def test_iterative_get_free_variables(self):
f = Symbol("x")
for _ in xrange(1000):
f = And(f, f)
cone = f.get_free_variables()
self.assertEqual(cone, set([Symbol("x")]))
def test_basic(self):
varA = Symbol("A")
f = And(varA, Not(varA))
self.assertEqual(f.size(), 4)
self.assertEqual(f.size(SizeOracle.MEASURE_TREE_NODES), 4)
self.assertEqual(f.size(SizeOracle.MEASURE_DAG_NODES), 3)
self.assertEqual(varA.size(SizeOracle.MEASURE_LEAVES), 1)
self.assertEqual(f.size(SizeOracle.MEASURE_DEPTH), 3)
self.assertEqual(f.size(SizeOracle.MEASURE_SYMBOLS), 1)
def test_leaf(self):
varA = Symbol("A")
self.assertEqual(varA.size(), 1)
self.assertEqual(varA.size(SizeOracle.MEASURE_TREE_NODES), 1)
self.assertEqual(varA.size(SizeOracle.MEASURE_DAG_NODES), 1)
self.assertEqual(varA.size(SizeOracle.MEASURE_LEAVES), 1)
self.assertEqual(varA.size(SizeOracle.MEASURE_DEPTH), 1)
self.assertEqual(varA.size(SizeOracle.MEASURE_SYMBOLS), 1)
def add_lt(x_str, v): global solver x = Symbol(x_str, REAL) solver.push() solver.add_assertion(x < v)
def add_opposite_eq(neg_obj_str, obj_str): global solver solver.push() neg_obj = Symbol(neg_obj_str, REAL) obj = Symbol(obj_str, REAL) solver.add_assertion(obj + neg_obj == 0)
def get_ceil(model, x_str): x = Symbol(x_str, REAL) ceilvalue = math.ceil(float(model.get_value(x).simplify())) return str(ceilvalue)
def get_model_value(model, x_str): x = Symbol(x_str, REAL) return str(model[x])
def __init__(self, name):
assert name in X86StackRegister.register_names
self.name = name
self.sym = Symbol(name, INT)
def test_node_id(self):
x = Symbol("x")
y = Symbol("y")
xx = Symbol("x")
self.assertEqual(x.node_id(), xx.node_id())
self.assertNotEqual(x.node_id(), y.node_id())
def test_msat_bool_back_conversion(self):
f = Symbol("A")
with Solver(name='msat') as solver:
solver.solve()
val = solver.get_value(Symbol("A"))
self.assertTrue(val.is_bool_constant())
def test_function_smtlib_print(self):
f_t = FunctionType(BOOL, [BOOL])
f0 = Symbol('f 0', f_t)
f0_of_false = Function(f0, [Bool(False)])
s = to_smtlib(f0_of_false, False)
self.assertEqual(s, '(|f 0| false)')
def test_empty_string_symbol(self):
with self.assertRaises(PysmtValueError):
Symbol("")
def test_substitute_to_real(self):
p = Symbol("p", INT)
f = LT(ToReal(p), Real(0))
new_f = f.substitute({p: Real(1)}).simplify()
self.assertEqual(new_f, Bool(False))
def test_cnf_as_set(self):
r = cnf_as_set(Symbol("x"))
self.assertTrue(type(r) == frozenset)
def test_error(self):
varA = Symbol("A")
with self.assertRaises(NotImplementedError):
varA.size("non-existent")
def test_prenex_simple_forall(self):
a, b = (Symbol(x) for x in "ab")
f = Or(b, ForAll([b], Implies(a, b)))
prenex = prenex_normal_form(f)
self.assertTrue(prenex.is_forall())
self.assertValid(Iff(f, prenex), logic=BOOL)
def test_node_id(self):
x = Symbol("x")
y = Symbol("y")
xx = Symbol("x")
self.assertEqual(x.node_id(), xx.node_id())
self.assertNotEqual(x.node_id(), y.node_id())
def setUp(self):
TestCase.setUp(self)
self.x, self.y = Symbol("x"), Symbol("y")
def test_real(self):
f = Plus([Real(1), Symbol("x", REAL), Symbol("y", REAL)])
self.assertEqual(f.to_smtlib(daggify=False), "(+ 1.0 x y)")
self.assertEqual(f.to_smtlib(daggify=True),
"(let ((.def_0 (+ 1.0 x y))) .def_0)")
