def simplify_constraints(spl_name, constraints, simplify_mode):
"""
This function simplifies the SMT constraint in input following the simplify_mode
:param spl_name: the name of the spl from which the constraint has been extracted
:param constraints: the extracted constraint (actually, a list of constraints)
:param simplify_mode: mode of simplification.
"default" means that
:return:
"""
if simplify_mode == "default":
formula = z3.simplify(smt_and(constraints))
if z3.is_false(formula):
logging.warning("Dependencies in package " + spl_name +
" make it uninstallable.")
return [formula]
elif simplify_mode == "individual":
formulas = []
for c in constraints:
formula = z3.simplify(c)
if z3.is_false(formula):
logging.warning("Dependencies in package " + spl_name +
" make it uninstallable.")
return [smt_false]
formulas.append(formula)
return formulas
def jumpi_(self, global_state):
state = global_state.mstate
disassembly = global_state.environment.code
states = []
op0, condition = state.stack.pop(), state.stack.pop()
try:
jump_addr = util.get_concrete_int(op0)
# FIXME: to broad exception handler
except:
logging.debug("Skipping JUMPI to invalid destination.")
return [global_state]
index = util.get_instruction_index(disassembly.instruction_list,
jump_addr)
if not index:
logging.debug("Invalid jump destination: " + str(jump_addr))
return [global_state]
instr = disassembly.instruction_list[index]
# True case
condi = simplify(condition) if type(
condition) == BoolRef else condition != 0
if instr['opcode'] == "JUMPDEST":
if (type(condi) == bool and condi) or (type(condi) == BoolRef
and not is_false(condi)):
new_state = copy(global_state)
new_state.mstate.pc = index
new_state.mstate.depth += 1
new_state.mstate.constraints.append(condi if type(condi) ==
bool else simplify(condi))
states.append(new_state)
else:
logging.debug("True, Pruned unreachable states. at %s" %
(state.pc))
# False case
negated = simplify(
Not(condition)) if type(condition) == BoolRef else condition == 0
if (type(negated) == bool and negated) or (type(negated) == BoolRef
and not is_false(negated)):
new_state = copy(global_state)
new_state.mstate.depth += 1
new_state.mstate.constraints.append(negated if type(negated) ==
bool else simplify(negated))
states.append(new_state)
else:
logging.debug("False, Pruned unreachable states. at %s" %
(state.pc))
return states
def is_false(a: Bool) -> bool:
"""Returns whether the provided bool can be simplified to false.
:param a:
:return:
"""
return z3.is_false(a.raw)
def is_false(self) -> bool:
"""Specifies whether this variable can be simplified to false.
:return:
"""
self.simplify()
return z3.is_false(self.raw)
def false(value):
"""Syntactic sugar for `z3.is_false(simplify(value))`.
i.e., return True iff `value` statically simplifies to False.
"""
return z3.is_false(simplify(value))
def marco(Pk):
print 'Starting to think about...', Pk
sys.stdout.flush()
solver = z3.Solver()
P = []
for line_number in conjecture_line_numbers:
P.append(z3.Bool('P_' + str(line_number)))
out = []
while True:
if solver.check() == z3.sat:
m = solver.model()
#seed = [conjecture_line_numbers[i] for i, Pi in enumerate(P) if m.eval(Pi, model_completion=True)]
seed = [conjecture_line_numbers[i] for i, Pi in enumerate(P) if not z3.is_false(m[Pi])]
#print 'Got seed:', seed
if query(Pk, set(seed), set()):
seed = shrink(Pk, seed)
#print 'Shrank to:', seed, 'which works'
out.append(seed)
block = z3.Or([z3.Not(P[i]) for i, line_number in enumerate(conjecture_line_numbers) if line_number in seed])
#print 'Blocking:', block
solver.add(block)
else:
seed = grow(Pk, seed)
#print 'Grew to:', seed, 'which does not work'
block = z3.Or([P[i] for i, line_number in enumerate(conjecture_line_numbers) if line_number not in seed])
#print 'Blocking:', block
solver.add(block)
else:
#print out
break
print 'Fully analyzed...', Pk
sys.stdout.flush()
return out
def _set(self, k, v):
"""An internal API used for actually building relations.
Not meant to be used from outside the module.
