def test_sub(self) -> None:
self.assertEqual(
Sub(Number(6), Number(4)).z3expr(),
z3.IntVal(6) - z3.IntVal(4))
self.assertEqual(
Sub(Number(12), Number(20)).z3expr(),
z3.IntVal(12) - z3.IntVal(20))
def basic_constraints(self):
""" Returns a list of constraints representing basic facts about the possible game states """
return [
# Number of impostors is number of impostors
self.n_impostors == sumbools(self.impostor)
# A number of impostors can be alive
,
self.n_alive_impostors == sumbools(
z3.And(self.alive[i], self.impostor[i])
for i in range(self.n_players))
# People that were murdered cannot be impostors
,
*[
z3.Implies(self.murdered[i], z3.Not(self.impostor[i]))
for i in range(self.n_players)
]
# Alive people have not been murdered and have not been ejected
,
*[
z3.And(z3.Not(self.murdered[i]), z3.Not(self.ejected[i]))
== self.alive[i] for i in range(self.n_players)
]
# There is at least one not-dead impostor
,
self.n_alive_impostors > z3.IntVal(0)
# Twice the number of alive impostors is less than the number of alive crewmates
,
sumbools(self.alive) > (self.n_alive_impostors * z3.IntVal(2))
]
def recover_value(value, uct_sort):
"""
Inverse of _extract_value. Given a pythonic value, returns a z3 embedding of it depending on its uct sort. The
explicit embedding scheme is as follows:
fgsort -> z3.ArithRef
fgsetsort -> z3.ArrayRef
intsort -> z3.ArithRef
intsetsort -> z3.ArrayRef
boolsort -> z3.BoolRef
:param value: any
:param uct_sort: naturalproofs.uct.UCTSort
:return: z3.ExprRef
"""
# TODO: typecheck all the arguments
if uct_sort in {fgsort, intsort}:
return z3.IntVal(value)
elif uct_sort == boolsort:
return z3.BoolVal(value)
elif uct_sort in {fgsetsort, intsetsort}:
expr = z3.EmptySet(z3.IntSort())
for elem in value:
expr = z3.SetAdd(expr, z3.IntVal(elem))
else:
raise ValueError(
'Sort not supported. Check for a list of available sorts in the naturalproofs.uct module.'
)
def test_mul(self) -> None:
self.assertEqual(
Mul(Number(6), Number(4)).z3expr(),
z3.IntVal(6) * z3.IntVal(4))
self.assertEqual(
Mul(Number(2), Number(4), Number(8)).z3expr(),
z3.IntVal(2) * z3.IntVal(4) * z3.IntVal(8),
)
def test_case() -> None:
assert_equal(
Case(Variable("x"), [(Number(5), Number(1)), (Number(10), Number(2))]).z3expr(),
z3.If(
z3.Int("x") == z3.IntVal(5),
z3.IntVal(1),
z3.If(z3.Int("x") == z3.IntVal(10), z3.IntVal(2), z3.BoolVal(False)),
),
)
def rename(self, srcname, dstname):
oldstate = self
src_ino = oldstate.fname_inode(srcname)
srcexists = src_ino != z3.IntVal(0)
dst_ino = oldstate.fname_inode(dstname)
dstexists = dst_ino != z3.IntVal(0)
return If(
z3.Not(srcexists), Result(z3.IntVal(-1), oldstate),
If(
srcname == dstname, Result(z3.IntVal(0), oldstate),
If(
dstexists,
Result(
z3.IntVal(0),
oldstate.write_nlink(
dst_ino,
self.inode_nlink(dst_ino) -
z3.IntVal(1)).write_dir(dstname,
src_ino).write_dir(
srcname,
z3.IntVal(0))),
Result(
z3.IntVal(0),
oldstate.write_dir(dstname, src_ino).write_dir(
srcname, z3.IntVal(0))))))
def generate():
for i, j in itertools.combinations(self.slots, 2):
ii, jj = z3.IntVal(i.id), z3.IntVal(j.id)
if fn(i, j):
yield z3fn(ii, jj)
yield z3fn(jj, ii)
else:
yield z3.Not(z3fn(ii, jj))
yield z3.Not(z3fn(jj, ii))
for i in self.slots:
ii = z3.IntVal(i.id)
yield z3fn(ii, ii)
