File size: 15,774 Bytes
65e48a9 cf82b1c 65e48a9 cf82b1c 65e48a9 cf82b1c 65e48a9 8d5ba38 65e48a9 8d5ba38 65e48a9 cf82b1c 65e48a9 1dc7ce1 8d5ba38 980b096 8d5ba38 65e48a9 cf82b1c 65e48a9 cf82b1c 65e48a9 cf82b1c 65e48a9 cf82b1c 65e48a9 cf82b1c 65e48a9 cf82b1c 65e48a9 cf82b1c 65e48a9 cf82b1c 65e48a9 cf82b1c 65e48a9 cf82b1c 65e48a9 cf82b1c 65e48a9 cf82b1c 65e48a9 cf82b1c 65e48a9 cf82b1c 65e48a9 cf82b1c 65e48a9 cf82b1c 65e48a9 cf82b1c 65e48a9 cf82b1c 8d5ba38 |
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 |
import json
import requests
import time
import os
from openai import OpenAI
import argparse
from utils import make_lean_repl, send_tactic, send_command_icanon, send_command_zsh, get_errs
def get_tactics_interactive(goal, prev_file):
print(f'output:<{goal}>')
print(f'file context: <{prev_file}>')
return [(input('give the next tactic to execute:'), 0)]
# the goal is to directly call the llmstep server.py
def get_tactics_llmstep(goal, prev_file):
# this is the function lean calls to interact with the server
def suggest(host, tactic_state, prefix, context):
data = {'tactic_state': tactic_state, 'prefix': prefix, 'context': context}
response = json.loads(requests.post(host, json=data).content)
return response['suggestions'] # modified to directly return the suggestion list
HOST='localhost'
PORT='6000'
default_host = f'http://{HOST}:{PORT}'
suggestions = suggest(default_host, goal, '', prev_file) # trying to match what the tactic sends
return suggestions
def send_prop_defn(lean_repl, pwd, prop_name, mathlib_out, mathlib_env):
print(prop_name)
successful_def = False
penult_env = None
while not successful_def:
successful_def = True
env = None
all_lines = []
for _loc, line in pwd[prop_name]:
penult_env = env
if line.strip() == 'import Mathlib':
outp, env = mathlib_out, mathlib_env
else:
outp, env = send_command(lean_repl, line, env=env)
if outp is None:
print('restarting repl')
successful_def = False
lean_repl.close()
lean_repl = make_lean_repl(repl_type=repl_type)
mathlib_out, mathlib_env = send_command(lean_repl, 'import Mathlib', env=None, first=True)
break
all_lines.append(line)
return lean_repl, mathlib_out, mathlib_env, outp, env, penult_env, all_lines
# for benchmarking 'get_tactics' functions that suggest several next possible steps for a given
# proofstate + optionally file context.
def benchmark_nextstep(pwd, get_tactics, send_command, search_depth=3, search_width=10, repl_type='zsh', logfile=None):
assert logfile is not None
def printl(*args, **kwargs):
print(*args, **kwargs)
print(*args, **kwargs, file=logfile)
lean_repl = make_lean_repl(repl_type=repl_type)
# get the first command out of the way which has a weird "expect" behavior using icanon mode
mathlib_out, mathlib_env = send_command(lean_repl, 'import Mathlib', env=None, first=True, timeout=30)
num_proved = 0
num_attempted = 0
for prop_name in pwd:
#time.sleep(5)
num_attempted += 1
#if num_attempted < 115:
# continue
lean_repl, mathlib_out, mathlib_env, outp, env, penult_env, all_lines = send_prop_defn(lean_repl, pwd, prop_name, mathlib_out, mathlib_env)
assert len(get_errs(outp)) == 0, str(outp.get('messages', []))
proofState = int(outp['sorries'][0]['proofState'])
goal = outp['sorries'][0]['goal']
prev_lines = '\n'.join(all_lines)
prev_lines = prev_lines.replace(':= by sorry', ':= by\n')
solution_tac_seq = None
old_ps = [(goal, proofState, [])]
new_ps = []
found_proof = False
for search_lvl in range(search_depth):
if search_lvl > 0:
print(f'search at level {search_lvl}')
for (curr_goal, ps, tac_seq) in old_ps:
next_tactics = get_tactics(curr_goal, prev_lines + '\n'.join(tac_seq))
for next_tactic, _scr in sorted(next_tactics, key=lambda p: -p[1])[:search_width]:
if prop_name in next_tactic:
continue # although this in theory Can be correct, LEAN DOES NOT CORRECTLY THROW ERRORS when the theorem name is used in a proof.
