parsers.py 50 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.

Juancarlo Añez: grako, a PEG parser generator in Python,
https://bitbucket.org/apalala/grako
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"""

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import abc
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import copy
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, Collection, cast, Dict, Iterator, List, Set, Tuple, Union
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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__ = ['ScannerFunc',
           'HistoryRecord',
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           'Parser',
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           'Grammar',
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           'RX_SCANNER_TOKEN',
           'BEGIN_SCANNER_TOKEN',
           'END_SCANNER_TOKEN',
           'make_token',
           'nil_scanner',
           'ScannerToken',
           '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
#
########################################################################


ScannerFunc = Union[Callable[[str], str], partial]


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LEFT_RECURSION_DEPTH = 10  # because of pythons recursion depth limit, this
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                           # value ought not to be set too high
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MAX_DROPOUTS = 25  # stop trying to recover parsing after so many errors


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(str(parser) for parser in self.call_stack)

    @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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    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__:
                # rollback variable changes for discarded branch of parsing tree
                while grammar.rollback__ and grammar.rollback__[-1][0] <= location:
                    grammar.rollback__[-1][1]()
                    grammar.rollback__.pop()
            grammar.moving_forward__ = True

            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:
                return parser.visited[location]
            # break left recursion at the maximum allowed depth
            if parser.recursion_counter.setdefault(location, 0) > LEFT_RECURSION_DEPTH:
                return None, text

            parser.recursion_counter[location] += 1

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

            if node is not None:
                # in case of a recursive call saves the result of the first
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                # (or left-most) call that matches; but not for variable manipulating parsers,
                # because caching would interfere with changes of variable state
                if not (grammar.rollback__ and grammar.rollback__[-1][0] <= location):
                    parser.visited[location] = (node, rest)
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                grammar.last_node__ = node   # store last node for Lookbehind operator
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            elif location in parser.visited:
                # if parser did non match but a saved result exits, assume
                # left recursion and use the saved result
                node, rest = parser.visited[location]

            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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    def __init__(cls, name, bases, attrs):
        # The following condition 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!
        guarded_parser_call = add_parser_guard(cls.__call__)
        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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    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):
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        return Series(self, other)
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    def __or__(self, other):
        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'):
        self._grammar = grammar
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        self._grammar_assigned_notifier()

    def _grammar_assigned_notifier(self):
        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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class Grammar:
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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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    @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.
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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
        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.
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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
        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)
                parser.apply(self._add_parser)
                # 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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        # 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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    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.

        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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        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 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
        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:
    """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 aparent.
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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)
#
########################################################################


RX_SCANNER_TOKEN = re.compile('\w+')
BEGIN_SCANNER_TOKEN = '\x1b'
END_SCANNER_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
    will be caught by the `ScannerToken`-parser.

    This function is a support function that should be used by scanners
    to inject scanner tokens into the source text.
    """
    assert RX_SCANNER_TOKEN.match(token)
    assert argument.find(BEGIN_SCANNER_TOKEN) < 0
    assert argument.find(END_SCANNER_TOKEN) < 0

    return BEGIN_SCANNER_TOKEN + token + argument + END_SCANNER_TOKEN


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def nil_scanner(text: str) -> str:
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    return text
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class ScannerToken(Parser):
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    """
    Parses tokens that have been inserted by a Scanner.
    