def z3ify_time_constraint(name: str, fn):
constraints = []
z3fn = z3.Function(name, z3.IntSort(), z3.IntSort(), z3.BoolSort())
for i, j in itertools.combinations(ALL_SLOTS, 2):
ii, jj = z3.IntVal(i.id), z3.IntVal(j.id)
if fn(i, j):
constraints += [z3fn(ii, jj), z3fn(jj, ii)]
else:
constraints += [z3.Not(z3fn(ii, jj)), z3.Not(z3fn(jj, ii))]
for i in ALL_SLOTS:
ii = z3.IntVal(i.id)
constraints += [z3fn(ii, ii)]
return z3fn, constraints
def test_if() -> None:
assert_equal(
If(
[
(Greater(Variable("a"), Number(5)), Number(1)),
(Greater(Variable("b"), Number(100)), Number(10)),
],
Number(100),
).z3expr(),
z3.If(
z3.Int("a") > z3.IntVal(5),
z3.IntVal(1),
z3.If(z3.Int("b") > z3.IntVal(100), z3.IntVal(10), z3.IntVal(100)),
),
)
def get_pred(self):
if self.is_ninf():
return copy.deepcopy(self)
if self.is_pzero():
return Float('-0',ne=self.ne,ns=self.ns).get_pred()
bv_str = self.get_bv_str()
#print(bv_str)
sign = bv_str[0]
if sign == '0':
succ = int(bv_str[1:],2) - 1
return Float(val=z3.simplify(z3.fpBVToFP(z3.Int2BV(z3.IntVal(succ),num_bits = self.ns + self.ne),z3.FPSort(self.ne,self.ns))),ne=self.ne, ns=self.ns)
else:
succ = int(bv_str[1:],2) + 1
return -Float(val=z3.simplify(z3.fpBVToFP(z3.Int2BV(z3.IntVal(succ),num_bits = self.ns + self.ne),z3.FPSort(self.ne,self.ns))),ne=self.ne, ns=self.ns)
def solve(s1, s2, s3):
global vars
vars = dict()
list1 = list(s1) #list=[s,e,n,d]
list2 = list(s2)
list3 = list(s3)
#initial list in z3
for i in list1:
mk_var(i)
for i in list2:
mk_var(i)
for i in list3:
mk_var(i)
#equation
lhs1 = reduce(lambda a, b: 10 * a + vars[b], list1, 0)
lhs2 = reduce(lambda a, b: 10 * a + vars[b], list2, 0)
rhs1 = reduce(lambda a, b: 10 * a + vars[b], list3, 0)
solver = z3.Solver()
#distinct
solver.add(z3.Distinct(get_vars()))
#equation
solver.add(lhs1 + lhs2 == rhs1)
solver.add(vars[list1[0]] != 0)
solver.add(vars[list2[0]] != 0)
solver.add(vars[list3[0]] != 0)
#digital range
for x in vars:
solver.add(vars[x] >= z3.IntVal(0))
solver.add(vars[x] <= z3.IntVal(9))
res = solver.check()
if res == z3.sat:
model = solver.model()
result = []
result.append(
int(reduce(lambda a, b: "%s%s" % (a, model[vars[b]]), list1, '')))
result.append(
int(reduce(lambda a, b: "%s%s" % (a, model[vars[b]]), list2, '')))
result.append(
int(reduce(lambda a, b: "%s%s" % (a, model[vars[b]]), list3, '')))
return result
else:
return None
def from_symmetries2programs(self, model, m_aux):
for t in range(len(self.typeVars) - 1):
k = self.typeVars[t]
m_aux[k] = self.model[k] # NEW
root_num = t + 1
type = int(str(self.model[k]))
new_node = int(str(model[z3.Int('x_' + str(root_num))]))
old_prod = self.line_productions[root_num - 1][type].id
new_prod = self.line_productions[new_node - 1][type].id
start = root_num * self.max_children
for i in range(start, len(self.leafs)):
n = self.leafs[i]
if self.model[n.var] == old_prod:
m_aux[n.var] = z3.IntVal(new_prod)
break
m_aux[self.typeVars[-1]] = self.model[self.typeVars[-1]]
n_model = dict(m_aux)
for v in model:
var, new_node_pos = v, int(str(model[v]))
node_pos = int(str(var).split("_")[1])
n_model[self.roots[new_node_pos -
1].var] = self.model[self.roots[node_pos -
1].var]
self.change_node(node_pos, new_node_pos, n_model, m_aux)
n_model[self.roots[-1].var] = self.model[self.roots[-1].var]
