-
Notifications
You must be signed in to change notification settings - Fork 14
/
search.py
218 lines (184 loc) · 7.99 KB
/
search.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
"""
Proof graph for proof search.
"""
from common import *
from prover.proof import ProofStep
import networkx as nx
class ProofGraph:
def __init__(
self, context: OrderedDict[str, str], hypothesis: str, eps: float = 1e-7
) -> None:
self.graph = nx.DiGraph()
self.graph.add_node("hypothesis", score=0.0, step_score=None, sent=hypothesis)
self.graph.add_nodes_from(
[(k, {"score": 1.0, "sent": v}) for k, v in context.items()]
)
self.assumptions = set(context.keys())
self.intermediates = set()
self.hypothesis = hypothesis
self.sent2node = {v: k for k, v in context.items()}
self.sent2node[hypothesis] = "hypothesis"
assert nx.is_directed_acyclic_graph(self.graph)
self.eps = eps
def initialize(self, proof_steps: List[ProofStep], scores: List[float]):
if len(proof_steps) == 0:
return
assert len(proof_steps) == len(scores)
for step, score in zip(proof_steps, scores):
self.expand(step, score)
def sample_proof_tree(self, exclude: Set[str]) -> Optional[str]:
"""
Sample a new partial proof tree not in `exclude`.
"""
reachable_nodes = set()
for node in self.assumptions:
reachable_nodes.update(nx.descendants(self.graph, node))
reachable_component = nx.subgraph(self.graph, reachable_nodes)
hypothesis_score = self.graph.nodes["hypothesis"]["score"]
for _ in range(10):
partial_proof = ""
nodes_included = set()
for node in reversed(list(nx.topological_sort(reachable_component))):
if (
node == "hypothesis"
or node in nodes_included
or self.graph.nodes[node]["score"] <= hypothesis_score + self.eps
):
continue
subproof = self.extract_proof(node, nodes_proved=nodes_included) + " "
if random.random() < 0.5: # Include node.
partial_proof += subproof
nodes_included.add(node)
nodes_included.update(nx.ancestors(self.graph, node))
prf = rename_ints(partial_proof.strip())
if prf not in exclude:
return prf
return None
def extract_proof(
self, node: str, rename: bool = False, nodes_proved: Set[str] = set()
) -> str:
ancestors = nx.ancestors(self.graph, node)
ancestors.add(node)
ancestors -= nodes_proved
ancestors_subgraph = nx.subgraph(self.graph, ancestors)
proof = ""
for x in nx.topological_sort(ancestors_subgraph):
if x not in self.assumptions:
try:
proof += self.extract_proof_step(x)
except ValueError:
return "INVALID_PROOF"
if rename:
proof = rename_ints(proof)
return proof.strip()
def extract_proof_step(self, node: str) -> str:
assert node == "hypothesis" or node in self.intermediates
predecessors = list(self.graph.predecessors(node))
if len(predecessors) == 0:
raise ValueError
premises = " & ".join(predecessors)
if node == "hypothesis":
return f"{premises} -> hypothesis; "
else:
return f"{premises} -> {node}: {self.graph.nodes[node]['sent']}; "
def expand(self, proof_step: ProofStep, score: float) -> bool:
premises = []
for ident, sent in zip(proof_step.premise_idents, proof_step.premise_sents):
if re.fullmatch(r"sent\d+", ident):
premises.append(ident)
else:
premises.append(self.sent2node[sent])
dst_score = self.calculate_score(score, premises)
if dst_score <= self.graph.nodes["hypothesis"]["score"] + self.eps: # Prune.
return False
# Create a node for the conclusion if necessasry.
if proof_step.conclusion_ident == "hypothesis":
dst = "hypothesis"
self.remove_inbound_edges(dst)
self.graph.nodes["hypothesis"]["score"] = dst_score
self.graph.nodes["hypothesis"]["step_score"] = score
else:
sent = proof_step.conclusion_sent
dst = None
if sent in self.sent2node:
dst = self.sent2node[sent]
if dst is not None: # The node exists.
if (
dst in self.assumptions
or dst_score <= self.graph.nodes[dst]["score"] + self.eps
): # Prune.
return False
self.graph.nodes[dst]["score"] = dst_score
self.graph.nodes[dst]["step_score"] = score
self.remove_inbound_edges(dst)
self.propagate_score(dst)
else: # Need to create a new node.
dst = f"int{1 + len(self.intermediates)}"
self.graph.add_node(dst, score=dst_score, step_score=score, sent=sent)
self.intermediates.add(dst)
self.sent2node[sent] = dst
# Add edges from the premises.
for p in premises:
if p.startswith("sent"):
assert p in self.assumptions
else: # int
assert p in self.intermediates
self.graph.add_edge(p, dst)
assert nx.is_directed_acyclic_graph(self.graph)
return True
def remove_inbound_edges(self, node):
self.graph.remove_edges_from(list(self.graph.in_edges(node)))
def propagate_score(self, node):
for u in self.graph.successors(node):
score_new = self.agg_op(
self.graph.nodes[u]["step_score"],
[self.graph.nodes[v]["score"] for v in self.graph.predecessors(u)],
)
if score_new > self.graph.nodes[u]["score"] + self.eps:
self.graph.nodes[u]["score"] = score_new
self.propagate_score(u)
def calculate_score(self, step_score: float, premises: str) -> None:
return self.agg_op(step_score, [self.graph.nodes[p]["score"] for p in premises])
def agg_op(self, step_score: float, input_scores: List[float]) -> float:
return min([step_score] + input_scores)
def to_pydot(self):
nodes_to_visualize = {
node
for node in self.graph.nodes
if node not in self.assumptions or self.graph.out_degree(node) > 0
}
graph = nx.nx_pydot.to_pydot(nx.subgraph(self.graph, nodes_to_visualize))
for node in graph.get_nodes():
name = node.get_name()
if not name.startswith("sent"):
node.set_shape("box")
nx_node = self.graph.nodes[name]
label = f"{name}: {nx_node['sent']}"
if name not in self.assumptions:
label += f"\nstep_score: {nx_node['step_score']}"
label += f"\nscore: {nx_node['score']}"
node.set_label(label)
return graph
def visualize(self, fname: str) -> None:
graph = self.to_pydot()
# Highlight the ancestors of the hypothesis.
ancestors = nx.ancestors(self.graph, "hypothesis")
ancestors.add("hypothesis")
for nx_node in ancestors:
graph.get_node(nx_node)[0].set_color("red")
graph.write_png(f"{fname}.png")
def visualize_proof_tree(self, proof, fname):
graph = self.to_pydot()
for proof_step in proof.split(";"):
proof_step = proof_step.strip()
if proof_step == "":
continue
premises, conclusion = proof_step.split(" -> ")
for p in premises.split(" & "):
if re.fullmatch(r"sent\d+", p):
graph.get_node(p)[0].set_color("red")
m = re.fullmatch(r"int\d+: (?P<sent>.+)", conclusion)
assert m is not None
name = self.sent2node[m["sent"]]
graph.get_node(name)[0].set_color("red")
graph.write_png(f"{fname}.png")