def test_stack_env(self):
env1 = get_env()
push_env()
push_env(env1)
self.assertEqual(env1, pop_env(), "Pushed environment was ignored.")
env2 = get_env()
self.assertIsNotNone(env2)
self.assertNotEqual(env1, pop_env(), "New environment was not created.")
def test_simplify_q(self):
simp = get_env().simplifier
Iff = get_env().formula_manager.Iff
for (f, _, _, logic) in get_example_formulae():
if logic.quantifier_free: continue
simp.validate_simplifications = True
sf = f.simplify()
simp.validate_simplifications = False
self.assertValid(Iff(f, sf), solver_name='z3',
msg="Simplification did not provide equivalent "+
"result:\n f= %s\n sf = %s" % (f, sf))
def test_with_env(self):
env1 = get_env()
a1 = Symbol("A", REAL)
with Environment():
env2 = get_env()
self.assertIsNotNone(env2, "Context should create an environment")
self.assertNotEqual(env1, env2, "Context should create a new environment")
a2 = Symbol("A", REAL)
self.assertNotEqual(a1, a2, "Symbols in different context should differ")
a3 = Symbol("A", REAL)
self.assertEqual(a1, a3, "Exiting a context should restore the previous environment")
def setUp(self):
super(TestSimpleTypeChecker, self).setUp()
self.tc = get_env().stc
self.x = Symbol("x", BOOL)
self.y = Symbol("y", BOOL)
self.p = Symbol("p", INT)
self.q = Symbol("q", INT)
self.r = Symbol("r", REAL)
self.s = Symbol("s", REAL)
self.qfo = get_env().qfo
def setUp(self):
super(TestSimpleTypeChecker, self).setUp()
self.tc = get_env().stc
self.x = Symbol("x", BOOL)
self.y = Symbol("y", BOOL)
self.p = Symbol("p", INT)
self.q = Symbol("q", INT)
self.r = Symbol("r", REAL)
self.s = Symbol("s", REAL)
self.qfo = get_env().qfo
def test_simplify_q(self):
simp = get_env().simplifier
Iff = get_env().formula_manager.Iff
for (f, _, _, logic) in get_example_formulae():
if logic.quantifier_free: continue
simp.validate_simplifications = True
sf = f.simplify()
simp.validate_simplifications = False
self.assertValid(Iff(f, sf),
solver_name='z3',
msg="Simplification did not provide equivalent " +
"result:\n f= %s\n sf = %s" % (f, sf))
def get_last_formula(self, mgr=None):
"""Returns the last formula of the execution of the Script.
This coincides with the conjunction of the assertions that are
left on the assertion stack at the end of the SMTLibScript.
"""
stack = []
backtrack = []
_And = mgr.And if mgr else get_env().formula_manager.And
for cmd in self.commands:
if cmd.name == smtcmd.ASSERT:
stack.append(cmd.args[0])
if cmd.name == smtcmd.RESET_ASSERTIONS:
stack = []
backtrack = []
elif cmd.name == smtcmd.PUSH:
for _ in xrange(cmd.args[0]):
backtrack.append(len(stack))
elif cmd.name == smtcmd.POP:
for _ in xrange(cmd.args[0]):
l = backtrack.pop()
stack = stack[:l]
return _And(stack)
def Solver(name: str, logic: tp.Optional[logics.Logic] = None) -> SolverT:
'''
Convience function for building a pysmt solver object with a switch backend.
Similar to `pysmt.shortcuts.Solver`.
'''
try:
cls = SWITCH_SOLVERS[name]
except KeyError:
raise NoSolverAvailableError(
f"Solver '{name}' is not available") from None
if isinstance(logic, str):
logic = logics.convert_logic_from_string(logic)
elif logic is None:
# Try to use the most general logic supported
try:
logic = logics.most_generic_logic(cls.LOGICS)
except NoLogicAvailableError:
# supported logics do not have a single "upper bound"
# Check for some reasonable ones
if logics.QF_UFLIRA in cls.LOGICS:
logic = logics.QF_UFLIRA
elif logics.QF_AUFBV in cls.LOGICS:
logic = logics.QF_AUFBV
else:
# use the first one
logic = cls.LOGICS[0]
return cls(environment=get_env(), logic=logic)
def test_solver_factory_preferences(self):
env = get_env()
factory = env.factory
self.assertEqual(factory.solver_preference_list,
pysmt.factory.DEFAULT_SOLVER_PREFERENCE_LIST)
for solver_name in factory.all_solvers(logic=logics.QF_UFLIRA):
factory.set_solver_preference_list([solver_name])
self.assertEqual(factory.solver_preference_list, [solver_name])
solver = factory.get_solver(logic=logics.QF_UFLIRA)
self.assertTrue(isinstance(solver, factory.all_solvers()[solver_name]))
factory.set_solver_preference_list(['nosolver'])
with self.assertRaises(NoSolverAvailableError):
factory.get_solver()
for qelim_name in factory.all_quantifier_eliminators():
factory.set_qelim_preference_list([qelim_name])
self.assertEqual(factory.qelim_preference_list, [qelim_name])
qelim = factory.get_quantifier_eliminator(logic=logics.BOOL)
self.assertTrue(isinstance(qelim, factory.all_quantifier_eliminators()[qelim_name]))
factory.set_qelim_preference_list(['nosolver'])
with self.assertRaises(NoSolverAvailableError):
factory.get_quantifier_eliminator()
def get_last_formula(self, mgr=None):
"""Returns the last formula of the execution of the Script.
This coincides with the conjunction of the assertions that are
left on the assertion stack at the end of the SMTLibScript.
"""
stack = []
backtrack = []
_And = mgr.And if mgr else get_env().formula_manager.And
for cmd in self.commands:
if cmd.name == smtcmd.ASSERT:
stack.append(cmd.args[0])
if cmd.name == smtcmd.RESET_ASSERTIONS:
stack = []
backtrack = []
elif cmd.name == smtcmd.PUSH:
for _ in xrange(cmd.args[0]):
backtrack.append(len(stack))
elif cmd.name == smtcmd.POP:
for _ in xrange(cmd.args[0]):
l = backtrack.pop()
stack = stack[:l]
return _And(stack)
def test_cannot_replace_global_walkers(self):
env = get_env()
# Check that environment contains standard walkers
self.assertIsNotNone(env.formula_manager)
self.assertIsNotNone(env.substituter)
self.assertIsNotNone(env.simplifier)
self.assertIsNotNone(env.serializer)
self.assertIsNotNone(env.stc)
# Cannot modify these elements
with self.assertRaises(AttributeError):
env.formula_manager = None
with self.assertRaises(AttributeError):
env.substituter = None
with self.assertRaises(AttributeError):
env.simplifier = None
with self.assertRaises(AttributeError):
env.serializer = None
with self.assertRaises(AttributeError):
env.stc = None
def from_graph(cls, graph, linear_energy_ranges, quadratic_energy_ranges):
"""Create Theta from a graph and energy ranges.