self.change_node(0, 0, n_model, m_aux)
return n_model
def incidence_sums(petrinet,
variables,
subnet_transitions="all",
reverse=False):
if subnet_transitions == "all":
subnet_transitions = set(range(petrinet.num_transitions))
sums = []
for p in range(petrinet.num_places()):
nonzero = petrinet.transitions_set({p}, reverse)
incidence_row = [(petrinet.get_post(p, t) - petrinet.get_pre(p, t),
variables[t]) for t in nonzero
if t in subnet_transitions]
sum_elements = [
expression(coeff, var) for coeff, var in incidence_row
if coeff != 0
]
curr_sum = z3.Sum(
sum_elements) if len(sum_elements) > 0 else z3.IntVal(0)
sums.append(curr_sum)
return sums
def pyval2z3val(val):
if type(val) is float:
return z3.RealVal(val)
elif type(val) is int:
return z3.IntVal(val)
else:
raise err.Fatal('unhandled python val type!')
def translate(self, term):
"""Translate a Maude term into an SMT formula"""
symbol = term.symbol()
# Variable
if str(symbol) == str(term.getSort()):
return smt.Const(str(term), self._smt_sort(term.getSort()))
# Integer constant
elif symbol == self.intlit_symb:
return smt.IntVal(int(term))
# Real constant
elif symbol == self.reallit_symb:
return smt.RealVal(float(term))
# Other symbols
else:
symb = self.ops_table.get(symbol)
# If the symbol is not in the table, it may be a
# polymorph for a custom type...
if symb is None:
symb = self._make_polymorph(symbol)
# ...or an uninterpreted function
if symb is None:
symb = self._make_function(symbol)
return symb(*[self.translate(arg) for arg in term.arguments()])
def bv_value_to_int_value(bv_value, bv_type, force_big_endian=False):
if bv_type == "intle:32" and not force_big_endian:
f = [
x for x in bitstring.BitArray(uint=bv_value.as_long(),
length=32).cut(8)
]
return z3.IntVal(
bitstring.pack('int:8, int:8, int:8, int:8', f[3].int, f[2].int,
f[1].int, f[0].int).int)
elif bv_type == "intbe:32" or (bv_type == "intle:32" and force_big_endian):
return z3.IntVal(bv_value.as_signed_long())
elif bv_type == "uintbe:32" or (bv_type == "uintle:32"
and force_big_endian):
return z3.IntVal(bv_value.as_long())
else:
raise NotImplementedError("unrecognized type: " + bv_type)
def _create_union_constraints(self):
""" Prevent union of twice the same subtree: (A|B) """
for node in self.nodes:
if node.children is None or len(node.children) == 0:
continue
test2 = node.children[0].children is None or len(
node.children[0].children) == 0
test3 = node.children[1].children is None or len(
node.children[1].children) == 0
if test2 or test3: continue
node_var = self.variables[node]
if self.dsl.get_function_production("union") is None: return
union_id = self.dsl.get_function_production("union").id
node_is_union = node_var == z3.IntVal(union_id)
subtree0, subtree1 = node.children[0].get_subtree(), \
node.children[1].get_subtree()
bigOr = []
for i in range(len(subtree0)):
var_i0 = self.variables[subtree0[i]]
var_i1 = self.variables[subtree1[i]]
bigOr.append(var_i0 != var_i1)
self.z3_solver.add(z3.Implies(node_is_union, z3.Or(bigOr)))
def get_transaction_info(test):
env_translate = dict(currentCoinbase='coinbase',
currentDifficulty='difficulty',
currentGasLimit='gaslimit',
currentNumber='number',
currentTimestamp='timestamp')
tstate = {}
for k, v in test['env'].items():
