# Source code for nltk.parse.viterbi

```# Natural Language Toolkit: Viterbi Probabilistic Parser
#
# Copyright (C) 2001-2022 NLTK Project
# Author: Edward Loper <edloper@gmail.com>
#         Steven Bird <stevenbird1@gmail.com>
# URL: <https://www.nltk.org/>

from functools import reduce

from nltk.parse.api import ParserI
from nltk.tree import ProbabilisticTree, Tree

##//////////////////////////////////////////////////////
##  Viterbi PCFG Parser
##//////////////////////////////////////////////////////

[docs]class ViterbiParser(ParserI):
"""
A bottom-up ``PCFG`` parser that uses dynamic programming to find
the single most likely parse for a text.  The ``ViterbiParser`` parser
parses texts by filling in a "most likely constituent table".
This table records the most probable tree representation for any
given span and node value.  In particular, it has an entry for
every start index, end index, and node value, recording the most
likely subtree that spans from the start index to the end index,
and has the given node value.

The ``ViterbiParser`` parser fills in this table incrementally.  It starts
by filling in all entries for constituents that span one element
of text (i.e., entries where the end index is one greater than the
start index).  After it has filled in all table entries for
constituents that span one element of text, it fills in the
entries for constitutants that span two elements of text.  It
continues filling in the entries for constituents spanning larger
and larger portions of the text, until the entire table has been
filled.  Finally, it returns the table entry for a constituent
spanning the entire text, whose node value is the grammar's start
symbol.

In order to find the most likely constituent with a given span and
node value, the ``ViterbiParser`` parser considers all productions that
could produce that node value.  For each production, it finds all
children that collectively cover the span and have the node values
specified by the production's right hand side.  If the probability
of the tree formed by applying the production to the children is
greater than the probability of the current entry in the table,
then the table is updated with this new tree.

A pseudo-code description of the algorithm used by
``ViterbiParser`` is:

| Create an empty most likely constituent table, *MLC*.
| For width in 1...len(text):
|   For start in 1...len(text)-width:
|     For prod in grammar.productions:
|       For each sequence of subtrees [t, t, ..., t[n]] in MLC,
|         where t[i].label()==prod.rhs[i],
|         and the sequence covers [start:start+width]:
|           old_p = MLC[start, start+width, prod.lhs]
|           new_p = P(t)P(t)...P(t[n])P(prod)
|           if new_p > old_p:
|             new_tree = Tree(prod.lhs, t, t, ..., t[n])
|             MLC[start, start+width, prod.lhs] = new_tree
| Return MLC[0, len(text), start_symbol]

:type _grammar: PCFG
:ivar _grammar: The grammar used to parse sentences.
:type _trace: int
:ivar _trace: The level of tracing output that should be generated
when parsing a text.
"""

[docs]    def __init__(self, grammar, trace=0):
"""
Create a new ``ViterbiParser`` parser, that uses ``grammar`` to
parse texts.

:type grammar: PCFG
:param grammar: The grammar used to parse texts.
:type trace: int
:param trace: The level of tracing that should be used when
parsing a text.  ``0`` will generate no tracing output;
and higher numbers will produce more verbose tracing
output.
"""
self._grammar = grammar
self._trace = trace

[docs]    def grammar(self):
return self._grammar

[docs]    def trace(self, trace=2):
"""
Set the level of tracing output that should be generated when
parsing a text.

:type trace: int
:param trace: The trace level.  A trace level of ``0`` will
generate no tracing output; and higher trace levels will
produce more verbose tracing output.
:rtype: None
"""
self._trace = trace

[docs]    def parse(self, tokens):
# Inherit docs from ParserI

tokens = list(tokens)
self._grammar.check_coverage(tokens)

# The most likely constituent table.  This table specifies the
# most likely constituent for a given span and type.
# Constituents can be either Trees or tokens.  For Trees,
# the "type" is the Nonterminal for the tree's root node
# value.  For Tokens, the "type" is the token's type.
# The table is stored as a dictionary, since it is sparse.
constituents = {}

# Initialize the constituents dictionary with the words from
# the text.
if self._trace:
print("Inserting tokens into the most likely" + " constituents table...")
for index in range(len(tokens)):
token = tokens[index]
constituents[index, index + 1, token] = token
if self._trace > 1:
self._trace_lexical_insertion(token, index, len(tokens))

# Consider each span of length 1, 2, ..., n; and add any trees
# that might cover that span to the constituents dictionary.
for length in range(1, len(tokens) + 1):
if self._trace:
print(
"Finding the most likely constituents"
+ " spanning %d text elements..." % length
)
for start in range(len(tokens) - length + 1):
span = (start, start + length)

# Return the tree that spans the entire text & have the right cat
tree = constituents.get((0, len(tokens), self._grammar.start()))
if tree is not None:
yield tree

"""
Find any constituents that might cover ``span``, and add them
to the most likely constituents table.

