") as f:
                    f.write("\n".join(history))
            elif os.path.exists(path):
                os.remove(path)

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        if not log_file_name:
            name = self.__class__.__name__
            log_file_name = name[:-7] if name.lower().endswith('grammar') else name
        full_history, match_history, errors_only = [], [], []
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        for record in self.history__:
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            line = ";  ".join(prepare_line(record))
            full_history.append(line)
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            if record.node and record.node.parser.ptype != WHITESPACE_PTYPE:
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                match_history.append(line)
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                if record.node.error_flag:
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                    errors_only.append(line)
        write_log(full_history, log_file_name + '_full')
        write_log(match_history, log_file_name + '_match')
        write_log(errors_only, log_file_name + '_errors')
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def dsl_error_msg(parser: Parser, error_str: str) -> str:
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    """
    Returns an error message for errors in the parser configuration,
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    e.g. errors that result in infinite loops.

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


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


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RX_PREPROCESSOR_TOKEN = re.compile('\w+')
BEGIN_TOKEN = '\x1b'
END_TOKEN = '\x1c'
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def make_token(token: str, argument: str = '') -> str:
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    """
    Turns the ``token`` and ``argument`` into a special token that
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    will be caught by the `PreprocessorToken`-parser.
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    This function is a support function that should be used by
    preprocessors to inject preprocessor tokens into the source text.
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    """
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    assert RX_PREPROCESSOR_TOKEN.match(token)
    assert argument.find(BEGIN_TOKEN) < 0
    assert argument.find(END_TOKEN) < 0
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    return BEGIN_TOKEN + token + argument + END_TOKEN
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def nil_preprocessor(text: str) -> str:
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    return text
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class PreprocessorToken(Parser):
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    """
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    Parses tokens that have been inserted by a preprocessor.
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    Preprocessors can generate Tokens with the ``make_token``-function.
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    These tokens start and end with magic characters that can only be
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    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.
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    """
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    def __init__(self, token: str) -> None:
        assert token and token.isupper()
        assert RX_PREPROCESSOR_TOKEN.match(token)
        super(PreprocessorToken, self).__init__(token)
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    def __call__(self, text: str) -> Tuple[Node, str]:
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        if text[0:1] == BEGIN_TOKEN:
            end = text.find(END_TOKEN, 1)
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            if end < 0:
                node = Node(self, '').add_error(
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                    'END_TOKEN delimiter missing from preprocessor token. '
                    '(Most likely due to a preprocessor bug!)')  # type: Node
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                return node, text[1:]
            elif end == 0:
                node = Node(self, '').add_error(
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                    'Preprocessor-token cannot have zero length. '
                    '(Most likely due to a preprocessor bug!)')
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                return node, text[2:]
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            elif text.find(BEGIN_TOKEN, 1, end) >= 0:
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                node = Node(self, text[len(self.name) + 1:end])
                node.add_error(
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                    'Preprocessor-tokens must not be nested or contain '
                    'BEGIN_TOKEN delimiter as part of their argument. '
                    '(Most likely due to a preprocessor bug!)')
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                return node, text[end:]
            if text[1:len(self.name) + 1] == self.name:
                return Node(self, text[len(self.name) + 1:end]), \
                       text[end + 1:]
        return None, text


class RegExp(Parser):
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    """
    Regular expression parser.
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    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.
    """
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    def __init__(self, regexp, name: str = '') -> None:
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        super(RegExp, self).__init__(name)
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        self.regexp = re.compile(regexp) if isinstance(regexp, str) else regexp

    def __deepcopy__(self, memo):
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        # `regex` supports deep copies, but not `re`
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        try:
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            regexp = copy.deepcopy(self.regexp, memo)
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        except TypeError:
            regexp = self.regexp.pattern
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        return RegExp(regexp, self.name)
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    def __call__(self, text: str) -> Tuple[Node, str]:
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        match = text[0:1] != BEGIN_TOKEN and self.regexp.match(text)  # ESC starts a preprocessor token.
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        if match:
            end = match.end()
            return Node(self, text[:end]), text[end:]
        return None, text