#
# In this example, we use four theories supported by pySMT:
# BitVectors, Integers, Reals, and Arrays.
#
#
from pysmt.shortcuts import Symbol, BV, Real, And, BVToNatural, ToReal
from pysmt.shortcuts import get_model
from pysmt.typing import BV8, REAL, INT, ArrayType
# We create a map from BitVectors to Reals, so that each bitvector
# value (interpreted as unary number) is equal to the Real
# value.
#
# The map is represented by an Array of type BV8 -> Real
map_type = ArrayType(BV8, REAL)
my_map = Symbol("my_map", map_type)
# Fill-up the map, by defining all 256 values:
for i in range(0, 255):
my_map = my_map.Store(BV(i, 8), Real(i))
# We want to find find a value for which our relation does not work.
# In other words, we ask if there is a value for the bitvector
# s.t. the corresponding value in the array is different from the
# unary interpretation of the bitvector.
bv_var = Symbol("bv", BV8)
int_var = Symbol("int", INT)
real_var = Symbol("real", REAL)
f = And(
# Convert the BV into INT
def variables(n):
# the Boolean network is represented by n*2^n Boolean variables
return [[Symbol("x{}_{}".format(i + 1, j + 1)) for j in range(n)]
for i in range(2**n)]
def test_toreal(self):
p = Symbol("p", INT)
rp = ToReal(p)
rp_string = self.print_to_string(rp)
self.assertEqual(rp_string, "(to_real p)")
def is_int(model, x_str): x = Symbol(x_str, REAL) tmp = (model.get_value(x) - Real(math.floor(float(model.get_value(x))))).simplify().is_zero() return tmp
def test_real(self):
f = Plus([Real(1), Symbol("x", REAL), Symbol("y", REAL)])
f_string = self.print_to_string(f)
self.assertEqual(f_string, "(+ 1.0 x y)")
def get_floor(model, x_str): x = Symbol(x_str, REAL) flvalue = math.floor(float(model.get_value(x).simplify())) return str(flvalue)
def test_boolean(self):
x, y, z = Symbol("x"), Symbol("y"), Symbol("z")
f = Or(And(Not(x), Iff(x, y)), Implies(x, z))
f_string = self.print_to_string(f)
self.assertEqual(f_string, "(or (and (not x) (= x y)) (=> x z))")
def exclude_interval(x, a, b): global solver solver.push() var = Symbol(x, REAL) solver.add_assertion(Or(LE(var, Real(float(a))), GE(var, Real(float(b)))))
def comb_attack(self):
# dis generator
solver_name = 'yices'
solver_obf = Solver(name=solver_name)
solver_key = Solver(name=solver_name)
self.solver_oracle = Solver(name=solver_name)
attack_formulas = FormulaGenerator(self.oracle_cir, self.obf_cir)
f = attack_formulas.dip_gen_ckt
# f = simplify(f)
solver_obf.add_assertion(f)
f = attack_formulas.key_inequality_ckt
# f = simplify(f)
solver_obf.add_assertion(f)
for l in self.oracle_cir.wire_objs:
self.solver_oracle.add_assertion(l.formula)
dip_list = []
stateful_keys = []
iteration = 0
while 1:
# query dip generator
if solver_obf.solve():
dip_formula = []
dip_boolean = []
for l in self.oracle_cir.input_wires:
s = Symbol(l.name)
if solver_obf.get_py_value(s):
dip_formula.append(s)
dip_boolean.append(TRUE())
else:
dip_formula.append(Not(s))
dip_boolean.append(FALSE())
logging.info(dip_formula)
# query oracle
dip_out = self.query_oracle(dip_formula)
logging.info(dip_out)
# check for stateful condition
if dip_formula in dip_list:
# ban stateful key
logging.info("found a repeated dip!")
# check outputs for both keys
key = None
for l in self.obf_cir.output_wires:
s1 = Symbol(l.name + '@dc1')
s2 = Symbol(l.name + '@dc2')
if solver_obf.get_py_value(
s1) != solver_obf.get_py_value(s2):
if solver_obf.get_py_value(
s1) != self.solver_oracle.get_py_value(
Symbol(l.name)):
key = '0'
else:
key = '1'
break
if key == None:
logging.critical(
'something is wrong when banning keys')
# find assigned keys
key_list = []
for l in self.obf_cir.key_wires:
k = Symbol(l.name + '_' + key)
if solver_obf.get_py_value(k):
key_list.append(k)
else:
key_list.append(Not(k))
stateful_keys.append(key_list)
# ban the stateful key
f = Not(And(key_list))
solver_obf.add_assertion(f)
solver_key.add_assertion(f)
if len(stateful_keys) % 5000 == 0:
logging.warning('current stateful keys: {}'.format(
