def get_coefficients(atom: FNode):
"""
obtain coefficient of variable x in atom of form a * x + b * y + const
note that when there is a * x + b * x, simplify() doesn't do multiplication
but still here we return (a + b)
:param atom: FNode, formula
:param x: FNode, symbol of variable
:return: dict with keys as variable symbol and values as coefficient in atom
"""
variables = list(get_real_variables(atom))
coefficients = defaultdict(int)
if len(variables) == 0:
return coefficients
const = get_constants(atom)
atom = simplify(Plus(atom, -const))
sub_dict = dict().fromkeys(variables, Real(0))
for i in range(len(variables)):
sub_dict[variables[i]] = Real(1)
coefficient = simplify(atom.substitute(sub_dict))
coefficients[variables[i]] = coefficient
sub_dict[variables[i]] = Real(0)
return coefficients
def two_comparator(input1, input2):
if SortingNetwork.simplify:
return [
simplify(Or(input1, input2)),
simplify(And(input1, input2))
]
else:
return [Or(input1, input2), And(input1, input2)]
def get_upper_bound_expectation_dnf(self, upper_bound_expectation, ignore_conjuncts_with_infinity = True):
"""
Takes a candidate upper bound expectation (as a String) and returns its DNF, i.e. a list of the form
[(guard_1, arith_1, ..., guard_n, arith_n)]. If ignore_conjuncts_with_infinity = False, then
the following holds
(1) for all i != j, the formula guard_i AND guard_j is UNSAT, and
(2) guard_1 OR ... OR guard_n is equivalent to TRUE.
:param upper_bound_expectation: The candidate upper bound that is to be checked.
:param ignore_conjuncts_with_infinity: For the refute-queries, conjuncts with arith_exp = infinity can be ignored since nothing is greater than infinity.
"""
probably_upper_bound_expectation = parse_expectation(upper_bound_expectation)
if type(probably_upper_bound_expectation) == CheckFail:
print(probably_upper_bound_expectation)
raise Exception("CheckFail.")
self.is_linear = self.is_linear and check_is_linear_expr(probably_upper_bound_expectation) == None
flattened_upper_bound_expectation = normalize_expectation_simple(self.program, probably_upper_bound_expectation)
logger.info(
"Flattened Upper Bound Expectation: %s" % flattened_upper_bound_expectation)
pysmt_upper_bound_snf = [(probably_expr_to_pysmt(bool_exp, self._pysmt_infinity_variable, True, self.monus_euf, False),
probably_expr_to_pysmt(arith_exp, self._pysmt_infinity_variable, True, self.rmonus_euf, True))
for bool_exp, arith_exp in flattened_upper_bound_expectation]
pysmt_upper_bound_dnf = []
for bin_seq in product([True, False], repeat=len(pysmt_upper_bound_snf)):
guard_seq, arith_seq = zip(
*list(map(self._construct_boolexp_arithexp_par, bin_seq, pysmt_upper_bound_snf)))
to_test = And(guard_seq + (self.non_negative_constraint,))
if self._sat_solver.is_sat(to_test):
# If arith_seq contains infinity, then the whole arithmetic expression is to be interpreted as infinity
# Since nothing is greater than infinity, states satisfying And(guard_seq) are always an upper bound and can thus be omitted.
if not self._pysmt_infinity_variable in arith_seq or not ignore_conjuncts_with_infinity:
resulting_arith = simplify(Plus(arith_seq))
pysmt_upper_bound_dnf.append(
(simplify(And(guard_seq)), resulting_arith))
logger.info("Upper Bound DNF (ignore_conjuncts_with_infinity = %s): %s" % (ignore_conjuncts_with_infinity, ["(%s,%s)" % (guard.serialize(), arith.serialize()) for (guard, arith) in pysmt_upper_bound_dnf]))
if not ignore_conjuncts_with_infinity:
logger.debug("Checking whether the Boolean expressions occurring in the DNF partition the state space if all variables are non-negative.")
# The k-induction encoding is not sound if this does not hold.
assert(not self._sat_solver.is_sat(And([self.non_negative_constraint, Not(Or([guard for (guard, arith) in pysmt_upper_bound_dnf]))])))
return pysmt_upper_bound_dnf
def _get_pysmt_loop_terminated_dnf(self, probably_summation_nf: SnfLoopExpectationTransformer, post_expectation):
"""
Computes the loop-terminated-part of the wp-characteristic functional in PySMT disjunctive normal form.