"""
# Typechecking
if not isinstance(k, tuple):
raise TypeError(k)
if not isinstance(v, z3.BoolRef) and not isinstance(v, bool):
raise TypeError(v)
# Make sure the arity of `k` matches the arity of other keys in self
if self.arity is None:
self.arity = len(k)
elif self.arity != len(k):
raise TypeError(f"`Relation` has arity {self.arity}, "
f"but adding a key of arity {len(k)}")
# No use adding `v` if it is known to be false.
if v is True:
# Convert Python type to z3 type
super().__setitem__(k, z3.BoolVal(True))
elif v is not False:
# v = simplify(v) # slower, but generates simpler expressions
if not z3.is_false(v):
super().__setitem__(k, v)
def elim_bool_ite(exp):
if z3.is_quantifier(exp):
(qvars, matrix) = strip_qblock(exp)
matrix = elim_bool_ite(matrix)
if exp.is_forall():
e = z3.ForAll(qvars, matrix)
else:
e = z3.Exists(qvars, matrix)
return e
if not z3.is_bool(exp): return exp
if z3.is_true(exp) or z3.is_false(exp): return exp
assert z3.is_app(exp)
decl = exp.decl()
args = map(elim_bool_ite, exp.children())
# need to worry about And and Or because they can take >2 args and
# decl(*args) doesn't seem to work with the py interface
if z3.is_and(exp):
return z3.And(*args)
elif z3.is_or(exp):
return z3.Or(*args)
elif is_ite(exp):
impl1 = z3.Implies(args[0], args[1])
impl2 = z3.Implies(z3.Not(args[0]), args[2])
return z3.And(impl1, impl2)
else:
return decl(*args)
def query(self, *query, **kwargs):
if 'max_solutions' in kwargs:
max_solutions = kwargs['max_solutions']
else:
max_solutions = -1
body_atms = [x.as_muz() for x in query]
self._solver.query(*body_atms)
ans = self._solver.get_answer()
query_vars = [x.get_variables() for x in query]
query_vars = reduce(lambda x, y: x + [v for v in y if v not in x],
query_vars, [])
if is_false(ans):
# no solution
return []
elif not (is_and(ans) or is_or(ans)):
# single solution, value of a single variable
val = int(ans.children()[1].as_long())
#varb = query.get_variables()[0]
varb = query_vars[0]
return [{varb: c_id_to_const(val, varb.get_type())}]
elif is_or(ans) and not (is_and(ans.children()[0])
or is_or(ans.children()[0])):
# multiple solutions of single variable
vals = [int(x.children()[1].as_long()) for x in ans.children()]
#varbs = query.get_variables()[0]
varbs = query_vars[0]
varbs = [varbs] * len(vals)
return [{
k: c_id_to_const(v, varbs[0].get_type())
} for k, v in zip(varbs, vals)]
elif is_and(ans):
# single solution of more than 1 variable
ans = [int(x.children()[1].as_long()) for x in ans.children()]
ans = [ans]
elif is_or(ans):
# multiple solutions of more than 1 variable
ans = ans.children()
ans = [[int(y.children()[1].as_long()) for y in x.children()]
for x in ans]
else:
raise Exception(f"don't know how to parse {ans}")
tmp_args = [v for x in query for v in x.get_variables()]
args = reduce(lambda x, y: x + [y] if y not in x else x, tmp_args, [])
answer = [
dict([(v, c_id_to_const(c,
v.get_type().name))
for v, c in zip(args, x)]) for x in ans
]
if max_solutions > 0:
return answer[:max_solutions]
else:
return answer
def num_clauses(formula):
if z3.is_and(formula):
return len(formula.children())
elif formula == True or z3.is_true(formula) or \
formula == False or z3.is_false(formula):
return 0
else:
return 1
def num_clauses(formula):
if z3.is_and(formula):
return len(formula.children())
elif formula == True or z3.is_true(formula) or \
formula == False or z3.is_false(formula):
return 0
else:
return 1
def _is_literal(z3ast):
if z3.is_int(z3ast):
return z3.is_int_value(z3ast)
if z3.is_bool(z3ast):
return z3.is_true(z3ast) or z3.is_false(z3ast)
if z3ast.sort_kind() == z3.Z3_UNINTERPRETED_SORT:
return z3.is_const(z3ast) and '!' in str(z3ast)
raise NotImplementedError('Don\'t know how to literal-check %s' % z3ast)
def is_bool_or_int_value(value):
if z3.is_int_value(value):
return True
if value.sort() == z3.BoolSort():
if z3.is_true(value) or z3.is_false(value):
return True
else:
return False
def _is_literal(z3ast):
if z3.is_int(z3ast):
return z3.is_int_value(z3ast)
if z3.is_bool(z3ast):
return z3.is_true(z3ast) or z3.is_false(z3ast)
if z3ast.sort_kind() == z3.Z3_UNINTERPRETED_SORT:
return z3.is_const(z3ast) and '!' in str(z3ast)
raise NotImplementedError('Don\'t know how to literal-check %s' % z3ast)
def get(self, v):
assert self._model is not None
assert type(v) is Z3BoolRef
v = self._model.eval(v.val, model_completion=True)
assert z3.is_bool(v)
t = z3.is_true(v)
f = z3.is_false(v)
assert t or f, f'bad {v}'
return int(t)
def try_bool(b):
b = try_simplify(b)
# HACK: z3 python interface has bug/weird behavior where (x == y) is
# always False for unknown x and y, so use is_true and is_false instead
if z3.is_true(b):
return True
if z3.is_false(b):
return False
return None
def get_value(r):
# https://stackoverflow.com/questions/12598408/z3-python-getting-python-values-from-model/12600208
"""
Convert from Z3 to python values.