Args:
graph (:obj:`networkx.Graph`):
Provides the structure for Theta.
linear_energy_ranges (dict):
A dict of the form {v: (min, max), ...} where min and max are the
range of values allowed to v.
quadratic_energy_ranges (dict):
A dict of the form {(u, v): (min, max), ...} where min and max
are the range of values allowed to (u, v).
Returns:
:obj:`.Theta`
"""
get_env(
).enable_infix_notation = True # not sure why we need this here
theta = cls.empty(dimod.SPIN)
theta.add_offset(Symbol('offset', REAL))
def Linear(v):
"""Create a Symbol for the linear bias including the energy range
constraints."""
bias = Symbol('h_{}'.format(v), REAL)
min_, max_ = linear_energy_ranges[v]
theta.assertions.add(LE(bias, limitReal(max_)))
theta.assertions.add(GE(bias, limitReal(min_)))
return bias
def Quadratic(u, v):
"""Create a Symbol for the quadratic bias including the energy range
constraints."""
bias = Symbol('J_{},{}'.format(u, v), REAL)
if (v, u) in quadratic_energy_ranges:
min_, max_ = quadratic_energy_ranges[(v, u)]
else:
min_, max_ = quadratic_energy_ranges[(u, v)]
theta.assertions.add(LE(bias, limitReal(max_)))
theta.assertions.add(GE(bias, limitReal(min_)))
return bias
for v in graph.nodes:
theta.add_variable(v, Linear(v))
for u, v in graph.edges:
theta.add_interaction(u, v, Quadratic(u, v))
return theta
def __init__(self, assignment, environment=None):
if environment is None:
environment = get_env()
Model.__init__(self, environment)
self.environment = environment
self.assignment = assignment
# Create a copy of the assignments to memoize completions
self.completed_assignment = dict(self.assignment)
def __call__(self, test_fun):
msg = "Quantifier Eliminator for %s not available" % self.logic
cond = len(get_env().factory.all_quantifier_eliminators(logic=self.logic)) == 0
@unittest.skipIf(cond, msg)
@wraps(test_fun)
def wrapper(*args, **kwargs):
return test_fun(*args, **kwargs)
return wrapper
def __init__(self, assignment, environment=None):
if environment is None:
environment = get_env()
Model.__init__(self, environment)
self.environment = environment
self.assignment = dict(assignment)
# Create a copy of the assignments to memoize completions
self.completed_assignment = dict(self.assignment)
def __call__(self, test_fun):
msg = "%s not available" % self.solver
cond = self.solver not in get_env().factory.all_solvers()
@unittest.skipIf(cond, msg)
@wraps(test_fun)
def wrapper(*args, **kwargs):
return test_fun(*args, **kwargs)
return wrapper
def __call__(self, test_fun):
msg = "Quantifier Eliminator %s not available" % self.qe
cond = self.qe not in get_env().factory.all_quantifier_eliminators()
@unittest.skipIf(cond, msg)
@wraps(test_fun)
def wrapper(*args, **kwargs):
return test_fun(*args, **kwargs)
return wrapper
def __call__(self, test_fun):
msg = "Solver for %s not available" % self.logic
cond = not get_env().factory.has_solvers(logic=self.logic)
@unittest.skipIf(cond, msg)
@wraps(test_fun)
def wrapper(*args, **kwargs):
return test_fun(*args, **kwargs)
return wrapper
def __call__(self, test_fun):
msg = "Unsat Core Solver for %s not available" % self.logic
cond = len(get_env().factory.all_unsat_core_solvers(logic=self.logic)) == 0
@unittest.skipIf(cond, msg)
@wraps(test_fun)
def wrapper(*args, **kwargs):
return test_fun(*args, **kwargs)
return wrapper
def check_installed(required_solvers, install_dir, bindings_dir, mirror_link):
"""Checks which solvers are visible to pySMT."""
# Check which solvers are accessible from the Factory
pypath_solvers = get_env().factory.all_solvers()
global_solvers_status = []
print("Installed Solvers:")
for i in INSTALLERS:
installer_ = i.InstallerClass(install_dir=install_dir,
bindings_dir=bindings_dir,
solver_version=i.version,
mirror_link=mirror_link,
**i.extra_params)
solver = installer_.SOLVER
version = installer_.get_installed_version()
is_installed = (version is not None)
global_solvers_status.append((solver, is_installed, version))
del installer_
for solver in required_solvers:
if solver not in pypath_solvers:
raise PysmtException("Was expecting to find %s installed" % solver)
#
# Output information
#
for (solver, is_installed, version) in global_solvers_status:
msg = " %s%s " % (solver.ljust(10), is_installed)
msg += ("(%s)" % version).ljust(20)
if solver not in pypath_solvers:
msg += "Not in Python's path!"
print(msg)
print("")
print("Solvers: %s" % ", ".join(name for name in pypath_solvers))
qes = get_env().factory.all_quantifier_eliminators()
print("Quantifier Eliminators: %s" % ", ".join(name for name in qes))
ucs = get_env().factory.all_unsat_core_solvers()
print("UNSAT-Cores: %s" % ", ".join(name for name in ucs))
interps = get_env().factory.all_interpolators()
print("Interpolators: %s" % ", ".join(name for name in interps))
def check_installed(required_solvers, install_dir, bindings_dir, mirror_link):
"""Checks which solvers are visible to pySMT."""
