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tlips.py
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tlips.py
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# -*- coding: utf-8 -*-
"""
Created on Sat Jul 15 18:01:55 2017
@author: Rafael C. Carrasco
"""
__author__ = 'Rafael C. Carrasco'
__copyright__ = 'Universidad de Alicante, 2017'
__license__ = "GPL"
__version__ = "2.0"
import re
from random import uniform, seed
from math import log
from collections import deque, Counter
# A tree has a label (str) and children (list).
# Children is None for a leaf tree (such as t = a)
class Tree(object):
def __init__(self, label, children = None):
self.label = label
self.children = children
# Return True if tree is a leaf (no children)
def is_leaf(self):
return self.children == None
# Return tuple of subtrees (empty for a leaf)
def subtrees(self):
if self.children:
return self.children
else:
return tuple()
# Return a string representation of the node such as 'a' or 'c(a b(d))'
def __str__(self):
if self.children:
content = ' '.join(str(child) for child in self.children)
return self.label + '(' + content + ')'
else:
return self.label
# Parse the string representation of a tree or subtree
@staticmethod
def parse_tree(s):
s = s.strip() # Neglect neighbouring whitespace
m = re.match('\w*', s)
label = m.group(0)
if len(label) == len(s): # leaf node
children = None
else: # internal node: remove brackets
children = Tree.parse_forest(s[len(label) + 1:-1])
return Tree(label, children)
# Parse the string representation of the content of a node (child subtrees)
@staticmethod
def parse_forest(s):
forest = list()
s = s.strip()
depth = 0
start = 0
for pos in range(len(s)):
if s[pos] == '(':
depth += 1
elif s[pos] == ')':
depth -= 1
elif s[pos] == ' ':
if depth == 0:
node = Tree.parse_tree(s[start:pos])
forest.append(node)
start = pos + 1
if start < len(s):
node = Tree.parse_tree(s[start:])
forest.append(node)
return forest
# Test tree implementation
s = 'aa(b(e(g xh(a) i) ex) cx(d))'
t = Tree.parse_tree(s)
assert(str(t)==s)
# A transition rule is lhs -> rhs with an associated weight (probability)
# lhs (str or int), rhs (tuple), weight(int or float)
# the rhs tuple starts with a label (str) followed by a list of arguments
class Rule(object):
def __init__(self, lhs, rhs, weight):
self._lhs = lhs
self._rhs = rhs
self._weight = weight
def label(self):
return self._rhs[0]
def args(self):
return self._rhs[1:]
def lhs(self):
return self._lhs
def rhs(self):
return self._rhs
def weight(self):
return self._weight
def arity(self):
return len(self._rhs) - 1
def add_to_weight(self, n):
self._weight += n
def __str__(self):
args = ' '.join(map(str, self.args()))
return str(self.lhs()) + ' <- ' + self.label() + '(' + args + ')'
# A bottom-up deterministic tree automaton with a single final state (axiom),
# a set of states and a list of transtion rules.
class DTA(object):
# Provide axiom and list of transition rules
def __init__(self, axiom, rules = []):
self.axiom = axiom
self.states = set(rule.lhs() for rule in rules) # No useless states expected
self.rules = rules
# Auxiliary data structures for quick access
self.transitions = {rule.rhs():rule for rule in rules}
self.rights = {state:set() for state in self.states}
self.lefts = {state:set() for state in self.states}
self.total = Counter()
for rule in rules:
self.lefts[rule.lhs()].add(rule)
self.total[rule.lhs()] += rule.weight()
for state in rule.args():
self.rights[state].add(rule)
# Return a string representation of the DTA
def __str__(self):
rules = ', '.join(map(str, self.rules))
return 'S = ' + str(self.axiom) + '\nR = [' + rules + ']'
# Generate a random subtree with output q (a DTA state)
def _gen(self, q):
z = uniform(0, 1) * self.total[q]
s = 0
for rule in self.lefts[q]:
s += rule.weight()
if z <= s:
label = rule.label()
if rule.arity() > 0:
children = [self._gen(state) for state in rule.args()]
return Tree(label, children)
else:
return Tree(label)
return None
# Generate a random tree using DTA probabilites (rule weights)
def gen(self):
return self._gen(self.axiom)
# Return the output delta(t) for a tree or subtree t
def delta(self, tree):
key = ((tree.label),) + tuple(self.delta(s) for s in tree.subtrees())
if key in self.transitions:
return self.transitions[key].lhs()
else:
return None
# Count number of occurrences when the DTA operates on a subtreee
def _add_tree_counts(self, tree):
key = ((tree.label),) + tuple(self.delta(s) for s in tree.subtrees())
if key in self.transitions:
rule = self.transitions[key]
lhs = rule.lhs()
self.total[lhs] += 1
rule.add_to_weight(1)
return lhs
else:
return None
# Compute weights from sample (maximum likelihood estimation)
def compute_weights(self, sample):
for rule in self.transitions.values():
rule.weight = 0
for tree in sample:
self._add_tree_counts(tree)
