aima-python/nlp4e.py at master · binlecode/aima-python · GitHub

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"""Natural Language Processing (Chapter 22)"""

from collections import defaultdict

from utils4e import weighted_choice

import copy

import operator

import heapq

from search import Problem

# ______________________________________________________________________________

# 22.2 Grammars

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 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(Article = "the | a | an")

{'Article': ['the', 'a', 'an']}

"""

for (lhs, rhs) in 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."""

self.name = name

self.rules = rules

self.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 cnf_rules(self):

"""Returns the tuple (X, Y, Z) for rules in the form:

X -> Y Z"""

cnf = []

for X, rules in self.rules.items():

for (Y, Z) in rules:

cnf.append((X, Y, Z))

return cnf

def generate_random(self, S='S'):

"""Replace each token in S by a random entry in grammar (recursively)."""

import random

def rewrite(tokens, into):

for token in tokens:

if token in self.rules:

rewrite(random.choice(self.rules[token]), into)

elif token in self.lexicon:

into.append(random.choice(self.lexicon[token]))

else:

into.append(token)

return into

return ' '.join(rewrite(S.split(), []))

def __repr__(self):

return '<Grammar {}>'.format(self.name)

def ProbRules(**rules):

"""Create a dictionary mapping symbols to alternative sequences,

with probabilities.

>>> ProbRules(A = "B C [0.3] | D E [0.7]")

{'A': [(['B', 'C'], 0.3), (['D', 'E'], 0.7)]}

"""

for (lhs, rhs) in rules.items():

rules[lhs] = []

rhs_separate = [alt.strip().split() for alt in rhs.split('|')]

for r in rhs_separate:

prob = float(r[-1][1:-1]) # remove brackets, convert to float

rhs_rule = (r[:-1], prob)

rules[lhs].append(rhs_rule)

return rules

def ProbLexicon(**rules):

"""Create a dictionary mapping symbols to alternative words,

with probabilities.

>>> ProbLexicon(Article = "the [0.5] | a [0.25] | an [0.25]")

{'Article': [('the', 0.5), ('a', 0.25), ('an', 0.25)]}

"""

for (lhs, rhs) in rules.items():

rules[lhs] = []

rhs_separate = [word.strip().split() for word in rhs.split('|')]

for r in rhs_separate:

prob = float(r[-1][1:-1]) # remove brackets, convert to float

word = r[:-1][0]

rhs_rule = (word, prob)

rules[lhs].append(rhs_rule)

return rules

class ProbGrammar:

def __init__(self, name, rules, lexicon):

"""A grammar has a set of rules and a lexicon.

Each rule has a probability."""

self.name = name

self.rules = rules

self.lexicon = lexicon

self.categories = defaultdict(list)

for lhs in lexicon:

for word, prob in lexicon[lhs]:

self.categories[word].append((lhs, prob))

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 [c for c, _ in self.categories[word]]

def cnf_rules(self):

"""Returns the tuple (X, Y, Z, p) for rules in the form:

X -> Y Z [p]"""

cnf = []

for X, rules in self.rules.items():

for (Y, Z), p in rules:

cnf.append((X, Y, Z, p))

return cnf

def generate_random(self, S='S'):

"""Replace each token in S by a random entry in grammar (recursively).

Returns a tuple of (sentence, probability)."""

def rewrite(tokens, into):

for token in tokens:

if token in self.rules:

non_terminal, prob = weighted_choice(self.rules[token])

into[1] *= prob

rewrite(non_terminal, into)

elif token in self.lexicon:

terminal, prob = weighted_choice(self.lexicon[token])

into[0].append(terminal)

into[1] *= prob

else:

into[0].append(token)

return into

rewritten_as, prob = rewrite(S.split(), [[], 1])

return (' '.join(rewritten_as), prob)

def __repr__(self):

return '<Grammar {}>'.format(self.name)

E0 = Grammar('E0',

Rules( # Grammar for E_0 [Figure 22.2]

S='NP VP | S Conjunction S',

VP='Verb | VP NP | VP Adjective | VP PP | VP Adverb',

PP='Preposition NP',

RelClause='That VP'),

Lexicon( # Lexicon for E_0 [Figure 22.3]

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'))

E_Prob = ProbGrammar('E_Prob', # The Probabilistic Grammar from the notebook

ProbRules(

S="NP VP [0.6] | S Conjunction S [0.4]",

NP="Pronoun [0.2] | Name [0.05] | Noun [0.2] | Article Noun [0.15] \

| Article Adjs Noun [0.1] | Digit [0.05] | NP PP [0.15] | NP RelClause [0.1]",

VP="Verb [0.3] | VP NP [0.2] | VP Adjective [0.25] | VP PP [0.15] | VP Adverb [0.1]",

