# Natural Language Toolkit: Dependency Grammars
#
# Copyright (C) 2001-2023 NLTK Project
# Author: Jason Narad <jason.narad@gmail.com>
#
# URL: <https://www.nltk.org/>
# For license information, see LICENSE.TXT
#
from collections import defaultdict
from functools import total_ordering
from itertools import chain
from nltk.grammar import (
DependencyGrammar,
DependencyProduction,
ProbabilisticDependencyGrammar,
)
from nltk.internals import raise_unorderable_types
from nltk.parse.dependencygraph import DependencyGraph
#################################################################
# Dependency Span
#################################################################
[docs]@total_ordering
class DependencySpan:
"""
A contiguous span over some part of the input string representing
dependency (head -> modifier) relationships amongst words. An atomic
span corresponds to only one word so it isn't a 'span' in the conventional
sense, as its _start_index = _end_index = _head_index for concatenation
purposes. All other spans are assumed to have arcs between all nodes
within the start and end indexes of the span, and one head index corresponding
to the head word for the entire span. This is the same as the root node if
the dependency structure were depicted as a graph.
"""
[docs] def __init__(self, start_index, end_index, head_index, arcs, tags):
self._start_index = start_index
self._end_index = end_index
self._head_index = head_index
self._arcs = arcs
self._tags = tags
self._comparison_key = (start_index, end_index, head_index, tuple(arcs))
self._hash = hash(self._comparison_key)
[docs] def head_index(self):
"""
:return: An value indexing the head of the entire ``DependencySpan``.
:rtype: int
"""
return self._head_index
def __repr__(self):
"""
:return: A concise string representatino of the ``DependencySpan``.
:rtype: str.
"""
return "Span %d-%d; Head Index: %d" % (
self._start_index,
self._end_index,
self._head_index,
)
def __str__(self):
"""
:return: A verbose string representation of the ``DependencySpan``.
:rtype: str
"""
str = "Span %d-%d; Head Index: %d" % (
self._start_index,
self._end_index,
self._head_index,
)
for i in range(len(self._arcs)):
str += "\n%d <- %d, %s" % (i, self._arcs[i], self._tags[i])
return str
def __eq__(self, other):
return (
type(self) == type(other) and self._comparison_key == other._comparison_key
)
def __ne__(self, other):
return not self == other
def __lt__(self, other):
if not isinstance(other, DependencySpan):
raise_unorderable_types("<", self, other)
return self._comparison_key < other._comparison_key
def __hash__(self):
"""
:return: The hash value of this ``DependencySpan``.
"""
return self._hash
#################################################################
# Chart Cell
#################################################################
[docs]class ChartCell:
"""
A cell from the parse chart formed when performing the CYK algorithm.
Each cell keeps track of its x and y coordinates (though this will probably
be discarded), and a list of spans serving as the cell's entries.
"""
[docs] def __init__(self, x, y):
"""
:param x: This cell's x coordinate.
:type x: int.
:param y: This cell's y coordinate.
:type y: int.
"""
self._x = x
self._y = y
self._entries = set()
[docs] def add(self, span):
"""
Appends the given span to the list of spans
representing the chart cell's entries.
:param span: The span to add.
:type span: DependencySpan
"""
self._entries.add(span)
def __str__(self):
"""
:return: A verbose string representation of this ``ChartCell``.
:rtype: str.
"""
return "CC[%d,%d]: %s" % (self._x, self._y, self._entries)
def __repr__(self):
"""
:return: A concise string representation of this ``ChartCell``.
:rtype: str.
"""
return "%s" % self
#################################################################
# Parsing with Dependency Grammars
#################################################################
[docs]class ProjectiveDependencyParser:
"""
A projective, rule-based, dependency parser. A ProjectiveDependencyParser
is created with a DependencyGrammar, a set of productions specifying
word-to-word dependency relations. The parse() method will then
return the set of all parses, in tree representation, for a given input
sequence of tokens. Each parse must meet the requirements of the both
the grammar and the projectivity constraint which specifies that the
branches of the dependency tree are not allowed to cross. Alternatively,
this can be understood as stating that each parent node and its children
in the parse tree form a continuous substring of the input sequence.
"""
[docs] def __init__(self, dependency_grammar):
"""
Create a new ProjectiveDependencyParser, from a word-to-word
dependency grammar ``DependencyGrammar``.
