File size: 11,913 Bytes
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from common.constants import CORE_OPTIONS, OPEN_HEADER, RPE_TACTICS, H_SUBMISSION_NAME, H_CONCLUSION_NAME
from common.utils import (
format_variable_sequence,
to_sync)
from common.pantograph.server import Server
from common.pantograph.dataclasses import GoalState, FormalProblem
class BaseSolvingServer:
def __init__(
self,
imports: List[str]=["Mathlib", "Aesop"],
project_path: Optional[str]=None,
timeout: int=300,
tag: str=''
) -> None:
self.sample : Optional[FormalProblem] = None
self.answer_mvarId : Optional[str] = None
self.server: Optional[Server] = None
self.imports = imports
self.project_path = project_path
self.timeout = timeout
self.tag = tag
async def init_backward_state_async(self, sample: Optional[FormalProblem]=None) -> GoalState:
await self.load_problem_async(sample)
self.answer_mvarId = None
V = [f" ({v.name or '_'} : {v.t})" for v in sample.independent_variables]
Phi = [f" ({v.name or '_'} : {v.t})" for v in sample.hypotheses]
Psi = sample.conclusions
self.formal_problem_framework = 'example\n' + \
'\n'.join(
V + \
[f' (answer : {self.sample.formal_answer_type})', f' ({H_SUBMISSION_NAME}: {self.sample.formal_answer})'] + \
Phi
) + \
'\n: ' + ' ∧ '.join(Psi) + '\n:= by\n' + \
'all_goals sorry'
units = await self.server.load_sorry_async((self.sample.header or OPEN_HEADER)+'\n'+self.formal_problem_framework)
assert len(units) >= 1 and 'error' not in str([x.messages for x in units]), f'formal_problem_framework:{(self.sample.header or OPEN_HEADER)}\n{self.formal_problem_framework}'
return units[-1].goal_state
init_backward_state = to_sync(init_backward_state_async)
async def load_problem_async(self, sample: Optional[FormalProblem]) -> None:
if sample is None:
return None
assert isinstance(sample, FormalProblem)
self.sample = sample
self.server = await Server.create(
imports=self.imports,
project_path=self.project_path,
core_options=CORE_OPTIONS,
timeout=self.timeout,
)
return None
load_problem = to_sync(load_problem_async)
async def get_submission_async(self, state: GoalState) -> Optional[str]:
assert self.answer_mvarId is not None
rs = await self.server.goal_print_async(state, False, False, False, [self.answer_mvarId])
answer = rs['extraMVars'][0]
return answer.get('pp', None)
get_submission = to_sync(get_submission_async)
# Answer as Term
class TermSolvingServer(BaseSolvingServer):
async def init_solving_state_async(self, sample: Optional[FormalProblem]=None) -> Tuple[GoalState, List[str]]:
await self.load_problem_async(sample)
self.answer_mvarId = None
V = [f" ({v.name or '_'} : {v.t})" for v in sample.independent_variables]
Phi = [f" ({v.name or '_'} : {v.t})" for v in sample.hypotheses]
Psi = sample.conclusions
init_steps = ([
'intros ' + ' '.join([v.name or '_' for v in self.sample.independent_variables])
] if len(self.sample.independent_variables) > 0 else []) + [
'apply Exists.intro ?Answer ?Proof',
'rotate_left',
] + ([
'intros ' + ' '.join([v.name or '_' for v in sample.hypotheses])
] if len(Phi) > 0 else [])
self.formal_problem_framework = 'example :\n' + \
(('∀ ' + '\n '.join(V) + ',\n') if len(V) > 0 else '\n') + \
f'∃ (answer : {self.sample.formal_answer_type}),' + \
(('\n∀ ' + '\n '.join(Phi) + ',\n') if len(Phi) > 0 else '\n') + \
' ∧ '.join(Psi) + '\n:= by\n' + \
'\n'.join(init_steps) + \
'\nall_goals sorry'
