""" Classes for representing hierarchical language structures, such as syntax
trees and morphological trees. This is an adaptation of the original tree.py
file from NLTK. Removed: probabilistic trees, binarization, tree drawing,
reading off CFG productions, &c. """
# Original notice:
# Natural Language Toolkit: Text Trees
#
# Copyright (C) 2001-2010 NLTK Project
# Author: Edward Loper <edloper@gradient.cis.upenn.edu>
#         Steven Bird <sb@csse.unimelb.edu.au>
#         Nathan Bodenstab <bodenstab@cslu.ogi.edu> (tree transforms)
# URL: <http://www.nltk.org/>
# For license information, see LICENSE.TXT
from __future__ import division, print_function, unicode_literals
import re
import sys
if sys.version[0] >= '3':
	basestring = str  # pylint: disable=W0622,C0103
 
 
class Tree(list):
	""" A hierarchical structure. Each Tree represents a single hierarchical
	grouping of leaves and subtrees. For example, each constituent in a syntax
	tree is represented by a single Tree.
	A tree's children are encoded as a list of leaves and subtrees, where a
	leaf is a basic (non-tree) value; and a subtree is a nested Tree.
	Any other properties that a Tree defines are known as node properties, and
	are used to add information about individual hierarchical groupings. For
	example, syntax trees use a label property to label syntactic constituents
	with phrase tags, such as "NP" and "VP".
	Several Tree methods use tree positions to specify children or descendants
	of a tree. Tree positions are defined as follows:
 
	- The tree position ``i`` specifies a Tree's ith child.
	- The tree position () specifies the Tree itself.
	- If ``p`` is the tree position of descendant d, then
		``p + (i,)`` specifies the ith child of d.
 
	i.e., every tree position is either a single index ``i``,
	specifying ``self[i]``; or a sequence ``(i1, i2, ..., iN)``,
	specifying ``self[i1][i2]...[iN]``.
 
	The constructor can be called in two ways:
 
	- ``Tree(label, children)`` constructs a new tree with the specified label
		and list of children.
	- ``Tree(s)`` constructs a new tree by parsing the string s. Equivalent to
		calling the class method ``Tree.parse(s)``. """
	def __new__(cls, label_or_str=None, children=None):
		if label_or_str is None:
			return list.__new__(cls)  # used by copy.deepcopy
		if children is None:
			if not isinstance(label_or_str, basestring):
				raise TypeError("%s: Expected a label and child list "
						"or a single string" % cls.__name__)
			return cls.parse(label_or_str)
		if (isinstance(children, basestring) or
				not hasattr(children, '__iter__')):
			raise TypeError("%s() argument 2 should be a list, not a "
					"string" % cls.__name__)
		return list.__new__(cls, label_or_str, children)
 
	def __init__(self, label_or_str, children=None):
		# Because __new__ may delegate to Tree.parse(), the __init__
		# method may end up getting called more than once (once when
		# constructing the return value for Tree.parse; and again when
		# __new__ returns). We therefore check if `children` is None
		# (which will cause __new__ to call Tree.parse()); if so, then
		# __init__ has already been called once, so just return.
		if children is None:
			return
		list.__init__(self, children)
		self.label = label_or_str
		self.source = self.bitset = None
 
	# === Comparison operators ==================================
	def __eq__(self, other):
		if not isinstance(other, Tree):
			return False
		return self.label == other.label and list.__eq__(self, other)
 
	def __ne__(self, other):
		return not (self == other)
 
	def __lt__(self, other):
		if not isinstance(other, Tree):
			return False
		return self.label < other.label or list.__lt__(self, other)
 
	def __le__(self, other):
		if not isinstance(other, Tree):
			return False
		return self.label <= other.label or list.__le__(self, other)
 
	def __gt__(self, other):
		if not isinstance(other, Tree):
			return True
		return self.label > other.label or list.__gt__(self, other)
 
	def __ge__(self, other):
		if not isinstance(other, Tree):
			return False
		return self.label >= other.label or list.__ge__(self, other)
 
	# === Disabled list operations ==============================
	def __mul__(self, _):
		raise TypeError('Tree does not support multiplication')
 
	def __rmul__(self, _):
		raise TypeError('Tree does not support multiplication')
 
	def __add__(self, _):
		raise TypeError('Tree does not support addition')
 
	def __radd__(self, _):
		raise TypeError('Tree does not support addition')
 