# in fact, Lean REPL will return a proofstate with empty goals and no errors! This creates false positives, so we skip these tactics.
#print('\n'.join(tac_seq + [next_tactic]))
outp, new_proofState = send_tactic(lean_repl, next_tactic, ps)
if outp is None:
continue # i.e. timeout/error on tactic sending
#print(outp)
error_msgs = get_errs(outp)
if len(error_msgs) > 0:
continue # invalid next proof step. sometimes there are invalid intermediate
# states that lead to successful proof, but for efficiency we enforce this.
if len(outp['goals']) == 0 and len(error_msgs) == 0:
#print(outp)
found_proof = True
solution_tac_seq = tac_seq + [next_tactic]
break
new_ps.append(('\n'.join(outp['goals']), new_proofState, tac_seq + [next_tactic]))
#print(f'final output: {outp}')
if found_proof:
break
if found_proof:
break
old_ps = new_ps
new_ps = []
if found_proof:
num_proved += 1
nl = '\n'
print(f'prop {prop_name} with goal <{goal}> solved by: <\n {nl.join([str(s) for s in solution_tac_seq])}\n>')
else:
print(f'failed to prove {prop_name}')
print(f'proved {num_proved}/{num_attempted}')
#exit()
def get_proof_gpt(theorem_defn, goal, context, num_gen=4):
#openai_api_key = os.environ['OPENAI_API_KEY']
client = OpenAI()
# decided I don't need the goal, it doesn't look very useful in most cases when the theorem statement
# and context are given. Future work can confirm or invalidate this.
encoded = f'<context>\n{context}\n</context>\n<theorem>\n{theorem_defn}\n</theorem>\n'
ret = client.chat.completions.create(
model=gpt_model, # see main block
n=num_gen,
messages=[{"role": "system", "content": "You are a Lean 4 expert tasked with completing proofs of program properties. You will be shown the relevant programs and definitions in <context>...</context> tags, the theorem to be proven in <theorem>...</theorem>. Please output your proof containing only Lean 4 proof code between <proof>...</proof> tags. The generated proof should never contain the word `sorry`. Here are some examples:"},
{"role": "user", "content": """<context>
import Mathlib
inductive MyTree (α: Type) where
| leaf : MyTree α
| node : MyTree α → α → MyTree α → MyTree α
def tree_size : MyTree α → ℕ
| .leaf => 1
| .node l _x r => 1 + (tree_size l) + (tree_size r)
def balanced : MyTree α → Prop
| .leaf => true
| .node l _x r => ((tree_size l) = (tree_size r)) ∧ (balanced l) ∧ (balanced r)
</context>
<theorem>
theorem balanced_tree_size_odd (t: MyTree α) (hb: balanced t): Odd (tree_size t) := by
</theorem>"""},
{"role": "assistant", "content": """<proof>
cases t with
| leaf => simp [tree_size]
| node p x q =>
unfold tree_size
unfold balanced at hb
simp [hb.1]
</proof>"""},
{"role": "user", "content": """<context>
import Mathlib
inductive MyTree (α: Type) where
| leaf : MyTree α
| node : MyTree α → α → MyTree α → MyTree α
def balanced : MyTree α → Prop
| .leaf => true
| .node l _x r => ((tree_size l) = (tree_size r)) ∧ (balanced l) ∧ (balanced r)
def swap_branches : MyTree α → MyTree α
| MyTree.leaf => MyTree.leaf
| MyTree.node p x q => MyTree.node q x p
</context>
<theorem>
theorem swap_preserves_balance (t: MyTree α) (hb: balanced t): balanced (swap_branches t) := by
</theorem>"""},