:rtype: None
:type span: tuple(int, int)
:param span: The section of the text for which we are
trying to find possible constituents.  The span is
specified as a pair of integers, where the first integer
is the index of the first token that should be included in
the constituent; and the second integer is the index of
the first token that should not be included in the
constituent.  I.e., the constituent should cover
``text[span:span]``, where ``text`` is the text
that we are parsing.

:type constituents: dict(tuple(int,int,Nonterminal) -> ProbabilisticToken or ProbabilisticTree)
:param constituents: The most likely constituents table.  This
table records the most probable tree representation for
any given span and node value.  In particular,
``constituents(s,e,nv)`` is the most likely
``ProbabilisticTree`` that covers ``text[s:e]``
and has a node value ``nv.symbol()``, where ``text``
is the text that we are parsing.  When
should contain all possible constituents that are shorter
than ``span``.

:type tokens: list of tokens
:param tokens: The text we are parsing.  This is only used for
trace output.
"""
# Since some of the grammar productions may be unary, we need to
# repeatedly try all of the productions until none of them add any
# new constituents.
changed = True
while changed:
changed = False

# Find all ways instantiations of the grammar productions that
# cover the span.
instantiations = self._find_instantiations(span, constituents)

# For each production instantiation, add a new
# ProbabilisticTree whose probability is the product
# of the childrens' probabilities and the production's
# probability.
for (production, children) in instantiations:
subtrees = [c for c in children if isinstance(c, Tree)]
p = reduce(lambda pr, t: pr * t.prob(), subtrees, production.prob())
node = production.lhs().symbol()
tree = ProbabilisticTree(node, children, prob=p)

# If it's new a constituent, then add it to the
# constituents dictionary.
c = constituents.get((span, span, production.lhs()))
if self._trace > 1:
if c is None or c != tree:
if c is None or c.prob() < tree.prob():
print("   Insert:", end=" ")
else:
self._trace_production(production, p, span, len(tokens))
if c is None or c.prob() < tree.prob():
constituents[span, span, production.lhs()] = tree
changed = True

def _find_instantiations(self, span, constituents):
"""
:return: a list of the production instantiations that cover a
given span of the text.  A "production instantiation" is
a tuple containing a production and a list of children,
where the production's right hand side matches the list of
children; and the children cover ``span``.  :rtype: list
of ``pair`` of ``Production``, (list of
(``ProbabilisticTree`` or token.

:type span: tuple(int, int)
:param span: The section of the text for which we are
trying to find production instantiations.  The span is
specified as a pair of integers, where the first integer
is the index of the first token that should be covered by
the production instantiation; and the second integer is
the index of the first token that should not be covered by
the production instantiation.
:type constituents: dict(tuple(int,int,Nonterminal) -> ProbabilisticToken or ProbabilisticTree)
:param constituents: The most likely constituents table.  This
table records the most probable tree representation for
any given span and node value.  See the module
"""
rv = []
for production in self._grammar.productions():
childlists = self._match_rhs(production.rhs(), span, constituents)

for childlist in childlists:
rv.append((production, childlist))
return rv

def _match_rhs(self, rhs, span, constituents):
"""
:return: a set of all the lists of children that cover ``span``
and that match ``rhs``.
:rtype: list(list(ProbabilisticTree or token)

:type rhs: list(Nonterminal or any)
:param rhs: The list specifying what kinds of children need to
cover ``span``.  Each nonterminal in ``rhs`` specifies
that the corresponding child should be a tree whose node
value is that nonterminal's symbol.  Each terminal in ``rhs``
specifies that the corresponding child should be a token
whose type is that terminal.
:type span: tuple(int, int)
:param span: The section of the text for which we are
trying to find child lists.  The span is specified as a
pair of integers, where the first integer is the index of
the first token that should be covered by the child list;
and the second integer is the index of the first token
that should not be covered by the child list.