:param initialization: The parsed variable declarations of the program.
:param probably_summation_nf: The probably summation normal form of the wp-characteristic functional.
:param post_expectation: The postexpectation that is to be parsed and processed.
:return: The PySMT dnf of the execute-loop-part.
"""
logger.info(probably_summation_nf.done)
pysmt_loop_done = probably_expr_to_pysmt(probably_summation_nf.done, self._pysmt_infinity_variable, True, self.monus_euf)
probably_postexpectation = parse_expectation(post_expectation)
self.is_linear = self.is_linear and check_is_linear_expr(probably_postexpectation)==None
flattened_postexpectation = normalize_expectation_simple(self.program, probably_postexpectation)
if type(flattened_postexpectation) == CheckFail:
print(flattened_postexpectation)
raise Exception("CheckFail.")
logger.info("Flattened Postexpectation: %s \n Loop Done Expression: %s"
% (flattened_postexpectation, pysmt_loop_done))
pysmt_postexpectation_snf = [(probably_expr_to_pysmt(bool_exp, self._pysmt_infinity_variable, True, self.monus_euf),
probably_expr_to_pysmt(arith_exp, self._pysmt_infinity_variable, True, self.rmonus_euf, True))
for bool_exp, arith_exp in flattened_postexpectation]
pysmt_loop_terminated_dnf = []
for bin_seq in product([True, False], repeat=len(pysmt_postexpectation_snf)):
guard_seq, arith_seq = zip(
*list(map(self._construct_boolexp_arithexp_par, bin_seq, pysmt_postexpectation_snf)))
to_test = And(guard_seq + (pysmt_loop_done, self.non_negative_constraint,))
if self._sat_solver.is_sat(to_test):
resulting_arith = simplify(Plus(arith_seq))
pysmt_loop_terminated_dnf.append(
(simplify(And(guard_seq + (pysmt_loop_done,))), resulting_arith))
self._pysmt_loop_done = pysmt_loop_done
logger.info("PySMT Loop-Terminated DNF: \n %s" % (pysmt_loop_terminated_dnf))
logger.debug("Checking that the conjunction of all guards is equivalent to True")
return pysmt_loop_terminated_dnf
def to_canonical(self, child_true: int,
child_false: int) -> Tuple['Decision', int, int]:
if self.is_canonical:
return self, child_true, child_false
if self.is_bool():
if self.test.is_symbol():
self.is_canonical = True
return self, child_true, child_false
else:
decision = Decision(simplify(~self.test), self._variables,
True)
print(decision)
assert decision.test.is_symbol()
return decision, child_false, child_true
inequality = LinearInequality.from_smt(self.test)
keys = sorted(inequality.inequality_dict.keys())
if len(keys) == 0:
print("IN", inequality)
factor = abs(inequality.inequality_dict[keys[0]])
result = {k: v / factor for k, v in inequality.inequality_dict.items()}
if result[keys[0]] < 0:
result = {k: -v for k, v in result.items()}
child_true, child_false = child_false, child_true
canonical_inequality = LinearInequality(result)
decision = Decision(canonical_inequality.to_smt(), self._variables,
True, canonical_inequality)
# canonical_inequality = LinearInequality.from_smt(self.test).normalize()
# if canonical_inequality.b() < 0:
# canonical_inequality = LinearInequality({k: -v for k, v, in canonical_inequality.inequality_dict.items()})
# child_true, child_false = child_false, child_true
# decision = Decision(canonical_inequality.to_smt(), self._variables, True, canonical_inequality)
return decision, child_true, child_false
def get_valid_branches(self) -> List[bool]:
"""
Returns the valid branches (True, False or both)
"""
simplified = self.test
if simplified not in [TRUE(), FALSE()]:
if self.is_bool():
simplified = simplify(simplified)
else:
simplified = simplify(self.inequality.to_smt())
if simplified == TRUE():
return [True]
elif simplified == FALSE():
return [False]
else:
return [True, False]
def _get_param_assignments(self, model, time, parameters, monotonic=True):
p_ass = []
fwd = False
for p in parameters:
p_time = model[TS.get_ptimed(p, 0)]