	# === Indexing (with support for tree positions) ============
	def __getitem__(self, index):
		if isinstance(index, (int, slice)):
			return list.__getitem__(self, index)
		else:
			if len(index) == 0:
				return self
			elif len(index) == 1:
				return self[int(index[0])]
			return self[int(index[0])][index[1:]]
 
	def __setitem__(self, index, value):
		if isinstance(index, (int, slice)):
			return list.__setitem__(self, index, value)
		else:
			if len(index) == 0:
				raise IndexError('The tree position () may not be '
						'assigned to.')
			elif len(index) == 1:
				self[index[0]] = value
			else:
				self[index[0]][index[1:]] = value
 
	def __delitem__(self, index):
		if isinstance(index, (int, slice)):
			return list.__delitem__(self, index)
		else:
			if len(index) == 0:
				raise IndexError('The tree position () may not be deleted.')
			elif len(index) == 1:
				del self[index[0]]
			else:
				del self[index[0]][index[1:]]
 
	# === Basic tree operations =================================
	def leaves(self):
		""" :returns: list containing this tree's leaves. The order reflects \
		the order of the leaves in the tree's hierarchical structure. """
		leaves = []
		for child in self:
			if isinstance(child, Tree):
				leaves.extend(child.leaves())
			else:
				leaves.append(child)
		return leaves
 
	def height(self):
		"""	:returns: The height of this tree. The height of a tree \
		containing no children is 1; the height of a tree containing only \
		leaves is 2; and the height of any other tree is one plus the maximum \
		of its children's heights. """
		max_child_height = 0
		for child in self:
			if isinstance(child, Tree):
				max_child_height = max(max_child_height, child.height())
			else:
				max_child_height = max(max_child_height, 1)
		return 1 + max_child_height
 
	def treepositions(self, order='preorder'):
		""" :param order: One of preorder, postorder, bothorder, leaves. """
		positions = []
		if order in ('preorder', 'bothorder'):
			positions.append(())
		for i, child in enumerate(self):
			if isinstance(child, Tree):
				childpos = child.treepositions(order)
				positions.extend((i, ) + p for p in childpos)
			else:
				positions.append((i, ))
		if order in ('postorder', 'bothorder'):
			positions.append(())
		return positions
 
	def subtrees(self, condition=None):
		""" Generate all the subtrees of this tree, optionally restricted
		to trees matching the condition function. NB: if the condition does not
		match a subtree, its children are still considered.
 
		:param condition: the function to filter all local trees """
		if condition is None or condition(self):
			yield self
		for child in self:
			if isinstance(child, Tree):
				for subtree in child.subtrees(condition):
					yield subtree
 
	def pos(self):
		""" :returns: a list of tuples containing leaves and pre-terminals \
		(part-of-speech tags). The order reflects the order of the leaves in \
		the tree's hierarchical structure. """
		pos = []
		for child in self:
			if isinstance(child, Tree):
				pos.extend(child.pos())
			else:
				pos.append((child, self.label))
		return pos
 
	def leaf_treeposition(self, index):
		""" :returns: The tree position of the index-th leaf in this tree; \
		i.e., if tp=self.leaf_treeposition(i), then self[tp]==self.leaves()[i].
		:raises IndexError: if this tree contains fewer than index+1 leaves, \
		or if index<0. """
		if index < 0:
			raise IndexError('index must be non-negative')
		stack = [(self, ())]
		while stack:
			value, treepos = stack.pop()
			if not isinstance(value, Tree):
				if index == 0:
					return treepos
				else:
					index -= 1
			else:
				for i in range(len(value) - 1, -1, -1):
					stack.append((value[i], treepos + (i, )))
		raise IndexError('index must be less than or equal to len(self)')
 
	def treeposition_spanning_leaves(self, start, end):
		""":returns: The tree position of the lowest descendant of this tree \
		that dominates self.leaves()[start:end].
		:raises ValueError: if end <= start """
		if end <= start:
			raise ValueError('end must be greater than start')
		# Find the tree positions of the start & end leaves,
		# and take the longest common subsequence.
		start_treepos = self.leaf_treeposition(start)
		end_treepos = self.leaf_treeposition(end - 1)
		# Find the first index where they mismatch:
		for i in range(len(start_treepos)):
			if i == len(end_treepos) or start_treepos[i] != end_treepos[i]:
				return start_treepos[:i]
		return start_treepos
 
	# === Convert, copy =========================================
	@classmethod
	def convert(cls, val):
		""" Convert a tree between different subtypes of Tree.
 