# Check which solvers are accessible from the Factory
pypath_solvers = get_env().factory.all_solvers()
global_solvers_status = []
print("Installed Solvers:")
for i in INSTALLERS:
installer_ = i.InstallerClass(install_dir=install_dir,
bindings_dir=bindings_dir,
solver_version=i.version,
mirror_link=mirror_link,
**i.extra_params)
solver = installer_.SOLVER
version = installer_.get_installed_version()
is_installed = (version is not None)
global_solvers_status.append((solver, is_installed, version))
del installer_
for solver in required_solvers:
if solver not in pypath_solvers:
raise PysmtException("Was expecting to find %s installed" % solver)
#
# Output information
#
for (solver, is_installed, version) in global_solvers_status:
msg = " %s%s " % (solver.ljust(10), is_installed)
msg += ("(%s)" % version).ljust(20)
if solver not in pypath_solvers:
msg += "Not in Python's path!"
print(msg)
print("")
print("Solvers: %s" % ", ".join(name for name in pypath_solvers))
qes = get_env().factory.all_quantifier_eliminators()
print("Quantifier Eliminators: %s" % ", ".join(name for name in qes))
ucs = get_env().factory.all_unsat_core_solvers()
print("UNSAT-Cores: %s" % ", ".join(name for name in ucs))
interps = get_env().factory.all_interpolators()
print("Interpolators: %s" % ", ".join(name for name in interps))
def __init__(self, stream, annotations=None):
TreeWalker.__init__(self)
self.stream = stream
self.write = self.stream.write
self.mgr = get_env().formula_manager
if not annotations:
self.annotations = Annotations()
else:
self.annotations = annotations
def __init__(self, stream, template=".def_%d"):
DagWalker.__init__(self, invalidate_memoization=True)
self.stream = stream
self.write = self.stream.write
self.openings = 0
self.name_seed = 0
self.template = template
self.names = None
self.mgr = get_env().formula_manager
def __call__(self, test_fun):
msg = "Quantifier Eliminator %s not available" % self.qe
cond = self.qe not in get_env().factory.all_quantifier_eliminators()
@unittest.skipIf(cond, msg)
@wraps(test_fun)
def wrapper(*args, **kwargs):
return test_fun(*args, **kwargs)
return wrapper
def __init__(self, env=None):
if env is None:
env = get_env()
self.env = env
self.mgr = env.formula_manager
self.get_type = env.stc.get_type
self.rules = []
self.scanner = None
self.eoi = EndOfInput()
def __call__(self, test_fun):
msg = "%s not available" % self.solver
cond = self.solver not in get_env().factory.all_solvers()
@unittest.skipIf(cond, msg)
@wraps(test_fun)
def wrapper(*args, **kwargs):
return test_fun(*args, **kwargs)
return wrapper
def __call__(self, test_fun):
msg = "Solver for %s not available" % self.logic
cond = not get_env().factory.has_solvers(logic=self.logic)
@unittest.skipIf(cond, msg)
@wraps(test_fun)
def wrapper(*args, **kwargs):
return test_fun(*args, **kwargs)
return wrapper
def get_strict_formula(self, mgr=None):
if self.contains_command(smtcmd.PUSH) or \
self.contains_command(smtcmd.POP):
raise Exception("Was not expecting push-pop commands")
assert self.count_command_occurrences(smtcmd.CHECK_SAT) == 1
_And = mgr.And if mgr else get_env().formula_manager.And
assertions = [cmd.args[0]
for cmd in self.filter_by_command_name([smtcmd.ASSERT])]
return _And(assertions)
def __init__(self, env=None):
if env is None:
env = get_env()
self.env = env
self.mgr = env.formula_manager
self.get_type = env.stc.get_type
self.rules = []
self.scanner = None
self.eoi = EndOfInput()
def skipIfNoSolverAvailable(test_fun):
"""Skip the test if no solver is available."""
msg = "No solver available"
cond = len(get_env().factory.all_solvers()) == 0
@unittest.skipIf(cond, msg)
@wraps(test_fun)
def wrapper(self, *args, **kwargs):
return test_fun(self, *args, **kwargs)
return wrapper
def __init__(self, stream, template=".def_%d"):
DagWalker.__init__(self, invalidate_memoization=True)
self.stream = stream
self.write = self.stream.write
self.openings = 0
self.name_seed = 0
self.template = template
self.names = None
self.mgr = get_env().formula_manager
self.set_function(partial(self._walk_nary, "and"), op.AND)
self.set_function(partial(self._walk_nary, "or"), op.OR)
self.set_function(partial(self._walk_nary, "not"), op.NOT)
self.set_function(partial(self._walk_nary, "=>"), op.IMPLIES)
self.set_function(partial(self._walk_nary, "="), op.IFF)
self.set_function(partial(self._walk_nary, "+"), op.PLUS)
self.set_function(partial(self._walk_nary, "-"), op.MINUS)
self.set_function(partial(self._walk_nary, "*"), op.TIMES)
self.set_function(partial(self._walk_nary, "pow"), op.POW)
self.set_function(partial(self._walk_nary, "="), op.EQUALS)
self.set_function(partial(self._walk_nary, "<="), op.LE)
self.set_function(partial(self._walk_nary, "<"), op.LT)
self.set_function(partial(self._walk_nary, "ite"), op.ITE)
self.set_function(partial(self._walk_nary, "to_real"), op.TOREAL)
self.set_function(partial(self._walk_nary, "/"), op.DIV)
self.set_function(partial(self._walk_nary, "bvand"), op.BV_AND)
self.set_function(partial(self._walk_nary, "bvor"), op.BV_OR)
self.set_function(partial(self._walk_nary, "bvnot"), op.BV_NOT)
self.set_function(partial(self._walk_nary, "bvxor"), op.BV_XOR)
self.set_function(partial(self._walk_nary, "bvadd"), op.BV_ADD)
self.set_function(partial(self._walk_nary, "bvsub"), op.BV_SUB)
self.set_function(partial(self._walk_nary, "bvneg"), op.BV_NEG)
self.set_function(partial(self._walk_nary, "bvmul"), op.BV_MUL)
self.set_function(partial(self._walk_nary, "bvudiv"), op.BV_UDIV)
self.set_function(partial(self._walk_nary, "bvurem"), op.BV_UREM)
self.set_function(partial(self._walk_nary, "bvshl"), op.BV_LSHL)
self.set_function(partial(self._walk_nary, "bvlshr"), op.BV_LSHR)
self.set_function(partial(self._walk_nary, "bvult"), op.BV_ULT)
self.set_function(partial(self._walk_nary, "bvule"), op.BV_ULE)
self.set_function(partial(self._walk_nary, "bvslt"), op.BV_SLT)
self.set_function(partial(self._walk_nary, "bvsle"), op.BV_SLE)
self.set_function(partial(self._walk_nary, "concat"), op.BV_CONCAT)
self.set_function(partial(self._walk_nary, "bvcomp"), op.BV_COMP)
self.set_function(partial(self._walk_nary, "bvashr"), op.BV_ASHR)
self.set_function(partial(self._walk_nary, "bvsdiv"), op.BV_SDIV)
self.set_function(partial(self._walk_nary, "bvsrem"), op.BV_SREM)
self.set_function(self.walk_bv_extract, op.BV_EXTRACT)
self.set_function(self.walk_bv_rotate, op.BV_ROR)
self.set_function(self.walk_bv_rotate, op.BV_ROL)
self.set_function(self.walk_bv_extend, op.BV_SEXT)
self.set_function(self.walk_bv_extend, op.BV_ZEXT)
self.set_function(partial(self._walk_nary, "select"), op.ARRAY_SELECT)
self.set_function(partial(self._walk_nary, "store"), op.ARRAY_STORE)
def _run_solver(idx, solver, logic, options, formula, signaling_queue,
ctrl_pipe):
"""Function used by the child Process to handle Portfolio requests.