"""
if z3.is_true(r):
return z3.is_true(r)
elif z3.is_false(r):
return z3.is_false(r)
elif z3.is_int_value(r):
return r.as_long()
elif z3.is_algebraic_value(r):
return round(num(r.approx(15)), 10)
elif z3.is_rational_value(r):
return r.as_decimal(20)
elif r is None:
None
else:
return num(r)
def l_get(self, ast):
val = self.solver.model().eval(ast.ast)
if val == None:
return esbmc.solve.tvt(esbmc.solve.tvt_enum.unknown)
elif z3.is_true(val):
return esbmc.solve.tvt(esbmc.solve.tvt_enum.true)
elif z3.is_false(val):
return esbmc.solve.tvt(esbmc.solve.tvt_enum.false)
else:
raise Exception("Unknown model eval value from l_get")
def l_get(self, ast):
val = self.solver.model().eval(ast.ast)
if val == None:
return esbmc.solve.tvt(esbmc.solve.tvt_enum.unknown)
elif z3.is_true(val):
return esbmc.solve.tvt(esbmc.solve.tvt_enum.true)
elif z3.is_false(val):
return esbmc.solve.tvt(esbmc.solve.tvt_enum.false)
else:
raise Exception("Unknown model eval value from l_get")
def ite(x, y, z):
if x is True:
return y
if x is False:
return z
x = z3.simplify(x)
if z3.is_true(x):
return y
if z3.is_false(x):
return z
return z3.If(x, y, z)
def _extract_var(self, z3model, var):
val = z3model[var]
if val is None:
return None
if z3.is_rational_value(val):
n = val.numerator_as_long()
d = val.denominator_as_long()
return float(n / d)
if z3.is_true(val):
return True
if z3.is_false(val):
return False
raise RuntimeError("var not supported")
def generalize_cube(z3_formula, model, all_vars):
assigned_vars = set([_v for _v in all_vars if model[_v] is not None])
my_model = MyModel({v: model[v] for v in assigned_vars})
go_over_vars = list(assigned_vars)
for _var in go_over_vars:
model_tag = MyModel(dict(my_model.assignment))
model_tag[_var] = BoolVal(is_false(my_model[_var]))
z3_assigned = simplify(
substitute(z3_formula,
*[(_v, model_tag[_v]) for _v in assigned_vars]))
if is_false(z3_assigned):
continue
s = SatSolverSelector.SatSolverCtor()
res = s.add(z3_assigned)
if res and s.check():
assigned_vars -= {_var}
my_model.unassign(_var)
return my_model
def branch(self, ctx, cond, cond_type, iftrue, iffalse):
self.assertion(ctx, not cond.is_poison(), "path condition is poison")
assert itypes.integer_size(cond_type) == 1
scond = util.simplify(cond)
can_be_true = not z3.is_false(scond)
can_be_false = not z3.is_true(scond)
if ctx['depth'] >= ctx['prune_depth']:
can_be_true = not z3.is_false(
scond) and not util.path_condition_implies(ctx, z3.Not(scond))
can_be_false = not can_be_true or (
not z3.is_true(scond)
and not util.path_condition_implies(ctx, scond))
true_branch_exc = None
false_branch_exc = None
trueval = None
falseval = None
if can_be_true:
try:
ctx.push(path_condition=scond)
trueval = iftrue()
except ex.UnreachableException, e:
stacktrace = getattr(e, 'stacktrace', None)
self.assertion(ctx,
util.path_condition_implies(ctx,
z3.BoolVal(False),
print_model=True),
"Panic " + repr(e),
stacktrace=stacktrace)
can_be_true = False
except BaseException, e:
true_branch_exc = e
def clause_model_simp(m, c):
""" Simplify a clause by dropping literals while maintaining its truth in a model. """
res = []
for l in c:
if not is_ground_lit(l):
res.append(l)
continue
# if isinstance(l.atom,ivy_logic.And):
# print "clause_model_simp: {}".format(c)
v = m.eval(literal_to_z3(l))
if z3.is_true(v):
return [l]
if not z3.is_false(v):
res.append(l)
return res
def clause_model_simp(m, c):
""" Simplify a clause by dropping literals while maintaining its truth in a model. """
res = []
for l in c:
if not is_ground_lit(l):
res.append(l)
continue
if isinstance(l.atom, ivy_logic.And):
print "clause_model_simp: {}".format(c)
v = m.eval(literal_to_z3(l))
if z3.is_true(v):
return [l]
if not z3.is_false(v):
res.append(l)
return res
def convert_patterns(pattern_repository, id_repository, patterns):
spls = set()
constraints = []
for pattern in patterns:
new_spls = pattern_repository.get_with_default(pattern).matched_spls
spls.update(new_spls)
#print(core_data.pattern_to_atom(pattern) + " => " + str([spl.name for spl in new_spls]))
constraint = z3.simplify(
smt_or([get_spl_smt(id_repository, spl.name) for spl in new_spls]))
if z3.is_false(constraint):