    Scanners can generate Tokens with the ``make_token``-function.
    These tokens start and end with magic characters that can only be
    matched by the ScannerToken Parser. Scanner tokens can be used to
    insert BEGIN - END delimiters at the beginning or ending of an 
    indented block. Otherwise indented block are difficult to handle 
    with parsing expression grammars.
    """
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    def __init__(self, scanner_token: str) -> None:
        assert scanner_token and scanner_token.isupper()
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        assert RX_SCANNER_TOKEN.match(scanner_token)
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        super(ScannerToken, self).__init__(scanner_token)
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    def __call__(self, text: str) -> Tuple[Node, str]:
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        if text[0:1] == BEGIN_SCANNER_TOKEN:
            end = text.find(END_SCANNER_TOKEN, 1)
            if end < 0:
                node = Node(self, '').add_error(
                    'END_SCANNER_TOKEN delimiter missing from scanner token. '
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                    '(Most likely due to a scanner bug!)')  # type: Node
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                return node, text[1:]
            elif end == 0:
                node = Node(self, '').add_error(
                    'Scanner token cannot have zero length. '
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                    '(Most likely due to a scanner bug!)')  # type: Node
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                return node, text[2:]
            elif text.find(BEGIN_SCANNER_TOKEN, 1, end) >= 0:
                node = Node(self, text[len(self.name) + 1:end])
                node.add_error(
                    'Scanner tokens must not be nested or contain '
                    'BEGIN_SCANNER_TOKEN delimiter as part of their argument. '
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                    '(Most likely due to a scanner bug!)')  # type: Node
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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_SCANNER_TOKEN and self.regexp.match(text)  # ESC starts a scanner token.
        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):
    """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.wL else ''
        wR = '~' if self.wR else ''
        return wL + '/%s/' % self.main.regexp.pattern + wR
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    # def __str__(self):
    #     if self.ptype == TOKEN_PTYPE:
    #         return 'Token "%s"' % self.main.regexp.pattern.replace('\\', '')
    #     return self.name or ('RE ' + ('~' if self.wL else '')
    #                          + '/%s/' % self.main.regexp.pattern + ('~' if self.wR else ''))
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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
    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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def mixin_comment(whitespace: str, comment: str) -> str:
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    """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).
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    """
    wspc = '(?:' + whitespace + '(?:' + comment + whitespace + ')*)'
    return wspc


########################################################################
#
# Combinator parser classes (i.e. trunk classes of the parser tree)
#
########################################################################


class UnaryOperator(Parser):
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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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    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)


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class Synonym(UnaryOperator):
    """Simply calls another parser and encapsulates the result in
    another node if that parser matches.

    This parser is needed to support synonyms in EBNF, e.g.
        jahr       = JAHRESZAHL
        JAHRESZAHL = /\d\d\d\d/
    Otherwise the first line could not be represented by any parser
    class, in which case it would be unclear whether the parser
    RE('\d\d\d\d') carries the name 'JAHRESZAHL' or 'jahr'
    """
    def __call__(self, text: str) -> Tuple[Node, str]:
        node, text = self.parser(text)
        if node:
            return Node(self, node), text
        return None, text

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    def __repr__(self):
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        return self.name or self.parser.repr
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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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    def __repr__(self):
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        return '[' + (self.parser.repr[1:-1] if isinstance(self.parser, Alternative)
                      and not self.parser.name else self.parser.repr) + ']'
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class ZeroOrMore(Optional):
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    def __call__(self, text: str) -> Tuple[Node, str]:
        results = ()  # type: Tuple[Node, ...]
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        n = len(text) + 1
        while text and len(text) < n:
            n = len(text)
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            node, text = self.parser(text)
            if not node:
                break
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            if len(text) == n:
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                node.add_error(dsl_error_msg(self, 'Infinite Loop detected.'))
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            results += (node,)
        return Node(self, results), text

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    def __repr__(self):
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        return '{' + (self.parser.repr[1:-1] if isinstance(self.parser, Alternative)
                      and not self.parser.name else self.parser.repr) + '}'
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class OneOrMore(UnaryOperator):
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    def __init__(self, parser: Parser, name: str = '') -> None:
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        super(OneOrMore, self).__init__(parser, name)
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        assert not isinstance(parser, Optional), \
            "Use ZeroOrMore instead of nesting OneOrMore and Optional: " \
            "%s(%s)" % (str(name), str(parser.name))

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    def __call__(self, text: str) -> Tuple[Node, str]:
        results = ()  # type: Tuple[Node, ...]
        text_ = text  # type: str
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        n = len(text) + 1
        while text_ and len(text_) < n:
            n = len(text_)
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            node, text_ = self.parser(text_)
            if not node:
                break
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            if len(text_) == n:
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                node.add_error(dsl_error_msg(self, 'Infinite Loop detected.'))
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            results += (node,)
        if results == ():
            return None, text
        return Node(self, results), text_

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    def __repr__(self):
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        return '{' + (self.parser.repr[1:-1] if isinstance(self.parser, Alternative)
                      and not self.parser.name else self.parser.repr) + '}+'
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class Series(NaryOperator):
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    def __init__(self, *parsers: Parser, name: str = '') -> None:
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        super(Series, self).__init__(*parsers, name=name)
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        assert len(self.parsers) >= 1

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    def __call__(self, text: str) -> Tuple[Node, str]:
        results = ()  # type: Tuple[Node, ...]
        text_ = text  # type: str
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        for parser in self.parsers:
            node, text_ = parser(text_)
            if not node:
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                return None, text
            results += (node,)
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            if node.error_flag:
                break
        assert len(results) <= len(self.parsers)
        return Node(self, results), text_

