class SlicedEarley(object):
"""
"""
def __init__(self, wcfg, wfsa, slice_vars):
"""
"""
self._wcfg = wcfg
self._wfsa = wfsa
self._agenda = Agenda(active_container_type=ActiveQueue)
self._predictions = set() # (LHS, start)
self._item_factory = ItemFactory()
self.slice_vars = slice_vars
def get_item(self, rule, dot, inner=[]):
return self._item_factory.get_item(rule, dot, inner)
def advance(self, item, dot):
"""returns a new item whose dot has been advanced"""
return self.get_item(item.rule, dot, item.inner + (item.dot,))
def axioms(self, symbol, start):
rules = self._wcfg.get(symbol, None)
if rules is None: # impossible to rewrite the symbol
return False
if (symbol, start) in self._predictions: # already predicted
return True
# otherwise add rewritings to the agenda
self._predictions.add((symbol, start))
self._agenda.extend(self.get_item(rule, start) for rule in rules)
return True
def prediction(self, item):
"""
This operation tris to create items from the rules associated with the nonterminal ahead of the dot.
It returns True when prediction happens, and False if it already happened before.
"""
if (item.next, item.dot) in self._predictions: # prediction already happened
return False
self._predictions.add((item.next, item.dot))
new_items = [self.get_item(rule, item.dot) for rule in self._wcfg.get(item.next, frozenset())]
self._agenda.extend(new_items)
return True
def scan(self, item):
"""
This operation tries to scan over as many terminals as possible,
but we only go as far as determinism allows.
If we get to a nondeterminism, we stop scanning and add the relevant items to the agenda.
"""
states = [item.dot]
for sym in item.nextsymbols():
if is_terminal(sym):
arcs = self._wfsa.get_arcs(origin=states[-1], symbol=sym)
if len(arcs) == 0: # cannot scan the symbol
return False
elif len(arcs) == 1: # symbol is scanned deterministically
sto, _ = arcs[0]
states.append(sto) # we do not create intermediate items, instead we scan as much as we can
else: # here we found a nondeterminism, we create all relevant items and add them to the agenda
# create items
for sto, w in arcs:
self._agenda.add(self.get_item(item.rule, sto, item.inner + tuple(states)))
return True
else: # that's it, scan bumped into a nonterminal symbol, time to wrap up
break
# here we should have scanned at least one terminal symbol
# and we defined a deterministic path
self._agenda.add(self.get_item(item.rule, states[-1], item.inner + tuple(states[:-1])))
return True
def complete_others(self, item):
"""
This operation creates new item by advancing the dot of passive items that are waiting for a certain given complete item.
It returns whether or not at least one passive item awaited for the given complete item.
"""
if self._agenda.is_generating(item.rule.lhs, item.start, item.dot):
return True
new_items = [self.advance(incomplete, item.dot) for incomplete in self._agenda.iterwaiting(item.rule.lhs, item.start)]
self._agenda.extend(new_items)
return len(new_items) > 0 # was there any item waiting for the complete one?
def complete_itself(self, item):
"""
This operation tries to merge a given incomplete item with a previosly completed one.
"""
new_items = [self.advance(item, sto) for sto in self._agenda.itercompletions(item.next, item.dot)]
self._agenda.extend(new_items)
return len(new_items) > 0
def do(self, root='[S]', goal='[GOAL]'):
wfsa = self._wfsa
wcfg = self._wcfg
agenda = self._agenda
# start items of the kind
# GOAL -> * ROOT, where * is an intial state of the wfsa
if not any(self.axioms(root, start) for start in wfsa.iterinitial()):
raise ValueError('No rule for the start symbol %s' % root)
new_roots = set()
while agenda:
item = agenda.pop() # always returns an active item
if item.is_complete():
# get slice variable for the current completed item
u = self.slice_vars.get(item.rule.lhs, item.start, item.dot)
# check whether the probability of the current completed item is above the threshold determined by
# the slice variable
if item.rule.log_prob > u:
# complete root item spanning from a start wfsa state to a final wfsa state
if item.rule.lhs == root and wfsa.is_initial(item.start) and wfsa.is_final(item.dot):
agenda.make_complete(item)
new_roots.add((root, item.start, item.dot))
agenda.make_passive(item)
else:
if self.complete_others(item):
agenda.make_complete(item)
agenda.make_passive(item)
else: # a complete state is only kept in case it could potentially complete others
agenda.discard(item)
else:
if is_terminal(item.next):
# fire the operation 'scan'
self.scan(item)
agenda.discard(item) # scanning renders incomplete items of this kind useless
else:
if not wcfg.can_rewrite(item.next): # if the NT does not exist this item is useless
agenda.discard(item)
else:
if not self.prediction(item): # try to predict, otherwise try to complete itself
self.complete_itself(item)
agenda.make_passive(item)
# converts complete items into rules
logging.debug('Making forest...')
return self.get_cfg(goal, root)
def get_intersected_rule(self, item):
lhs = make_symbol(item.rule.lhs, item.start, item.dot)
positions = item.inner + (item.dot,)
rhs = [make_symbol(sym, positions[i], positions[i + 1]) for i, sym in enumerate(item.rule.rhs)]
return Rule(lhs, rhs, item.rule.log_prob)
def get_cfg(self, goal, root):
"""
Constructs the CFG by visiting complete items in a top-down fashion.