{"role": "assistant", "content": """<proof>
cases t with
| leaf => simp [swap_branches]
| node p x q =>
simp [swap_branches, balanced] at hb ⊢
split
{ simp [← hb.1] }
{ split; assumption }
</proof>"""},
{"role": "user", "content": """<context>
import Mathlib
inductive PairList where
| empty : PairList
| node : Nat → Nat → PairList → PairList
def len_pairlist : PairList → Nat
| .empty => 0
| .node _n1 _n2 l => len_pairlist l + 2
lemma even_plus_two (x: Nat) (h: Even x): Even (x + 2) := by
unfold Even at h
rcases h with ⟨y, hy⟩
use y + 1
linarith [hy]
</context>
<theorem>
theorem len_pairlist_even (l: PairList): Even (len_pairlist l) := by
</theorem>"""},
{"role": "assistant", "content": """<proof>
generalize hl: len_pairlist l = pl
induction pl using Nat.strong_induction_on generalizing l with
| h n ih => cases l with
| empty => simp [len_pairlist] at hl; simp [←hl];
| node n1 n2 l2 =>
unfold len_pairlist at hl
simp [←hl]
apply even_plus_two
exact ih (len_pairlist l2) (by linarith [hl]) l2 (by rfl)
</proof>"""},
{"role": "user", "content": encoded}]
)#.choices[0].message.content.replace('<proof>','').replace('</proof>', '').strip()
return [m.message.content.replace('<proof>','').replace('</proof>', '').strip() for m in ret.choices]
# for benchmarking full proof generation methods, where input is
# file context, theorem definition, and initial proof state, and output is a full proof of the theorem.
def benchmark_full_proofgen(pwd, get_proof, send_command, num_gen=8, repl_type='icanon', logfile=None):
assert logfile is not None, 'pass in a file object to write results to'
def printl(*args, **kwargs):
print(*args, **kwargs)
print(*args, **kwargs, file=logfile)
lean_repl = make_lean_repl(repl_type=repl_type)
# get the first command out of the way which has a weird "expect" behavior using icanon mode
mathlib_out, mathlib_env = send_command(lean_repl, 'import Mathlib', env=None, first=True)
num_proved = 0
num_attempted = 0
for prop_name in pwd:
num_attempted += 1
#time.sleep(5)
#if num_attempted < 30:
# continue
lean_repl, mathlib_out, mathlib_env, outp, env, penult_env, all_lines = send_prop_defn(lean_repl, pwd, prop_name, mathlib_out, mathlib_env)
assert len(get_errs(outp)) == 0, str(outp.get('messages', []))
context = '\n\n'.join([line for _loc, line in pwd[prop_name][:-1]])
theorem_defn = pwd[prop_name][-1][1].replace('by sorry', 'by\n') # give the llm a clean place to begin generating
goal = outp['sorries'][0]['goal']
found_proof = False
sugg_proofs = get_proof(theorem_defn, goal, context, num_gen=num_gen)
for gen_i, suggested_proof in enumerate(sugg_proofs):
printl(f'generated proof {gen_i}')
if prop_name in suggested_proof:
printl('suggested proof used proof name, skipping')
continue # although this in theory Can be correct, LEAN DOES NOT CORRECTLY THROW ERRORS when the theorem name is used in a proof.
# in fact, Lean REPL will return a proofstate with empty goals and no errors! This creates false positives, so we skip these proofs.
if 'sorry' in suggested_proof or 'admit' in suggested_proof:
printl('suggested proof uses sorry/admit, skipping')
continue # this also isn't perfect, as I'm throwing out proofs with 'sorry' in a comment, for example.
