def make_coq_formulae(premise_interpretations, conclusion, reverse=False):
interpretations = premise_interpretations + [conclusion]
interpretations = [
normalize_interpretation(interp) for interp in interpretations
]
if reverse:
interpretations.reverse()
coq_formulae = ' -> '.join(interpretations)
return coq_formulae
def prove_statements(premise_interpretations, conclusion, dynamic_library = ''):
# Transform these interpretations into coq format:
# interpretation1 -> interpretation2 -> ... -> conclusion
interpretations = premise_interpretations + [conclusion]
interpretations = [normalize_interpretation(interp) for interp in interpretations]
coq_formulae = ' -> '.join(interpretations)
# Input these formulae to coq and retrieve the results.
input_coq_script = ('echo \"Require Export coqlib.\n'
'{0}\nTheorem t1: {1}. {2}.\" | coqtop').format(
dynamic_library, coq_formulae, _tactics)
input_coq_script = substitute_invalid_chars(input_coq_script, 'replacement.txt')
process = subprocess.Popen(\
input_coq_script, \
shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT)
output_lines = [str(line).strip().split() for line in process.stdout.readlines()]
return is_theorem_defined(output_lines), input_coq_script
def prove_statements(premise_interpretations, conclusion, dynamic_library=''):
# Transform these interpretations into coq format:
# interpretation1 -> interpretation2 -> ... -> conclusion
interpretations = premise_interpretations + [conclusion]
interpretations = [
normalize_interpretation(interp) for interp in interpretations
]
coq_formulae = ' -> '.join(interpretations)
# Input these formulae to coq and retrieve the results.
tactics = get_tactics()
input_coq_script = ('echo \"Require Export coqlib.\n'
'{0}\nTheorem t1: {1}. {2}.\" | coqtop').format(
dynamic_library, coq_formulae, tactics)
input_coq_script = substitute_invalid_chars(input_coq_script,
'replacement.txt')
process = subprocess.Popen(\
input_coq_script, \
shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT)
output_lines = [
str(line).strip().split() for line in process.stdout.readlines()
]
return is_theorem_defined(output_lines), input_coq_script
def test_negation_predicate(self):
nltk_expr = lexpr(r'-(P)')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(not P)'
self.assertEqual(expected_coq_expr, coq_expr)
def test_predicate1_arg(self):
nltk_expr = lexpr(r'P(x)')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(P x)'
self.assertEqual(expected_coq_expr, coq_expr)
def test_universal_args2(self):
nltk_expr = lexpr(r'all x y. P(x,y)')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(forall x y, (P x y))'
self.assertEqual(expected_coq_expr, coq_expr)
def test_existentialArgs2(self):
nltk_expr = lexpr(r'exists x y. P(x,y)')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(exists x y, (P x y))'
self.assertEqual(expected_coq_expr, coq_expr)
def test_lambda3_args2_pred1(self):
nltk_expr = lexpr(r'\x y P. P(x, y)')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(fun x y P => (P x y))'
self.assertEqual(expected_coq_expr, coq_expr)
def test_lambda1_proposition(self):
nltk_expr = lexpr(r'\x. A')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(fun x => A)'
self.assertEqual(expected_coq_expr, coq_expr)
def test_predicate3_args1Pred(self):
nltk_expr = lexpr(r'P(x,y,R(z))')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(P x y (R z))'
self.assertEqual(expected_coq_expr, coq_expr)
def test_implication_proposition2(self):
nltk_expr = lexpr(r'P -> Q')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(P -> Q)'
self.assertEqual(expected_coq_expr, coq_expr)
def test_disjunction_predicate2_arg1and1(self):
nltk_expr = lexpr(r'(P(x) | Q(y))')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(or (P x) (Q y))'
self.assertEqual(expected_coq_expr, coq_expr)
def test_disjunction_predicates2(self):
nltk_expr = lexpr(r'(P | Q)')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(or P Q)'
self.assertEqual(expected_coq_expr, coq_expr)
def test_conjunction_predicate2_arg1(self):
nltk_expr = lexpr(r'(P(x) & Q)')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(and (P x) Q)'
self.assertEqual(expected_coq_expr, coq_expr)
def test_Negationpredicate2_args(self):