This is effectively a reachability test and it serves the purpose of filtering nonterminal symbols
that could never be reached from the root.
Note that bottom-up intersection typically does enumerate a lot of useless (unreachable) items.
This is the recursive procedure described in the paper (Nederhof and Satta, 2008).
"""
G = WCFG()
processed = set()
fsa = self._wfsa
itergenerating = self._agenda.itergenerating
itercomplete = self._agenda.itercomplete
def make_rules(lhs, start, end):
if (start, lhs, end) in processed:
return
processed.add((lhs, start, end))
for item in itercomplete(lhs, start, end):
G.add(self.get_intersected_rule(item))
fsa_states = item.inner + (item.dot,)
for i, sym in itertools.ifilter(lambda (_, s): is_nonterminal(s), enumerate(item.rule.rhs)):
if (sym, fsa_states[i], fsa_states[
i + 1]) not in processed: # Nederhof does not perform this test, but in python it turned out crucial
make_rules(sym, fsa_states[i], fsa_states[i + 1])
# create goal items
for start, ends in itergenerating(root):
if not fsa.is_initial(start):
continue
for end in itertools.ifilter(lambda q: fsa.is_final(q), ends):
make_rules(root, start, end)
G.add(Rule(make_symbol(goal, None, None),
[make_symbol(root, start, end)], 0.0))
return G
class Nederhof(object):
"""
This is an implementation of the CKY-inspired intersection due to Nederhof and Satta (2008).
"""
def __init__(self, wcfg, wfsa):
self._wcfg = wcfg
self._wfsa = wfsa
self._agenda = Agenda(active_container_type=ActiveQueue)
self._firstsym = defaultdict(
set) # index rules by their first RHS symbol
self._item_factory = ItemFactory()
def get_item(self, rule, dot, inner=[]):
return self._item_factory.get_item(rule, dot, inner)
def advance(self, item, dot):
"""returns a new item whose dot has been advanced"""
return self.get_item(item.rule, dot, item.inner + (item.dot, ))
def add_symbol(self, sym, sfrom, sto):
"""
This operation:
1) completes items waiting for `sym` from `sfrom`
2) instantiate delayed axioms
Returns False if the annotated symbol had already been added, True otherwise
"""
if self._agenda.is_generating(sym, sfrom, sto):
return False
# every item waiting for `sym` from `sfrom`
for item in self._agenda.iterwaiting(sym, sfrom):
self._agenda.add(self.advance(item, sto))
# you may interpret this as a delayed axiom
# every compatible rule in the grammar
for r in self._firstsym.get(sym, set()):
self._agenda.add(self.get_item(
r, sto, inner=(sfrom, ))) # can be interpreted as a lazy axiom
return True
def axioms(self):
"""
The axioms of the program are based on the FSA transitions.
"""
# you may interpret the following as a sort of lazy axiom (based on grammar rules)
for r in self._wcfg:
self._firstsym[r.rhs[0]].add(r)
# these are axioms based on the transitions of the automaton
for sfrom, sto, sym, w in self._wfsa.iterarcs():
self.add_symbol(sym, sfrom, sto)
def inference(self):
"""Exhausts the queue of active items"""
agenda = self._agenda
while agenda:
item = agenda.pop() # always returns an ACTIVE item
# complete other items (by calling add_symbol), in case the input item is complete
if item.is_complete():
self.add_symbol(item.rule.lhs, item.start,
item.dot) # prove the symbol
agenda.make_complete(item) # mark the item as complete
else:
# merges the input item with previously completed items effectively moving the input item's dot forward
agenda.make_passive(item)
for sto in agenda.itercompletions(item.next, item.dot):
agenda.add(self.advance(item, sto)) # move the dot forward
def do(self, root='[S]', goal='[GOAL]'):
"""Runs the program and returns the intersected CFG"""
self.axioms()
self.inference()
return get_cfg(goal, root, self._wfsa, self._agenda)
class SlicedEarley(object):
"""
"""
def __init__(self, wcfg, wfsa, slice_vars):
"""
"""
self._wcfg = wcfg
self._wfsa = wfsa
self._agenda = Agenda(active_container_type=ActiveQueue)
self._predictions = set() # (LHS, start)
self._item_factory = ItemFactory()
self.slice_vars = slice_vars
def get_item(self, rule, dot, inner=[]):
return self._item_factory.get_item(rule, dot, inner)
def advance(self, item, dot):
"""returns a new item whose dot has been advanced"""
return self.get_item(item.rule, dot, item.inner + (item.dot, ))
def axioms(self, symbol, start):
rules = self._wcfg.get(symbol, None)
if rules is None: # impossible to rewrite the symbol
return False
if (symbol, start) in self._predictions: # already predicted
return True
# otherwise add rewritings to the agenda
self._predictions.add((symbol, start))
self._agenda.extend(self.get_item(rule, start) for rule in rules)
return True
def prediction(self, item):
"""
This operation tris to create items from the rules associated with the nonterminal ahead of the dot.