tstate[env_translate[k]] = z3.BitVecVal(int(v, 0), 256)
exec_translate = dict(gasPrice='gasprice',
value='callvalue',
caller='caller',
gas='initial_gas')
for k, v in test['exec'].items():
if k in exec_translate:
if k == 'gas':
v = z3.IntVal(int(v, 0))
else:
v = z3.BitVecVal(int(v, 0), 256)
tstate[exec_translate[k]] = v
code = symevm.code.Code(test['exec']['code'])
tstate['calldata'], tstate['calldatasize'] = mem_from_str(
test['exec']['data'])
return code, tstate
def z3_val(val, ctx):
if isinstance(val, int):
return z3.IntVal(val, ctx)
elif isinstance(val, str):
return z3.StringVal(val, ctx)
else:
raise ValueError(f'z3_val: unsupported typ ({type(val)})')
def _py2expr(a, ctx=None):
if isinstance(a, bool):
return z3.BoolVal(a, ctx)
if isinstance(a, int):
return z3.IntVal(a, ctx)
if isinstance(a, float):
return z3.RealVal(a, ctx)
def generate():
for i in self.slots:
ii = z3.IntVal(i.id)
if fn(i):
yield z3fn(ii)
else:
yield z3.Not(z3fn(ii))
def get_model_constraint(self):
block = []
for x in self.variables:
block.append(x != z3.Int('val_' + str(x)))
self.modelConstraint = z3.Or(block)
for m in self.model:
self.cleanedModel[m()] = z3.IntVal(0)
def enum(self, t):
res = term_to_z3(t)
if isinstance(t, Constant) and t.rep not in self.numbering:
num = z3.IntVal(self.next_number)
self.next_number += 1
self.numbering[t.rep] = num
cnst = self.enum_func(res) == num
self.temp_solver.add(cnst)
return res
def visit_IntConst(self, node, *args, **kwargs):
#print ("visiting int_const")
#print ("node.val=", node.val, "type(node.val)=", type(node.val))
#if type(node.val)!=int:
# print ("wtf...")
# return node.val
#else:
# print ("a classic int")
return z3.IntVal(node.val)
def get_z3_val(valtype, value, name, datatype_name=None, ctx=None):
val = None
if isinstance(valtype, z3.z3.DatatypeSortRef): # discrete values datatype
val = getattr(valtype, value)
elif valtype is Types.INT:
try:
val = z3.BitVecVal(value, 32, ctx=ctx)
except Exception as exc:
raise ValueError(
f"Error during INT conversion. Cannot convert value: {value}, type: {type(value)}, name: {name}"
)
elif valtype is Types.INTEGER:
try:
val = z3.IntVal(value, ctx=ctx)
except Exception as exc:
raise ValueError(
f"Error during INTEGER conversion. Cannot convert value: {value}, type: {type(value)}, name: {name}"
)
elif valtype is Types.FLOAT:
try:
val = z3.FPVal(value, z3.Float32(), ctx=ctx)
except Exception as exc:
raise ValueError(
f"Error during FLOAT conversion. Cannot convert value: {value}, type: {type(value)}, name: {name}"
)
elif valtype is Types.REAL:
try:
val = z3.RealVal(value, ctx=ctx)
except Exception as exc:
raise ValueError(
f"Error during REAL conversion. Cannot convert value: {value}, type: {type(value)}, name: {name}"
)
elif valtype is Types.BOOL:
try:
val = z3.BoolVal(value, ctx=ctx)
except Exception as exc:
raise ValueError(
f"Error during BOOL conversion of value to INT. value: {value}, type: {type(value)}, name: {name}"
)
elif valtype is Types.STRING:
try:
val = z3.StringVal(value, ctx=ctx)
except Exception as exc:
raise ValueError(
f"Error during STRING conversion of value to INT. value: {value}, type: {type(value)}, name: {name}"
)
elif isinstance(valtype, list):
datatype = _get_datatype_from_list(valtype, datatype_name)
val = getattr(datatype, value)