		:param cls: the class that will be used for the new tree.
		:param val: The tree that should be converted. """
		if isinstance(val, Tree):
			children = [cls.convert(child) for child in val]
			return cls(val.label, children)
		return val
 
	def copy(self, deep=False):
		""" Create a copy of this tree. """
		if not deep:
			return self.__class__(self.label, self)
		return self.__class__.convert(self)
 
	def _frozen_class(self):
		""" The frozen version of this class. """
		return ImmutableTree
 
	def freeze(self, leaf_freezer=None):
		""" :returns: an immutable version of this tree. """
		frozen_class = self._frozen_class()
		if leaf_freezer is None:
			newcopy = frozen_class.convert(self)
		else:
			newcopy = self.copy(deep=True)
			for pos in newcopy.treepositions('leaves'):
				newcopy[pos] = leaf_freezer(newcopy[pos])
			newcopy = frozen_class.convert(newcopy)
		hash(newcopy)  # Make sure the leaves are hashable.
		return newcopy
 
	# === Parsing ===============================================
	@classmethod
	def parse(cls, s, brackets='()', parse_label=None, parse_leaf=None,
			label_pattern=None, leaf_pattern=None,
			remove_empty_top_bracketing=False):
		""" Parse a bracketed tree string and return the resulting tree.
		Trees are represented as nested brackettings, such as:
		``(S (NP (NNP John)) (VP (V runs)))``
 
		:param s: The string to parse
		:param brackets: The two bracket characters used to mark the
			beginning and end of trees and subtrees.
		:param parse_label, parse_leaf: If specified, these functions are
			applied to the substrings of s corresponding to labels and leaves
			(respectively) to obtain the values for those labels and leaves.
			They should have the following signature: parse_label(str) -> value
		:param label_pattern, leaf_pattern: Regular expression patterns used to
			find label and leaf substrings in s. By default, both label and
			leaf patterns are defined to match any sequence of non-whitespace
			non-bracket characters.
		:param remove_empty_top_bracketing: If the resulting tree has an empty
			node label, and is length one, then return its single child
			instead. This is useful for treebank trees, which sometimes contain
			an extra level of bracketing.
		:returns: A tree corresponding to the string representation s.
			If this class method is called using a subclass of Tree, then it
			will return a tree of that type. """
		if not isinstance(brackets, basestring) or len(brackets) != 2:
			raise TypeError('brackets must be a length-2 string')
		if re.search(r'\s', brackets):
			raise TypeError('whitespace brackets not allowed')
		# Construct a regexp that will tokenize the string.
		open_b, close_b = brackets
		open_pattern, close_pattern = (re.escape(open_b), re.escape(close_b))
		if label_pattern is None:
			label_pattern = r'[^\s%s%s]+' % (open_pattern, close_pattern)
		if leaf_pattern is None:
			leaf_pattern = r'[^\s%s%s]+' % (open_pattern, close_pattern)
		token_re = re.compile(r'%s\s*(%s)?|%s|(%s)' % (
			open_pattern, label_pattern, close_pattern, leaf_pattern))
		# Walk through each token, updating a stack of trees.
		stack = [(None, [])]  # list of (label, children) tuples
		for match in token_re.finditer(s):
			token = match.group()
			if token[0] == open_b:  # Beginning of a tree/subtree
				if len(stack) == 1 and len(stack[0][1]) > 0:
					cls._parse_error(s, match, 'end-of-string')
				label = token[1:].lstrip()
				if parse_label is not None:
					label = parse_label(label)
				stack.append((label, []))
			elif token == close_b:  # End of a tree/subtree
				if len(stack) == 1:
					if len(stack[0][1]) == 0:
						cls._parse_error(s, match, open_b)
					else:
						cls._parse_error(s, match, 'end-of-string')
				label, children = stack.pop()
				stack[-1][1].append(cls(label, children))
			else:  # Leaf node
				if len(stack) == 1:
					cls._parse_error(s, match, open_b)
				if parse_leaf is not None:
					token = parse_leaf(token)
				stack[-1][1].append(token)
		# check that we got exactly one complete tree.
		if len(stack) > 1:
			cls._parse_error(s, 'end-of-string', close_b)
		elif len(stack[0][1]) == 0:
			cls._parse_error(s, 'end-of-string', open_b)
		else:
			assert stack[0][0] is None and len(stack[0][1]) == 1
		tree = stack[0][1][0]
		# If the tree has an extra level with label='', then get rid of
		# it. E.g.: "((S (NP ...) (VP ...)))"
		if remove_empty_top_bracketing and tree.label == '' and len(tree) == 1:
			tree = tree[0]
		return tree
 
	@classmethod
	def _parse_error(cls, s, match, expecting):
		""" Display a friendly error message when parsing a tree string fails.
 