# A DTA which accepts a sample of trees.
# State 0 (the axiom) is the only final state
class Acceptor(object):
def __init__(self, trees):
self.axiom = 0
self.states = {self.axiom}
self.rules = list()
# Create indices
self.transitions = dict()
self.lefts = {0:set()}
self.rights = {0:set()}
self.total = Counter()
for tree in trees:
# add all transitions required to parse the tree
root = self.add_tree(tree)
# add a root-to-axiom transition
self.add_final(root)
# Auxiliary sets for the inference process
self.kern = list()
self.frontier = deque()
self.merged = dict()
self.kern_rules = set()
# Return number of states in the acceptor
def __len__(self):
return len(self.states)
# Add a new state to the acceptor
def add_state(self, state):
if state not in self.states:
self.states.add(state)
self.rights[state] = set()
self.lefts[state] = set()
# Add a final (accepting) state
def add_final(self, state):
self.add_state(state)
key = ('ROOT', state)
if key in self.transitions:
self.transitions[key].add_to_weight(1)
else:
rule = Rule(0, key, 1)
self.add_rule(rule)
# Add a new transition rule to the aceptor
def add_rule(self, rule):
self.rules.append(rule)
self.transitions[rule.rhs()] = rule
lhs = rule.lhs()
self.add_state(lhs)
self.lefts[lhs].add(rule)
self.total[lhs] += rule.weight()
for state in rule.args():
self.add_state(state)
self.rights[state].add(rule)
# Return a string representation
def __str__(self):
rules = '\n'.join(str(r) + ':' + str(r.weight()) for r in self.rules)
return 'S = ' + str(self.axiom) \
+ '\nQ = ' + str(self.states) \
+ '\nR=\n' + rules
# Add all rules required to parse a subtree
def add_tree(self, tree):
key = ((tree.label),) + tuple(self.add_tree(s) for s in tree.subtrees())
if key in self.transitions:
rule = self.transitions[key]
rule.add_to_weight(1)
self.total[rule.lhs()] += 1
return rule.lhs()
else:
# new state is required
state = len(self.states)
rule = Rule(state, key, 1)
self.add_rule(rule)
return state
# Compare two Bernoulli outcomes: n1 out of t1 and n2 out of t2
@staticmethod
def differ(n1, t1, n2, t2, gamma):
if t1 > 0 and t2 > 0:
delta = abs(n1 / t1 - n2 / t2)
err = gamma * (1 / t1 + 1 / t2) ** 0.5
return delta > err
else:
return False
# Check if kern_state is compatible with this state
def compatible(self, kern_state, state, gamma):
t1 = self.total[kern_state]
t2 = self.total[state]
for rule in self.rights[state]:
n2 = rule.weight()
rhs2 = rule.rhs()
for pos in range(1, len(rhs2)):
if rhs2[pos] == state:
rhs1 = list(rhs2)
rhs1[pos] = kern_state
key = tuple(rhs1)
if key in self.transitions:
kern_rule = self.transitions[key]
n1 = kern_rule.weight()
else:
kern_rule = None
n1 = 0
if self.differ(n1, t1, n2, t2, gamma):
#print(kern_state, state, n1, t1, n2, t2)
return False
elif kern_rule and not self.compatible(kern_rule.lhs(), rule.lhs(), gamma):
return False
for kern_rule in self.rights[kern_state]:
n1 = kern_rule.weight()
rhs1 = kern_rule.rhs()