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    def __repr__(self):
        return " ".join(parser.repr for parser in self.parsers)

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    def __add__(self, other: Parser) -> 'Series':
        other_parsers = cast('Series', other).parsers if isinstance(other, Series) else (other,)
        return Series(*(self.parsers + other_parsers))
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    def __radd__(self, other: Parser) -> 'Series':
        other_parsers = cast('Series', other).parsers if isinstance(other, Series) else (other,)
        return Series(*(other_parsers + self.parsers))
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    def __iadd__(self, other):
        other_parsers = cast('Series', other).parsers if isinstance(other, Series) else (other,)
        self.parsers += other_parsers
        return self
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class Alternative(NaryOperator):
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    """Matches if at least 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.

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    # the order of the sub-expression matters!
    >>> number = RE('\d+') | RE('\d+') + RE('\.') + RE('\d+')
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    >>> Grammar(number)("3.1416").show()
    '3 <<< Error on ".1416" | Parser stopped before end! trying to recover... >>> '
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    # the most selective expression should be put first:
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    >>> number = RE('\d+') + RE('\.') + RE('\d+') | RE('\d+')
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    >>> Grammar(number)("3.1416").show()
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    '3.1416'
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    """
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    def __init__(self, *parsers: Parser, name: str = '') -> None:
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        super(Alternative, self).__init__(*parsers, name=name)
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        assert len(self.parsers) >= 1
        assert all(not isinstance(p, Optional) for p in self.parsers)

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    def __call__(self, text: str) -> Tuple[Node, str]:
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        for parser in self.parsers:
            node, text_ = parser(text)
            if node:
                return Node(self, node), text_
        return None, text

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    def __repr__(self):
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        return '(' + ' | '.join(parser.repr for parser in self.parsers) + ')'
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    def __or__(self, other: Parser) -> 'Alternative':
        other_parsers = cast('Alternative', other).parsers \
                        if isinstance(other, Alternative) else (other,)
        return Alternative(*(self.parsers + other_parsers))
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    def __ror__(self, other: Parser) -> 'Alternative':
        other_parsers = cast('Alternative', other).parsers \
                        if isinstance(other, Alternative) else (other,)
        return Alternative(*(other_parsers + self.parsers))
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    def __ior__(self, other):
        other_parsers = cast('Alternative', other.parsers) \
                        if isinstance(other, Alternative) else (other,)
        self.parsers += other_parsers
        return self
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########################################################################
#
# Flow control operators
#
########################################################################


class FlowOperator(UnaryOperator):
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    def __init__(self, parser: Parser, name: str = '') -> None:
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        super(FlowOperator, self).__init__(parser, name)
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class Required(FlowOperator):
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    # Add constructor that checks for logical errors, like `Required(Optional(...))` constructs ?
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    def __call__(self, text: str) -> Tuple[Node, str]:
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        node, text_ = self.parser(text)
        if not node:
            m = re.search(r'\s(\S)', text)
            i = max(1, m.regs[1][0]) if m else 1
            node = Node(self, text[:i])
            text_ = text[i:]
            # assert False, "*"+text[:i]+"*"
            node.add_error('%s expected; "%s..." found!' %
                           (str(self.parser), text[:10]))
        return node, text_

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    def __repr__(self):
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        return '§' + self.parser.repr
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class Lookahead(FlowOperator):
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    def __init__(self, parser: Parser, name: str = '') -> None:
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        super(Lookahead, self).__init__(parser, name)
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    def __call__(self, text: str) -> Tuple[Node, str]:
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        node, text_ = self.parser(text)
        if self.sign(node is not None):
            return Node(self, ''), text
        else:
            return None, text

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    def __repr__(self):
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    def sign(self, bool_value) -> bool:
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        return bool_value


class NegativeLookahead(Lookahead):
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    def __repr__(self):
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        return '!' + self.parser.repr
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    def sign(self, bool_value) -> bool:
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        return not bool_value


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def iter_right_branch(node) -> Iterator[Node]:
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    """
    Iterates over the right branch of `node` starting with node itself.
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    Iteration is stopped if either there are no child nodes any more or
    if the parser of a node is a Lookahead parser. (Reason is: Since
    lookahead nodes do not advance the parser, it does not make sense
    to look back to them.)
    """
    while node and not isinstance(node.parser, Lookahead):  # the second condition should not be necessary
        yield node  # for well-formed EBNF code
        node = node.children[-1] if node.children else None


class Lookbehind(FlowOperator):