		:param s: The string we're parsing.
		:param match: regexp match of the problem token.
		:param expecting: what we expected to see instead. """
		# Construct a basic error message
		if match == 'end-of-string':
			pos, token = len(s), 'end-of-string'
		else:
			pos, token = match.start(), match.group()
		msg = '%s.parse(): expected %r but got %r\n%sat index %d.' % (
			cls.__name__, expecting, token, ' ' * 12, pos)
		# Add a display showing the error token itsels:
		s = s.replace('\n', ' ').replace('\t', ' ')
		offset = pos
		if len(s) > pos + 10:
			s = s[:pos + 10] + '...'
		if pos > 10:
			s = '...' + s[pos - 10:]
			offset = 13
		msg += '\n%s"%s"\n%s^' % (' ' * 16, s, ' ' * (17 + offset))
		raise ValueError(msg)
 
	# === String Representation =================================
	def __repr__(self):
		childstr = ", ".join(repr(c) for c in self)
		return '%s(%r, [%s])' % (self.__class__.__name__, self.label, childstr)
 
	def __str__(self):
		return self._pprint_flat('', '()', False)
 
	def pprint(self, margin=70, indent=0, labelsep='', brackets='()',
			quotes=False):
		"""	:returns: A pretty-printed string representation of this tree.
		:param margin: The right margin at which to do line-wrapping.
		:param indent: The indentation level at which printing begins. This
			number is used to decide how far to indent subsequent lines.
		:param labelsep: A string that is used to separate the label from the
			children; e.g., the value ':' gives trees like::
 
				(S: (NP: I) (VP: (V: saw) (NP: it))). """
		# Try writing it on one line.
		s = self._pprint_flat(labelsep, brackets, quotes)
		if len(s) + indent < margin:
			return s
		# If it doesn't fit on one line, then write it on multi-lines.
		if isinstance(self.label, basestring):
			s = '%s%s%s' % (brackets[0], self.label, labelsep)
		else:
			s = '%s%r%s' % (brackets[0], self.label, labelsep)
		for child in self:
			if isinstance(child, Tree):
				s += '\n' + ' ' * (indent + 2) + child.pprint(margin,
						indent + 2, labelsep, brackets, quotes)
			elif isinstance(child, tuple):
				s += '\n' + ' ' * (indent + 2) + '/'.join(child)
			elif isinstance(child, basestring) and not quotes:
				s += '\n' + ' ' * (indent + 2) + '%s' % child
			else:
				s += '\n' + ' ' * (indent + 2) + '%r' % child
		return s + brackets[1]
 
	def _pprint_flat(self, labelsep, brackets, quotes):
		""" pretty-printing helper function. """
		childstrs = []
		for child in self:
			if isinstance(child, Tree):
				childstrs.append(child._pprint_flat(labelsep, brackets, quotes))
			elif isinstance(child, tuple):
				childstrs.append("/".join(child))
			elif isinstance(child, basestring) and not quotes:
				childstrs.append('%s' % child)
			else:
				childstrs.append('%r' % child)
		if isinstance(self.label, basestring):
			return '%s%s%s %s%s' % (brackets[0], self.label, labelsep,
									' '.join(childstrs), brackets[1])
		return '%s%r%s %s%s' % (brackets[0], self.label, labelsep,
								' '.join(childstrs), brackets[1])
 
	def draw(self):
		""" :returns: an ASCII art visualization of tree. """
		from discodop.treedraw import DrawTree
		return DrawTree(self, [str(a) for a in self.leaves()]).text()
 
 
class ImmutableTree(Tree):
	""" A tree which may not be modified. Has a hash() value. """
	def __init__(self, label_or_str, children=None):
		if children is None:
			return  # see note in Tree.__init__()
		super(ImmutableTree, self).__init__(label_or_str, children)
		# Precompute our hash value. This ensures that we're really
		# immutable. It also means we only have to calculate it once.
		try:
			self._hash = hash((self.label, tuple(self)))
		except (TypeError, ValueError) as err:
			raise ValueError("ImmutableTree's label and children "
					"must be immutable:\n%s %r\n%r" % (self.label, self, err))
		else:
			self._leaves = Tree.leaves(self)
			self._subtrees = tuple(Tree.subtrees(self))
 
	def leaves(self):
		return self._leaves
 
	def subtrees(self, condition=None):
		if condition is None:
			return self._subtrees
		return filter(condition, self._subtrees)
 
	def __setitem__(self, _index, _value):
		raise ValueError('ImmutableTrees may not be modified')
 
	def __setslice__(self, _start, _stop, _value):
		raise ValueError('ImmutableTrees may not be modified')
 
	def __delitem__(self, _index):
		raise ValueError('ImmutableTrees may not be modified')
 
	def __delslice__(self, _start, _stop):
		raise ValueError('ImmutableTrees may not be modified')
 
	def __iadd__(self):
		raise ValueError('ImmutableTrees may not be modified')
 
	def __imul__(self):
		raise ValueError('ImmutableTrees may not be modified')
 