logging.warning("atom \"" + (core_data.pattern_to_atom(pattern)) +
"\" is satisfied by no ebuild")
return set(), []
constraints.append(constraint)
return spls, smt_list_to_strings(constraints)
def try_bool(b):
# Just ignore attributes here
if isinstance(b, Value):
b = b.value
if z3.is_bv(b) or isinstance(b, int):
b = (b != 0)
b = try_simplify(b)
if isinstance(b, bool):
return (b, None)
# HACK: z3 python interface has bug/weird behavior where (x == y) is
# always False for unknown x and y, so use is_true and is_false instead
if z3.is_true(b):
return (True, None)
if z3.is_false(b):
return (False, None)
return (None, b)
def simplify_z3_constraints(constraints):
"""
Simplifies the constraint list, only by expressions that can be determined to evaluate to a a specific boolean value
:param constraints:
:return:
"""
simp_const = constraints
# Currently not running the individual simplification algorithm on every simplification call for
# simp_const = simplify_constraints_individually(constraints)
simp_const = list(
filter(lambda c: not is_bool(c) or not is_true(c), simp_const))
falses = list(filter(lambda c: is_bool(c) and is_false(c), simp_const))
if len(falses) > 0:
return [deepcopy(falses[0])]
return simp_const
def build_rule(self, rule, env):
vars = {}
head = self.compile_atom(vars, rule.head, env)
body = [
self.compile_atom(vars, atom, env)
for atom in rule.body
if atom is not None]
if any(z3.is_false(at) for at in body):
return
body = [at for at in body if not z3.is_true(at)]
body_conj = body[0] if len(body) == 1 else z3.And(*body)
term1 = head if body == [] else z3.Implies(body_conj, head)
term2 = (
term1 if vars == {}
else z3.ForAll(list(vars.values()), term1))
self.context.rule(term2)
def val(self, exp):
'''Evaluate a z3 ref to a python value based on this solution.
'''
v = self.model.eval(exp)
if z3.is_true(v):
return True
if z3.is_false(v):
return False
if z3.is_algebraic_value(v):
v = v.approx(20)
if z3.is_int_value(v):
return v.as_long()
if z3.is_rational_value(v):
return v.numerator_as_long() / v.denominator_as_long()
return z3.is_true(v)
def get_py_val_from_z3_val(z3_result):
if z3_result is not None:
if z3.is_int_value(z3_result):
return z3_result.as_long()
elif z3.is_real(z3_result):
return float(z3_result.numerator_as_long()) / float(
z3_result.denominator_as_long())
elif z3.is_true(z3_result):
return True
elif z3.is_false(z3_result):
return False
elif z3.is_string_value(z3_result):
return z3_result.as_string()
else:
raise NotImplementedError(
"Z3 model result other than int, real, bool, string is not supported yet!"
)
def z3ToPoint(self, point):
res = []
# get the variables corresponding to the axis names
for idx, i in enumerate(self.axis_names):
locals()[i] = Globals.z3variables[i]
if i in Globals.z3types: # non-numeric points -> coord to value
value = Globals.z3types[i][point[locals()[i]].as_long()]
elif None == point[locals()[i]]:
info("no value for %s, take %r (incomplete model)" %
(self.axis_names[idx], self.axis_val_ranges[idx][0]))
value = self.axis_val_ranges[idx][0]
elif z3.is_int_value(point[locals()[i]]):
value = point[locals()[i]].as_long()
elif z3.is_true(point[locals()[i]]) or z3.is_false(
point[locals()[i]]):
value = z3.is_true(point[locals()[i]])
res.append(value)
return res
def mk_const(self, c):
if z3.is_int_value(c):
return ii(c.as_long())
if z3.is_rational_value(c):
# TODO: what should we convert a rational to?
return rr(Fraction(c.numerator_as_long(), \
c.denominator_as_long()))
elif z3.is_true(c):
return true
elif z3.is_false(c):
return false
else:
try:
return self.context.decls[str(c)]
except KeyError:
#Constant is not found in the context
typ = self.mk_sort(c.sort())
return const(str(c), typ)
def tfFlags(self, pred, flags_len):
"""
return two lists, one for true and one false flags
"""
false_idxs = list()
true_idxs = list ()
if debug_cex: print "Get list of failing flags from : ", pred
ch = pred.children()
i=0
for val in ch[0:flags_len]:
if z3.is_false(val):
false_idxs.append(i)
i+=1
elif z3.is_true(val):
true_idxs.append(i)
i+=1
else: i+=1
return true_idxs, false_idxs
def mk_const(self, c):
if z3.is_int_value(c):
return ii(c.as_long())
if z3.is_rational_value(c):
