# Source code for nltk.tree.transforms

```# Natural Language Toolkit: Tree Transformations
#
# Author: Nathan Bodenstab <bodenstab@cslu.ogi.edu>
# URL: <https://www.nltk.org/>

r"""
A collection of methods for tree (grammar) transformations used
in parsing natural language.

Although many of these methods are technically grammar transformations
(ie. Chomsky Norm Form), when working with treebanks it is much more
natural to visualize these modifications in a tree structure.  Hence,
we will do all transformation directly to the tree itself.
Transforming the tree directly also allows us to do parent annotation.
A grammar can then be simply induced from the modified tree.

The following is a short tutorial on the available transformations.

1. Chomsky Normal Form (binarization)

It is well known that any grammar has a Chomsky Normal Form (CNF)
equivalent grammar where CNF is defined by every production having
either two non-terminals or one terminal on its right hand side.
When we have hierarchically structured data (ie. a treebank), it is
natural to view this in terms of productions where the root of every
subtree is the head (left hand side) of the production and all of
its children are the right hand side constituents.  In order to
convert a tree into CNF, we simply need to ensure that every subtree
has either two subtrees as children (binarization), or one leaf node
(non-terminal).  In order to binarize a subtree with more than two
children, we must introduce artificial nodes.

There are two popular methods to convert a tree into CNF: left
factoring and right factoring.  The following example demonstrates
the difference between them.  Example::

Original       Right-Factored     Left-Factored

A              A                      A
/ | \          /   \                  /   \
B  C  D   ==>  B    A|<C-D>   OR   A|<B-C>  D
/  \          /  \
C    D        B    C

2. Parent Annotation

In addition to binarizing the tree, there are two standard
modifications to node labels we can do in the same traversal: parent
annotation and Markov order-N smoothing (or sibling smoothing).

The purpose of parent annotation is to refine the probabilities of
productions by adding a small amount of context.  With this simple
addition, a CYK (inside-outside, dynamic programming chart parse)
can improve from 74% to 79% accuracy.  A natural generalization from
parent annotation is to grandparent annotation and beyond.  The
tradeoff becomes accuracy gain vs. computational complexity.  We
must also keep in mind data sparcity issues.  Example::

Original       Parent Annotation

A                A^<?>
/ | \             /   \
B  C  D   ==>  B^<A>    A|<C-D>^<?>     where ? is the
/  \          parent of A
C^<A>   D^<A>

3. Markov order-N smoothing

Markov smoothing combats data sparcity issues as well as decreasing
computational requirements by limiting the number of children
included in artificial nodes.  In practice, most people use an order
2 grammar.  Example::

Original       No Smoothing       Markov order 1   Markov order 2   etc.

__A__            A                      A                A
/ /|\ \         /   \                  /   \            /   \
B C D E F  ==>  B    A|<C-D-E-F>  ==>  B   A|<C>  ==>   B  A|<C-D>
/   \               /   \            /   \
C    ...            C    ...         C    ...

Annotation decisions can be thought about in the vertical direction
(parent, grandparent, etc) and the horizontal direction (number of
siblings to keep).  Parameters to the following functions specify

Dan Klein and Chris Manning (2003) "Accurate Unlexicalized
Parsing", ACL-03.  https://www.aclweb.org/anthology/P03-1054

4. Unary Collapsing

Collapse unary productions (ie. subtrees with a single child) into a
new non-terminal (Tree node).  This is useful when working with
algorithms that do not allow unary productions, yet you do not wish
to lose the parent information.  Example::

A
|
B   ==>   A+B
/ \        / \
C   D      C   D

"""

from nltk.tree.tree import Tree

[docs]def chomsky_normal_form(
tree, factor="right", horzMarkov=None, vertMarkov=0, childChar="|", parentChar="^"
):
# assume all subtrees have homogeneous children
# assume all terminals have no siblings

# A semi-hack to have elegant looking code below.  As a result,
# any subtree with a branching factor greater than 999 will be incorrectly truncated.
if horzMarkov is None:
horzMarkov = 999

# Traverse the tree depth-first keeping a list of ancestor nodes to the root.
# I chose not to use the tree.treepositions() method since it requires
# two traversals of the tree (one to get the positions, one to iterate
# over them) and node access time is proportional to the height of the node.
# This method is 7x faster which helps when parsing 40,000 sentences.

nodeList = [(tree, [tree.label()])]
while nodeList != []:
node, parent = nodeList.pop()
if isinstance(node, Tree):

# parent annotation
parentString = ""
originalNode = node.label()
if vertMarkov != 0 and node != tree and isinstance(node, Tree):
parentString = "{}<{}>".format(parentChar, "-".join(parent))
node.set_label(node.label() + parentString)
parent = [originalNode] + parent[: vertMarkov - 1]

# add children to the agenda before we mess with them
for child in node:
nodeList.append((child, parent))

# chomsky normal form factorization
if len(node) > 2:
childNodes = [child.label() for child in node]
nodeCopy = node.copy()
node[0:] = []  # delete the children

curNode = node
numChildren = len(nodeCopy)
for i in range(1, numChildren - 1):
if factor == "right":
originalNode,
childChar,
"-".join(
childNodes[i : min([i + horzMarkov, numChildren])]
),
parentString,
curNode[0:] = [nodeCopy.pop(0), newNode]
else:
originalNode,
childChar,
"-".join(
childNodes[max([numChildren - i - horzMarkov, 0]) : -i]
),
parentString,
)
curNode[0:] = [newNode, nodeCopy.pop()]

curNode = newNode

curNode[0:] = [child for child in nodeCopy]

[docs]def un_chomsky_normal_form(
tree, expandUnary=True, childChar="|", parentChar="^", unaryChar="+"
):