nltk_expr = lexpr(r'-(P(x,y))')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(not (P x y))'
self.assertEqual(expected_coq_expr, coq_expr)
def test_negation_predicate(self):
nltk_expr = lexpr(r'-(P)')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(not P)'
self.assertEqual(expected_coq_expr, coq_expr)
def test_conjunction_predicate2_arg1(self):
nltk_expr = lexpr(r'(P(x) & Q)')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(and (P x) Q)'
self.assertEqual(expected_coq_expr, coq_expr)
def test_disjunction_predicate2_arg1and1(self):
nltk_expr = lexpr(r'(P(x) | Q(y))')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(or (P x) (Q y))'
self.assertEqual(expected_coq_expr, coq_expr)
def test_implication_predicate2(self):
nltk_expr = lexpr(r'P(x) -> Q(y)')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '((P x) -> (Q y))'
self.assertEqual(expected_coq_expr, coq_expr)
def test_implication_predicate2(self):
nltk_expr = lexpr(r'P(x) -> Q(y)')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '((P x) -> (Q y))'
self.assertEqual(expected_coq_expr, coq_expr)
def test_lambda1_proposition(self):
nltk_expr = lexpr(r'\x. A')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(fun x => A)'
self.assertEqual(expected_coq_expr, coq_expr)
def test_lambda1_arg1(self):
nltk_expr = lexpr(r'\x. P(x)')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(fun x => (P x))'
self.assertEqual(expected_coq_expr, coq_expr)
def test_lambda1_arg1(self):
nltk_expr = lexpr(r'\x. P(x)')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(fun x => (P x))'
self.assertEqual(expected_coq_expr, coq_expr)
def test_existentialArg1Proposition(self):
nltk_expr = lexpr(r'exists x. P')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(exists x, P)'
self.assertEqual(expected_coq_expr, coq_expr)
def test_lambda3_args2_pred1(self):
nltk_expr = lexpr(r'\x y P. P(x, y)')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(fun x y P => (P x y))'
self.assertEqual(expected_coq_expr, coq_expr)
def test_universal_arg1_proposition(self):
nltk_expr = lexpr(r'all x. P')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(forall x, P)'
self.assertEqual(expected_coq_expr, coq_expr)
def test_existentialArg1Proposition(self):
nltk_expr = lexpr(r'exists x. P')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(exists x, P)'
self.assertEqual(expected_coq_expr, coq_expr)
def test_tautology(self):
nltk_expr = lexpr(r'all x y.TrueP')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(forall x y, True)'
self.assertEqual(expected_coq_expr, coq_expr)
def test_existentialArgs2(self):
nltk_expr = lexpr(r'exists x y. P(x,y)')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(exists x y, (P x y))'
self.assertEqual(expected_coq_expr, coq_expr)
def test_predicate3_args1Pred(self):
nltk_expr = lexpr(r'P(x,y,R(z))')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(P x y (R z))'
self.assertEqual(expected_coq_expr, coq_expr)
def test_universal_arg1_proposition(self):
nltk_expr = lexpr(r'all x. P')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(forall x, P)'
self.assertEqual(expected_coq_expr, coq_expr)
def test_Negationpredicate2_args(self):
nltk_expr = lexpr(r'-(P(x,y))')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(not (P x y))'
self.assertEqual(expected_coq_expr, coq_expr)
def test_universal_args2(self):
nltk_expr = lexpr(r'all x y. P(x,y)')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(forall x y, (P x y))'
self.assertEqual(expected_coq_expr, coq_expr)
def test_disjunction_predicates2(self):
nltk_expr = lexpr(r'(P | Q)')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(or P Q)'
self.assertEqual(expected_coq_expr, coq_expr)
def test_implication_proposition2(self):
nltk_expr = lexpr(r'P -> Q')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(P -> Q)'
self.assertEqual(expected_coq_expr, coq_expr)
def test_tautology(self):
nltk_expr = lexpr(r'all x y.TrueP')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(forall x y, True)'
self.assertEqual(expected_coq_expr, coq_expr)
def test_predicate1_arg(self):
nltk_expr = lexpr(r'P(x)')
coq_expr = normalize_interpretation(nltk_expr)
expected_coq_expr = '(P x)'
self.assertEqual(expected_coq_expr, coq_expr)