:param dependency_grammar: A word-to-word relation dependencygrammar.
:type dependency_grammar: DependencyGrammar
"""
self._grammar = dependency_grammar
[docs] def parse(self, tokens):
"""
Performs a projective dependency parse on the list of tokens using
a chart-based, span-concatenation algorithm similar to Eisner (1996).
:param tokens: The list of input tokens.
:type tokens: list(str)
:return: An iterator over parse trees.
:rtype: iter(Tree)
"""
self._tokens = list(tokens)
chart = []
for i in range(0, len(self._tokens) + 1):
chart.append([])
for j in range(0, len(self._tokens) + 1):
chart[i].append(ChartCell(i, j))
if i == j + 1:
chart[i][j].add(DependencySpan(i - 1, i, i - 1, [-1], ["null"]))
for i in range(1, len(self._tokens) + 1):
for j in range(i - 2, -1, -1):
for k in range(i - 1, j, -1):
for span1 in chart[k][j]._entries:
for span2 in chart[i][k]._entries:
for newspan in self.concatenate(span1, span2):
chart[i][j].add(newspan)
for parse in chart[len(self._tokens)][0]._entries:
conll_format = ""
# malt_format = ""
for i in range(len(tokens)):
# malt_format += '%s\t%s\t%d\t%s\n' % (tokens[i], 'null', parse._arcs[i] + 1, 'null')
# conll_format += '\t%d\t%s\t%s\t%s\t%s\t%s\t%d\t%s\t%s\t%s\n' % (i+1, tokens[i], tokens[i], 'null', 'null', 'null', parse._arcs[i] + 1, 'null', '-', '-')
# Modify to comply with the new Dependency Graph requirement (at least must have an root elements)
conll_format += "\t%d\t%s\t%s\t%s\t%s\t%s\t%d\t%s\t%s\t%s\n" % (
i + 1,
tokens[i],
tokens[i],
"null",
"null",
"null",
parse._arcs[i] + 1,
"ROOT",
"-",
"-",
)
dg = DependencyGraph(conll_format)
# if self.meets_arity(dg):
yield dg.tree()
[docs] def concatenate(self, span1, span2):
"""
Concatenates the two spans in whichever way possible. This
includes rightward concatenation (from the leftmost word of the
leftmost span to the rightmost word of the rightmost span) and
leftward concatenation (vice-versa) between adjacent spans. Unlike
Eisner's presentation of span concatenation, these spans do not
share or pivot on a particular word/word-index.
:return: A list of new spans formed through concatenation.
:rtype: list(DependencySpan)
"""
spans = []
if span1._start_index == span2._start_index:
print("Error: Mismatched spans - replace this with thrown error")
if span1._start_index > span2._start_index:
temp_span = span1
span1 = span2
span2 = temp_span
# adjacent rightward covered concatenation
new_arcs = span1._arcs + span2._arcs
new_tags = span1._tags + span2._tags
if self._grammar.contains(
self._tokens[span1._head_index], self._tokens[span2._head_index]
):
# print('Performing rightward cover %d to %d' % (span1._head_index, span2._head_index))
new_arcs[span2._head_index - span1._start_index] = span1._head_index
spans.append(
DependencySpan(
span1._start_index,
span2._end_index,
span1._head_index,
new_arcs,
new_tags,
)
)
# adjacent leftward covered concatenation
new_arcs = span1._arcs + span2._arcs
if self._grammar.contains(
self._tokens[span2._head_index], self._tokens[span1._head_index]
):
# print('performing leftward cover %d to %d' % (span2._head_index, span1._head_index))
new_arcs[span1._head_index - span1._start_index] = span2._head_index
spans.append(
DependencySpan(
span1._start_index,
span2._end_index,
span2._head_index,
new_arcs,
new_tags,
)
)
return spans
#################################################################
# Parsing with Probabilistic Dependency Grammars
#################################################################
[docs]class ProbabilisticProjectiveDependencyParser:
"""A probabilistic, projective dependency parser.
This parser returns the most probable projective parse derived from the
probabilistic dependency grammar derived from the train() method. The
probabilistic model is an implementation of Eisner's (1996) Model C, which
conditions on head-word, head-tag, child-word, and child-tag. The decoding
uses a bottom-up chart-based span concatenation algorithm that's identical
to the one utilized by the rule-based projective parser.