if p.symbol_type() == BOOL:
if monotonic:
if p_time == TRUE():
p_ass.append(p)
else:
p_ass.append(p if p_time == TRUE() else Not(p))
else:
p_ass.append(EqualsOrIff(p, p_time))
p_ass = And(p_ass)
self.region = simplify(Or(self.region, p_ass))
if self.models is None:
self.models = []
self.models.append((model, time))
Logger.msg("+", 0, not (Logger.level(1)))
self.cs_count += 1
Logger.log(
"Found assignment \"%s\"" % (p_ass.serialize(threshold=100)), 1)
return (p_ass, False)
def operator_to_bound(self, inequality: LinearInequality, var_name: str):
result = Real(inequality.b())
for other in inequality.variables:
if other != var_name:
result += Symbol(other,
REAL) * Real(-inequality.coefficient(other))
return simplify(result * Real(1 / inequality.coefficient(var_name)))
def walk_literal(self, l, node):
vertex_id = self.get_id(node.id)
if self.literals.is_number_boolean(l):
label = "[{}] {}".format(node.id, ("~" if l < 0 else "") +
str(self.literals.number_to_val(l)))
if node.id in self.node_annotations:
label += ": {}".format(self.node_annotations[node.id])
return (
vertex_id,
{
'{} [label="{}",color=black,shape=rectangle];'.format(
vertex_id, label)
},
set(),
node.id,
)
else:
inequality = self.literals.number_to_val(l)
if l < 0:
inequality = smt.simplify(~inequality)
label = "[{}] {}".format(node.id, str(inequality))
if node.id in self.node_annotations:
label += ": {}".format(self.node_annotations[node.id])
return (
vertex_id,
{
'{} [label="{}",color=black,shape=rectangle];'.format(
vertex_id, label)
},
set(),
node.id,
)
def _get_param_assignments(self, model, time, parameters, monotonic=True):
p_ass = []
fwd = False
for p in parameters:
# search the trace for any enabled faults
ever_true = False
for t in range(time + 1):
p_time = model[TS.get_ptimed(p, 0)]
if p.symbol_type() == BOOL:
if p_time == TRUE():
ever_true = True
break
if ever_true:
p_ass.append(p)
elif not monotonic:
p_ass.append(EqualsOrIff(p, FALSE()))
p_ass = And(p_ass)
self.region = simplify(Or(self.region, p_ass))
if self.models is None:
self.models = []
self.models.append((model, time))
Logger.msg("+", 0, not (Logger.level(1)))
self.cs_count += 1
Logger.log(
"Found assignment \"%s\"" % (p_ass.serialize(threshold=100)), 1)
return (p_ass, False)
def categorize_bounds(formula: FNode, sender_symbol: FNode):
"""
categorize symbolic bounds for a given variable
:param formula: FNode formula in CNF form
:param sender_symbol: FNode of the bounded variable
:return: upper_bounds, lower_bounds, parent_atoms
"""
clauses = set()
formula = simplify(formula)
if formula.is_or() or is_literal(formula):
clauses.add(formula)
else: # formula of CNF form
for clause in formula.args():
assert is_literal(clause) or clause.is_or()
clauses.add(clause)
bounds = defaultdict(list)
for clause in clauses:
if clause.is_le() or clause.is_lt(): # single literal clause
bound, bound_type = atom_to_bound(clause, sender_symbol)
bounds[bound_type].append(bound)
continue
for atom in clause.get_atoms(): # atom: inequality a * x + b * y < c
assert atom.is_le() or atom.is_lt()
bound, bound_type = atom_to_bound(atom, sender_symbol)
bounds[bound_type].append(bound)
return list(set(bounds[UPPER])), list(set(bounds[LOWER])), \
list(set(bounds[NEITHER]))
def validateModel(smtFile, modelFile):
try:
if (not path.exists(smtFile)):
raise Exception("File not found: {}".format(smtFile))
if (not path.exists(modelFile)):
raise Exception("File not found: {}".format(modelFile))
parser = SmtLibParser()
formula = readSmtFile(parser, smtFile)
symbols = getSymbols(parser)
model = readModel(parser, modelFile)
checkFullModel(model, symbols)
result = simplify(formula.substitute(model))
if (not result.is_constant()):
print("INVALID: Did not provide a full model.")
elif (not result.is_true()):
print("INVALID: Model does not evaluate to true.")