len(stateful_keys)))
continue
else:
dip_list.append(dip_formula)
# add dip checker
f = []
f.append(
attack_formulas.gen_dip_chk(iteration * 2, '_0',
dip_boolean))
f.append(
attack_formulas.gen_dip_chk(iteration * 2 + 1, '_1',
dip_boolean))
for i in range(len(self.obf_cir.output_wires)):
l = self.obf_cir.output_wires[i].name
f.append(
And(
Iff(dip_out[i],
Symbol(l + '@{}'.format(iteration * 2))),
Iff(dip_out[i],
Symbol(l + '@{}'.format(iteration * 2 + 1)))))
f = And(f)
solver_obf.add_assertion(f)
solver_key.add_assertion(f)
iteration += 1
logging.warning('iteration: {}'.format(iteration))
else:
logging.warning('print keys')
logging.warning('stateful keys: {}'.format(len(stateful_keys)))
if solver_key.solve():
key = ''
for l in self.obf_cir.key_wires:
if solver_key.get_py_value(Symbol(l.name + '_0')):
key += '1'
else:
key += '0'
print("key=%s" % key)
else:
logging.critical('key solver returned UNSAT')
return
def get_float(model, x, accuracy): val = model.get_py_value(Symbol(x, REAL)) decdigits = int(-math.log(accuracy, 10)) + 2 return float(val)
from pysmt.shortcuts import Symbol, LE, GE, And, Int
from pysmt.typing import INT
h = Symbol("H", INT)
# domain = (1 <= h) & (10 >= h)
domain = And(LE(Int(1), h), GE(Int(10), h))
def test_prenex_simple_exists(self):
a, b = (Symbol(x) for x in "ab")
f = And(b, Exists([b], Implies(a, b)))
prenex = prenex_normal_form(f)
self.assertTrue(prenex.is_exists())
self.assertValid(Iff(f, prenex), logic=BOOL)
def setUp(self):
self.x, self.y = Symbol("x"), Symbol("y")
def test_prenex_negated_forall(self):
a, b = (Symbol(x) for x in "ab")
f = Implies(ForAll([b], Implies(a, b)), b)
prenex = prenex_normal_form(f)
self.assertTrue(prenex.is_exists())
self.assertValid(Iff(f, prenex), logic=BOOL)
def generate_model(formula):
"""
This function will invoke PySMT APIs to solve the provided formula and return the byte list of the model
Arguments:
formula: smtlib formatted formula
"""
emitter.debug("extracting z3 model")
model = get_model(formula)
if model is None:
return None
path_script = "/tmp/z3_script_model"
write_smtlib(formula, path_script)
with open(path_script, "r") as script_file:
script_lines = script_file.readlines()
script = "".join(script_lines)
var_list = set(re.findall("\(declare-fun (.+?) \(\)", script))
sym_var_list = dict()
for var_name in var_list:
# sym_var_list[var_name] = dict()
if "const_" in var_name and not "const_arr" in var_name:
sym_def = Symbol(var_name, BV32)
if sym_def not in model:
continue
x = model[sym_def]
byte_list = dict()
default_value = x.bv_signed_value()
byte_list[0] = default_value
else:
sym_def = Symbol(var_name, ArrayType(BV32, BV8))
if sym_def not in model:
continue
x = model[sym_def].simplify()
byte_list = dict()
value_array_map = x.array_value_assigned_values_map()
default_value = int(str(x.array_value_default()).split("_")[0])
if not value_array_map:
byte_list[0] = default_value
else:
for idx, val in value_array_map.items():
index = int(str(idx).split("_")[0])
value = int(str(val).split("_")[0])
byte_list[index] = value
max_index = max(list(byte_list.keys()))
if var_name in values.LIST_BIT_LENGTH:
array_size = values.LIST_BIT_LENGTH[var_name] - 1
if var_name in ["A-data"]:
array_size = max_index
else:
array_size = max_index + 1 # TODO: this could be wrong calculation
if max_index == 0:
array_size = 2
if var_name not in ["A-data"]:
for i in range(0, array_size):
if i not in byte_list:
byte_list[i] = default_value
if var_name not in ["A-data", "A-data-stat"]:
for i in range(array_size - 1, -1, -1):
if byte_list[i] == 0:
byte_list.pop(i)
else:
break
sym_var_list[var_name] = byte_list
emitter.data("model var list", sym_var_list)
return sym_var_list
def test_bv(self):
mgr = self.env.formula_manager
BV = mgr.BV
# Constants
one = BV(1, 32)
zero = BV(0, 32)
big = BV(127, 128)
binary = BV("111")
binary2 = BV("#b111")
binary3 = BV(0b111, 3) # In this case we need to explicit the width
self.assertEqual(binary, binary2)
self.assertEqual(binary2, binary3)