solver : name of the solver
options : options for the solver
formula : formula to assert
signaling_queue: queue in which to write to indicate completion of solve
ctrl_pipe: Pipe to communicate with parent process *after* solve
"""
from pysmt.environment import get_env
Solver = get_env().factory.Solver
with Solver(name=solver, logic=logic, **options) as s:
s.add_assertion(formula)
try:
local_res = s.solve()
except Exception as ex:
signaling_queue.put((solver, ex))
return
signaling_queue.put((idx, local_res))
_exit = False
while not _exit:
try:
cmd = ctrl_pipe.recv()
except EOFError:
break
if type(cmd) == tuple:
cmd, args = cmd
if cmd == "exit":
_exit = True
elif cmd == "get_model":
# MG: Can we pickle the EagerModel directly?
# Note: contextualization happens on the receiver side
model = list(s.get_model())
ctrl_pipe.send(model)
elif cmd == "get_value":
args = get_env().formula_manager.normalize(args)
ctrl_pipe.send(s.get_value(args))
else:
raise ValueError("Unknown command '%s'" % cmd)
def __init__(self, LexerClass, env=None):
if env is None:
env = get_env()
self.env = env
self.mgr = env.formula_manager
self.get_type = env.stc.get_type
self.lexer = LexerClass(env)
self.token = None
self.tokenizer = None
def test_boolean(self):
varA = Symbol("At", INT)
varB = Symbol("Bt", INT)
f = And(LT(varA, Plus(varB, Int(1))), GT(varA, Minus(varB, Int(1))))
g = Equals(varA, varB)
h = Iff(f, g)
tc = get_env().stc
res = tc.walk(h)
self.assertEqual(res, BOOL)
def get_strict_formula(self, mgr=None):
if self.contains_command(smtcmd.PUSH) or \
self.contains_command(smtcmd.POP):
raise PysmtValueError("Was not expecting push-pop commands")
if self.count_command_occurrences(smtcmd.CHECK_SAT) != 1:
raise PysmtValueError("Was expecting exactly one check-sat command")
_And = mgr.And if mgr else get_env().formula_manager.And
assertions = [cmd.args[0]
for cmd in self.filter_by_command_name([smtcmd.ASSERT])]
return _And(assertions)
def __call__(self, test_fun):
msg = "Quantifier Eliminator for %s not available" % self.logic
cond = len(get_env().factory.all_quantifier_eliminators(
logic=self.logic)) == 0
@unittest.skipIf(cond, msg)
@wraps(test_fun)
def wrapper(*args, **kwargs):
return test_fun(*args, **kwargs)
return wrapper
def test_simplify_qf(self):
simp = get_env().simplifier
for (f, _, _, logic) in get_example_formulae():
if logic.is_quantified(): continue
sname = "z3" if not logic.theory.strings else "cvc4"
simp.validate_simplifications = sname
sf = f.simplify()
simp.validate_simplifications = None
self.assertValid(Iff(f, sf), solver_name=sname,
msg="Simplification did not provide equivalent "+
"result:\n f= %s\n sf = %s" % (f, sf))
def __init__(self, LexerClass, env=None):
if env is None:
env = get_env()
self.env = env
self.mgr = env.formula_manager
self.get_type = env.stc.get_type
self.lexer = LexerClass(env)
self.token = None
self.tokenizer = None
def __call__(self, test_fun):
msg = "Unsat Core Solver for %s not available" % self.logic
cond = len(
get_env().factory.all_unsat_core_solvers(logic=self.logic)) == 0
@unittest.skipIf(cond, msg)
@wraps(test_fun)
def wrapper(*args, **kwargs):
return test_fun(*args, **kwargs)
return wrapper
def _run_solver(idx, solver, options, formula, signaling_queue, ctrl_pipe):
"""Function used by the child Process to handle Portfolio requests.
solver : name of the solver
options : options for the solver
formula : formula to assert
signaling_queue: queue in which to write to indicate completion of solve
ctrl_pipe: Pipe to communicate with parent process *after* solve
"""
from pysmt.environment import get_env
Solver = get_env().factory.Solver
with Solver(name=solver, **options) as s:
s.add_assertion(formula)
try:
local_res = s.solve()
except Exception as ex:
signaling_queue.put((solver, ex))
return
signaling_queue.put((idx, local_res))
_exit = False
while not _exit:
try:
cmd = ctrl_pipe.recv()
except EOFError:
break
if type(cmd) == tuple:
cmd, args = cmd
if cmd == "exit":
_exit = True
elif cmd == "get_model":
# MG: Can we pickle the EagerModel directly?
# Note: contextualization happens on the receiver side
model = list(s.get_model())
ctrl_pipe.send(model)
elif cmd == "get_value":
args = get_env().formula_manager.normalize(args)
ctrl_pipe.send(s.get_value(args))
else:
raise ValueError("Unknown command '%s'" % cmd)
def __init__(self, environment=None):
self.pysmt_env = get_env() if environment is None else environment
# Placeholders for fields filled by self._reset
self._current_env = None
self.cache = None
self.logic = None
self._reset()
# Special tokens appearing in expressions
self.parentheses = set(["(", ")"])
self.specials = set(["let", "!", "exists", "forall"])
def __init__(self, environment=None):
self.pysmt_env = get_env() if environment is None else environment
# Placeholders for fields filled by self._reset
self._current_env = None
self.cache = None
self.logic = None
self._reset()
# Special tokens appearing in expressions
self.parentheses = set(["(", ")"])
self.specials = set(["let", "!", "exists", "forall"])
def test_simplify_qf(self):
simp = get_env().simplifier
for (f, _, _, logic) in get_example_formulae():
if logic.is_quantified(): continue
sname = "z3" if not logic.theory.strings else "cvc4"
simp.validate_simplifications = sname
sf = f.simplify()
simp.validate_simplifications = None
self.assertValid(Iff(f, sf),
solver_name=sname,
msg="Simplification did not provide equivalent " +
"result:\n f= %s\n sf = %s" % (f, sf))
def test_boolean(self):
varA = Symbol("At", INT)
varB = Symbol("Bt", INT)
f = And(LT(varA, Plus(varB, Int(1))),
GT(varA, Minus(varB, Int(1))))
g = Equals(varA, varB)
h = Iff(f, g)
tc = get_env().stc
res = tc.walk(h)
self.assertEqual(res, BOOL)
def skipIfNoSolverAvailable(test_fun):
"""Skip the test if no solver is available."""