:type constituents: dict(tuple(int,int,Nonterminal) -> ProbabilisticToken or ProbabilisticTree)
:param constituents: The most likely constituents table.  This
table records the most probable tree representation for
any given span and node value.  See the module
"""
(start, end) = span

# Base case
if start >= end and rhs == ():
return [[]]
if start >= end or rhs == ():
return []

# Find everything that matches the 1st symbol of the RHS
childlists = []
for split in range(start, end + 1):
l = constituents.get((start, split, rhs))
if l is not None:
rights = self._match_rhs(rhs[1:], (split, end), constituents)
childlists += [[l] + r for r in rights]

return childlists

def _trace_production(self, production, p, span, width):
"""
Print trace output indicating that a given production has been
applied at a given location.

:param production: The production that has been applied
:type production: Production
:param p: The probability of the tree produced by the production.
:type p: float
:param span: The span of the production
:type span: tuple
:rtype: None
"""

str = "|" + "." * span
str += "=" * (span - span)
str += "." * (width - span) + "| "
str += "%s" % production
if self._trace > 2:
str = f"{str:<40} {p:12.10f} "

print(str)

def _trace_lexical_insertion(self, token, index, width):
str = "   Insert: |" + "." * index + "=" + "." * (width - index - 1) + "| "
str += f"{token}"
print(str)

def __repr__(self):
return "<ViterbiParser for %r>" % self._grammar

##//////////////////////////////////////////////////////
##  Test Code
##//////////////////////////////////////////////////////

[docs]def demo():
"""
A demonstration of the probabilistic parsers.  The user is
prompted to select which demo to run, and how many parses should
be found; and then each parser is run on the same demo, and a
summary of the results are displayed.
"""
import sys
import time

from nltk import tokenize
from nltk.grammar import PCFG
from nltk.parse import ViterbiParser

toy_pcfg1 = PCFG.fromstring(
"""
S -> NP VP [1.0]
NP -> Det N [0.5] | NP PP [0.25] | 'John' [0.1] | 'I' [0.15]
Det -> 'the' [0.8] | 'my' [0.2]
N -> 'man' [0.5] | 'telescope' [0.5]
VP -> VP PP [0.1] | V NP [0.7] | V [0.2]
V -> 'ate' [0.35] | 'saw' [0.65]
PP -> P NP [1.0]
P -> 'with' [0.61] | 'under' [0.39]
"""
)

toy_pcfg2 = PCFG.fromstring(
"""
S    -> NP VP         [1.0]
VP   -> V NP          [.59]
VP   -> V             [.40]
VP   -> VP PP         [.01]
NP   -> Det N         [.41]
NP   -> Name          [.28]
NP   -> NP PP         [.31]
PP   -> P NP          [1.0]
V    -> 'saw'         [.21]
V    -> 'ate'         [.51]
V    -> 'ran'         [.28]
N    -> 'boy'         [.11]
N    -> 'table'       [.13]
N    -> 'telescope'   [.14]
N    -> 'hill'        [.5]
Name -> 'Jack'        [.52]
Name -> 'Bob'         [.48]
P    -> 'with'        [.61]
P    -> 'under'       [.39]
Det  -> 'the'         [.41]
Det  -> 'a'           [.31]
Det  -> 'my'          [.28]
"""
)

# Define two demos.  Each demo has a sentence and a grammar.
demos = [
("I saw the man with my telescope", toy_pcfg1),
("the boy saw Jack with Bob under the table with a telescope", toy_pcfg2),
]

# Ask the user which demo they want to use.
print()
for i in range(len(demos)):
print(f"{i + 1:>3}: {demos[i]}")
print("     %r" % demos[i])
print()
print("Which demo (%d-%d)? " % (1, len(demos)), end=" ")
try:
sent, grammar = demos[snum]
except:
return

# Tokenize the sentence.
tokens = sent.split()

parser = ViterbiParser(grammar)
all_parses = {}

print(f"\nsent: {sent}\nparser: {parser}\ngrammar: {grammar}")
parser.trace(3)
t = time.time()
parses = parser.parse_all(tokens)
time = time.time() - t
average = (
reduce(lambda a, b: a + b.prob(), parses, 0) / len(parses) if parses else 0
)
num_parses = len(parses)
for p in parses:
all_parses[p.freeze()] = 1

# Print some summary statistics
print()
print("Time (secs)   # Parses   Average P(parse)")
print("-----------------------------------------")
print("%11.4f%11d%19.14f" % (time, num_parses, average))
parses = all_parses.keys()
if parses:
p = reduce(lambda a, b: a + b.prob(), parses, 0) / len(parses)
else:
p = 0
print("------------------------------------------")
print("%11s%11d%19.14f" % ("n/a", len(parses), p))

# Ask the user if we should draw the parses.
print()
print("Draw parses (y/n)? ", end=" ")
from nltk.draw.tree import draw_trees