	def append(self, _):
		raise ValueError('ImmutableTrees may not be modified')
 
	def extend(self, _):
		raise ValueError('ImmutableTrees may not be modified')
 
	def pop(self, _=None):
		raise ValueError('ImmutableTrees may not be modified')
 
	def remove(self, _):
		raise ValueError('ImmutableTrees may not be modified')
 
	def reverse(self):
		raise ValueError('ImmutableTrees may not be modified')
 
	def sort(self):
		raise ValueError('ImmutableTrees may not be modified')
 
	def __hash__(self):
		return self._hash
 
	def _set_label(self, label):
		""" Set self._label. This will only succeed the first time the label is
		set, which should occur in Tree.__init__(). """
		if hasattr(self, '_label'):
			raise ValueError('ImmutableTrees may not be modified')
		self._label = label  # pylint: disable=W0201
 
	def _get_label(self):
		""" Get node label. """
		return self._label
	label = property(_get_label, _set_label, doc=_get_label.__doc__)
 
 
class AbstractParentedTree(Tree):
	""" An abstract base class for Trees that automatically maintain pointers
	to their parents. These parent pointers are updated whenever any change is
	made to a tree's structure. Two subclasses are currently defined:
 
	- ParentedTree is used for tree structures where each subtree has at most
		one parent. This class should be used in cases where there is
		no "sharing" of subtrees.
	- MultiParentedTree is used for tree structures where a subtree may have
		zero or more parents. This class should be used in cases where subtrees
		may be shared.
 
	The AbstractParentedTree class redefines all operations that modify a
	tree's structure to call two methods, which are used by subclasses to
	update parent information:
 
	- ``_setparent()`` is called whenever a new child is added.
	- ``_delparent()`` is called whenever a child is removed. """
	def __init__(self, label_or_str, children=None):
		if children is None:
			return  # see note in Tree.__init__()
		super(AbstractParentedTree, self).__init__(label_or_str, children)
		# iterate over self, and *not* children, because children
		# might be an iterator.
		for i, child in enumerate(self):
			if isinstance(child, Tree):
				self._setparent(child, i, dry_run=True)
		for i, child in enumerate(self):
			if isinstance(child, Tree):
				self._setparent(child, i)
 
	# === Parent management =====================================
	def _setparent(self, _child, _index, dry_run=False):
		""" Update child's parent pointer to point to self. This method is only
		called if child's type is Tree; i.e., it is not called when adding a
		leaf to a tree. This method is always called before the child is
		actually added to self's child list. Typically, if child is a tree,
		then its type needs to match self's type. This prevents mixing of
		different tree types (single-, multi-, and non-parented).
 
		:param index: The index of child in self.
		:param dry_run: If true, the don't actually set the child's parent
			pointer; just check for any error conditions, and raise an
			exception if one is found.
		:raises TypeError: if child is a tree with an inappropriate type. """
		raise NotImplementedError('Abstract base class')
 
	def _delparent(self, _child, _index):
		""" Update child's parent pointer to not point to self. This method is
		only called if child's type is Tree; i.e., it is not called when
		removing a leaf from a tree. This method is always called before the
		child is actually removed from self's child list.
 
		:param index: The index of child in self. """
		raise NotImplementedError('Abstract base class')
 
	# === Methods that add/remove children ======================
	# Every method that adds or removes a child must make
	# appropriate calls to _setparent() and _delparent().
 
	def __delitem__(self, index):
		if isinstance(index, slice):  # del ptree[start:stop]
			start, stop = slice_bounds(self, index)
			# Clear all the children pointers.
			for i in range(start, stop):
				if isinstance(self[i], Tree):
					self._delparent(self[i], i)
			# Delete the children from our child list.
			super(AbstractParentedTree, self).__delitem__(index)
		elif isinstance(index, int):  # del ptree[i]
			if index < 0:
				index += len(self)
			if index < 0:
				raise IndexError('index out of range')
			# Clear the child's parent pointer.
			if isinstance(self[index], Tree):
				self._delparent(self[index], index)
			# Remove the child from our child list.
			super(AbstractParentedTree, self).__delitem__(index)
		elif len(index) == 0:  # del ptree[()]
			raise IndexError('The tree position () may not be deleted.')
		elif len(index) == 1:  # del ptree[(i, )]
			del self[index[0]]
		else:  # del ptree[i1, i2, i3]
			del self[index[0]][index[1:]]
 