# TODO: what should we convert a rational to?
return rr(Fraction(c.numerator_as_long(), \
c.denominator_as_long()))
elif z3.is_true(c):
return true
elif z3.is_false(c):
return false
else:
try:
return self.context.decls[str(c)]
except KeyError:
#Constant is not found in the context
typ = self.mk_sort(c.sort())
return const(str(c), typ)
def tfFlags(self, pred, flags_len):
"""
return two lists, one for true and one false flags
"""
false_idxs = list()
true_idxs = list()
if verbose: print "Get list of failing flags from : ", pred
ch = pred.children()
i = 0
for val in ch[0:flags_len]:
if z3.is_false(val):
false_idxs.append(i)
i += 1
elif z3.is_true(val):
true_idxs.append(i)
i += 1
else:
i += 1
return true_idxs, false_idxs
def z3_to_val(z3_expr):
"""Send a z3 expression to it's value
as a python expression, if it has one,
otherwise return the expresson itself.
Arguments:
- `z3_expr`: a z3 AST
"""
if z3.is_int_value(z3_expr):
return z3_expr.as_long()
if z3.is_rational_value(z3_expr):
return Fraction(z3_expr.numerator_as_long(), \
z3_expr.denominator_as_long())
elif z3.is_true(z3_expr):
return True
elif z3.is_false(z3_expr):
return False
elif isinstance(z3_expr, z3.FuncInterp):
return z3_to_fun(z3_expr)
else:
return z3_expr
def constant_from_z3(sort, c):
if z3.is_true(c):
return ivy_logic.And()
if z3.is_false(c):
return ivy_logic.Or()
return ivy_logic.Constant(ivy_logic.Symbol(repr(c), sort))
print c4.result
stop = time.time()
print stop - start
print "Running simple compression test"
ResetZ3()
start = time.time()
out = TrivialWanOptimizer()
result = out.check.CheckIsolationProperty(out.a, out.b)
assert z3.sat == result.result, \
"Nothing is blocking the way, packets should get from A -> B"
assert is_true(result.model.eval(out.ctx.send(out.w.z3Node, out.b.z3Node, result.violating_packet))), \
"Violating packet was never sent"
assert is_true(result.model.eval(out.ctx.recv(out.w.z3Node, out.b.z3Node, result.violating_packet))), \
"Violating packet was never received"
assert is_false(result.model.eval(out.ctx.recv(out.a.z3Node, out.w.z3Node, result.violating_packet))), \
"The packet should not get to b unmodified"
assert is_false(result.model.eval(out.ctx.send(out.a.z3Node, out.w.z3Node, result.violating_packet))), \
"The packet should not get to b unmodified"
stop = time.time()
print stop - start
print "Running simple compression-decompression test"
ResetZ3()
start = time.time()
out = TrivialWanOptimizerDeOptimizer()
result = out.check.CheckIsolatedIf(lambda p: z3.Not(out.ctx.send(out.w0.z3Node, out.w1.z3Node, p)), out.a, out.b)
assert z3.sat == result.result, \
"Nothing is blocking the way, packets should get from A -> B"
assert is_true(result.model.eval(out.ctx.send(out.w1.z3Node, out.b.z3Node, result.violating_packet))), \
"Violating packet was never sent"
def _back_single_term(self, expr, args, model=None):
assert z3.is_expr(expr)
if z3.is_quantifier(expr):
raise NotImplementedError(
"Quantified back conversion is currently not supported")
res = None
if z3.is_and(expr):
res = self.mgr.And(args)
elif z3.is_or(expr):
res = self.mgr.Or(args)
elif z3.is_add(expr):
res = self.mgr.Plus(args)
elif z3.is_div(expr):
res = self.mgr.Div(args[0], args[1])
elif z3.is_eq(expr):
if self._get_type(args[0]).is_bool_type():
res = self.mgr.Iff(args[0], args[1])
else:
res = self.mgr.Equals(args[0], args[1])
elif z3.is_iff(expr):
res = self.mgr.Iff(args[0], args[1])
elif z3.is_xor(expr):
res = self.mgr.Xor(args[0], args[1])
elif z3.is_false(expr):
res = self.mgr.FALSE()
elif z3.is_true(expr):
res = self.mgr.TRUE()
elif z3.is_gt(expr):
res = self.mgr.GT(args[0], args[1])
elif z3.is_ge(expr):
res = self.mgr.GE(args[0], args[1])
elif z3.is_lt(expr):
res = self.mgr.LT(args[0], args[1])
elif z3.is_le(expr):
res = self.mgr.LE(args[0], args[1])
elif z3.is_mul(expr):
res = self.mgr.Times(args[0], args[1])
elif z3.is_uminus(expr):
tp = self._get_type(args[0])