Usage example
>>> from nltk.parse.dependencygraph import conll_data2
>>> graphs = [
... DependencyGraph(entry) for entry in conll_data2.split('\\n\\n') if entry
... ]
>>> ppdp = ProbabilisticProjectiveDependencyParser()
>>> ppdp.train(graphs)
>>> sent = ['Cathy', 'zag', 'hen', 'wild', 'zwaaien', '.']
>>> list(ppdp.parse(sent))
[Tree('zag', ['Cathy', 'hen', Tree('zwaaien', ['wild', '.'])])]
"""
[docs] def __init__(self):
"""
Create a new probabilistic dependency parser. No additional
operations are necessary.
"""
[docs] def parse(self, tokens):
"""
Parses the list of tokens subject to the projectivity constraint
and the productions in the parser's grammar. This uses a method
similar to the span-concatenation algorithm defined in Eisner (1996).
It returns the most probable parse derived from the parser's
probabilistic dependency grammar.
"""
self._tokens = list(tokens)
chart = []
for i in range(0, len(self._tokens) + 1):
chart.append([])
for j in range(0, len(self._tokens) + 1):
chart[i].append(ChartCell(i, j))
if i == j + 1:
if tokens[i - 1] in self._grammar._tags:
for tag in self._grammar._tags[tokens[i - 1]]:
chart[i][j].add(
DependencySpan(i - 1, i, i - 1, [-1], [tag])
)
else:
print(
"No tag found for input token '%s', parse is impossible."
% tokens[i - 1]
)
return []
for i in range(1, len(self._tokens) + 1):
for j in range(i - 2, -1, -1):
for k in range(i - 1, j, -1):
for span1 in chart[k][j]._entries:
for span2 in chart[i][k]._entries:
for newspan in self.concatenate(span1, span2):
chart[i][j].add(newspan)
trees = []
max_parse = None
max_score = 0
for parse in chart[len(self._tokens)][0]._entries:
conll_format = ""
malt_format = ""
for i in range(len(tokens)):
malt_format += "%s\t%s\t%d\t%s\n" % (
tokens[i],
"null",
parse._arcs[i] + 1,
"null",
)
# conll_format += '\t%d\t%s\t%s\t%s\t%s\t%s\t%d\t%s\t%s\t%s\n' % (i+1, tokens[i], tokens[i], parse._tags[i], parse._tags[i], 'null', parse._arcs[i] + 1, 'null', '-', '-')
# Modify to comply with recent change in dependency graph such that there must be a ROOT element.
conll_format += "\t%d\t%s\t%s\t%s\t%s\t%s\t%d\t%s\t%s\t%s\n" % (
i + 1,
tokens[i],
tokens[i],
parse._tags[i],
parse._tags[i],
"null",
parse._arcs[i] + 1,
"ROOT",
"-",
"-",
)
dg = DependencyGraph(conll_format)
score = self.compute_prob(dg)
trees.append((score, dg.tree()))
trees.sort()
return (tree for (score, tree) in trees)
[docs] def concatenate(self, span1, span2):
"""
Concatenates the two spans in whichever way possible. This
includes rightward concatenation (from the leftmost word of the
leftmost span to the rightmost word of the rightmost span) and
leftward concatenation (vice-versa) between adjacent spans. Unlike
Eisner's presentation of span concatenation, these spans do not
share or pivot on a particular word/word-index.
:return: A list of new spans formed through concatenation.
:rtype: list(DependencySpan)
"""
spans = []
if span1._start_index == span2._start_index:
print("Error: Mismatched spans - replace this with thrown error")
if span1._start_index > span2._start_index:
temp_span = span1
span1 = span2
span2 = temp_span
# adjacent rightward covered concatenation
new_arcs = span1._arcs + span2._arcs
new_tags = span1._tags + span2._tags
if self._grammar.contains(
self._tokens[span1._head_index], self._tokens[span2._head_index]
):
new_arcs[span2._head_index - span1._start_index] = span1._head_index
spans.append(
DependencySpan(
span1._start_index,
span2._end_index,
span1._head_index,
new_arcs,
new_tags,
)
)
# adjacent leftward covered concatenation
new_arcs = span1._arcs + span2._arcs
new_tags = span1._tags + span2._tags
if self._grammar.contains(
self._tokens[span2._head_index], self._tokens[span1._head_index]
):
new_arcs[span1._head_index - span1._start_index] = span2._head_index
spans.append(
DependencySpan(
span1._start_index,
span2._end_index,
span2._head_index,
new_arcs,
new_tags,
)
)
return spans
[docs] def train(self, graphs):
"""
Trains a ProbabilisticDependencyGrammar based on the list of input
DependencyGraphs. This model is an implementation of Eisner's (1996)
Model C, which derives its statistics from head-word, head-tag,
child-word, and child-tag relationships.