	def __setitem__(self, index, value):
		if isinstance(index, slice):  # ptree[start:stop] = value
			start, stop = slice_bounds(self, index)
			# make a copy of value, in case it's an iterator
			if not isinstance(value, (list, tuple)):
				value = list(value)
			# Check for any error conditions, so we can avoid ending
			# up in an inconsistent state if an error does occur.
			for i, child in enumerate(value):
				if isinstance(child, Tree):
					self._setparent(child, start + i, dry_run=True)
			# clear the child pointers of all parents we're removing
			for i in range(start, stop):
				if isinstance(self[i], Tree):
					self._delparent(self[i], i)
			# set the child pointers of the new children. We do this
			# after clearing *all* child pointers, in case we're e.g.
			# reversing the elements in a tree.
			for i, child in enumerate(value):
				if isinstance(child, Tree):
					self._setparent(child, start + i)
			# finally, update the content of the child list itself.
			super(AbstractParentedTree, self).__setitem__(index, value)
		elif isinstance(index, int):  # ptree[i] = value
			if index < 0:
				index += len(self)
			if index < 0:
				raise IndexError('index out of range')
			# if the value is not changing, do nothing.
			if value is self[index]:
				return
			# Set the new child's parent pointer.
			if isinstance(value, Tree):
				self._setparent(value, index)
			# Remove the old child's parent pointer
			if isinstance(self[index], Tree):
				self._delparent(self[index], index)
			# Update our child list.
			super(AbstractParentedTree, self).__setitem__(index, value)
		elif len(index) == 0:  # ptree[()] = value
			raise IndexError('The tree position () may not be assigned to.')
		elif len(index) == 1:  # ptree[(i, )] = value
			self[index[0]] = value
		else:  # ptree[i1, i2, i3] = value
			self[index[0]][index[1:]] = value
 
	def append(self, child):
		if isinstance(child, Tree):
			self._setparent(child, len(self))
		super(AbstractParentedTree, self).append(child)
 
	def extend(self, children):
		for child in children:
			if isinstance(child, Tree):
				self._setparent(child, len(self))
			super(AbstractParentedTree, self).append(child)
 
	def insert(self, index, child):
		# Handle negative indexes. Note that if index < -len(self),
		# we do *not* raise an IndexError, unlike __getitem__. This
		# is done for consistency with list.__getitem__ and list.index.
		if index < 0:
			index += len(self)
		if index < 0:
			index = 0
		# Set the child's parent, and update our child list.
		if isinstance(child, Tree):
			self._setparent(child, index)
		super(AbstractParentedTree, self).insert(index, child)
 
	def pop(self, index=-1):
		if index < 0:
			index += len(self)
		if index < 0:
			raise IndexError('index out of range')
		if isinstance(self[index], Tree):
			self._delparent(self[index], index)
		return super(AbstractParentedTree, self).pop(index)
 
	# NB: like `list`, this is done by equality, not identity!
	# To remove a specific child, use del ptree[i].
	def remove(self, child):
		index = self.index(child)
		if isinstance(self[index], Tree):
			self._delparent(self[index], index)
		super(AbstractParentedTree, self).remove(child)
 
	# We need to implement __getslice__ and friends, even though
	# they're deprecated, because otherwise list.__getslice__ will get
	# called (since we're subclassing from list). Just delegate to
	# __getitem__ etc., but use max(0, start) and max(0, stop) because
	# because negative indices are already handled *before*
	# __getslice__ is called; and we don't want to double-count them.
	if hasattr(list, '__getslice__'):
		def __getslice__(self, start, stop):
			return self.__getitem__(slice(max(0, start), max(0, stop)))
 
		def __delslice__(self, start, stop):
			return self.__delitem__(slice(max(0, start), max(0, stop)))
 
		def __setslice__(self, start, stop, value):
			return self.__setitem__(slice(max(0, start), max(0, stop)), value)
 
 
class ParentedTree(AbstractParentedTree):
	""" A Tree that automatically maintains parent pointers for single-parented
	trees. The following read-only property values are automatically updated
	whenever the structure of a parented tree is modified: parent,
	parent_index, left_sibling, right_sibling, root, treeposition.
	Each ParentedTree may have at most one parent. In particular, subtrees may
	not be shared. Any attempt to reuse a single ParentedTree as a child of
	more than one parent (or as multiple children of the same parent) will
	cause a ValueError exception to be raised.
	ParentedTrees should never be used in the same tree as Trees or
	MultiParentedTrees. Mixing tree implementations may result in incorrect
	parent pointers and in TypeError exceptions. """
	def __init__(self, label_or_str, children=None):
		if children is None:
			return  # see note in Tree.__init__()
		self._parent = None
		super(ParentedTree, self).__init__(label_or_str, children)
 
	def _frozen_class(self):
		return ImmutableParentedTree
 
	# === Properties =================================================
	def _get_parent_index(self):
		""" The index of this tree in its parent;
		i.e., ptree.parent[ptree.parent_index] is ptree.
		Note that ptree.parent_index is not necessarily equal to
		ptree.parent.index(ptree), since the index() method
		returns the first child that is _equal_ to its argument. """
		if self._parent is None:
			return None
		for i, child in enumerate(self._parent):
			if child is self:
				return i
		raise ValueError('expected to find self in self._parent!')
 