if tp.is_real_type():
minus_one = self.mgr.Real(-1)
else:
assert tp.is_int_type()
minus_one = self.mgr.Int(-1)
res = self.mgr.Times(args[0], minus_one)
elif z3.is_sub(expr):
res = self.mgr.Minus(args[0], args[1])
elif z3.is_not(expr):
res = self.mgr.Not(args[0])
elif z3.is_implies(expr):
res = self.mgr.Implies(args[0], args[1])
elif z3.is_quantifier(expr):
raise NotImplementedError
elif z3.is_const(expr):
if z3.is_rational_value(expr):
n = expr.numerator_as_long()
d = expr.denominator_as_long()
f = Fraction(n, d)
res = self.mgr.Real(f)
elif z3.is_int_value(expr):
n = expr.as_long()
res = self.mgr.Int(n)
elif z3.is_bv_value(expr):
n = expr.as_long()
w = expr.size()
res = self.mgr.BV(n, w)
elif z3.is_as_array(expr):
if model is None:
raise NotImplementedError("As-array expressions cannot be" \
" handled as they are not " \
"self-contained")
else:
interp_decl = z3.get_as_array_func(expr)
interp = model[interp_decl]
default = self.back(interp.else_value(), model=model)
assign = {}
for i in xrange(interp.num_entries()):
e = interp.entry(i)
assert e.num_args() == 1
idx = self.back(e.arg_value(0), model=model)
val = self.back(e.value(), model=model)
assign[idx] = val
arr_type = self._z3_to_type(expr.sort())
res = self.mgr.Array(arr_type.index_type, default, assign)
elif z3.is_algebraic_value(expr):
# Algebraic value
return self.mgr._Algebraic(Numeral(expr))
else:
# it must be a symbol
res = self.mgr.get_symbol(str(expr))
elif z3.is_ite(expr):
res = self.mgr.Ite(args[0], args[1], args[2])
elif z3.is_function(expr):
res = self.mgr.Function(self.mgr.get_symbol(expr.decl().name()), args)
elif z3.is_to_real(expr):
res = self.mgr.ToReal(args[0])
elif z3.is_bv_and(expr):
res = self.mgr.BVAnd(args[0], args[1])
elif z3.is_bv_or(expr):
res = self.mgr.BVOr(args[0], args[1])
elif z3.is_bv_xor(expr):
res = self.mgr.BVXor(args[0], args[1])
elif z3.is_bv_not(expr):
res = self.mgr.BVNot(args[0])
elif z3.is_bv_neg(expr):
res = self.mgr.BVNeg(args[0])
elif z3.is_bv_concat(expr):
res = self.mgr.BVConcat(args[0], args[1])
elif z3.is_bv_ult(expr):
res = self.mgr.BVULT(args[0], args[1])
elif z3.is_bv_uleq(expr):
res = self.mgr.BVULE(args[0], args[1])
elif z3.is_bv_slt(expr):
res = self.mgr.BVSLT(args[0], args[1])
elif z3.is_bv_sleq(expr):
res = self.mgr.BVSLE(args[0], args[1])
elif z3.is_bv_ugt(expr):
res = self.mgr.BVUGT(args[0], args[1])
elif z3.is_bv_ugeq(expr):
res = self.mgr.BVUGE(args[0], args[1])
elif z3.is_bv_sgt(expr):
res = self.mgr.BVSGT(args[0], args[1])
elif z3.is_bv_sgeq(expr):
res = self.mgr.BVSGE(args[0], args[1])
elif z3.is_bv_extract(expr):
end = z3.get_payload(expr, 0)
start = z3.get_payload(expr, 1)
res = self.mgr.BVExtract(args[0], start, end)
elif z3.is_bv_add(expr):
res = self.mgr.BVAdd(args[0], args[1])
elif z3.is_bv_mul(expr):
res = self.mgr.BVMul(args[0], args[1])
elif z3.is_bv_udiv(expr):
res = self.mgr.BVUDiv(args[0], args[1])
elif z3.is_bv_sdiv(expr):
res = self.mgr.BVSDiv(args[0], args[1])
elif z3.is_bv_urem(expr):
res = self.mgr.BVURem(args[0], args[1])
elif z3.is_bv_srem(expr):
res = self.mgr.BVSRem(args[0], args[1])
elif z3.is_bv_lshl(expr):
res = self.mgr.BVLShl(args[0], args[1])
elif z3.is_bv_lshr(expr):
res = self.mgr.BVLShr(args[0], args[1])
elif z3.is_bv_ashr(expr):
res = self.mgr.BVAShr(args[0], args[1])
elif z3.is_bv_sub(expr):
res = self.mgr.BVSub(args[0], args[1])
elif z3.is_bv_rol(expr):
amount = z3.get_payload(expr, 0)
res = self.mgr.BVRol(args[0], amount)
elif z3.is_bv_ror(expr):
amount = z3.get_payload(expr, 0)
res = self.mgr.BVRor(args[0], amount)
elif z3.is_bv_ext_rol(expr):
amount = args[1].bv_unsigned_value()
res = self.mgr.BVRol(args[0], amount)
elif z3.is_bv_ext_ror(expr):
amount = args[1].bv_unsigned_value()
res = self.mgr.BVRor(args[0], amount)
elif z3.is_bv_sext(expr):
amount = z3.get_payload(expr, 0)
res = self.mgr.BVSExt(args[0], amount)
elif z3.is_bv_zext(expr):
amount = z3.get_payload(expr, 0)