self.assertEqual(one, mgr.BVOne(32))
self.assertEqual(zero, mgr.BVZero(32))
# Type Equality
self.assertTrue(BV32 != BV128)
self.assertFalse(BV32 != BV32)
self.assertFalse(BV32 == BV128)
self.assertTrue(BV32 == BV32)
with self.assertRaises(PysmtValueError):
# Negative numbers are not supported
BV(-1, 10)
with self.assertRaises(PysmtValueError):
# Number should fit in the width
BV(10, 2)
# Variables
b128 = Symbol("b", BV128) # BV1, BV8 etc. are defined in pysmt.typing
b32 = Symbol("b32", BV32)
hexample = BV(0x10, 32)
bcustom = Symbol("bc", BVType(42))
self.assertIsNotNone(hexample)
self.assertIsNotNone(bcustom)
self.assertEqual(bcustom.bv_width(), 42)
self.assertEqual(hexample.constant_value(), 16)
not_zero32 = mgr.BVNot(zero)
not_b128 = mgr.BVNot(b128)
self.assertTrue(not_b128.is_bv_not())
f1 = Equals(not_zero32, b32)
f2 = Equals(not_b128, big)
self.assertTrue(is_sat(f1, logic=QF_BV))
self.assertTrue(is_sat(f2, logic=QF_BV))
zero_and_one = mgr.BVAnd(zero, one)
self.assertTrue(zero_and_one.is_bv_and())
zero_or_one = mgr.BVOr(zero, one)
self.assertTrue(zero_or_one.is_bv_or())
zero_xor_one = mgr.BVXor(zero, one)
self.assertTrue(zero_xor_one.is_bv_xor())
zero_xor_one.simplify()
self.assertTrue(zero_xor_one.is_bv_op())
f1 = Equals(zero_and_one, b32)
f2 = Equals(zero_or_one, b32)
f3 = Equals(zero_xor_one, b32)
f4 = Equals(zero_xor_one, one)
self.assertTrue(is_sat(f1, logic=QF_BV), f1)
self.assertTrue(is_sat(f2, logic=QF_BV), f2)
self.assertTrue(is_sat(f3, logic=QF_BV), f3)
self.assertTrue(is_valid(f4, logic=QF_BV), f4)
with self.assertRaises(PysmtTypeError):
mgr.BVAnd(b128, zero)
f = mgr.BVAnd(b32, zero)
f = mgr.BVOr(f, b32)
f = mgr.BVXor(f, b32)
f = Equals(f, zero)
self.assertTrue(is_sat(f, logic=QF_BV), f)
zero_one_64 = mgr.BVConcat(zero, one)
one_zero_64 = mgr.BVConcat(one, zero)
one_one_64 = mgr.BVConcat(one, one)
self.assertTrue(one_one_64.is_bv_concat())
self.assertFalse(one_one_64.is_bv_and())
self.assertTrue(zero_one_64.bv_width() == 64)
f1 = Equals(mgr.BVXor(one_zero_64, zero_one_64),
one_one_64)
self.assertTrue(is_sat(f1, logic=QF_BV), f1)
# MG: BV indexes grow to the left.
# This is confusing and we should address this.
extraction = mgr.BVExtract(zero_one_64, 32, 63)
self.assertTrue(is_valid(Equals(extraction, zero)))
ult = mgr.BVULT(zero, one)
self.assertTrue(ult.is_bv_ult())
neg = mgr.BVNeg(one)
self.assertTrue(neg.is_bv_neg())
self.assertTrue(is_valid(ult, logic=QF_BV), ult)
test_eq = Equals(neg, one)
self.assertTrue(is_unsat(test_eq, logic=QF_BV))
f = zero
addition = mgr.BVAdd(f, one)
self.assertTrue(addition.is_bv_add())
multiplication = mgr.BVMul(f, one)
self.assertTrue(multiplication.is_bv_mul())
udiv = mgr.BVUDiv(f, one)
self.assertTrue(udiv.is_bv_udiv())
self.assertTrue(is_valid(Equals(addition, one), logic=QF_BV), addition)
self.assertTrue(is_valid(Equals(multiplication, zero), logic=QF_BV), multiplication)
self.assertTrue(is_valid(Equals(udiv, zero), logic=QF_BV), udiv)
three = mgr.BV(3, 32)
two = mgr.BV(2, 32)
self.assertEqual(3, three.bv2nat())
reminder = mgr.BVURem(three, two)
self.assertTrue(reminder.is_bv_urem())
shift_l_a = mgr.BVLShl(one, one)
self.assertTrue(shift_l_a.is_bv_lshl())
shift_l_b = mgr.BVLShl(one, 1)
self.assertTrue(is_valid(Equals(reminder, one)), reminder)
self.assertEqual(shift_l_a, shift_l_b)
self.assertTrue(is_valid(Equals(shift_l_a, two)))
shift_r_a = mgr.BVLShr(one, one)
self.assertTrue(shift_r_a.is_bv_lshr())
shift_r_b = mgr.BVLShr(one, 1)
self.assertEqual(shift_r_a, shift_r_b)
self.assertTrue(is_valid(Equals(shift_r_a, zero)))
ashift_r_a = mgr.BVAShr(one, one)
ashift_r_b = mgr.BVAShr(one, 1)
self.assertEqual(ashift_r_a, ashift_r_b)
self.assertTrue(ashift_r_a.is_bv_ashr())
rotate_l = mgr.BVRol(one, 3)
self.assertTrue(rotate_l.is_bv_rol())
rotate_r = mgr.BVRor(rotate_l, 3)
self.assertTrue(rotate_r.is_bv_ror())
self.assertTrue(is_valid(Equals(one, rotate_r)))
zero_ext = mgr.BVZExt(one, 64)
self.assertTrue(zero_ext.is_bv_zext())
signed_ext = mgr.BVSExt(one, 64)