msg = "No solver available"
cond = len(get_env().factory.all_solvers()) == 0
@unittest.skipIf(cond, msg)
@wraps(test_fun)
def wrapper(self, *args, **kwargs):
return test_fun(self, *args, **kwargs)
return wrapper
def get_strict_formula(self, mgr=None):
if self.contains_command(smtcmd.PUSH) or \
self.contains_command(smtcmd.POP):
raise PysmtValueError("Was not expecting push-pop commands")
if self.count_command_occurrences(smtcmd.CHECK_SAT) != 1:
raise PysmtValueError(
"Was expecting exactly one check-sat command")
_And = mgr.And if mgr else get_env().formula_manager.And
assertions = [
cmd.args[0] for cmd in self.filter_by_command_name([smtcmd.ASSERT])
]
return _And(assertions)
def test_plus_algebraic(self):
from pysmt.constants import Numeral
env = get_env()
mgr = env.formula_manager
r0 = Symbol("r0", REAL)
p_2 = Real(2)
m_5 = mgr._Algebraic(Numeral(-5))
m_3 = mgr._Algebraic(Numeral(-3))
# r0 + 2 - 5
expr = Plus(r0, p_2, m_5)
res = expr.simplify()
self.assertValid(Equals(expr, res))
self.assertIn(m_3, res.args())
def test_times_algebraic(self):
from pysmt.constants import Numeral
env = get_env()
mgr = env.formula_manager
r0 = Symbol("r0", REAL)
p_2 = Real(2)
m_5 = mgr._Algebraic(Numeral(-5))
m_10 = mgr._Algebraic(Numeral(-10))
# -5 * r0 * 2
expr = Times(m_5, r0, p_2)
res = expr.simplify()
self.assertValid(Equals(expr, res))
self.assertIn(m_10, res.args())
def smtlibscript_from_formula(formula, logic=None):
script = SmtLibScript()
if logic is None:
# Get the simplest SmtLib logic that contains the formula
f_logic = get_logic(formula)
smt_logic = None
try:
smt_logic = get_closer_smtlib_logic(f_logic)
except NoLogicAvailableError:
warnings.warn("The logic %s is not reducible to any SMTLib2 " \
"standard logic. Proceeding with non-standard " \
"logic '%s'" % (f_logic, f_logic),
stacklevel=3)
smt_logic = f_logic
elif not (isinstance(logic, Logic) or isinstance(logic, str)):
raise UndefinedLogicError(str(logic))
else:
if logic not in SMTLIB2_LOGICS:
warnings.warn("The logic %s is not reducible to any SMTLib2 " \
"standard logic. Proceeding with non-standard " \
"logic '%s'" % (logic, logic),
stacklevel=3)
smt_logic = logic
script.add(name=smtcmd.SET_LOGIC,
args=[smt_logic])
# Declare all types
types = get_env().typeso.get_types(formula, custom_only=True)
for type_ in types:
script.add(name=smtcmd.DECLARE_SORT, args=[type_.decl])
deps = formula.get_free_variables()
# Declare all variables
for symbol in deps:
assert symbol.is_symbol()
script.add(name=smtcmd.DECLARE_FUN, args=[symbol])
# Assert formula
script.add_command(SmtLibCommand(name=smtcmd.ASSERT,
args=[formula]))
# check-sat
script.add_command(SmtLibCommand(name=smtcmd.CHECK_SAT,
args=[]))
return script
def __init__(self, stream):
TreeWalker.__init__(self)
self.stream = stream
self.write = self.stream.write
self.mgr = get_env().formula_manager
self.set_function(partial(self._walk_nary, "and"), op.AND)
self.set_function(partial(self._walk_nary, "or"), op.OR)
self.set_function(partial(self._walk_nary, "not"), op.NOT)
self.set_function(partial(self._walk_nary, "=>"), op.IMPLIES)
self.set_function(partial(self._walk_nary, "="), op.IFF)
self.set_function(partial(self._walk_nary, "+"), op.PLUS)
self.set_function(partial(self._walk_nary, "-"), op.MINUS)
self.set_function(partial(self._walk_nary, "*"), op.TIMES)
self.set_function(partial(self._walk_nary, "="), op.EQUALS)
self.set_function(partial(self._walk_nary, "<="), op.LE)
self.set_function(partial(self._walk_nary, "<"), op.LT)
self.set_function(partial(self._walk_nary, "ite"), op.ITE)
self.set_function(partial(self._walk_nary, "to_real"), op.TOREAL)
self.set_function(partial(self._walk_nary, "bvand"), op.BV_AND)
self.set_function(partial(self._walk_nary, "bvor"), op.BV_OR)
self.set_function(partial(self._walk_nary, "bvnot"), op.BV_NOT)
self.set_function(partial(self._walk_nary, "bvxor"), op.BV_XOR)
self.set_function(partial(self._walk_nary, "bvadd"), op.BV_ADD)
self.set_function(partial(self._walk_nary, "bvsub"), op.BV_SUB)
self.set_function(partial(self._walk_nary, "bvneg"), op.BV_NEG)
self.set_function(partial(self._walk_nary, "bvmul"), op.BV_MUL)
self.set_function(partial(self._walk_nary, "bvudiv"), op.BV_UDIV)
self.set_function(partial(self._walk_nary, "bvurem"), op.BV_UREM)
self.set_function(partial(self._walk_nary, "bvshl"), op.BV_LSHL)
self.set_function(partial(self._walk_nary, "bvlshr"), op.BV_LSHR)
self.set_function(partial(self._walk_nary, "bvult"), op.BV_ULT)
self.set_function(partial(self._walk_nary, "bvule"), op.BV_ULE)
self.set_function(partial(self._walk_nary, "bvslt"), op.BV_SLT)
self.set_function(partial(self._walk_nary, "bvsle"), op.BV_SLE)
self.set_function(partial(self._walk_nary, "concat"), op.BV_CONCAT)
self.set_function(partial(self._walk_nary, "bvcomp"), op.BV_COMP)
self.set_function(partial(self._walk_nary, "bvashr"), op.BV_ASHR)
self.set_function(partial(self._walk_nary, "bvsdiv"), op.BV_SDIV)
self.set_function(partial(self._walk_nary, "bvsrem"), op.BV_SREM)
self.set_function(self.walk_bv_extract, op.BV_EXTRACT)
self.set_function(self.walk_bv_rotate, op.BV_ROR)
self.set_function(self.walk_bv_rotate, op.BV_ROL)
self.set_function(self.walk_bv_extend, op.BV_ZEXT)
self.set_function(self.walk_bv_extend, op.BV_SEXT)
def test_functions(self):
vi = Symbol("At", INT)
vr = Symbol("Bt", REAL)
f = Symbol("f", FunctionType(INT, [REAL]))
g = Symbol("g", FunctionType(REAL, [INT]))
tc = get_env().stc
self.assertEqual(tc.walk(Function(f, [vr])), INT)
self.assertEqual(tc.walk(Function(g, [vi])), REAL)
self.assertEqual(tc.walk(Function(f, [Function(g, [vi])])), INT)
self.assertEqual(tc.walk(LE(Plus(vi, Function(f, [Real(4)])), Int(8))), BOOL)
self.assertEqual(tc.walk(LE(Plus(vr, Function(g, [Int(4)])), Real(8))), BOOL)
with self.assertRaises(TypeError):
LE(Plus(vr, Function(g, [Real(4)])), Real(8))
with self.assertRaises(TypeError):
LE(Plus(vi, Function(f, [Int(4)])), Int(8))
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)