for pos in range(1, len(rhs1)):
if rhs1[pos] == kern_state:
rhs2 = list(rhs1)
rhs2[pos] = state
key = tuple(rhs2)
if key in self.transitions:
rule = self.transitions[key]
n2 = rule.weight()
else:
rule = None
n2 = 0
if self.differ(n1, t1, n2, t2, gamma):
#print(kern_state, state, n1, t1, n2, t2)
return False
elif rule and not self.compatible(kern_rule.lhs(), rule.lhs(), gamma):
return False
return True
# Return the first state in kern which is compatible with this state (None if none found)
def first_compatible_state_in_kern(self, state, gamma):
for kern_state in self.kern:
#print(kern_state)
if kern_state > 0 and self.compatible(kern_state, state, gamma):
return kern_state
return None
# Add to kern and update frontier with lhs-states if rhs is fully in kern
def add_to_kern(self, state):
self.kern.add(state)
for rule in self.rights[state]:
if set(rule.args()) <= self.kern:
q = rule.lhs()
if q not in self.kern and q not in self.merged:
self.frontier.append(q)
self.kern_rules.add(rule)
# The key algorithm
# alpha(float) = significance level
def infer(self, alpha):
gamma = (0.5 * log(2 / alpha))
self.kern = {0}
self.frontier = deque(rule.lhs() for rule in self.rules if rule.arity() == 0)
self.kern_rules = {rule for rule in self.rules if rule.arity() == 0}
while len(self.frontier) > 0:
state = self.frontier.popleft()
kern_state = self.first_compatible_state_in_kern(state, gamma)
if kern_state != None:
self.merged[state] = kern_state
else:
#print('addded', state, 'to K = ', self.kern)
self.add_to_kern(state)
rules = self.projected_kern_rules()
print('Merged', len(self.states), 'states into',
len(self.kern) - 1, 'states and', len(rules), 'rules')
return str(list(self.kern)), rules
def projected_kern_rules(self):
rules = set(self.kern_rules)
for rule in rules:
if rule.lhs() in self.merged:
rule._lhs = self.merged[rule.lhs()]
return [str(rule) for rule in rules]
# Main code
G = DTA(1,
[Rule(1, ('b',), 0.5),
Rule(1, ('', 2, 2), 0.5),
Rule(2, ('a',), 0.8),
Rule(2, ('', 1, 1), 0.2)
])
#print(G)
t = Tree.parse_tree('((b (a ((a a) ((b (a a)) a)))) a)')
t = Tree.parse_tree('b')
print(t, ' -> ', G.delta(t))
assert(G.delta(t)==1)
#seed(1)
sample = [G.gen() for n in range(1000)]
"""
with open('tlips.pkl', 'wb') as f:
pickle.dump(sample, f)
with open('tlips.pkl', 'rb') as f:
sample2 = pickle.load(f)
"""
a = Acceptor(sample)
#print(a)
res = a.infer(1/len(sample))
print('Kern=', res[0])
print('Rules=', res[1])
G = DTA(1,
[Rule(1, ('if-then-else-endif', 2, 1, 1), 0.2),
Rule(1, ('if-then-endif', 2, 1), 0.2),
Rule(1, ('print', 2), 0.6),
Rule(2, ('operator', 2, 3), 0.3),
Rule(2, ('', 3), 0.7),
Rule(3, ('exp n', 3), 0.1),
Rule(3, ('', 4), 0.9),
Rule(4, ('lpar-rpar', 3), 0.2),
Rule(4, ('n',), 0.8),
])
sample = [G.gen() for n in range(500)]
#print('t=', [str(t) for t in sample])
a = Acceptor(sample)
#print(a)
res = a.infer(1/len(a))
print('Kern=', res[0])
print('Rules=', res[1])