else:
print("VALID")
except Exception as e:
print(e)
sys.exit(1)
def clause_to_intervals(clause: FNode, sender_symbol: FNode,
test_point: float):
"""
turn clause into a list of intervals,
where there are at most two intervals
:param clause: OR FNode or a single atom
:param sender_symbol:
:param test_point: an initiation value for recipient variable
:return: list of tuples of form [lower, upper]
"""
upper_bounds, lower_bounds, recipient_atoms = categorize_bounds(
clause, sender_symbol)
if recipient_atoms:
parent_symbol = list(get_real_variables(recipient_atoms[0]))
for atom in recipient_atoms:
bound = simplify(
substitute(atom, {parent_symbol[0]: Real(test_point)}))
if bound.is_true():
return []
num_uppers = [initiate_bound(upper, test_point) for upper in upper_bounds]
num_lowers = [initiate_bound(lower, test_point) for lower in lower_bounds]
if not num_uppers and not num_lowers:
return []
if not num_uppers:
return [[min(num_lowers), float('inf')]]
if not num_lowers:
return [[float('-inf'), max(num_uppers)]]
max_upper, min_lower = max(num_uppers), min(num_lowers)
if max_upper < min_lower:
return [[float('-inf'), max_upper], [min_lower, float('inf')]]
else:
return []
def _get_pysmt_dnf_loop_execute(self, pysmt_summation_nf):
"""
Computes the execute-loop-part of the wp-characteristic functional in PySMT disjunctive normal form
:param pysmt_summation_nf: The wp-characteristic functional in summation normal form.
:return: The PySMT dnf of the execute-loop-part.
"""
pysmt_dnf_loop_execute = []
for bin_seq in product([True, False], repeat=len(pysmt_summation_nf)):
guard_seq, prob_seq, sub_seq, tick_seq = zip(*list(map(self._construct_guard_prob_tick_triple, bin_seq, pysmt_summation_nf)))
conjuncted_B = And(guard_seq)
to_test = And(guard_seq + (self.non_negative_constraint,))
# We only want to add them, if they are satisfiable
if self._sat_solver.is_sat(to_test):
prob_sub_tick_list = [(prob_seq[i], sub_seq[i], tick_seq[i]) for i in range(0, len(prob_seq)) if
not prob_seq[i] == Real(0)]
# if the prob_sub_list is empty, then this entry of the dnf corresponds to the (not guard) part of
# the wp-characteristic functional. Omit this part in the loop_execute part.
if len(prob_sub_tick_list) != 0:
pysmt_dnf_loop_execute.append((simplify(conjuncted_B),
prob_sub_tick_list))
logger.info("PySMT Disjunctive NF (length = %s): \n %s \n" % (
len(pysmt_dnf_loop_execute),
[(guard.serialize(), prob_subs_ticks) for (guard, prob_subs_ticks) in pysmt_dnf_loop_execute]))
return pysmt_dnf_loop_execute
def compile_ftrans(self):
if self.ftrans is None:
return None
ret_trans = TRUE()
ret_invar = TRUE()
use_ites = False
if use_ites:
for var, cond_assign_list in self.ftrans.items():
if TS.has_next(var):
ite_list = TS.to_prev(var)
else:
ite_list = var
for (condition, value) in reversed(cond_assign_list):
if condition == TRUE():
ite_list = value
else:
ite_list = Ite(condition, value, ite_list)
if TS.has_next(ite_list):
ret_trans = And(ret_trans, EqualsOrIff(var, ite_list))
else:
ret_invar = And(ret_invar, EqualsOrIff(var, ite_list))
else:
for var, cond_assign_list in self.ftrans.items():
effects = []
all_neg_cond = []
for (condition, value) in cond_assign_list:
effects.append(
simplify(Implies(condition, EqualsOrIff(var, value))))
all_neg_cond.append(Not(condition))
if not TS.has_next(var) and not TS.has_next(condition):
ret_invar = And(ret_invar, And(effects))
else:
ret_trans = And(ret_trans, And(effects))
if TS.has_next(var):
no_change = EqualsOrIff(var, TS.to_prev(var))
ret_trans = And(
ret_trans,
simplify(Implies(And(all_neg_cond), no_change)))
return (ret_invar, ret_trans)
def add_ts(self, ts):
if self.en_simplify:
ts.init = simplify(ts.init)
ts.invar = simplify(ts.invar)
ts.trans = simplify(ts.trans)
self.tss.add(ts)
for v in ts.vars:
self.vars.add(v)
for v in ts.state_vars:
self.state_vars.add(v)
for v in ts.input_vars:
self.input_vars.add(v)
for v in ts.output_vars:
self.output_vars.add(v)
self.update_logic(ts.logic)
def add_ts(self, ts, add_vars=True, reset=True):
if self.en_simplify:
ts.init = simplify(ts.init)
ts.invar = simplify(ts.invar)
ts.trans = simplify(ts.trans)
self.tss.add(ts)
if add_vars:
for v in ts.vars:
self.vars.add(v)
if (v in ts.state_vars) and (v not in self.input_vars):