It returns True when prediction happens, and False if it already happened before.
"""
if (item.next,
item.dot) in self._predictions: # prediction already happened
return False
self._predictions.add((item.next, item.dot))
new_items = [
self.get_item(rule, item.dot)
for rule in self._wcfg.get(item.next, frozenset())
]
self._agenda.extend(new_items)
return True
def scan(self, item):
"""
This operation tries to scan over as many terminals as possible,
but we only go as far as determinism allows.
If we get to a nondeterminism, we stop scanning and add the relevant items to the agenda.
"""
states = [item.dot]
for sym in item.nextsymbols():
if is_terminal(sym):
arcs = self._wfsa.get_arcs(origin=states[-1], symbol=sym)
if len(arcs) == 0: # cannot scan the symbol
return False
elif len(arcs) == 1: # symbol is scanned deterministically
sto, _ = arcs[0]
states.append(
sto
) # we do not create intermediate items, instead we scan as much as we can
else: # here we found a nondeterminism, we create all relevant items and add them to the agenda
# create items
for sto, w in arcs:
self._agenda.add(
self.get_item(item.rule, sto,
item.inner + tuple(states)))
return True
else: # that's it, scan bumped into a nonterminal symbol, time to wrap up
break
# here we should have scanned at least one terminal symbol
# and we defined a deterministic path
self._agenda.add(
self.get_item(item.rule, states[-1],
item.inner + tuple(states[:-1])))
return True
def complete_others(self, item):
"""
This operation creates new item by advancing the dot of passive items that are waiting for a certain given complete item.
It returns whether or not at least one passive item awaited for the given complete item.
"""
if self._agenda.is_generating(item.rule.lhs, item.start, item.dot):
return True
new_items = [
self.advance(incomplete,
item.dot) for incomplete in self._agenda.iterwaiting(
item.rule.lhs, item.start)
]
self._agenda.extend(new_items)
return len(
new_items) > 0 # was there any item waiting for the complete one?
def complete_itself(self, item):
"""
This operation tries to merge a given incomplete item with a previosly completed one.
"""
new_items = [
self.advance(item, sto)
for sto in self._agenda.itercompletions(item.next, item.dot)
]
self._agenda.extend(new_items)
return len(new_items) > 0
def do(self, root='[S]', goal='[GOAL]'):
wfsa = self._wfsa
wcfg = self._wcfg
agenda = self._agenda
# start items of the kind
# GOAL -> * ROOT, where * is an intial state of the wfsa
if not any(self.axioms(root, start) for start in wfsa.iterinitial()):
raise ValueError('No rule for the start symbol %s' % root)
new_roots = set()
while agenda:
item = agenda.pop() # always returns an active item
if item.is_complete():
# get slice variable for the current completed item
u = self.slice_vars.get(item.rule.lhs, item.start, item.dot)
# check whether the probability of the current completed item is above the threshold determined by
# the slice variable
if item.rule.log_prob > u:
# complete root item spanning from a start wfsa state to a final wfsa state
if item.rule.lhs == root and wfsa.is_initial(
item.start) and wfsa.is_final(item.dot):
agenda.make_complete(item)
new_roots.add((root, item.start, item.dot))
agenda.make_passive(item)
else:
if self.complete_others(item):
agenda.make_complete(item)
agenda.make_passive(item)
else: # a complete state is only kept in case it could potentially complete others
agenda.discard(item)
else:
if is_terminal(item.next):
# fire the operation 'scan'
self.scan(item)
agenda.discard(
item
) # scanning renders incomplete items of this kind useless
else:
if not wcfg.can_rewrite(
item.next
): # if the NT does not exist this item is useless
agenda.discard(item)
else:
if not self.prediction(
item
): # try to predict, otherwise try to complete itself
self.complete_itself(item)
agenda.make_passive(item)
# converts complete items into rules
logging.debug('Making forest...')
return self.get_cfg(goal, root)
def get_intersected_rule(self, item):
lhs = make_symbol(item.rule.lhs, item.start, item.dot)
positions = item.inner + (item.dot, )
rhs = [
make_symbol(sym, positions[i], positions[i + 1])
for i, sym in enumerate(item.rule.rhs)
]
return Rule(lhs, rhs, item.rule.log_prob)
def get_cfg(self, goal, root):
"""
Constructs the CFG by visiting complete items in a top-down fashion.