# but, it's better than having false positives.
# although I explicitly warn against sorry in the prompt, they still pop up sometimes.
full_thm = theorem_defn + suggested_proof
printl('suggested proof: ' + full_thm)
outp, _result_env = send_command(lean_repl, full_thm, env=penult_env)
if len(get_errs(outp)) == 0:
num_proved += 1
found_proof = True
printl('successful proof!')
printl(f'prop {prop_name} with goal <{goal}> solved by: <\n {suggested_proof}\n>')
break
else:
printl('errors:', get_errs(outp))
if not found_proof:
printl(f'failed to prove {prop_name}')
printl(f'proved {num_proved}/{num_attempted}')
def parse_benchmark_output(fname, pwd, loc2comm):
with open(fname, 'r') as f:
lines = f.readlines()
failures = set()
for line in lines:
if 'failed to prove' in line:
failures.add(line.strip().split(' ')[-1])
by_score = {i: [0,0] for i in range(1, 6)}
by_custom = [0, 0]
custom_proved = []
all_proved = []
results = {}
for i in range(1, 87):
key = f'prop_{i}' if i >=10 else f'prop_0{i}'
if key not in pwd:
continue
loc = [loc[0] for loc, line in pwd[key] if key in line][0]
line_str = int(loc.strip().split(':')[1])
comm = loc2comm[line_str-1]
print(comm)
score = int(comm.split(':')[1].strip().split('/')[0].strip())
is_custom = 'custom' in comm
results[key] = {'score': score, 'result': key not in failures, 'custom': is_custom}
if key in failures:
by_score[score][1] += 1
if is_custom:
by_custom[1] += 1
print(f'could not prove {key}')
else:
by_score[score][0] += 1
if is_custom:
by_custom[0] += 1
custom_proved.append(key)
all_proved.append((score, key))
print(f'proved {key}')
print('by score', by_score)
print('by custom', by_custom)
print('custom proved', custom_proved)
print('all proved 5', [name for score, name in all_proved if score == 5])
print(f'total: {len(all_proved)}/{len(pwd)}')
return results, by_score
def parse_benchmark_input(fname):
with open(fname, 'r') as f:
lines = f.readlines()
jl = [json.loads(line.strip()) for line in lines if len(line.strip()) > 0]
# dummy locations via enumerate, since they're unused during baseline calculation
return {dct['full_name']: list(enumerate(dct['deps'].split('\n\n') + [dct['prop_defn']])) for dct in jl}
if __name__ == '__main__':
# if any single command is >1024 characters, use_icanon=True is necessary.
# unfortunately there may still be some bugs where a theorem is actually proven,
# but the messages from Lean REPL indicate an error when using this mode.
use_icanon = True
parser = argparse.ArgumentParser()
parser.add_argument('bench_type', type=str, default='fullproof')
parser.add_argument('gpt_model', type=str, default='gpt-4-turbo')
parser.add_argument('bench_file', type=str, default='codeprops_bench_ps.jsonl')
args = parser.parse_args()
assert args.bench_type in ['fullproof', 'nextstep']
bench_type = args.bench_type
gpt_model = args.gpt_model
if use_icanon:
send_command = send_command_icanon
repl_type = 'icanon'
else:
send_command = send_command_zsh
repl_type = 'zsh'
#benchmark_nextstep(pwd, get_tactics_interactive, send_command, repl_type=repl_type) # get_tactics_interactive for testing
pwd = parse_benchmark_input(args.bench_file)
if bench_type == 'nextstep':
with open(f'logfile_nextstep.txt', 'w') as logf:
benchmark_nextstep(pwd, get_tactics_llmstep, send_command, repl_type=repl_type, logfile=logf) # get_tactics_llmstep for benchmarking
elif bench_type == 'fullproof':
with open(f'logfile_{gpt_model}.txt', 'w') as logf:
benchmark_full_proofgen(pwd, get_proof_gpt, send_command, repl_type=repl_type, logfile=logf)
|