self.state_vars.add(v)
if v in ts.input_vars:
self.input_vars.add(v)
if (v in ts.output_vars) and (v not in self.input_vars):
self.output_vars.add(v)
self.update_logic(ts.logic)
if reset:
init = True
trans = True
invar = True
ftrans = True
if (ts.init is None) or (ts.init == TRUE()):
init = False
if (ts.invar is None) or (ts.invar == TRUE()):
invar = False
if (ts.trans is None) or (ts.trans == TRUE()):
trans = False
if (ts.ftrans is None) or (ts.ftrans == {}):
ftrans = False
self.reset_formulae(init=init,
invar=invar,
trans=trans,
ftrans=ftrans)
def literal_to_bounds(f: FNode):
"""
obtain bounds on variable x from inequality atom
:param literal: ax + by + c < dx + ey + f
:param x: variable
:return: symbolic bound for x, is_lower, k_inclduded
for example, given literal 3x + 2y + 4 < x + y + 1,
first move all terms to left hand side: 2x + y + 3 < 0,
then it returns [-1/2 y - 3/2, False]
since the literal is equivalent to x < -1/2 y - 3/2
"""
assert (is_literal(f))
assert f.is_le() or f.is_lt()
variables = list(get_real_variables(f))
k_included = f.is_le()
f = simplify(f)
lhs, rhs = f.arg(0), f.arg(1)
lhs_coef, lhs_const = get_coefficients(lhs), get_constants(lhs)
rhs_coef, rhs_const = get_coefficients(rhs), get_constants(rhs)
# move all terms to lhs
const = simplify(lhs_const - rhs_const)
coef = dict()
for v in variables:
coef[v] = simplify(lhs_coef[v] - rhs_coef[v])
bounds = dict()
for v in variables:
if float(coef[v].constant_value()) == 0:
continue
bound_terms = [simplify(const * Real(-1) / coef[v])]
for w in variables:
if w == v or float(coef[w].constant_value()) == 0:
continue
new_w_coef = simplify(coef[w] * Real(-1) / coef[v])
bound_terms.append(Times(new_w_coef, w))
bound = Plus(bound_terms)
is_lower = coef[v].constant_value() < 0
bounds[v] = bound, is_lower, k_included
return bounds
def get_constants(atom: FNode):
"""
obtain constant term in a linear real arithmetics
:param atom: FNode formula of form a * x + b * y + c
:return:
"""
variables = list(get_real_variables(atom))
new_atom = atom
for var in variables:
new_atom = new_atom.substitute({var: Real(0)})
return simplify(new_atom)
def __init__(self, parent, child, formula):
"""
:param formula: clause must be of form that child variable on one side
and other variables and constant on the other side, e.g. root+c <= child
:param child: TNode object
"""
self.parent = parent
self.child = child
self.formula = simplify(formula)
self.check_formula()
self.upper_bounds, self.lower_bounds, self.critical_points = self.collect_bounds(
)
def atom_to_bound(atom: FNode, x_symbol: FNode):
"""
obtain bounds on variable x from inequality atom
:param atom: must be of plus form or a single term on each side
:param x_symbol:
:return:
"""
assert atom.is_le() or atom.is_lt()
variables = list(get_real_variables(atom))
if x_symbol not in variables:
return [atom, NEITHER]
lhs, rhs = atom.arg(0), atom.arg(1)
lhs_coef, lhs_const = get_coefficients(lhs), get_constants(lhs)
rhs_coef, rhs_const = get_coefficients(rhs), get_constants(rhs)
lhs_x_coef = lhs_coef[x_symbol] if lhs_coef.get(x_symbol) else Real(0)
rhs_x_coef = rhs_coef[x_symbol] if rhs_coef.get(x_symbol) else Real(0)
x_coef_diff = simplify(lhs_x_coef - rhs_x_coef)
assert float(x_coef_diff.constant_value()) != 0
flag = simplify(x_coef_diff > 0)
bound = simplify((rhs_const - lhs_const) / x_coef_diff)
bound_type = UPPER if flag.is_true() else LOWER
if len(variables) == 1:
return [bound, bound_type]
y_symbol = variables[0] if x_symbol == variables[1] else variables[1]
lhs_y_coef = lhs_coef[y_symbol] if lhs_coef.get(y_symbol) else Real(0)
rhs_y_coef = rhs_coef[y_symbol] if rhs_coef.get(y_symbol) else Real(0)
y_coef_diff = simplify(lhs_y_coef - rhs_y_coef)
if float(y_coef_diff.constant_value()) == 0:
return [bound, bound_type]
new_y_coef = simplify(y_coef_diff * Real(-1) / x_coef_diff)
bound = Plus(bound, Times(new_y_coef, y_symbol))
return [bound, bound_type]
def parse_univariate_literal(f):
"""
Not complete. Given a univariate literal f, returns:
- the variable x
- the simplified endpoint k
- a flag that is True iff f is a lower bound to x
- a flag that is True iff the endpoint k is included
WARNING: again, not complete, i.e. it doesn't work for arbitrary
univariate literals.