self.assertTrue(signed_ext.is_bv_sext())
signed_ext2 = mgr.BVSExt(mgr.BVNeg(one), 64)
self.assertNotEqual(signed_ext2, signed_ext)
self.assertTrue(is_valid(Equals(zero_ext, signed_ext), logic=QF_BV))
x = Symbol("x")
g = And(x, mgr.BVULT(zero, one))
res = is_sat(g, logic=QF_BV)
self.assertTrue(res)
model = get_model(g, logic=QF_BV)
self.assertTrue(model[x] == TRUE())
gt_1 = mgr.BVUGT(zero, one)
gt_2 = mgr.BVULT(one, zero)
self.assertEqual(gt_1, gt_2)
gte_1 = mgr.BVULE(zero, one)
gte_2 = mgr.BVUGE(one, zero)
self.assertEqual(gte_1, gte_2)
self.assertTrue(is_valid(gte_2, logic=QF_BV))
ide = Equals(mgr.BVNeg(BV(10, 32)), mgr.SBV(-10, 32))
self.assertValid(ide, logic=QF_BV)
# These should work without exceptions
mgr.SBV(-2, 2)
mgr.SBV(-1, 2)
mgr.SBV(0, 2)
mgr.SBV(1, 2)
# Overflow and Underflow
with self.assertRaises(PysmtValueError):
mgr.SBV(2, 2)
with self.assertRaises(PysmtValueError):
mgr.SBV(-3, 2)
# These should work without exceptions
mgr.BV(0, 2)
mgr.BV(1, 2)
mgr.BV(2, 2)
mgr.BV(3, 2)
# Overflow
with self.assertRaises(PysmtValueError):
mgr.BV(4, 2)
# No negative number allowed
with self.assertRaises(PysmtValueError):
mgr.BV(-1, 2)
# SBV should behave as BV for positive numbers
self.assertEqual(mgr.SBV(10, 16), mgr.BV(10, 16))
# Additional is_bv_* tests
f = mgr.BVSub(one, one)
self.assertTrue(f.is_bv_sub())
f = mgr.BVSLT(one, one)
self.assertTrue(f.is_bv_slt())
f = mgr.BVSLE(one, one)
self.assertTrue(f.is_bv_sle())
f = mgr.BVComp(one, one)
self.assertTrue(f.is_bv_comp())
f = mgr.BVSDiv(one, one)
self.assertTrue(f.is_bv_sdiv())
f = mgr.BVSRem(one, one)
self.assertTrue(f.is_bv_srem())
f = mgr.BVULE(one, one)
self.assertTrue(f.is_bv_ule())
def get_full_example_formulae(environment=None):
"""Return a list of Examples using the given environment."""
if environment is None:
environment = get_env()
with environment:
x = Symbol("x", BOOL)
y = Symbol("y", BOOL)
p = Symbol("p", INT)
q = Symbol("q", INT)
r = Symbol("r", REAL)
s = Symbol("s", REAL)
aii = Symbol("aii", ARRAY_INT_INT)
arb = Symbol("arb", ArrayType(REAL, BV8))
abb = Symbol("abb", ArrayType(BV8, BV8))
nested_a = Symbol("a_arb_aii",
ArrayType(ArrayType(REAL, BV8), ARRAY_INT_INT))
rf = Symbol("rf", FunctionType(REAL, [REAL, REAL]))
rg = Symbol("rg", FunctionType(REAL, [REAL]))
ih = Symbol("ih", FunctionType(INT, [REAL, INT]))
ig = Symbol("ig", FunctionType(INT, [INT]))
bf = Symbol("bf", FunctionType(BOOL, [BOOL]))
bg = Symbol("bg", FunctionType(BOOL, [BOOL]))
bv8 = Symbol("bv1", BV8)
bv16 = Symbol("bv2", BV16)
result = [
# Formula, is_valid, is_sat, is_qf
Example(hr="(x & y)",
expr=And(x, y),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
Example(hr="(x <-> y)",
expr=Iff(x, y),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
Example(hr="((x | y) & (! (x | y)))",
expr=And(Or(x, y), Not(Or(x, y))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BOOL),
Example(hr="(x & (! y))",
expr=And(x, Not(y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
Example(hr="(False -> True)",
expr=Implies(FALSE(), TRUE()),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
#
# LIA
#
Example(hr="((q < p) & (x -> y))",
expr=And(GT(p, q), Implies(x, y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_IDL),
Example(hr="(((p + q) = 5) & (q < p))",
expr=And(Equals(Plus(p, q), Int(5)), GT(p, q)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA),
Example(hr="((q <= p) | (p <= q))",
expr=Or(GE(p, q), LE(p, q)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_IDL),
Example(hr="(! (p < (q * 2)))",
expr=Not(LT(p, Times(q, Int(2)))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA),
Example(hr="(p < (p - (5 - 2)))",
expr=GT(Minus(p, Minus(Int(5), Int(2))), p),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_IDL),
Example(hr="((x ? 7 : ((p + -1) * 3)) = q)",
expr=Equals(
Ite(x, Int(7), Times(Plus(p, Int(-1)), Int(3))), q),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA),
Example(hr="(p < (q + 1))",
