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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.)
# ______________________________________________________________________________
# Grammars and Lexicons
"""Create a dictionary mapping symbols to alternative sequences.
>>> Rules(A = "B C | D E")
{'A': [['B', 'C'], ['D', 'E']]}
"""
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']}
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 __repr__(self):
return '<Grammar %s>' % self.name
E0 = Grammar('E0',
Rules( # Grammar for E_0 [Figure 22.4]
NP='Pronoun | Name | Noun | Article Noun | Digit Digit | NP PP | NP RelClause', # noqa
VP='Verb | VP NP | VP Adjective | VP PP | VP Adverb',
PP='Preposition NP',
RelClause='That VP'),
Lexicon( # Lexicon for E_0 [Figure 22.3]
Noun="stench | breeze | glitter | nothing | wumpus | pit | pits | gold | east", # noqa
Verb="is | see | smell | shoot | fell | stinks | go | grab | carry | kill | turn | feel", # noqa
Adjective="right | left | east | south | back | smelly",
Adverb="here | there | nearby | ahead | right | left | east | south | back", # noqa
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. [Figure 22.7]
>>> 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]]."""
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:
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." # noqa
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:]])
"Add to chart any rules for B that could help extend this 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:]])