ari = Symbol("ari", ArrayType(REAL, 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]))
bv3 = Symbol("bv3", BVType(3))
bv8 = Symbol("bv8", BV8)
bv16 = Symbol("bv16", 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
),
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
),
#
# 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="((! bv3) = 5_3)",
expr=Equals(BVNot(bv3),
BV("101")),
is_valid=False,
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="((7_3 xor bv3) = (6_3 xor bv3))",
expr=Equals(BVXor(BV("111"), bv3),
BVXor(BV("110"), bv3)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV
),
Example(hr="((bv8::bv8) u< 0_16)",
expr=BVULT(BVConcat(bv8, bv8),
BVZero(16)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV
),
Example(hr="((bv8::bv8) u< (bv8::9_8))",
expr=BVULT(BVConcat(bv8, bv8),
BVConcat(bv8, BV(9, 8))),
is_valid=False,
is_sat=True,
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< (((bv8 + 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<= bv16)",
expr=BVUGE(bv16, BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV
),
Example(hr="(0_16 s<= bv16)",
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) = 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
),
Example(hr="((bv16 ROL 1) = (bv16 ROR 2))",
expr=Equals(BVRol(bv16, 1),
BVRor(bv16, 2)),
is_valid=False,
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="((bv8 ZEXT 19) = (bv16 SEXT 11))",
expr=Equals(BVZExt(bv8, 19),
BVSExt(bv16, 11)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV
),
Example(hr="((bv16 - bv16) = 0_16)",
expr=Equals(BVSub(bv16, bv16), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV
),
Example(hr="((bv16 - bv16)[0:7] = bv8)",
expr=Equals(BVExtract(BVSub(bv16, bv16), 0, 7), bv8),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV
),
Example(hr="((bv16[0:7] bvcomp bv8) = 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="((bv16 bvcomp bv16) = 0_1)",
expr=Equals(BVComp(bv16, bv16), BVZero(1)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV
),
Example(hr="(bv16 s< bv16)",
expr=BVSLT(bv16, bv16),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV
),
Example(hr="(bv16 s< 0_16)",
expr=BVSLT(bv16, BVZero(16)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV
),
Example(hr="((bv16 s< 0_16) | (0_16 s<= bv16))",
expr=Or(BVSGT(BVZero(16), bv16), BVSGE(bv16, BVZero(16))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV
),
Example(hr="(bv16 u< bv16)",
expr=BVULT(bv16, bv16),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV
),
Example(hr="(bv16 u< 0_16)",
expr=BVULT(bv16, BVZero(16)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV
),
Example(hr="((bv16 | 0_16) = bv16)",
expr=Equals(BVOr(bv16, BVZero(16)), bv16),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV
),
Example(hr="((bv16 | 5_16) = bv16)",
expr=Equals(BVOr(bv16, BV(5, 16)), bv16),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV
),
Example(hr="((bv16 & 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="((bv16 & 7_16) = 0_16)",
expr=Equals(BVAnd(bv16, BV(7, 16)), BVZero(16)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV
),
Example(hr="((0_16 s< bv16) & ((bv16 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< bv16) & ((bv16 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="((bv16 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="((bv16 u% bv16) = 0_16)",
expr=Equals(BVURem(bv16, bv16), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV
),
Example(hr="((bv16 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="((bv16 s% bv16) = 0_16)",
expr=Equals(BVSRem(bv16, bv16), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV
),
Example(hr="((bv16 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="(bv16 s< (- bv16))",
expr=BVSGT(BVNeg(bv16), bv16),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV
),
Example(hr="((bv16 a>> 0_16) = bv16)",
expr=Equals(BVAShr(bv16, BVZero(16)), bv16),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV
),
Example(hr="((0_16 s<= bv16) & ((bv16 a>> 1_16) = (bv16 >> 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, (q + 3))) | (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((p - 3)) = r) & (ToReal(q) = r)) -> ((p < ih(ToReal((p - 3)), (q + 3))) | (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((p - 3)) = r) & (ToReal(q) = r)) -> ((p < ih(ToReal((p - 3)), (q + 3))) | (ih(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="((Array{Int, Int}(0)[1 := 3] = aii) & (aii[1] = 3))",
expr=And(Equals(Array(INT, Int(0), {Int(1) : Int(3)}), aii), Equals(Select(aii, Int(1)), Int(3))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.get_logic_by_name("QF_ALIA*")
),
Example(hr="((Array{Real, Int}(10) = ari) & (ari[6/5] = 0))",
expr=And(Equals(Array(REAL, Int(10)), ari), Equals(Select(ari, Real((6, 5))), Int(0))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.get_logic_by_name("QF_AUFBVLIRA*")
),
Example(hr="((Array{Real, Int}(0)[1.0 := 10][2.0 := 20][3.0 := 30][4.0 := 40] = ari) & (! ((ari[0.0] = 0) & (ari[1.0] = 10) & (ari[2.0] = 20) & (ari[3.0] = 30) & (ari[4.0] = 40))))",
expr=And(Equals(Array(REAL, Int(0), {Real(1) : Int(10), Real(2) : Int(20), Real(3) : Int(30), Real(4) : Int(40)}), ari),
Not(And(Equals(Select(ari, Real(0)), Int(0)),
Equals(Select(ari, Real(1)), Int(10)),
Equals(Select(ari, Real(2)), Int(20)),
Equals(Select(ari, Real(3)), Int(30)),
Equals(Select(ari, Real(4)), Int(40))))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.get_logic_by_name("QF_AUFBVLIRA*")
),
Example(hr="((Array{Real, Int}(0)[1.0 := 10][2.0 := 20][3.0 := 30][4.0 := 40][5.0 := 50] = ari) & (! ((ari[0.0] = 0) & (ari[1.0] = 10) & (ari[2.0] = 20) & (ari[3.0] = 30) & (ari[4.0] = 40) & (ari[5.0] = 50))))",
expr=And(Equals(Array(REAL, Int(0), {Real(1) : Int(10), Real(2) : Int(20), Real(3) : Int(30), Real(4) : Int(40), Real(5) : Int(50)}), ari),
Not(And(Equals(Select(ari, Real(0)), Int(0)),
Equals(Select(ari, Real(1)), Int(10)),
Equals(Select(ari, Real(2)), Int(20)),
Equals(Select(ari, Real(3)), Int(30)),