valtype = datatype
else:
raise ValueError(
f"I do not know how to create a z3-value for type {valtype}")
assert val is not None, f"Value wasn't converted: valtype: {valtype}, value: {value}, name: {name}"
val.type = valtype
return val
def expression(coeff, var):
if coeff == 1:
return var
elif coeff == -1:
return -var
elif coeff != 0:
return coeff * var
else:
return z3.IntVal(0)
def test_add(self) -> None:
self.assertEqual(
Add(Number(42), Number(1)).z3expr(),
z3.IntVal(0) + z3.IntVal(42) + z3.IntVal(1))
self.assertEqual(
Add(Number(42), Number(1), Number(10)).z3expr(),
z3.IntVal(0) + z3.IntVal(42) + z3.IntVal(1) + z3.IntVal(10),
)
def _resolve_char_must_occur_predicate(self, pred):
self._check_arg_types(pred, [Node, int])
program = pred.args[0]
big_or = []
for node in self.nodes_until_depth(self.depth - program.depth() + 1):
big_or.append(
self.variables[node] == z3.IntVal(program.production.id))
self.z3_solver.add(z3.Or(big_or))
def getZ3ValFromJSVal(val):
if type(val) == str:
return z3.StringVal(val)
if type(val) == bool:
return z3.BoolVal(val)
if type(val) == int:
return z3.IntVal(val)
if type(val) == int:
return z3.IntVal(val)
if type(val) == list:
arr = z3.Array('ignore_helper_constant_array_' + randomString(), z3.IntSort(), z3.StringSort())
for i, arg in enumerate(val):
GLOBAL_CONSTRAINTS.append(z3.Select(arr, i) == createZ3ExpressionFromConstraint(arg, {}))
ARRAY_LENGTHS[str(arr.decl())] = len(val)
return arr
if type(val) == dict:
raise NotSupportedException('Complex Objects as base for operations with proxy strings are not yet supported!')
raise Exception('Could not transform Js val to Z3 Val' + repr(val))
def coerceTypesIfPossible(var, other_var):
if z3.is_or(other_var) and not z3.is_bool(var):
other_var = transformNonBooleanLazyEvaluations(other_var)
if z3.is_or(var) and not z3.is_bool(other_var):
var = transformNonBooleanLazyEvaluations(var)
if z3.is_and(other_var) and not z3.is_bool(var):
other_var = transformNonBooleanLazyEvaluations(other_var)
if z3.is_and(var) and not z3.is_bool(other_var):
var = transformNonBooleanLazyEvaluations(var)
if var.decl().kind() == z3.Z3_OP_UNINTERPRETED:
if z3.is_bool(other_var) and not z3.is_bool(var):
infered_types[str(var)] = 'boolean'
return z3.Bool(str(var)), other_var
if z3.is_string(other_var) and not z3.is_string(var):
if other_var.as_string() == '':
# we probably dont want to coerce in this specific case as this is merely a non empty check
if z3.is_bool(var):
return var, z3.BoolVal(False)
if z3.is_int(var):
return var, z3.IntVal(0)
else:
infered_types[str(var)] = 'string'
return z3.String(str(var)), other_var
if z3.is_int(other_var) and not z3.is_int(var):
infered_types[str(var)] = 'number'
return z3.Int(str(var)), other_var
elif var.decl().kind() == z3.Z3_OP_UNINTERPRETED:
if z3.is_bool(var):
infered_types[str(var)] = 'boolean'
if z3.is_string(var):
infered_types[str(var)] = 'string'
if z3.is_int(var):
infered_types[str(var)] = 'number'
else:
# this means that it is non-interpreted and we need to coerce other var to the type of var
if z3.is_string(var) and z3.is_int_value(other_var):
other_var = z3.StringVal(str(other_var))
if z3.is_arith(var) and z3.is_string(other_var):
other_var = z3.IntVal(int(other_var.as_string()))
return var, other_var