	def _get_left_sibling(self):
		""" The left sibling of this tree, or None if it has none. """
		parent_index = self._get_parent_index()
		if self._parent and parent_index > 0:
			return self._parent[parent_index - 1]
		return None  # no left sibling
 
	def _get_right_sibling(self):
		""" The right sibling of this tree, or None if it has none. """
		parent_index = self._get_parent_index()
		if self._parent and parent_index < (len(self._parent) - 1):
			return self._parent[parent_index + 1]
		return None  # no right sibling
 
	def _get_treeposition(self):
		""" The tree position of this tree, relative to the root of the
		tree; i.e., ptree.root[ptree.treeposition] is ptree. """
		if self._parent is None:
			return ()
		return (self._parent._get_treeposition() +
				(self._get_parent_index(), ))
 
	def _get_root(self):
		""" The root of this tree; i.e., the unique ancestor of this tree whose
		parent is None. If ptree.parent is None, then ptree is its own root. """
		if self._parent is None:
			return self
		return self._parent._get_root()
 
	parent = property(lambda self: self._parent, doc="""\
		The parent of this tree, or None if it has no parent. """)
	parent_index = property(_get_parent_index, doc=_get_parent_index.__doc__)
	left_sibling = property(_get_left_sibling, doc=_get_left_sibling.__doc__)
	right_sibling = property(_get_right_sibling, doc=_get_right_sibling.__doc__)
	root = property(_get_root, doc=_get_root.__doc__)
	treeposition = property(_get_treeposition, doc=_get_treeposition.__doc__)
 
	# === Parent Management ==========================================
	def _delparent(self, child, index):
		assert isinstance(child, ParentedTree)
		assert self[index] is child and child._parent is self
		child._parent = None
 
	def _setparent(self, child, _index, dry_run=False):
		if not isinstance(child, ParentedTree):
			raise TypeError('Cannot insert a non-ParentedTree '
					'into a ParentedTree')
		if child._parent is not None:
			raise ValueError('Cannot insert a subtree that already '
					'has a parent.')
		if not dry_run:
			child._parent = self
 
 
class ImmutableParentedTree(ImmutableTree, ParentedTree):
	""" Combination of an Immutable and Parented Tree. """
	def __init__(self, label_or_str, children=None):
		if children is None:
			return  # see note in Tree.__init__()
		super(ImmutableParentedTree, self).__init__(label_or_str, children)
 
 
class MultiParentedTree(AbstractParentedTree):
	""" A Tree that automatically maintains parent pointers for multi-parented
	trees. The following read-only property values are automatically updated
	whenever the structure of a multi-parented tree is modified: parents,
	parent_indices, left_siblings, right_siblings, roots, treepositions. Each
	MultiParentedTree may have zero or more parents. In particular, subtrees
	may be shared. If a single MultiParentedTree is used as multiple children
	of the same parent, then that parent will appear multiple times in its
	parents property.
	MultiParentedTrees should never be used in the same tree as Trees or
	ParentedTrees. Mixing tree implementations may result in incorrect parent
	pointers and in TypeError exceptions. """
	def __init__(self, label_or_str, children=None):
		if children is None:
			return  # see note in Tree.__init__()
		# This list should not contain duplicates, even if a parent contains
		# this tree multiple times.
		self._parents = []
		super(MultiParentedTree, self).__init__(label_or_str, children)
 
	def _frozen_class(self):
		return ImmutableMultiParentedTree
 
	# === Properties =================================================
	def _get_parent_indices(self):
		""" Collect tuples of (parent, index) for all parents in a list. """
		return [(parent, index)
				for parent in self._parents
				for index, child in enumerate(parent)
				if child is self]
 
	def _get_left_siblings(self):
		""" A list of all left siblings of this tree, in any of its parent
		trees. A tree may be its own left sibling if it is used as multiple
		contiguous children of the same parent. A tree may appear multiple
		times in this list if it is the left sibling of this tree with respect
		to multiple parents. """
		return [parent[index - 1]
				for (parent, index) in self._get_parent_indices()
				if index > 0]
 
	def _get_right_siblings(self):
		""" A list of all right siblings of this tree, in any of its parent
		trees. A tree may be its own right sibling if it is used as multiple
		contiguous children of the same parent. A tree may appear multiple
		times in this list if it is the right sibling of this tree with respect
		to multiple parents. """
		return [parent[index + 1]
				for (parent, index) in self._get_parent_indices()
				if index < (len(parent) - 1)]
 