:param graphs: A list of dependency graphs to train from.
:type: list(DependencyGraph)
"""
productions = []
events = defaultdict(int)
tags = {}
for dg in graphs:
for node_index in range(1, len(dg.nodes)):
# children = dg.nodes[node_index]['deps']
children = list(
chain.from_iterable(dg.nodes[node_index]["deps"].values())
)
nr_left_children = dg.left_children(node_index)
nr_right_children = dg.right_children(node_index)
nr_children = nr_left_children + nr_right_children
for child_index in range(
0 - (nr_left_children + 1), nr_right_children + 2
):
head_word = dg.nodes[node_index]["word"]
head_tag = dg.nodes[node_index]["tag"]
if head_word in tags:
tags[head_word].add(head_tag)
else:
tags[head_word] = {head_tag}
child = "STOP"
child_tag = "STOP"
prev_word = "START"
prev_tag = "START"
if child_index < 0:
array_index = child_index + nr_left_children
if array_index >= 0:
child = dg.nodes[children[array_index]]["word"]
child_tag = dg.nodes[children[array_index]]["tag"]
if child_index != -1:
prev_word = dg.nodes[children[array_index + 1]]["word"]
prev_tag = dg.nodes[children[array_index + 1]]["tag"]
if child != "STOP":
productions.append(DependencyProduction(head_word, [child]))
head_event = "(head ({} {}) (mods ({}, {}, {}) left))".format(
child,
child_tag,
prev_tag,
head_word,
head_tag,
)
mod_event = "(mods ({}, {}, {}) left))".format(
prev_tag,
head_word,
head_tag,
)
events[head_event] += 1
events[mod_event] += 1
elif child_index > 0:
array_index = child_index + nr_left_children - 1
if array_index < nr_children:
child = dg.nodes[children[array_index]]["word"]
child_tag = dg.nodes[children[array_index]]["tag"]
if child_index != 1:
prev_word = dg.nodes[children[array_index - 1]]["word"]
prev_tag = dg.nodes[children[array_index - 1]]["tag"]
if child != "STOP":
productions.append(DependencyProduction(head_word, [child]))
head_event = "(head ({} {}) (mods ({}, {}, {}) right))".format(
child,
child_tag,
prev_tag,
head_word,
head_tag,
)
mod_event = "(mods ({}, {}, {}) right))".format(
prev_tag,
head_word,
head_tag,
)
events[head_event] += 1
events[mod_event] += 1
self._grammar = ProbabilisticDependencyGrammar(productions, events, tags)
[docs] def compute_prob(self, dg):
"""
Computes the probability of a dependency graph based
on the parser's probability model (defined by the parser's
statistical dependency grammar).
:param dg: A dependency graph to score.
:type dg: DependencyGraph
:return: The probability of the dependency graph.