res = self.mgr.BVZExt(args[0], amount)
elif z3.is_array_select(expr):
res = self.mgr.Select(args[0], args[1])
elif z3.is_array_store(expr):
res = self.mgr.Store(args[0], args[1], args[2])
elif z3.is_const_array(expr):
arr_ty = self._z3_to_type(expr.sort())
k = args[0]
res = self.mgr.Array(arr_ty.index_type, k)
elif z3.is_power(expr):
res = self.mgr.Pow(args[0], args[1])
if res is None:
raise ConvertExpressionError(message=("Unsupported expression: %s" %
str(expr)),
expression=expr)
return res
def _back_single_term(self, expr, args):
assert z3.is_expr(expr)
if z3.is_quantifier(expr):
raise NotImplementedError(
"Quantified back conversion is currently not supported")
res = None
if z3.is_and(expr):
res = self.mgr.And(args)
elif z3.is_or(expr):
res = self.mgr.Or(args)
elif z3.is_add(expr):
res = self.mgr.Plus(args)
elif z3.is_div(expr):
res = self.mgr.Div(args[0], args[1])
elif z3.is_eq(expr):
if self._get_type(args[0]).is_bool_type():
res = self.mgr.Iff(args[0], args[1])
else:
res = self.mgr.Equals(args[0], args[1])
elif z3.is_iff(expr):
res = self.mgr.Iff(args[0], args[1])
elif z3.is_xor(expr):
res = self.mgr.Xor(args[0], args[1])
elif z3.is_false(expr):
res = self.mgr.FALSE()
elif z3.is_true(expr):
res = self.mgr.TRUE()
elif z3.is_gt(expr):
res = self.mgr.GT(args[0], args[1])
elif z3.is_ge(expr):
res = self.mgr.GE(args[0], args[1])
elif z3.is_lt(expr):
res = self.mgr.LT(args[0], args[1])
elif z3.is_le(expr):
res = self.mgr.LE(args[0], args[1])
elif z3.is_mul(expr):
res = self.mgr.Times(args[0], args[1])
elif z3.is_uminus(expr):
tp = self._get_type(args[0])
if tp.is_real_type():
minus_one = self.mgr.Real(-1)
else:
assert tp.is_int_type()
minus_one = self.mgr.Int(-1)
res = self.mgr.Times(args[0], minus_one)
elif z3.is_sub(expr):
res = self.mgr.Minus(args[0], args[1])
elif z3.is_not(expr):
res = self.mgr.Not(args[0])
elif z3.is_implies(expr):
res = self.mgr.Implies(args[0], args[1])
elif z3.is_quantifier(expr):
raise NotImplementedError
elif z3.is_const(expr):
if z3.is_rational_value(expr):
n = expr.numerator_as_long()
d = expr.denominator_as_long()
f = Fraction(n, d)
res = self.mgr.Real(f)
elif z3.is_int_value(expr):
n = expr.as_long()
res = self.mgr.Int(n)
elif z3.is_bv_value(expr):
n = expr.as_long()
w = expr.size()
res = self.mgr.BV(n, w)
else:
# it must be a symbol
res = self.mgr.get_symbol(str(expr))
elif z3.is_ite(expr):
res = self.mgr.Ite(args[0], args[1], args[2])
elif z3.is_function(expr):
res = self.mgr.Function(self.mgr.get_symbol(expr.decl().name()), args)
elif z3.is_to_real(expr):
res = self.mgr.ToReal(args[0])
elif z3.is_bv_and(expr):
res = self.mgr.BVAnd(args[0], args[1])
elif z3.is_bv_or(expr):
res = self.mgr.BVOr(args[0], args[1])
elif z3.is_bv_xor(expr):
res = self.mgr.BVXor(args[0], args[1])
elif z3.is_bv_not(expr):
res = self.mgr.BVNot(args[0])
elif z3.is_bv_neg(expr):
res = self.mgr.BVNeg(args[0])
elif z3.is_bv_concat(expr):
res = self.mgr.BVConcat(args[0], args[1])
elif z3.is_bv_ult(expr):
res = self.mgr.BVULT(args[0], args[1])
elif z3.is_bv_uleq(expr):
res = self.mgr.BVULE(args[0], args[1])
elif z3.is_bv_slt(expr):
res = self.mgr.BVSLT(args[0], args[1])
elif z3.is_bv_sleq(expr):
res = self.mgr.BVSLE(args[0], args[1])
elif z3.is_bv_ugt(expr):
res = self.mgr.BVUGT(args[0], args[1])
elif z3.is_bv_ugeq(expr):
res = self.mgr.BVUGE(args[0], args[1])
elif z3.is_bv_sgt(expr):
res = self.mgr.BVSGT(args[0], args[1])
elif z3.is_bv_sgeq(expr):
res = self.mgr.BVSGE(args[0], args[1])
elif z3.is_bv_extract(expr):
end = z3.get_payload(expr, 0)
start = z3.get_payload(expr, 1)
res = self.mgr.BVExtract(args[0], start, end)
elif z3.is_bv_add(expr):
res = self.mgr.BVAdd(args[0], args[1])
elif z3.is_bv_mul(expr):
res = self.mgr.BVMul(args[0], args[1])
elif z3.is_bv_udiv(expr):
res = self.mgr.BVUDiv(args[0], args[1])
elif z3.is_bv_sdiv(expr):
res = self.mgr.BVSDiv(args[0], args[1])
elif z3.is_bv_urem(expr):
res = self.mgr.BVURem(args[0], args[1])