Equals(Select(ari, Real(4)), Int(40)),
Equals(Select(ari, Real(5)), Int(50))))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.get_logic_by_name("QF_AUFBVLIRA*")
),
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[bv8 := y_][bv8 := z_] = abb[bv8 := 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
def get_example_formulae(environment=None):
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)
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]))
bv8 = Symbol("bv1", BV8)
bv16 =Symbol("bv2", BV16)
result = [
# Formula, is_valid, is_sat, is_qf
# x /\ y
Example(expr=And(x, y),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BOOL
),
# x <-> y
Example(expr=Iff(x, y),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BOOL
),
# (x \/ y ) /\ ! ( x \/ y )
Example(expr=And(Or(x, y), Not(Or(x, y))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BOOL
),
# (x /\ !y)
Example(expr=And(x, Not(y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
# False -> True
Example(expr=Implies(FALSE(),TRUE()),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BOOL
),
#
# LIA
#
# (p > q) /\ x -> y
Example(expr=And(GT(p, q), Implies(x, y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_IDL
),
# (p + q) = 5 /\ (p > q)
Example(expr=And(Equals(Plus(p,q),Int(5)) , GT(p, q)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA
),
# (p >= q) \/ ( p <= q)
Example(expr=Or(GE(p, q), LE(p, q)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_IDL
),
# !( p < q * 2 )
Example(expr=Not(LT(p, Times(q, Int(2)))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA
),
# p - (5 - 2) > p
Example(expr=GT(Minus(p, Minus(Int(5), Int(2))), p),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_IDL
),
# x ? 7: (p + -1) * 3 = q
Example(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(expr=LT(p, Plus(q, Int(1))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA
),
#
# LRA
#
# (r > s) /\ x -> y
Example(expr=And(GT(r, s), Implies(x, y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_RDL
),
# (r + s) = 5.6 /\ (r > s)
Example(expr=And(Equals(Plus(r,s), Real(Fraction("5.6"))) , GT(r, s)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA
),
# (r >= s) \/ ( r <= s)
Example(expr=Or(GE(r, s), LE(r, s)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_RDL
),
# !( (r / (1/2)) < s * 2 )
Example(expr=Not(LT(Div(r, Real((1,2))), Times(s, Real(2)))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA
),
# ! ( r - (5 - 2) > r )
Example(expr=Not(GT(Minus(r, Minus(Real(5), Real(2))), r)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_RDL
),
# x ? 7: (s + -1) * 3 = r
Example(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
#
# rf(5, rg(2)) = 0
Example(expr=Equals(Function(rf, (Real(5), Function(rg, (r,)))), Real(0)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_UFLRA
),
# (rg(r) = 5 + 2) <-> (rg(r) = 7)
Example(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
),
# (r = s + 1) & (rg(s) = 5) & (rg(r - 1) = 7)
Example(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
#
# bv_one & bv_zero == bv_zero
Example(expr=Equals(BVAnd(BVOne(32), BVZero(32)),
BVZero(32)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# ~(010) == 101
Example(expr=Equals(BVNot(BV("010")),
BV("101")),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# "111" xor "000" == "000"
Example(expr=Equals(BVXor(BV("111"), BV("000")),
BV("000")),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
# bv8 :: bv8 < bv_zero
Example(expr=BVULT(BVConcat(bv8, bv8),
BVZero(16)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
# bv_one[:7] == bv_one
Example(expr=Equals(BVExtract(BVOne(32), end=7),
BVOne(8)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# (((bv8 + bv_one) * bv(5)) / bv(5)) > bv(0)
Example(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),
# bv16 >=u bv(0)
Example(expr=BVUGE(bv16, BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# bv16 >=s bv(0)
Example(expr=BVSGE(bv16, BVZero(16)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
# (BV(5) rem BV(2) > bv_zero) /\ (BV(5) rem BV(2) < bv_one)
Example(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),
# ((bv_one + (- bv_one)) << 1) >> 1 == bv_one
Example(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),
# bv_one - bv_one == bv_zero
Example(expr=Equals(BVSub(BVOne(32), BVOne(32)), BVZero(32)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# Rotations
Example(expr=Equals(BVRor(BVRol(BVOne(32), 1),1), BVOne(32)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# Extensions
Example(expr=Equals(BVZExt(BVZero(5), 11),
BVSExt(BVZero(1), 15)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# bv16 - bv16 = 0_16
Example(expr=Equals(BVSub(bv16, bv16), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# (bv16 - bv16)[0:7] = bv8
Example(expr=Equals(BVExtract(BVSub(bv16, bv16), 0, 7), bv8),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
# (bv16[0,7] comp bv8) = bv1
Example(expr=Equals(BVComp(BVExtract(bv16, 0, 7), bv8), BVOne(1)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
# (bv16 comp bv16) = bv0
Example(expr=Equals(BVComp(bv16, bv16), BVZero(1)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
# (bv16 s< bv16)
Example(expr=BVSLT(bv16, bv16),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
# (bv16 s< 0_16)
Example(expr=BVSLT(bv16, BVZero(16)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
# (bv16 u< bv16)
Example(expr=BVULT(bv16, bv16),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
# (bv16 s< 0_16)
Example(expr=BVULT(bv16, BVZero(16)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
# (bv16 | 0_16) = bv16
Example(expr=Equals(BVOr(bv16, BVZero(16)), bv16),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# (bv16 & 0_16) = 0_16
Example(expr=Equals(BVAnd(bv16, BVZero(16)), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# 0_16 s< bv16 & ((bv16 s/ -1) s< 0)
Example(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),
# 0_16 s< bv16 & ((bv16 s% -1) s< 0)
Example(expr=And(BVSLT(BVZero(16), bv16),
