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nlp.py
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nlp.py
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"""A chart parser and some grammars. (Chapter 22)"""
# (Written for the second edition of AIMA; expect some discrepanciecs
# from the third edition until this gets reviewed.)
from utils import *
from collections import defaultdict
#______________________________________________________________________________
# Grammars and Lexicons
def Rules(**rules):
"""Create a dictionary mapping symbols to alternative sequences.
>>> Rules(A = "B C | D E")
{'A': [['B', 'C'], ['D', 'E']]}
"""
for (lhs, rhs) in list(rules.items()):
rules[lhs] = [alt.strip().split() for alt in rhs.split('|')]
return rules
def Lexicon(**rules):
"""Create a dictionary mapping symbols to alternative words.
>>> Lexicon(Art = "the | a | an")
{'Art': ['the', 'a', 'an']}
"""
for (lhs, rhs) in list(rules.items()):
rules[lhs] = [word.strip() for word in rhs.split('|')]
return rules
class Grammar:
def __init__(self, name, rules, lexicon):
"A grammar has a set of rules and a lexicon."
update(self, name=name, rules=rules, lexicon=lexicon)
self.categories = defaultdict(list)
for lhs in lexicon:
for word in lexicon[lhs]:
self.categories[word].append(lhs)
def rewrites_for(self, cat):
"Return a sequence of possible rhs's that cat can be rewritten as."
return self.rules.get(cat, ())
def isa(self, word, cat):
"Return True iff word is of category cat"
return cat in self.categories[word]
def __repr__(self):
return '<Grammar %s>' % self.name
E0 = Grammar('E0',
Rules( # Grammar for E_0 [Fig. 22.4]
S='NP VP | S Conjunction S',
NP='Pronoun | Name | Noun | Article Noun | Digit Digit | NP PP | NP RelClause',
VP='Verb | VP NP | VP Adjective | VP PP | VP Adverb',
PP='Preposition NP',
RelClause='That VP'),
Lexicon( # Lexicon for E_0 [Fig. 22.3]
Noun="stench | breeze | glitter | nothing | wumpus | pit | pits | gold | east",
Verb="is | see | smell | shoot | fell | stinks | go | grab | carry | kill | turn | feel",
Adjective="right | left | east | south | back | smelly",
Adverb="here | there | nearby | ahead | right | left | east | south | back",
Pronoun="me | you | I | it",
Name="John | Mary | Boston | Aristotle",
Article="the | a | an",
Preposition="to | in | on | near",
Conjunction="and | or | but",
Digit="0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9",
That="that"
))
E_ = Grammar('E_', # Trivial Grammar and lexicon for testing
Rules(
S='NP VP',
NP='Art N | Pronoun',
VP='V NP'),
Lexicon(
Art='the | a',
N='man | woman | table | shoelace | saw',
Pronoun='I | you | it',
V='saw | liked | feel'
))
E_NP_ = Grammar('E_NP_', # another trivial grammar for testing
Rules(NP='Adj NP | N'),
Lexicon(Adj='happy | handsome | hairy',
N='man'))
def generate_random(grammar=E_, s='S'):
"""Replace each token in s by a random entry in grammar (recursively).
This is useful for testing a grammar, e.g. generate_random(E_)"""
import random
def rewrite(tokens, into):
for token in tokens:
if token in grammar.rules:
rewrite(random.choice(grammar.rules[token]), into)
elif token in grammar.lexicon:
into.append(random.choice(grammar.lexicon[token]))
else:
into.append(token)
return into
return ' '.join(rewrite(s.split(), []))
#______________________________________________________________________________
# Chart Parsing
class Chart:
"""Class for parsing sentences using a chart data structure. [Fig 22.7]
>>> chart = Chart(E0);
>>> len(chart.parses('the stench is in 2 2'))
1
"""
def __init__(self, grammar, trace=False):
"""A datastructure for parsing a string; and methods to do the parse.
self.chart[i] holds the edges that end just before the i'th word.
Edges are 5-element lists of [start, end, lhs, [found], [expects]]."""
update(self, grammar=grammar, trace=trace)
def parses(self, words, S='S'):
"""Return a list of parses; words can be a list or string.
>>> chart = Chart(E_NP_)
>>> chart.parses('happy man', 'NP')
[[0, 2, 'NP', [('Adj', 'happy'), [1, 2, 'NP', [('N', 'man')], []]], []]]
"""
if isinstance(words, str):
words = words.split()
self.parse(words, S)
# Return all the parses that span the whole input
# 'span the whole input' => begin at 0, end at len(words)
return [[i, j, S, found, []]
for (i, j, lhs, found, expects) in self.chart[len(words)]
# assert j == len(words)
if i == 0 and lhs == S and expects == []]
def parse(self, words, S='S'):
"""Parse a list of words; according to the grammar.