elif z3.is_bv_srem(expr):
res = self.mgr.BVSRem(args[0], args[1])
elif z3.is_bv_lshl(expr):
res = self.mgr.BVLShl(args[0], args[1])
elif z3.is_bv_lshr(expr):
res = self.mgr.BVLShr(args[0], args[1])
elif z3.is_bv_ashr(expr):
res = self.mgr.BVAShr(args[0], args[1])
elif z3.is_bv_sub(expr):
res = self.mgr.BVSub(args[0], args[1])
elif z3.is_bv_rol(expr):
amount = z3.get_payload(expr, 0)
res = self.mgr.BVRol(args[0], amount)
elif z3.is_bv_ror(expr):
amount = z3.get_payload(expr, 0)
res = self.mgr.BVRor(args[0], amount)
elif z3.is_bv_ext_rol(expr):
amount = args[1].bv_unsigned_value()
res = self.mgr.BVRol(args[0], amount)
elif z3.is_bv_ext_ror(expr):
amount = args[1].bv_unsigned_value()
res = self.mgr.BVRor(args[0], amount)
elif z3.is_bv_sext(expr):
amount = z3.get_payload(expr, 0)
res = self.mgr.BVSExt(args[0], amount)
elif z3.is_bv_zext(expr):
amount = z3.get_payload(expr, 0)
res = self.mgr.BVZExt(args[0], amount)
if res is None:
raise ConvertExpressionError(message=("Unsupported expression: %s" %
str(expr)),
expression=expr)
return res
def maxSAT(self, solver, var_weight_pairs):
# A classic argmax loop, holding on to our best cost and the
# cooresponding solution.
min_cost = None
best_solution = None
# The variables that keep us from trying a solution we've
# already tried, or a subset of that solution.
conflictVars = []
# Get our first solver result, the solution if we don't need
# to accomplish any of our weighted vars.
next_solver_result = solver.check()
while(next_solver_result == z3.sat):
# The cost of this solution.
cost = 0
# Get the solvers model.
model = solver.model()
# For each soft variable that was set to false in the
# current solution, incur a cost.
for var, weight in var_weight_pairs:
if self.debugPrint:
print "adding cost of " + str(var) + ": " + str(weight) + " * "\
+ str(not z3.is_false(model[var]))
if z3.is_false(model[var]):
cost += weight
# Extract a solution object. We would just save the model,
# but it turns out z3 models are invalidated when you next
# run the solver.
solution = self.modelToSolution(model)
# If our new cost is the best cost we've seen so far,
# update our best.
if min_cost == None or cost < min_cost:
min_cost = cost
best_solution = solution
if self.debugPrint:
print "found solution: "
self.printSolution(solution)
print "with cost " + str(cost)
# Create a fresh variable that blocks any future solution
# that does not include at least one of the tasks that
# were excluded from this solution. That statement may
# take a bit of unpacking. Basically the idea is, if we
# have some solution, then there exists no better solution
# which only does a subset of the tasks which this
# solution does. So, we block all solutions which don't
# include at least one other task that this solution
# doesn't have. I got the algorithm from this paper:
# http://research.microsoft.com/en-US/peopleb/nbjorner/scss2014.pdf
# The paper actually shows that another algorithm is more
# efficient, but this one is simpler, so we use this one
# until we hit a performance bottleneck with it.
fresh_var_name = "block"
interp = [v for v,w in var_weight_pairs \
if z3.is_false(model[v])]
for v in interp:
fresh_var_name += "_" + str(v)
fresh_var = z3.Bool(fresh_var_name)
# Tie our blocking constraint to a new "conflict
# variable," and add that variable to our set of
# assumptions.
block_constraint = Or(Not(fresh_var), *interp)
if self.debugPrint:
print "adding block constraint " + str(block_constraint)
solver.add(block_constraint)
conflictVars.append(fresh_var)
# Get a new result for the next time around the while loop.
next_solver_result = solver.check(*conflictVars)
if self.debugPrint:
print "best solution was "
self.printSolution(best_solution)
print "with cost " + str(min_cost)
return best_solution
def evaluate(self, t):
s = self.solver.model().eval(t.z3Node())
assert z3.is_true(s) or z3.is_false(s)
return z3.is_true(s)