# Traverse the tree-depth first keeping a pointer to the parent for modification purposes.
nodeList = [(tree, [])]
while nodeList != []:
node, parent = nodeList.pop()
if isinstance(node, Tree):
# if the node contains the 'childChar' character it means that
# it is an artificial node and can be removed, although we still need
# to move its children to its parent
childIndex = node.label().find(childChar)
if childIndex != -1:
nodeIndex = parent.index(node)
parent.remove(parent[nodeIndex])
# Generated node was on the left if the nodeIndex is 0 which
# means the grammar was left factored.  We must insert the children
# at the beginning of the parent's children
if nodeIndex == 0:
parent.insert(0, node)
parent.insert(1, node)
else:
parent.extend([node, node])

# parent is now the current node so the children of parent will be added to the agenda
node = parent
else:
parentIndex = node.label().find(parentChar)
if parentIndex != -1:
# strip the node name of the parent annotation
node.set_label(node.label()[:parentIndex])

# expand collapsed unary productions
if expandUnary == True:
unaryIndex = node.label().find(unaryChar)
if unaryIndex != -1:
newNode = Tree(
node.label()[unaryIndex + 1 :], [i for i in node]
)
node.set_label(node.label()[:unaryIndex])
node[0:] = [newNode]

for child in node:
nodeList.append((child, node))

[docs]def collapse_unary(tree, collapsePOS=False, collapseRoot=False, joinChar="+"):
"""
Collapse subtrees with a single child (ie. unary productions)
into a new non-terminal (Tree node) joined by 'joinChar'.
This is useful when working with algorithms that do not allow
unary productions, and completely removing the unary productions
would require loss of useful information.  The Tree is modified
directly (since it is passed by reference) and no value is returned.

:param tree: The Tree to be collapsed
:type  tree: Tree
:param collapsePOS: 'False' (default) will not collapse the parent of leaf nodes (ie.
Part-of-Speech tags) since they are always unary productions
:type  collapsePOS: bool
:param collapseRoot: 'False' (default) will not modify the root production
if it is unary.  For the Penn WSJ treebank corpus, this corresponds
to the TOP -> productions.
:type collapseRoot: bool
:param joinChar: A string used to connect collapsed node values (default = "+")
:type  joinChar: str
"""

if collapseRoot == False and isinstance(tree, Tree) and len(tree) == 1:
nodeList = [tree]
else:
nodeList = [tree]

# depth-first traversal of tree
while nodeList != []:
node = nodeList.pop()
if isinstance(node, Tree):
if (
len(node) == 1
and isinstance(node, Tree)
and (collapsePOS == True or isinstance(node[0, 0], Tree))
):
node.set_label(node.label() + joinChar + node.label())
node[0:] = [child for child in node]
# since we assigned the child's children to the current node,
# evaluate the current node again
nodeList.append(node)
else:
for child in node:
nodeList.append(child)

#################################################################
# Demonstration
#################################################################

def demo():
"""
A demonstration showing how each tree transform can be used.
"""

from copy import deepcopy

from nltk.draw.tree import draw_trees
from nltk.tree.tree import Tree

# original tree from WSJ bracketed text
sentence = """(TOP
(S
(S
(VP
(VBN Turned)
(PP
(IN in)
(NP
(NP (NNP Shane) (NNP Longman) (POS 's))
(NN room)))))
(, ,)
(NP (DT the) (NN yuppie) (NNS dealers))
(VP (AUX do) (NP (NP (RB little)) (ADJP (RB right))))
(. .)))"""
t = Tree.fromstring(sentence, remove_empty_top_bracketing=True)

# collapse subtrees with only one child
collapsedTree = deepcopy(t)
collapse_unary(collapsedTree)

# convert the tree to CNF
cnfTree = deepcopy(collapsedTree)
chomsky_normal_form(cnfTree)

# convert the tree to CNF with parent annotation (one level) and horizontal smoothing of order two
parentTree = deepcopy(collapsedTree)
chomsky_normal_form(parentTree, horzMarkov=2, vertMarkov=1)

# convert the tree back to its original form (used to make CYK results comparable)
original = deepcopy(parentTree)
un_chomsky_normal_form(original)

# convert tree back to bracketed text
sentence2 = original.pprint()
print(sentence)
print(sentence2)
print("Sentences the same? ", sentence == sentence2)

draw_trees(t, collapsedTree, cnfTree, parentTree, original)

if __name__ == "__main__":
demo()

__all__ = ["chomsky_normal_form", "un_chomsky_normal_form", "collapse_unary"]
```