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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _apply_query(self, query, document):
 """ Applies a query to a document. Returns True if the document meets the criteria of the supplied query. The ``query`` argument generally follows mongodb style syntax and consists of the following logical checks and operators. Logical: $and, $or, $nor, $not Operators: $eq, $ne, $gt, $gte, $lt, $lte, $mod, $in, $nin, $all If no logical operator is supplied, it assumed that all field checks must pass. For example, these are equivalent: {'foo': 'bar', 'baz': 'qux'} {'$and': [{'foo': 'bar'}, {'baz': 'qux'}]} Both logical and operational queries can be nested in a complex fashion: { 'bar': 'baz', '$or': [ { 'foo': { '$gte': 0, '$lte': 10, '$mod': [2, 0] } }, { 'foo': { '$gt': 10, '$mod': [2, 1] } }, ] } In the previous example, this will return any document where the 'bar' key is equal to 'baz' and either the 'foo' key is an even number between 0 and 10 or is an odd number greater than 10. """

        matches = []  # A list of booleans
        reapply = lambda q: self._apply_query(q, document)

        for field, value in query.items():
            # A more complex query type $and, $or, etc
            if field == '$and':
                matches.append(all(map(reapply, value)))
            elif field == '$or':
                matches.append(any(map(reapply, value)))
            elif field == '$nor':
                matches.append(not any(map(reapply, value)))
            elif field == '$not':
                matches.append(not self._apply_query(value, document))

            # Invoke a query operator
            elif isinstance(value, dict):
                for operator, arg in value.items():
                    if not self._get_operator_fn(operator)(field, arg, document):
                        matches.append(False)
                        break
                else:
                    matches.append(True)

            # Standard
            elif value != document.get(field, None):
                # check if field contains a dot
                if '.' in field:
                    nodes = field.split('.')
                    document_section = document

                    try:
                        for path in nodes[:-1]:
                            document_section = document_section.get(path, None)
                    except AttributeError:
                        document_section = None

                    if document_section is None:
                        matches.append(False)
                    else:
                        if value != document_section.get(nodes[-1], None):
                            matches.append(False)
                else:
                    matches.append(False)

        return all(matches)