expr=LT(p, Plus(q, Int(1))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA),
#
# LRA
#
Example(hr="((s < r) & (x -> y))",
expr=And(GT(r, s), Implies(x, y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_RDL),
Example(hr="(((r + s) = 28/5) & (s < r))",
expr=And(Equals(Plus(r, s), Real(Fraction("5.6"))),
GT(r, s)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA),
Example(hr="((s <= r) | (r <= s))",
expr=Or(GE(r, s), LE(r, s)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_RDL),
Example(hr="(! ((r * 2.0) < (s * 2.0)))",
expr=Not(LT(Div(r, Real((1, 2))), Times(s, Real(2)))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA),
Example(hr="(! (r < (r - (5.0 - 2.0))))",
expr=Not(GT(Minus(r, Minus(Real(5), Real(2))), r)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_RDL),
Example(hr="((x ? 7.0 : ((s + -1.0) * 3.0)) = r)",
expr=Equals(
Ite(x, Real(7), Times(Plus(s, Real(-1)), Real(3))), r),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA),
#
# EUF
#
Example(hr="(bf(x) <-> bg(x))",
expr=Iff(Function(bf, (x, )), Function(bg, (x, ))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_UF),
Example(hr="(rf(5.0, rg(r)) = 0.0)",
expr=Equals(Function(rf, (Real(5), Function(rg, (r, )))),
Real(0)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_UFLRA),
Example(hr="((rg(r) = (5.0 + 2.0)) <-> (rg(r) = 7.0))",
expr=Iff(Equals(Function(rg, [r]), Plus(Real(5), Real(2))),
Equals(Function(rg, [r]), Real(7))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_UFLRA),
Example(
hr="((r = (s + 1.0)) & (rg(s) = 5.0) & (rg((r - 1.0)) = 7.0))",
expr=And([
Equals(r, Plus(s, Real(1))),
Equals(Function(rg, [s]), Real(5)),
Equals(Function(rg, [Minus(r, Real(1))]), Real(7))
]),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_UFLRA),
#
# BV
#
Example(hr="((1_32 & 0_32) = 0_32)",
expr=Equals(BVAnd(BVOne(32), BVZero(32)), BVZero(32)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((! 2_3) = 5_3)",
expr=Equals(BVNot(BV("010")), BV("101")),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((7_3 xor 0_3) = 0_3)",
expr=Equals(BVXor(BV("111"), BV("000")), BV("000")),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="((bv1::bv1) u< 0_16)",
expr=BVULT(BVConcat(bv8, bv8), BVZero(16)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="(1_32[0:7] = 1_8)",
expr=Equals(BVExtract(BVOne(32), end=7), BVOne(8)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="(0_8 u< (((bv1 + 1_8) * 5_8) u/ 5_8))",
expr=BVUGT(
BVUDiv(BVMul(BVAdd(bv8, BVOne(8)), BV(5, width=8)),
BV(5, width=8)), BVZero(8)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="(0_16 u<= bv2)",
expr=BVUGE(bv16, BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="(0_16 s<= bv2)",
expr=BVSGE(bv16, BVZero(16)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(
hr="((0_32 u< (5_32 u% 2_32)) & ((5_32 u% 2_32) u<= 1_32))",
expr=And(
BVUGT(BVURem(BV(5, width=32), BV(2, width=32)),
BVZero(32)),
BVULE(BVURem(BV(5, width=32), BV(2, width=32)),
BVOne(32))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((((1_32 + (- ...)) << 1_32) >> 1_32) = 1_32)",
expr=Equals(
BVLShr(BVLShl(BVAdd(BVOne(32), BVNeg(BVOne(32))), 1),
1), BVOne(32)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="((1_32 - 1_32) = 0_32)",
expr=Equals(BVSub(BVOne(32), BVOne(32)), BVZero(32)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# Rotations
Example(hr="(((1_32 ROL 1) ROR 1) = 1_32)",
expr=Equals(BVRor(BVRol(BVOne(32), 1), 1), BVOne(32)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# Extensions
Example(hr="((0_5 ZEXT 11) = (0_1 SEXT 15))",
expr=Equals(BVZExt(BVZero(5), 11), BVSExt(BVZero(1), 15)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 - bv2) = 0_16)",
expr=Equals(BVSub(bv16, bv16), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 - bv2)[0:7] = bv1)",
expr=Equals(BVExtract(BVSub(bv16, bv16), 0, 7), bv8),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2[0:7] bvcomp bv1) = 1_1)",
expr=Equals(BVComp(BVExtract(bv16, 0, 7), bv8), BVOne(1)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 bvcomp bv2) = 0_1)",