"""
assert (is_literal(f))
assert (len(f.get_free_variables()) == 1)
# TODO: is this needed, given that we flip every xRA literal as a
# preprocessing step?
if f.is_not():
f = flip_ra_atom(f.args()[0])
f = simplify(f)
x = list(f.get_free_variables())[0]
k_included = f.is_le()
l, r = f.args()
if l.is_real_constant():
is_lower = True
k = l.constant_value()
ax = r
elif r.is_real_constant():
is_lower = False
k = r.constant_value()
ax = l
else:
raise ValueError(f"Can't parse the univariate literal {f.serialize()}")
if ax.is_times():
assert (len(ax.args()) == 2)
assert (ax.args()[0].is_symbol())
assert (ax.args()[1].is_real_constant())
k = k / ax.args()[1].constant_value()
elif ax.is_plus():
assert (len(ax.args()) == 2)
assert (ax.args()[0].is_symbol())
assert (ax.args()[1].is_real_constant())
k = k - ax.args()[1].constant_value()
elif not ax.is_symbol():
raise ValueError(f"Can't parse the univariate literal {f.serialize()}")
return x, k, is_lower, k_included
def get_x_coefficient(atom: FNode):
"""
obtain coefficient of variable in univariate LRA
:param atom: FNode atom
:return: coeffcient of variable, type FNode
"""
variable = list(get_real_variables(atom))
assert len(variable) == 1
var = variable[0]
const = get_constants(atom)
new_atom = Plus(atom, -const)
new_atom = new_atom.substitute({var: Real(1)})
return simplify(new_atom)
def __init__(self, value=SMYBOLIC, *, name=AUTOMATIC, prefix=AUTOMATIC):
if (name is not AUTOMATIC
or prefix is not AUTOMATIC) and value is not SMYBOLIC:
raise TypeError('Can only name symbolic variables')
elif name is not AUTOMATIC and prefix is not AUTOMATIC:
raise ValueError('Can only set either name or prefix not both')
elif name is not AUTOMATIC:
if not isinstance(name, str):
raise TypeError('Name must be string')
elif name in _name_table:
raise ValueError(f'Name {name} already in use')
elif _name_re.fullmatch(name):
warnings.warn(
'Name looks like an auto generated name, this might break things'
)
_name_table[name] = self
elif prefix is not AUTOMATIC:
name = _gen_name(prefix)
_name_table[name] = self
elif name is AUTOMATIC and value is SMYBOLIC:
name = _gen_name()
_name_table[name] = self
if value is SMYBOLIC:
self._value = smt.Symbol(name, BOOL)
elif isinstance(value, pysmt.fnode.FNode):
if value.get_type().is_bool_type():
self._value = value
else:
raise TypeError(f'Expected bool type not {value.get_type()}')
elif isinstance(value, SMTBit):
if name is not AUTOMATIC and name != value.name:
warnings.warn(
'Changing the name of a SMTBit does not cause a new underlying smt variable to be created'
)
self._value = value._value
elif isinstance(value, bool):
self._value = smt.Bool(value)
elif isinstance(value, int):
if value not in {0, 1}:
raise ValueError(
'Bit must have value 0 or 1 not {}'.format(value))
self._value = smt.Bool(bool(value))
elif hasattr(value, '__bool__'):
self._value = smt.Bool(bool(value))
else:
raise TypeError("Can't coerce {} to Bit".format(type(value)))
self._name = name
self._value = smt.simplify(self._value)
def initiate_bound(bound: FNode, initiation: float) -> float:
"""
initiate an atom with only one variable with value initiation
:param bound: FNode atom
:param initiation: initiation of variable, type float
:return: initiated bound, type float
"""