units = await self.server.load_sorry_async((self.sample.header or OPEN_HEADER)+'\n'+self.formal_problem_framework)
assert len(units) >= 1 and 'error' not in str([x.messages for x in units]), f'formal_problem_framework:{(self.sample.header or OPEN_HEADER)}\n{self.formal_problem_framework}'
init_solution_state = units[-1].goal_state
assert len(init_solution_state.goals) == 2 and [g.name for g in init_solution_state.goals] == ['Proof', 'Answer'], f'Invalid solving_state:\n{init_solution_state}'
rs = await self.server.goal_print_async(init_solution_state, False, False, True)
answer_mvarId = [g['name'] for g in rs['goals'] if g['userName'] == 'Answer']
assert len(answer_mvarId) == 1, f'Invalid answer_mvarId in init_solution_state: {[init_solution_state]}'
self.answer_mvarId = answer_mvarId[0]
return init_solution_state, init_steps
init_solving_state = to_sync(init_solving_state_async)
async def prove_eq_async(self, submission: str) -> Optional[str]:
await self.server.restart_async()
rpe_proof = ''' try ext
try funext
repeat''' + ' {\n' + '\n'.join((' try ' + tac + ';') for tac in RPE_TACTICS) + '\n }'
rpe_code = 'example' + \
((' ' + format_variable_sequence(self.sample.independent_variables) + '\n') if len(self.sample.independent_variables) > 0 else '\n') + \
f' (answer : {self.sample.formal_answer_type}) : (answer = (\n{submission} : {self.sample.formal_answer_type}\n)) ↔ (\n{self.sample.formal_answer}\n)' + ' := by\n' + rpe_proof
try:
units = await self.server.load_sorry_async((self.sample.header or OPEN_HEADER)+'\n'+rpe_code)
assert 'error' not in str([x.messages for x in units]) and all((u.goal_state is None or u.goal_state.is_solved) for u in units), f'formal_problem_framework:\n{(self.sample.header or OPEN_HEADER)}\n{rpe_code}\nmessage:\n{str([x.messages for x in units])}'
return rpe_proof
except:
return None
prove_eq = to_sync(prove_eq_async)
# Answer as Prop
class PropSolvingServer(BaseSolvingServer):
async def init_solving_state_async(self, sample: Optional[FormalProblem]=None) -> Tuple[GoalState, List[str]]:
await self.load_problem_async(sample)
self.answer_mvarId = None
V = [f" ({v.name or '_'} : {v.t})" for v in sample.independent_variables]
Phi = [f" ({v.name or '_'} : {v.t})" for v in sample.hypotheses]
Psi = sample.conclusions
# From FPS to D-FPS
V.append(f' (answer : {self.sample.formal_answer_type})')
Psi = '(' + ' ∧ '.join(Psi) + f' ↔ {H_SUBMISSION_NAME})'
init_steps = [
'intros ' + ' '.join([v.name or '_' for v in self.sample.independent_variables] + ['answer']),
'apply Exists.intro ?Answer ?Proof',
'rotate_left'
] + \
(['intros ' + ' '.join([v.name or '_' for v in sample.hypotheses])] if len(Phi) > 0 else []) + \
[
'refine @Iff.intro ?_ _ ?Forward ?Backward',
'rotate_left',
f'intros {H_SUBMISSION_NAME}',
'rotate_right',
f'intros {H_CONCLUSION_NAME}'
]
self.formal_problem_framework = 'example :\n' + \
(('∀ ' + '\n '.join(V) + ',\n') if len(V) > 0 else '\n') + \
f'∃ ({H_SUBMISSION_NAME} : Prop),' + \
(('\n∀ ' + '\n '.join(Phi) + ',\n') if len(Phi) > 0 else '\n') + \
Psi + '\n:= by\n' + \
'\n'.join(init_steps) + \
'\nall_goals sorry'
units = await self.server.load_sorry_async((self.sample.header or OPEN_HEADER)+'\n'+self.formal_problem_framework)
assert len(units) >= 1 and 'error' not in str([x.messages for x in units]), f'formal_problem_framework:{(self.sample.header or OPEN_HEADER)}\n{self.formal_problem_framework}'