Leave results in the chart."""
self.chart = [[] for i in range(len(words)+1)]
self.add_edge([0, 0, 'S_', [], [S]])
for i in range(len(words)):
self.scanner(i, words[i])
return self.chart
def add_edge(self, edge):
"Add edge to chart, and see if it extends or predicts another edge."
start, end, lhs, found, expects = edge
if edge not in self.chart[end]:
self.chart[end].append(edge)
if self.trace:
print('%10s: added %s' % (caller(2), edge))
if not expects:
self.extender(edge)
else:
self.predictor(edge)
def scanner(self, j, word):
"For each edge expecting a word of this category here, extend the edge."
for (i, j, A, alpha, Bb) in self.chart[j]:
if Bb and self.grammar.isa(word, Bb[0]):
self.add_edge([i, j+1, A, alpha + [(Bb[0], word)], Bb[1:]])
def predictor(self, xxx_todo_changeme):
"Add to chart any rules for B that could help extend this edge."
(i, j, A, alpha, Bb) = xxx_todo_changeme
B = Bb[0]
if B in self.grammar.rules:
for rhs in self.grammar.rewrites_for(B):
self.add_edge([j, j, B, [], rhs])
def extender(self, edge):
"See what edges can be extended by this edge."
(j, k, B, _, _) = edge
for (i, j, A, alpha, B1b) in self.chart[j]:
if B1b and B == B1b[0]:
self.add_edge([i, k, A, alpha + [edge], B1b[1:]])
# TODO:
# 1. Parsing with augmentations -- requires unification, etc.
# 2. Sequitor
__doc__ += """
>>> chart = Chart(E0)
>>> chart.parses('the wumpus that is smelly is near 2 2')
[[0, 9, 'S', [[0, 5, 'NP', [[0, 2, 'NP', [('Article', 'the'), ('Noun', 'wumpus')], []], [2, 5, 'RelClause', [('That', 'that'), [3, 5, 'VP', [[3, 4, 'VP', [('Verb', 'is')], []], ('Adjective', 'smelly')], []]], []]], []], [5, 9, 'VP', [[5, 6, 'VP', [('Verb', 'is')], []], [6, 9, 'PP', [('Preposition', 'near'), [7, 9, 'NP', [('Digit', '2'), ('Digit', '2')], []]], []]], []]], []]]
### There is a built-in trace facility (compare [Fig. 22.9])
>>> Chart(E_, trace=True).parses('I feel it')
parse: added [0, 0, 'S_', [], ['S']]
predictor: added [0, 0, 'S', [], ['NP', 'VP']]
predictor: added [0, 0, 'NP', [], ['Art', 'N']]
predictor: added [0, 0, 'NP', [], ['Pronoun']]
scanner: added [0, 1, 'NP', [('Pronoun', 'I')], []]
extender: added [0, 1, 'S', [[0, 1, 'NP', [('Pronoun', 'I')], []]], ['VP']]
predictor: added [1, 1, 'VP', [], ['V', 'NP']]
scanner: added [1, 2, 'VP', [('V', 'feel')], ['NP']]
predictor: added [2, 2, 'NP', [], ['Art', 'N']]
predictor: added [2, 2, 'NP', [], ['Pronoun']]
scanner: added [2, 3, 'NP', [('Pronoun', 'it')], []]
extender: added [1, 3, 'VP', [('V', 'feel'), [2, 3, 'NP', [('Pronoun', 'it')], []]], []]
extender: added [0, 3, 'S', [[0, 1, 'NP', [('Pronoun', 'I')], []], [1, 3, 'VP', [('V', 'feel'), [2, 3, 'NP', [('Pronoun', 'it')], []]], []]], []]
extender: added [0, 3, 'S_', [[0, 3, 'S', [[0, 1, 'NP', [('Pronoun', 'I')], []], [1, 3, 'VP', [('V', 'feel'), [2, 3, 'NP', [('Pronoun', 'it')], []]], []]], []]], []]
[[0, 3, 'S', [[0, 1, 'NP', [('Pronoun', 'I')], []], [1, 3, 'VP', [('V', 'feel'), [2, 3, 'NP', [('Pronoun', 'it')], []]], []]], []]]
"""