expr=Equals(BVComp(bv16, bv16), BVZero(1)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="(bv2 s< bv2)",
expr=BVSLT(bv16, bv16),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="(bv2 s< 0_16)",
expr=BVSLT(bv16, BVZero(16)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 s< 0_16) | (0_16 s<= bv2))",
expr=Or(BVSGT(BVZero(16), bv16), BVSGE(bv16, BVZero(16))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="(bv2 u< bv2)",
expr=BVULT(bv16, bv16),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="(bv2 u< 0_16)",
expr=BVULT(bv16, BVZero(16)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 | 0_16) = bv2)",
expr=Equals(BVOr(bv16, BVZero(16)), bv16),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 & 0_16) = 0_16)",
expr=Equals(BVAnd(bv16, BVZero(16)), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((0_16 s< bv2) & ((bv2 s/ 65535_16) s< 0_16))",
expr=And(BVSLT(BVZero(16), bv16),
BVSLT(BVSDiv(bv16, SBV(-1, 16)), BVZero(16))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((0_16 s< bv2) & ((bv2 s% 1_16) s< 0_16))",
expr=And(BVSLT(BVZero(16), bv16),
BVSLT(BVSRem(bv16, BVOne(16)), BVZero(16))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 u% 1_16) = 0_16)",
expr=Equals(BVURem(bv16, BVOne(16)), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 s% 1_16) = 0_16)",
expr=Equals(BVSRem(bv16, BVOne(16)), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 s% (- 1_16)) = 0_16)",
expr=Equals(BVSRem(bv16, BVNeg(BVOne(16))), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv2 a>> 0_16) = bv2)",
expr=Equals(BVAShr(bv16, BVZero(16)), bv16),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((0_16 s<= bv2) & ((bv2 a>> 1_16) = (bv2 >> 1_16)))",
expr=And(
BVSLE(BVZero(16), bv16),
Equals(BVAShr(bv16, BVOne(16)),
BVLShr(bv16, BVOne(16)))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
#
# Quantification
#
Example(hr="(forall y . (x -> y))",
expr=ForAll([y], Implies(x, y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.BOOL),
Example(hr="(forall p, q . ((p + q) = 0))",
expr=ForAll([p, q], Equals(Plus(p, q), Int(0))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.LIA),
Example(
hr="(forall r, s . (((0.0 < r) & (0.0 < s)) -> ((r - s) < r)))",
expr=ForAll([r, s],
Implies(And(GT(r, Real(0)), GT(s, Real(0))),
(LT(Minus(r, s), r)))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.LRA),
Example(hr="(exists x, y . (x -> y))",
expr=Exists([x, y], Implies(x, y)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.BOOL),
Example(hr="(exists p, q . ((p + q) = 0))",
expr=Exists([p, q], Equals(Plus(p, q), Int(0))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.LIA),
Example(hr="(exists r . (forall s . (r < (r - s))))",
expr=Exists([r], ForAll([s], GT(Minus(r, s), r))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.LRA),
Example(hr="(forall r . (exists s . (r < (r - s))))",
expr=ForAll([r], Exists([s], GT(Minus(r, s), r))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.LRA),
Example(hr="(x & (forall r . ((r + s) = 5.0)))",
expr=And(x, ForAll([r], Equals(Plus(r, s), Real(5)))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.LRA),
Example(hr="(exists x . ((x <-> (5.0 < s)) & (s < 3.0)))",
expr=Exists([x],
(And(Iff(x, GT(s, Real(5))), LT(s, Real(3))))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.LRA),
#
# UFLIRA
#
Example(hr="((p < ih(r, q)) & (x -> y))",
expr=And(GT(Function(ih, (r, q)), p), Implies(x, y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_UFLIRA),
Example(
hr=
"(((p - 3) = q) -> ((p < ih(r, (... + ...))) | (ih(r, p) <= p)))",
expr=Implies(
Equals(Minus(p, Int(3)), q),
Or(GT(Function(ih, (r, Plus(q, Int(3)))), p),
LE(Function(ih, (r, p)), p))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_UFLIRA),
Example(
hr=
"(((ToReal((... - ...)) = r) & (ToReal(q) = r)) -> ((p < ih(ToReal(...), (... + ...))) | (ih(r, p) <= p)))",
expr=Implies(
And(Equals(ToReal(Minus(p, Int(3))), r),