init_solution_state = units[-1].goal_state
assert len(init_solution_state.goals) == 3 and [g.name for g in init_solution_state.goals] == ['Forward', 'Backward', 'Answer'], f'Invalid solving_state:\n{init_solution_state}'
rs = await self.server.goal_print_async(init_solution_state, False, False, True)
answer_mvarId = [g['name'] for g in rs['goals'] if g['userName'] == 'Answer']
assert len(answer_mvarId) == 1, f'Invalid answer_mvarId in init_solution_state: {[init_solution_state]}'
self.answer_mvarId = answer_mvarId[0]
return init_solution_state, init_steps
init_solving_state = to_sync(init_solving_state_async)
async def init_forward_solving_state_async(self, sample: Optional[FormalProblem]=None) -> GoalState:
await self.load_problem_async(sample)
self.answer_mvarId = None
init_steps = [
'intros ' + ' '.join([v.name or '_' for v in self.sample.independent_variables] + ['answer']),
'apply Exists.intro ?Answer ?Proof',
'rotate_left',
] + ([
'intros ' + ' '.join([v.name or '_' for v in sample.hypotheses])
] if len(sample.hypotheses) > 0 else [])
self.formal_problem_framework = 'example :\n' + \
(('∀ ' + format_variable_sequence(self.sample.independent_variables) + ',\n') if len(self.sample.independent_variables) > 0 else '') + \
f'∀ (answer : {self.sample.formal_answer_type}), ∃ ({H_SUBMISSION_NAME} : Prop), \n' + \
(('∀ ' + format_variable_sequence(self.sample.hypotheses) + ',\n') if len(self.sample.hypotheses) > 0 else '') + \
f'({H_SUBMISSION_NAME})' + '\n:= by\n' + \
'\n'.join(init_steps) + \
'\nall_goals sorry'
units = await self.server.load_sorry_async((self.sample.header or OPEN_HEADER)+'\n'+self.formal_problem_framework)
assert len(units) >= 1 and 'error' not in str([x.messages for x in units]), f'formal_problem_framework:{(self.sample.header or OPEN_HEADER)}\n{self.formal_problem_framework}'
init_solution_state = units[-1].goal_state
assert [g.name for g in init_solution_state.goals] == ['Proof', 'Answer'], f'Invalid solving_state:\n{init_solution_state}'
rs = await self.server.goal_print_async(init_solution_state, False, False, True)
answer_mvarId = [g['name'] for g in rs['goals'] if g['userName'] == 'Answer']
assert len(answer_mvarId) == 1, f'Invalid answer_mvarId in init_solution_state: {[init_solution_state]}'
self.answer_mvarId = answer_mvarId[0]
return init_solution_state, init_steps
init_forward_solving_state = to_sync(init_forward_solving_state_async)
async def prove_eq_async(self, submission: str) -> Optional[str]:
await self.server.restart_async()
rpe_proof = ''' try ext
try funext
repeat''' + ' {\n' + '\n'.join((' try ' + tac + ';') for tac in RPE_TACTICS) + '\n }'
rpe_code = 'example' + \
((' ' + format_variable_sequence(self.sample.independent_variables) + '\n') if len(self.sample.independent_variables) > 0 else '\n') + \
f' (answer : {self.sample.formal_answer_type}) : (\n{submission}\n) ↔ (\n{self.sample.formal_answer}\n)' + ' := by\n' + rpe_proof
try:
units = await self.server.load_sorry_async((self.sample.header or OPEN_HEADER)+'\n'+rpe_code)
assert 'error' not in str([x.messages for x in units]) and all((u.goal_state is None or u.goal_state.is_solved) for u in units), f'formal_problem_framework:\n{(self.sample.header or OPEN_HEADER)}\n{rpe_code}\nmessage:\n{str([x.messages for x in units])}'
return rpe_proof
except:
return None
prove_eq = to_sync(prove_eq_async)
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