	def _get_roots(self):
		""" The set of all roots of this tree. This set is formed by tracing
		all possible parent paths until trees with no parents are found. """
		return list(self._get_roots_helper({}).values())
 
	def _get_roots_helper(self, result):
		""" Collect all roots for this node. """
		if self._parents:
			for parent in self._parents:
				parent._get_roots_helper(result)
		else:
			result[id(self)] = self
		return result
 
	parents = property(lambda self: list(self._parents), doc="""\
		The set of parents of this tree. If this tree has no parents, then
		parents is the empty set. To check if a tree is used as multiple
		children of the same parent, use the parent_indices property. """)
	left_siblings = property(_get_left_siblings, doc=_get_left_siblings.__doc__)
	right_siblings = property(_get_right_siblings,
			doc=_get_right_siblings.__doc__)
	roots = property(_get_roots, doc=_get_roots.__doc__)
 
	def parent_indices(self, parent):
		""" :returns: a list of the indices where this tree occurs as a child \
		of parent.
 
		If this child does not occur as a child of parent, then the
		empty list is returned. The following is always true::
 
			for parent_index in ptree.parent_indices(parent):
				parent[parent_index] is ptree """
		if parent not in self._parents:
			return []
		return [index for (index, child) in enumerate(parent)
				if child is self]
 
	def treepositions(self, root):
		"""	:returns: a list of all tree positions that can be used to reach \
			this multi-parented tree starting from root.
 
		i.e., the following holds::
 
			for treepos in ptree.treepositions(root):
				root[treepos] is ptree """
		if self is root:
			return [()]
		return [treepos + (index, ) for parent in self._parents
				for treepos in parent.treepositions(root)
				for (index, child) in enumerate(parent) if child is self]
 
	# === Parent Management ==========================================
	def _delparent(self, child, index):
		assert isinstance(child, MultiParentedTree) and self[index] is child
		assert len([p for p in child._parents if p is self]) == 1
		# If the only copy of child in self is at index, then delete
		# self from child's parent list.
		for i, c in enumerate(self):
			if c is child and i != index:
				break
		else:
			child._parents.remove(self)
 
	def _setparent(self, child, _index, dry_run=False):
		if not isinstance(child, MultiParentedTree):
			raise TypeError('Cannot insert a non-MultiParentedTree '
					'into a MultiParentedTree')
		# Add self as a parent pointer if it's not already listed.
		if not dry_run:
			for parent in child._parents:
				if parent is self:
					break
			else:
				child._parents.append(self)
 
 
class ImmutableMultiParentedTree(ImmutableTree, MultiParentedTree):
	""" Combination of an Immutable and Multi Parented Tree. """
	def __init__(self, label_or_str, children=None):
		if children is None:
			return  # see note in Tree.__init__()
		super(ImmutableMultiParentedTree, self).__init__(label_or_str, children)
 
 
def slice_bounds(seq, slice_obj, allow_step=False):
	""" Given a slice, return the corresponding (start, stop) bounds, taking
	into account None indices and negative indices. The following holds
	for the returned start and stop values: 0 <= start <= stop <= len(seq).
 
	:raises ValueError: if slice_obj.step is not None.
	:param allow_step: If true, then the slice object may have a non-None step.
		If it does, then return a tuple (start, stop, step). """
	start, stop = (slice_obj.start, slice_obj.stop)
	if allow_step:
		slice_obj.step = 1 if slice_obj.step is None else slice_obj.step
		# Use a recursive call without allow_step to find the slice
		# bounds. If step is negative, then the roles of start and
		# stop (in terms of default values, etc), are swapped.
		if slice_obj.step < 0:
			start, stop = slice_bounds(seq, slice(stop, start))
		else:
			start, stop = slice_bounds(seq, slice(start, stop))
		return start, stop, slice_obj.step
	elif slice_obj.step not in (None, 1):
		raise ValueError('slices with steps are not supported by %s' %
				seq.__class__.__name__)
	start = 0 if start is None else start
	stop = len(seq) if stop is None else stop
	start = max(0, len(seq) + start) if start < 0 else start
	stop = max(0, len(seq) + stop) if stop < 0 else stop
	if stop > 0:  # Make sure stop doesn't go past the end of the list.
		# Try to avoid calculating len(seq), since that can be expensive for
		# lazy sequences.
		try:
			seq[stop - 1]
		except IndexError:
			stop = len(seq)
	start = min(start, stop)
	return start, stop
 
 
def test():
	""" Not implemented. """