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    def __repr__(self):
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        return '/%s/' % self.regexp.pattern
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class Whitespace(RegExp):
    assert WHITESPACE_PTYPE == ":Whitespace"
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class RE(Parser):
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    """
    Regular Expressions with optional leading or trailing whitespace.
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    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.
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    """
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    def __init__(self, regexp, wL=None, wR=None, name=''):
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        """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.
        """
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        super(RE, self).__init__(name)
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        self.wL = wL
        self.wR = wR
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        self.wspLeft = Whitespace(wL) if wL else ZOMBIE_PARSER
        self.wspRight = Whitespace(wR) if wR else ZOMBIE_PARSER
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        self.main = RegExp(regexp)

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    def __deepcopy__(self, memo={}):
        try:
            regexp = copy.deepcopy(self.main.regexp, memo)
        except TypeError:
            regexp = self.main.regexp.pattern
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        return self.__class__(regexp, self.wL, self.wR, self.name)
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    def __call__(self, text: str) -> Tuple[Node, str]:
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        # assert self.main.regexp.pattern != "@"
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        t = text    # type: str
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        wL, t = self.wspLeft(t)
        main, t = self.main(t)
        if main:
            wR, t = self.wspRight(t)
            result = tuple(nd for nd in (wL, main, wR)
                           if nd and nd.result != '')
            return Node(self, result), t
        return None, text

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    def __repr__(self):
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        wL = '~' if self.wspLeft != ZOMBIE_PARSER else ''
        wR = '~' if self.wspRight != ZOMBIE_PARSER else ''
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        return wL + '/%s/' % self.main.regexp.pattern + wR
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    def _grammar_assigned_notifier(self):
        if self.grammar:
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            # use default whitespace parsers if not otherwise specified
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            if self.wL is None:
                self.wspLeft = self.grammar.wsp_left_parser__
            if self.wR is None:
                self.wspRight = self.grammar.wsp_right_parser__

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    def apply(self, func: Parser.ApplyFunc):
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        if super(RE, self).apply(func):
            if self.wL:
                self.wspLeft.apply(func)
            if self.wR:
                self.wspRight.apply(func)
            self.main.apply(func)


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class Token(RE):
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    """
    Class Token parses simple strings. Any regular regular
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    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.
    """
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    assert TOKEN_PTYPE == ":Token"

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

    def __deepcopy__(self, memo={}):
        return self.__class__(self.token, self.wL, self.wR, self.name)
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    def __repr__(self):
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        return '"%s"' % self.token if self.token.find('"') < 0 else "'%s'" % self.token
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########################################################################
#
# Combinator parser classes (i.e. trunk classes of the parser tree)
#
########################################################################


class UnaryOperator(Parser):
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    """
    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.
    """
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    def __init__(self, parser: Parser, name: str = '') -> None:
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        super(UnaryOperator, self).__init__(name)
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        # assert isinstance(parser, Parser)
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        self.parser = parser  # type: Parser
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    def __deepcopy__(self, memo):
        parser = copy.deepcopy(self.parser, memo)
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        return self.__class__(parser, self.name)
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    def apply(self, func: Parser.ApplyFunc):
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        if super(UnaryOperator, self).apply(func):
            self.parser.apply(func)


class NaryOperator(Parser):
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    """
    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.
    """
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    def __init__(self, *parsers: Parser, name: str = '') -> None:
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        super(NaryOperator, self).__init__(name)
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        # assert all([isinstance(parser, Parser) for parser in parsers]), str(parsers)
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        self.parsers = parsers  # type: Tuple[Parser, ...]
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    def __deepcopy__(self, memo):
        parsers = copy.deepcopy(self.parsers, memo)
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        return self.__class__(*parsers, name=self.name)
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    def apply(self, func: Parser.ApplyFunc):
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        if super(NaryOperator, self).apply(func):
            for parser in self.parsers:
                parser.apply(func)


class Optional(UnaryOperator):
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    def __init__(self, parser: Parser, name: str = '') -> None:
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        super(Optional, self).__init__(parser, name)
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        # assert isinstance(parser, Parser)
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        assert not isinstance(parser, Optional), \
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            "Redundant nesting of options: %s(%s)" % \
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            (str(name), str(parser.name))
        assert not isinstance(parser, Required), \
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            "Nesting options with required elements is contradictory: " \
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            "%s(%s)" % (str(name), str(parser.name))

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

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