This is effectively a reachability test and it serves the purpose of filtering nonterminal symbols
that could never be reached from the root.
Note that bottom-up intersection typically does enumerate a lot of useless (unreachable) items.
This is the recursive procedure described in the paper (Nederhof and Satta, 2008).
"""
G = WCFG()
processed = set()
fsa = self._wfsa
itergenerating = self._agenda.itergenerating
itercomplete = self._agenda.itercomplete
def make_rules(lhs, start, end):
if (start, lhs, end) in processed:
return
processed.add((lhs, start, end))
for item in itercomplete(lhs, start, end):
G.add(self.get_intersected_rule(item))
fsa_states = item.inner + (item.dot, )
for i, sym in itertools.ifilter(
lambda (_, s): is_nonterminal(s),
enumerate(item.rule.rhs)):
if (
sym, fsa_states[i], fsa_states[i + 1]
) not in processed: # Nederhof does not perform this test, but in python it turned out crucial
make_rules(sym, fsa_states[i], fsa_states[i + 1])
# create goal items
for start, ends in itergenerating(root):
if not fsa.is_initial(start):
continue
for end in itertools.ifilter(lambda q: fsa.is_final(q), ends):
make_rules(root, start, end)
G.add(
Rule(make_symbol(goal, None, None),
[make_symbol(root, start, end)], 0.0))
return G
class SlicedNederhof(object):
"""
This is an implementation of the CKY-inspired intersection due to Nederhof and Satta (2008).
"""
def __init__(self, wcfg, wfsa, slice_vars):
self._wcfg = wcfg
self._wfsa = wfsa
self._agenda = Agenda(active_container_type=ActiveQueue)
self._firstsym = defaultdict(set) # index rules by their first RHS symbol
self._item_factory = ItemFactory()
self.slice_vars = slice_vars
def get_item(self, rule, dot, inner=[]):
return self._item_factory.get_item(rule, dot, inner)
def advance(self, item, dot):
"""returns a new item whose dot has been advanced"""
return self.get_item(item.rule, dot, item.inner + (item.dot,))
def add_symbol(self, sym, sfrom, sto):
"""
This operation:
1) completes items waiting for `sym` from `sfrom`
2) instantiate delayed axioms
Returns False if the annotated symbol had already been added, True otherwise
"""
if self._agenda.is_generating(sym, sfrom, sto):
return False
# every item waiting for `sym` from `sfrom`
for item in self._agenda.iterwaiting(sym, sfrom):
self._agenda.add(self.advance(item, sto))
# you may interpret this as a delayed axiom
# every compatible rule in the grammar
for r in self._firstsym.get(sym, set()):
self._agenda.add(self.get_item(r, sto, inner=(sfrom,))) # can be interpreted as a lazy axiom
return True
def axioms(self):
"""
The axioms of the program are based on the FSA transitions.
"""
# you may interpret the following as a sort of lazy axiom (based on grammar rules)
for r in self._wcfg:
self._firstsym[r.rhs[0]].add(r)
# these are axioms based on the transitions of the automaton
for sfrom, sto, sym, w in self._wfsa.iterarcs():
self.add_symbol(sym, sfrom, sto)
def inference(self):
"""Exhausts the queue of active items"""
agenda = self._agenda
while agenda:
item = agenda.pop() # always returns an ACTIVE item
# complete other items (by calling add_symbol), in case the input item is complete
if item.is_complete():
u = self.slice_vars.get(item.rule.lhs, item.start, item.dot)
# check whether the probability of the current completed item is above the threshold determined by
# the slice variable
if item.rule.log_prob > u:
self.add_symbol(item.rule.lhs, item.start, item.dot) # prove the symbol
agenda.make_complete(item) # mark the item as complete
else:
# merges the input item with previously completed items effectively moving the input item's dot forward
agenda.make_passive(item)
for sto in agenda.itercompletions(item.next, item.dot):
agenda.add(self.advance(item, sto)) # move the dot forward
def do(self, root='[S]', goal='[GOAL]'):
"""Runs the program and returns the intersected CFG"""
self.axioms()
self.inference()
return get_cfg(goal, root, self._wfsa, self._agenda)
