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'\n{context}\n\n\n{theorem_defn}\n\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 ... tags, the theorem to be proven in .... Please output your proof containing only Lean 4 proof code between ... tags. The generated proof should never contain the word `sorry`. Here are some examples:"},
{"role": "user", "content": """
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)
theorem balanced_tree_size_odd (t: MyTree α) (hb: balanced t): Odd (tree_size t) := by
"""},
{"role": "assistant", "content": """
cases t with
| leaf => simp [tree_size]
| node p x q =>
unfold tree_size
unfold balanced at hb
simp [hb.1]
"""},
{"role": "user", "content": """
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
theorem swap_preserves_balance (t: MyTree α) (hb: balanced t): balanced (swap_branches t) := by
"""},
{"role": "assistant", "content": """
cases t with
| leaf => simp [swap_branches]
| node p x q =>
simp [swap_branches, balanced] at hb ⊢
split
{ simp [← hb.1] }
{ split; assumption }
"""},
{"role": "user", "content": """
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]
theorem len_pairlist_even (l: PairList): Even (len_pairlist l) := by
"""},
{"role": "assistant", "content": """
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)
"""},
{"role": "user", "content": encoded}]
)#.choices[0].message.content.replace('','').replace('', '').strip()
return [m.message.content.replace('','').replace('', '').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)