Adjs="Adjective [0.5] | Adjective Adjs [0.5]",

PP="Preposition NP [1]",

RelClause="RelPro VP [1]"

ProbLexicon(

Verb="is [0.5] | say [0.3] | are [0.2]",

Noun="robot [0.4] | sheep [0.4] | fence [0.2]",

Adjective="good [0.5] | new [0.2] | sad [0.3]",

Adverb="here [0.6] | lightly [0.1] | now [0.3]",

Pronoun="me [0.3] | you [0.4] | he [0.3]",

RelPro="that [0.5] | who [0.3] | which [0.2]",

Name="john [0.4] | mary [0.4] | peter [0.2]",

Article="the [0.5] | a [0.25] | an [0.25]",

Preposition="to [0.4] | in [0.3] | at [0.3]",

Conjunction="and [0.5] | or [0.2] | but [0.3]",

Digit="0 [0.35] | 1 [0.35] | 2 [0.3]"

))

E_Chomsky = Grammar('E_Prob_Chomsky', # A Grammar in Chomsky Normal Form

Rules(

S='NP VP',

NP='Article Noun | Adjective Noun',

VP='Verb NP | Verb Adjective',

Lexicon(

Article='the | a | an',

Noun='robot | sheep | fence',

Adjective='good | new | sad',

Verb='is | say | are'

))

E_Prob_Chomsky = ProbGrammar('E_Prob_Chomsky', # A Probabilistic Grammar in CNF

ProbRules(

S='NP VP [1]',

NP='Article Noun [0.6] | Adjective Noun [0.4]',

VP='Verb NP [0.5] | Verb Adjective [0.5]',

ProbLexicon(

Article='the [0.5] | a [0.25] | an [0.25]',

Noun='robot [0.4] | sheep [0.4] | fence [0.2]',

Adjective='good [0.5] | new [0.2] | sad [0.3]',

Verb='is [0.5] | say [0.3] | are [0.2]'

))

E_Prob_Chomsky_ = ProbGrammar('E_Prob_Chomsky_',

ProbRules(

S='NP VP [1]',

NP='NP PP [0.4] | Noun Verb [0.6]',

PP='Preposition NP [1]',

VP='Verb NP [0.7] | VP PP [0.3]',

ProbLexicon(

Noun='astronomers [0.18] | eyes [0.32] | stars [0.32] | telescopes [0.18]',

Verb='saw [0.5] | \'\' [0.5]',

Preposition='with [1]'

))

# ______________________________________________________________________________

# 22.3 Parsing

class Chart:

"""Class for parsing sentences using a chart data structure.

>>> chart = Chart(E0)

>>> len(chart.parses('the stench is in 2 2'))

"""

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]]."""

self.grammar = grammar

self.trace = trace

def parses(self, words, S='S'):

"""Return a list of parses; words can be a list or string."""

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('Chart: added {}'.format(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, edge):

"""Add to chart any rules for B that could help extend this edge."""

(i, j, A, alpha, Bb) = edge

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:]])

# ______________________________________________________________________________

# CYK Parsing

class Tree:

def __init__(self, root, *args):

self.root = root

self.leaves = [leaf for leaf in args]

def CYK_parse(words, grammar):

""" [Figure 22.6] """

# We use 0-based indexing instead of the book's 1-based.

P = defaultdict(float)

T = defaultdict(Tree)

# Insert lexical categories for each word.

for (i, word) in enumerate(words):

for (X, p) in grammar.categories[word]:

P[X, i, i] = p

T[X, i, i] = Tree(X, word)

# Construct X(i:k) from Y(i:j) and Z(j+1:k), shortest span first

for i, j, k in subspan(len(words)):

for (X, Y, Z, p) in grammar.cnf_rules():

PYZ = P[Y, i, j] * P[Z, j+1, k] * p

if PYZ > P[X, i, k]:

P[X, i, k] = PYZ

T[X, i, k] = Tree(X, T[Y, i, j], T[Z, j+1, k])

return T

def subspan(N):

"""returns all tuple(i, j, k) covering a span (i, k) with i <= j < k"""

for length in range(2, N+1):

for i in range(1, N+2-length):

k = i + length - 1

for j in range(i, k):

yield (i, j, k)

# using search algorithms in the searching part

class TextParsingProblem(Problem):

def __init__(self, initial, grammar, goal='S'):

"""

:param initial: the initial state of words in a list.