BVSLT(BVSRem(bv16, BVOne(16)), BVZero(16))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
# bv16 u% 1 = 0_16
Example(expr=Equals(BVURem(bv16, BVOne(16)), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# bv16 s% 1 = 0_16
Example(expr=Equals(BVSRem(bv16, BVOne(16)), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# bv16 s% -1 = 0_16
Example(expr=Equals(BVSRem(bv16, BVNeg(BVOne(16))), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# bv16 a>> 0 = bv16
Example(expr=Equals(BVAShr(bv16, BVZero(16)), bv16),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# 0 s<= bv16 & bv16 a>> 1 = bv16 >> 1
Example(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
#
# forall y . x -> y
Example(expr=ForAll([y], Implies(x,y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.BOOL
),
# forall p,q . p + q = 0
Example(expr=ForAll([p,q], Equals(Plus(p,q), Int(0))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.LIA
),
# forall r,s . ((r > 0) & (s > 0)) -> (r - s < r)
Example(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
),
# exists x,y . x -> y
Example(expr=Exists([x,y], Implies(x,y)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.BOOL
),
# exists p,q . p + q = 0
Example(expr=Exists([p,q], Equals(Plus(p,q), Int(0))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.LIA
),
# exists r . forall s . (r - s > r)
Example(expr=Exists([r], ForAll([s], GT(Minus(r,s), r))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.LRA
),
# forall r . exists s . (r - s > r)
Example(expr=ForAll([r], Exists([s], GT(Minus(r,s), r))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.LRA
),
# x /\ forall r. (r + s = 5)
Example(expr=And(x, ForAll([r], Equals(Plus(r,s), Real(5)))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.LRA
),
#
# UFLIRA
#
# ih(r,q) > p /\ (x -> y)
Example(expr=And(GT(Function(ih, (r, q)), p), Implies(x, y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_UFLIRA
),
# ( (p - 3) = q ) -> ( ih(r, q + 3) > p \/ ih(r, p) <= p )
Example(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
),
# ( (ToReal(p - 3) = r) /\ (ToReal(q) = r) ) ->
# ( ( ih(ToReal(p - 3), q + 3) > p ) \/ (ih(r, p) <= p) )
Example(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
),
# ! ( (ToReal(p - 3) = r /\ ToReal(q) = r) ->
# ( ih(ToReal(p - 3), q + 3) > p \/
# ih(r,p) <= p ) )
Example(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
),
]
return result
def __init__(self, environment=None, interactive=False):
self.env = get_env() if environment is None else environment
self.interactive = interactive
# Placeholders for fields filled by self._reset
self.cache = None
self.logic = None
self._reset()
# Tokens representing interpreted functions appearing in expressions
# Each token is handled by a dedicated function that takes the
# recursion stack, the token stream and the parsed token
# Common tokens are handled in the _reset function
mgr = self.env.formula_manager
self.interpreted = {
"let": self._enter_let,
"!": self._enter_annotation,
"exists": self._enter_quantifier,
"forall": self._enter_quantifier,
"+": self._operator_adapter(mgr.Plus),
"-": self._operator_adapter(self._minus_or_uminus),
"*": self._operator_adapter(mgr.Times),
"/": self._operator_adapter(self._division),
">": self._operator_adapter(mgr.GT),
"<": self._operator_adapter(mgr.LT),
">=": self._operator_adapter(mgr.GE),
"<=": self._operator_adapter(mgr.LE),
"=": self._operator_adapter(self._equals_or_iff),
"not": self._operator_adapter(mgr.Not),
"and": self._operator_adapter(mgr.And),
"or": self._operator_adapter(mgr.Or),
"xor": self._operator_adapter(mgr.Xor),
"=>": self._operator_adapter(mgr.Implies),
"<->": self._operator_adapter(mgr.Iff),
"ite": self._operator_adapter(mgr.Ite),
"to_real": self._operator_adapter(mgr.ToReal),
"concat": self._operator_adapter(mgr.BVConcat),
"bvnot": self._operator_adapter(mgr.BVNot),
"bvand": self._operator_adapter(mgr.BVAnd),
"bvor": self._operator_adapter(mgr.BVOr),
"bvneg": self._operator_adapter(mgr.BVNeg),
"bvadd": self._operator_adapter(mgr.BVAdd),
"bvmul": self._operator_adapter(mgr.BVMul),
"bvudiv": self._operator_adapter(mgr.BVUDiv),
"bvurem": self._operator_adapter(mgr.BVURem),
"bvshl": self._operator_adapter(mgr.BVLShl),
"bvlshr": self._operator_adapter(mgr.BVLShr),
"bvsub": self._operator_adapter(mgr.BVSub),
"bvult": self._operator_adapter(mgr.BVULT),
"bvxor": self._operator_adapter(mgr.BVXor),
"_": self._operator_adapter(self._smtlib_underscore),
# Extended Functions
"bvnand": self._operator_adapter(mgr.BVNand),
"bvnor": self._operator_adapter(mgr.BVNor),
"bvxnor": self._operator_adapter(mgr.BVXnor),
"bvcomp": self._operator_adapter(mgr.BVComp),
"bvsdiv": self._operator_adapter(mgr.BVSDiv),
"bvsrem": self._operator_adapter(mgr.BVSRem),
"bvsmod": self._operator_adapter(mgr.BVSMod),
"bvashr": self._operator_adapter(mgr.BVAShr),
"bvule": self._operator_adapter(mgr.BVULE),
"bvugt": self._operator_adapter(mgr.BVUGT),
"bvuge": self._operator_adapter(mgr.BVUGE),
"bvslt": self._operator_adapter(mgr.BVSLT),
"bvsle": self._operator_adapter(mgr.BVSLE),
"bvsgt": self._operator_adapter(mgr.BVSGT),
"bvsge": self._operator_adapter(mgr.BVSGE),
}
# Command tokens
self.commands = {
smtcmd.SET_INFO: self._cmd_set_info,
smtcmd.SET_OPTION: self._cmd_set_option,
smtcmd.ASSERT: self._cmd_assert,
smtcmd.CHECK_SAT: self._cmd_check_sat,
smtcmd.PUSH: self._cmd_push,
smtcmd.POP: self._cmd_pop,
smtcmd.EXIT: self._cmd_exit,
smtcmd.SET_LOGIC: self._cmd_set_logic,
smtcmd.DECLARE_CONST: self._cmd_declare_const,
smtcmd.GET_VALUE: self._cmd_get_value,
smtcmd.DECLARE_FUN: self._cmd_declare_fun,
smtcmd.DEFINE_FUN: self._cmd_define_fun,
}
Example(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
),
# ! ( (ToReal(p - 3) = r /\ ToReal(q) = r) ->
# ( ih(ToReal(p - 3), q + 3) > p \/
# ih(r,p) <= p ) )
Example(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
),
]
return result
EXAMPLE_FORMULAS = get_example_formulae(get_env())
EXAMPLE_FORMULAE = EXAMPLE_FORMULAS