:rtype: int
"""
prob = 1.0
for node_index in range(1, len(dg.nodes)):
# children = dg.nodes[node_index]['deps']
children = list(chain.from_iterable(dg.nodes[node_index]["deps"].values()))
nr_left_children = dg.left_children(node_index)
nr_right_children = dg.right_children(node_index)
nr_children = nr_left_children + nr_right_children
for child_index in range(0 - (nr_left_children + 1), nr_right_children + 2):
head_word = dg.nodes[node_index]["word"]
head_tag = dg.nodes[node_index]["tag"]
child = "STOP"
child_tag = "STOP"
prev_word = "START"
prev_tag = "START"
if child_index < 0:
array_index = child_index + nr_left_children
if array_index >= 0:
child = dg.nodes[children[array_index]]["word"]
child_tag = dg.nodes[children[array_index]]["tag"]
if child_index != -1:
prev_word = dg.nodes[children[array_index + 1]]["word"]
prev_tag = dg.nodes[children[array_index + 1]]["tag"]
head_event = "(head ({} {}) (mods ({}, {}, {}) left))".format(
child,
child_tag,
prev_tag,
head_word,
head_tag,
)
mod_event = "(mods ({}, {}, {}) left))".format(
prev_tag,
head_word,
head_tag,
)
h_count = self._grammar._events[head_event]
m_count = self._grammar._events[mod_event]
# If the grammar is not covered
if m_count != 0:
prob *= h_count / m_count
else:
prob = 0.00000001 # Very small number
elif child_index > 0:
array_index = child_index + nr_left_children - 1
if array_index < nr_children:
child = dg.nodes[children[array_index]]["word"]
child_tag = dg.nodes[children[array_index]]["tag"]
if child_index != 1:
prev_word = dg.nodes[children[array_index - 1]]["word"]
prev_tag = dg.nodes[children[array_index - 1]]["tag"]
head_event = "(head ({} {}) (mods ({}, {}, {}) right))".format(
child,
child_tag,
prev_tag,
head_word,
head_tag,
)
mod_event = "(mods ({}, {}, {}) right))".format(
prev_tag,
head_word,
head_tag,
)
h_count = self._grammar._events[head_event]
m_count = self._grammar._events[mod_event]
if m_count != 0:
prob *= h_count / m_count
else:
prob = 0.00000001 # Very small number
return prob
#################################################################
# Demos
#################################################################
[docs]def demo():
projective_rule_parse_demo()
# arity_parse_demo()
projective_prob_parse_demo()
[docs]def projective_rule_parse_demo():
"""
A demonstration showing the creation and use of a
``DependencyGrammar`` to perform a projective dependency
parse.
"""
grammar = DependencyGrammar.fromstring(
"""
'scratch' -> 'cats' | 'walls'
'walls' -> 'the'
'cats' -> 'the'
"""
)
print(grammar)
pdp = ProjectiveDependencyParser(grammar)
trees = pdp.parse(["the", "cats", "scratch", "the", "walls"])
for tree in trees:
print(tree)
[docs]def arity_parse_demo():
"""
A demonstration showing the creation of a ``DependencyGrammar``
in which a specific number of modifiers is listed for a given
head. This can further constrain the number of possible parses
created by a ``ProjectiveDependencyParser``.
"""
print()
print("A grammar with no arity constraints. Each DependencyProduction")
print("specifies a relationship between one head word and only one")
print("modifier word.")
grammar = DependencyGrammar.fromstring(
"""
'fell' -> 'price' | 'stock'
'price' -> 'of' | 'the'
'of' -> 'stock'
'stock' -> 'the'
"""
)
print(grammar)
print()
print("For the sentence 'The price of the stock fell', this grammar")
print("will produce the following three parses:")
pdp = ProjectiveDependencyParser(grammar)
trees = pdp.parse(["the", "price", "of", "the", "stock", "fell"])
for tree in trees:
print(tree)
print()
print("By contrast, the following grammar contains a ")
print("DependencyProduction that specifies a relationship")
print("between a single head word, 'price', and two modifier")
print("words, 'of' and 'the'.")
grammar = DependencyGrammar.fromstring(
"""
'fell' -> 'price' | 'stock'
'price' -> 'of' 'the'
'of' -> 'stock'
'stock' -> 'the'
"""
)
print(grammar)
print()
print(
"This constrains the number of possible parses to just one:"
) # unimplemented, soon to replace
pdp = ProjectiveDependencyParser(grammar)
trees = pdp.parse(["the", "price", "of", "the", "stock", "fell"])
for tree in trees:
print(tree)
[docs]def projective_prob_parse_demo():
"""
A demo showing the training and use of a projective
dependency parser.
"""
from nltk.parse.dependencygraph import conll_data2
graphs = [DependencyGraph(entry) for entry in conll_data2.split("\n\n") if entry]
ppdp = ProbabilisticProjectiveDependencyParser()
print("Training Probabilistic Projective Dependency Parser...")
ppdp.train(graphs)
sent = ["Cathy", "zag", "hen", "wild", "zwaaien", "."]
print("Parsing '", " ".join(sent), "'...")
print("Parse:")
for tree in ppdp.parse(sent):
print(tree)
if __name__ == "__main__":
demo()