:param grammar: a grammar object

:param goal: the goal state, usually S

"""

super(TextParsingProblem, self).__init__(initial, goal)

self.grammar = grammar

self.combinations = defaultdict(list) # article combinations

# backward lookup of rules

for rule in grammar.rules:

for comb in grammar.rules[rule]:

self.combinations[' '.join(comb)].append(rule)

def actions(self, state):

actions = []

categories = self.grammar.categories

# first change each word to the article of its category

for i in range(len(state)):

word = state[i]

if word in categories:

for X in categories[word]:

state[i] = X

actions.append(copy.copy(state))

state[i] = word

# if all words are replaced by articles, replace combinations of articles by inferring rules.

if not actions:

for start in range(len(state)):

for end in range(start, len(state)+1):

# try combinations between (start, end)

articles = ' '.join(state[start:end])

for c in self.combinations[articles]:

actions.append(state[:start] + [c] + state[end:])

return actions

def result(self, state, action):

return action

def h(self, state):

# heuristic function

return len(state)

def astar_search_parsing(words, gramma):

"""bottom-up parsing using A* search to find whether a list of words is a sentence"""

# init the problem

problem = TextParsingProblem(words, gramma, 'S')

state = problem.initial

# init the searching frontier

frontier = [(len(state)+problem.h(state), state)]

heapq.heapify(frontier)

while frontier:

# search the frontier node with lowest cost first

cost, state = heapq.heappop(frontier)

actions = problem.actions(state)

for action in actions:

new_state = problem.result(state, action)

# update the new frontier node to the frontier

if new_state == [problem.goal]:

return problem.goal

if new_state != state:

heapq.heappush(frontier, (len(new_state)+problem.h(new_state), new_state))

return False

def beam_search_parsing(words, gramma, b=3):

"""bottom-up text parsing using beam search"""

# init problem

problem = TextParsingProblem(words, gramma, 'S')

# init frontier

frontier = [(len(problem.initial), problem.initial)]

heapq.heapify(frontier)

# explore the current frontier and keep b new states with lowest cost

def explore(frontier):

new_frontier = []

for cost, state in frontier:

# expand the possible children states of current state

if not problem.goal_test(' '.join(state)):

actions = problem.actions(state)

for action in actions:

new_state = problem.result(state, action)

if [len(new_state), new_state] not in new_frontier and new_state != state:

new_frontier.append([len(new_state), new_state])

else:

return problem.goal

heapq.heapify(new_frontier)

# only keep b states

return heapq.nsmallest(b, new_frontier)

while frontier:

frontier = explore(frontier)

if frontier == problem.goal:

return frontier

return False

# ______________________________________________________________________________

# 22.4 Augmented Grammar

g = Grammar("arithmetic_expression", # A Grammar of Arithmetic Expression

rules={

'Number_0': 'Digit_0', 'Number_1': 'Digit_1', 'Number_2': 'Digit_2',

'Number_10': 'Number_1 Digit_0', 'Number_11': 'Number_1 Digit_1',

'Number_100': 'Number_10 Digit_0',

'Exp_5': ['Number_5', '( Exp_5 )', 'Exp_1, Operator_+ Exp_4', 'Exp_2, Operator_+ Exp_3',

'Exp_0, Operator_+ Exp_5', 'Exp_3, Operator_+ Exp_2', 'Exp_4, Operator_+ Exp_1',

'Exp_5, Operator_+ Exp_0', 'Exp_1, Operator_* Exp_5'], # more possible combinations

'Operator_+': operator.add, 'Operator_-': operator.sub, 'Operator_*':operator.mul, 'Operator_/': operator.truediv,

'Digit_0': 0, 'Digit_1': 1, 'Digit_2': 2, 'Digit_3': 3, 'Digit_4': 4

lexicon={})

g = Grammar("Ali loves Bob", # A example grammer of Ali loves Bob example

rules={

"S_loves_ali_bob": "NP_ali, VP_x_loves_x_bob", "S_loves_bob_ali": "NP_bob, VP_x_loves_x_ali",

"VP_x_loves_x_bob": "Verb_xy_loves_xy NP_bob", "VP_x_loves_x_ali": "Verb_xy_loves_xy NP_ali",

"NP_bob": "Name_bob", "NP_ali": "Name_ali"

lexicon={

"Name_ali":"Ali", "Name_bob": "Bob", "Verb_xy_loves_xy": "loves"

})

aima-python/nlp4e.py at master · binlecode/aima-python · GitHub

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