Equals(ToReal(q), r)),
Or(
GT(
Function(
ih,
(ToReal(Minus(p, Int(3))), Plus(q, Int(3)))),
p), LE(Function(ih, (r, p)), p))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_UFLIRA),
Example(
hr=
"(! (((ToReal(...) = r) & (ToReal(...) = r)) -> ((p < ...(..., ...)) | (...(..., ...) <= p))))",
expr=Not(
Implies(
And(Equals(ToReal(Minus(p, Int(3))), r),
Equals(ToReal(q), r)),
Or(
GT(
Function(ih, (ToReal(Minus(
p, Int(3))), Plus(q, Int(3)))), p),
LE(Function(ih, (r, p)), p)))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_UFLIRA),
Example(
hr=
"""("Did you know that any string works? #yolo" & "10" & "|#somesolverskeepthe||" & " ")""",
expr=And(Symbol("Did you know that any string works? #yolo"),
Symbol("10"), Symbol("|#somesolverskeepthe||"),
Symbol(" ")),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
#
# Arrays
#
Example(hr="((q = 0) -> (aii[0 := 0] = aii[0 := q]))",
expr=Implies(
Equals(q, Int(0)),
Equals(Store(aii, Int(0), Int(0)),
Store(aii, Int(0), q))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_ALIA),
Example(hr="(aii[0 := 0][0] = 0)",
expr=Equals(Select(Store(aii, Int(0), Int(0)), Int(0)),
Int(0)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_ALIA),
Example(hr="((Array{Int, Int}(0)[1 := 1] = aii) & (aii[1] = 0))",
expr=And(Equals(Array(INT, Int(0), {Int(1): Int(1)}), aii),
Equals(Select(aii, Int(1)), Int(0))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.get_logic_by_name("QF_ALIA*")),
Example(
hr=
"((a_arb_aii = Array{Array{Real, BV{8}}, Array{Int, Int}}(Array{Int, Int}(7))) -> (a_arb_aii[arb][42] = 7))",
expr=Implies(
Equals(nested_a,
Array(ArrayType(REAL, BV8), Array(INT, Int(7)))),
Equals(Select(Select(nested_a, arb), Int(42)), Int(7))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.get_logic_by_name("QF_AUFBVLIRA*")),
Example(hr="(abb[bv1 := y_][bv1 := z_] = abb[bv1 := z_])",
expr=Equals(
Store(Store(abb, bv8, Symbol("y_", BV8)), bv8,
Symbol("z_", BV8)),
Store(abb, bv8, Symbol("z_", BV8))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_ABV),
Example(hr="((r / s) = (r * s))",
expr=Equals(Div(r, s), Times(r, s)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_NRA),
Example(hr="(2.0 = (r * r))",
expr=Equals(Real(2), Times(r, r)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_NRA),
Example(hr="((p ^ 2) = 0)",
expr=Equals(Pow(p, Int(2)), Int(0)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_NIA),
Example(hr="((r ^ 2.0) = 0.0)",
expr=Equals(Pow(r, Real(2)), Real(0)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_NRA),
Example(hr="((r * r * r) = 25.0)",
expr=Equals(Times(r, r, r), Real(25)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_NRA),
Example(hr="((5.0 * r * 5.0) = 25.0)",
expr=Equals(Times(Real(5), r, Real(5)), Real(25)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA),
Example(hr="((p * p * p) = 25)",
expr=Equals(Times(p, p, p), Int(25)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_NIA),
Example(hr="((5 * p * 5) = 25)",
expr=Equals(Times(Int(5), p, Int(5)), Int(25)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA),
Example(hr="(((1 - 1) * p * 1) = 0)",
expr=Equals(Times(Minus(Int(1), Int(1)), p, Int(1)),
Int(0)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_LIA),
# Huge Fractions:
Example(
hr=
"((r * 1606938044258990275541962092341162602522202993782792835301376/7) = -20480000000000000000000000.0)",
expr=Equals(Times(r, Real(Fraction(2**200, 7))),
Real(-200**11)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA),
Example(hr="(((r + 5.0 + s) * (s + 2.0 + r)) = 0.0)",
expr=Equals(
Times(Plus(r, Real(5), s), Plus(s, Real(2), r)),
Real(0)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_NRA),
Example(
hr=
"(((p + 5 + q) * (p - (q - 5))) = ((p * p) + (10 * p) + 25 + (-1 * q * q)))",
expr=Equals(
Times(Plus(p, Int(5), q), Minus(p, Minus(q, Int(5)))),
Plus(Times(p, p), Times(Int(10), p), Int(25),
Times(Int(-1), q, q))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_NIA),
]
return result