real_variables = list(get_real_variables(bound))
assert len(real_variables) < 2
if real_variables:
# print(real_variables[0], Real(initiation))
bound = simplify(
substitute(bound, {real_variables[0]: Real(initiation)}))
return float(bound.constant_value())
def __print_single_ts(self, ts):
has_comment = len(ts.comment) > 0
if has_comment:
lenstr = len(ts.comment) + 3
self.write("\n%s\n" % ("-" * lenstr))
self.write("# %s\n" % ts.comment)
self.write("%s\n" % ("-" * lenstr))
sections = [("VAR", [x for x in ts.vars if x not in list(ts.state_vars)+list(ts.input_vars)+list(ts.output_vars)]),\
("STATE", ts.state_vars),\
("INPUT", ts.input_vars),\
("OUTPUT", ts.output_vars)]
for (sname, vars) in sections:
if len(vars) > 0: self.write("%s\n" % sname)
for var in vars:
sname = self.names(var.symbol_name())
if var.symbol_type() == BOOL:
self.write("%s : Bool;\n" % (sname))
else:
self.write("%s : BV(%s);\n" %
(sname, var.symbol_type().width))
self.write("\n")
sections = [((ts.init), "INIT"), ((ts.invar), "INVAR"),
((ts.trans), "TRANS")]
for (formula, keyword) in sections:
if formula not in [TRUE(), FALSE()]:
self.write("%s\n" % keyword)
cp = list(conjunctive_partition(formula))
if self.simplify:
cp = self._simplify_cp(cp)
for i in range(len(cp)):
f = simplify(cp[i])
if f == TRUE():
continue
self.printer(f)
self.write(";\n")
if f == FALSE():
break
self.write("\n")
if has_comment:
self.write("\n%s\n" % ("-" * lenstr))
def check_clause(formula: FNode):
"""
check if formula is either an atom or disjunctive of atoms
:param formula:
:return:
"""
flag = True
formula = simplify(formula)
if len(formula.get_atoms()) == 1:
return True
if not formula.is_or():
return False
for atom in formula.get_atoms():
flag = flag and (atom in atom.get_atoms())
return flag
def _simplify_cp(self, cp):
random.shuffle(cp)
newcp = []
last = False
step = 3
for i in range(0, len(cp) - (step - 1), step):
if i == len(cp) - step:
last = True
formula = simplify(And([cp[i + j] for j in range(step)]))
newcp += list(conjunctive_partition(formula))
if not last:
for i in range(-1, -step, -1):
newcp.append(cp[i])
return newcp
def with_evidence(self, substitutions):
# type: (T, Dict[FNode, FNode]) -> T
variables_to_remove = set()
for k, v in substitutions.items():
assert k.is_symbol()
assert k.symbol_type() == BOOL
assert v.is_constant()
variables_to_remove.add(k.symbol_name())
variables = [
v for v in self.domain.variables if v not in variables_to_remove
]
domain = Domain(variables,
{v: self.domain.var_types[v]
for v in variables}, self.domain.var_domains)
support = self.support.substitute(substitutions)
weight = simplify(self.weight.substitute(substitutions))
return self.copy(domain, support, weight)
def mutual_exclusive(n):
domain = make_domain(n)
symbols = domain.get_symbols(domain.real_vars)
x, symbols = symbols[0], symbols[1:]
bounds = make_distinct_bounds(domain)
terms = [x <= v for v in symbols]
disjunction = smt.TRUE()
for i in range(n):
for j in range(i + 1, n):
disjunction &= ~terms[i] | ~terms[j]
disjunction = smt.simplify(disjunction) & smt.Or(*terms)
flipped_domain = Domain(list(reversed([v for v in domain.variables if v != "x"])) + ["x"], domain.var_types, domain.var_domains)
return FileDensity(flipped_domain, disjunction & bounds, smt.Real(1.0))
