def __init__(self, file, bound=0, period=0, realPeroid=0): ccsl = CCSL(file) tmp = ccsl.workOnCCSL() self.oldClocks = tmp["oldClocks"] self.newClocks = tmp["newClocks"] self.newCCSLConstraintList = tmp["newCCSLConstraintList"] self.oldCCSLConstraintList = tmp["oldCCSLConstraintList"] self.parameter = tmp["parameter"] self.bound = bound self.period = period self.realPeroid = realPeroid self.parameterRange = [] self.solver = z3.SolverFor("AUFLIRA") z3.set_param("smt.random_seed", random.randint(100, 1000000)) self.solver.set(unsat_core=True) # self.solver.set(produce_models=True) # self.solver.set(print_success=False) self.printParameter = {} self.tickStep = {} self.n = z3.Int("n") if self.period > 0: self.k = z3.Int("k") self.l = z3.Int("l") self.p = z3.Int("p") self.tickDict = {} self.historyDict = {} self.Tick_result = {} self.cnt = 0
def addHistory(self): for clock in self.newClocks: history = None tick = self.tickDict["t_%s" % (clock)] if ("h_%s" % (clock)) not in self.historyDict.keys(): history = z3.Function("h_%s" % (clock), z3.IntSort(), z3.IntSort()) self.historyDict["h_%s" % (clock)] = history else: history = self.historyDict["h_%s" % (clock)] # self.solver.add(history(0) == z3.IntVal(0)) self.solver.add(history(1) == z3.IntVal(0)) if self.bound > 0: # If the bound is finite, we define the history of the clock with a fixed bound. for i in range(1, self.bound + 1): self.solver.add( z3.If(tick(i), history(i + 1) == history(i) + 1, history(i + 1) == history(i))) # self.solver.add(z3.If(tick(i), # history(i + 1) == history(i) + 1, # history(i + 1) == history(i))) elif self.bound == 0: x = z3.Int("x") # If the bound is infinite, we define the history of the clock infinitely. self.solver.add( z3.ForAll( x, z3.Implies( x >= 1, z3.If(tick(x), history(x + 1) == history(x) + 1, history(x + 1) == history(x)))))
def verifyExpr(self, expr): self.funcproto.expr = expr counterexample = self.z3checker.check(str(self.funcproto), self.moreconstraint) def testDelete(): if len(self.moreconstraint) == 0: return None self.moreconstraint.pop(-1) counterexample = self.z3checker.check(str(self.funcproto), self.moreconstraint) if counterexample is None: return testDelete() return counterexample if counterexample is None: counterexample = testDelete() if counterexample is None: return None, None # counterexample = self.z3checker.check(str(self.funcproto), randomConstraint) symtab = {} for i in range(len(self.inputlist)): s = self.inputlist[i] if self.inputtylist[i] == 'Int': symtab[s] = int(str(counterexample.eval(z3.Int(s), True))) else: symtab[s] = int(str(counterexample.eval(z3.Bool(s), True))) innersymtab = self.semchecker.getSymtab(symtab) symtab = [symtab] * len(innersymtab) return innersymtab, symtab
def addTickSMT(self): for each in self.newClocks: self.tickDict["t_%s" % (each)] = z3.Function( "t_%s" % (each), z3.IntSort(), z3.BoolSort()) tick = self.tickDict["t_%s" % (each)] if self.bound > 0: y = z3.Int("y") if self.period > 0: for y in range(1, self.bound + 1): self.solver.add( z3.Implies( y >= self.k, tick((y - self.l) % self.p + self.l) == tick(y))) # self.solver.add( # z3.ForAll(y,z3.Implies( # z3.And(y >= self.k,y <= self.bound), # tick((y - self.l) % self.p + self.l) == tick(y)))) elif self.bound == 0: x = z3.Int("x") if self.period > 0: y = z3.Int("y") self.solver.add( z3.ForAll( y, z3.Implies( y >= self.k, tick((y - self.l) % self.p + self.l) == tick(y)))) clockListTmp = [] x = z3.Int("x") for each in self.tickDict.keys(): tick = self.tickDict[each] clockListTmp.append(tick(x)) if self.bound == 0: self.solver.add( z3.ForAll(x, z3.Implies(x >= 1, z3.Or(clockListTmp)))) else: for i in range(1, self.bound + 1): tmp = [] for tick in self.tickDict.values(): tmp.append(tick(i)) self.solver.add(z3.Or(tmp))
def addTickStep(self, clock): tick = self.tickDict["t_%s" % (clock)] history = self.historyDict["h_%s" % (clock)] if "s_%s" % (clock) not in self.tickStep.keys(): tickStep = z3.Function("s_%s" % (clock), z3.IntSort(), z3.IntSort()) self.tickStep["s_%s" % (clock)] = tickStep if self.bound > 0: x = z3.Int("x") # If the bound is infinite, we define the history of the clock infinitely. for i in range(1, self.bound + 1): self.solver.add( z3.Implies(tick(i), tickStep(history(i) + 1) == i)) elif self.bound == 0: x = z3.Int("x") # If the bound is infinite, we define the history of the clock infinitely. self.solver.add( z3.ForAll( x, z3.Implies(z3.And(x >= 1, tick(x)), tickStep(history(x) + 1) == x)))
def addTickForever(self): """ Adding a clock msec, which ticks every step, represents the real-time. :return: """ if "msec" in self.oldClocks: tick = self.tickDict["t_%s" % ("msec")] if self.bound > 0: for i in range(1, self.bound + 1): self.solver.add(tick(i) == True) else: x = z3.Int("x") self.solver.add( z3.ForAll(x, z3.Implies(x >= 1, tick(x) == True)))
def new_from_sort(self, key): if isinstance(key, Bool): key = key.name val = z3.Bool(key) return val elif isinstance(key, Int): key = key.name val = z3.Int(key) return val elif isinstance(key, String): key = key.name val = z3.String(key) return val elif isinstance(key, BitVec): name = key.name size = key.size val = z3.BitVec(name, size) return val raise TypeError("%s not supported!" %type(key))
def translate(expr, xid): substitutions = dict() def raw(s): return '_'.join(s.split('_')[:-1]) for v in get_vars_non_recursive(expr): if v not in substitutions: v_name = raw(v.decl().name()) if v.sort_kind() == z3.Z3_INT_SORT: substitutions[v] = z3.Int('%s_%d' % (v_name, xid)) elif v.sort_kind() == z3.Z3_BOOL_SORT: substitutions[v] = z3.Bool('%s_%d' % (v_name, xid)) elif v.sort_kind() == z3.Z3_BV_SORT: substitutions[v] = z3.BitVec('%s_%d' % (v_name, xid), v.size()) elif v.sort_kind() == z3.Z3_ARRAY_SORT: substitutions[v] = z3.Array('%s_%d' % (v_name, xid), v.domain(), v.range()) else: raise Exception('CANNOT CONVERT %s (%d)' % (v, v.sort_kind())) subst = list(substitutions.items()) return z3.substitute(expr, subst)
def verifyExpr(self, expr): randomConstraint = [['constraint', ['>=', 'x', '5']], ['constraint', ['>=', 'y', '5']], ['constraint', ['>=', 'z', '5']], ['constraint', ['>=', 'w', '5']], ['constraint', ['true']]] self.funcproto.expr = expr counterexample = self.z3checker.check(str(self.funcproto), []) if counterexample is None: return None, None # counterexample = self.z3checker.check(str(self.funcproto), randomConstraint) symtab = {} for i in range(len(self.inputlist)): s = self.inputlist[i] if self.inputtylist[i] == 'Int': symtab[s] = int(str(counterexample.eval(z3.Int(s), True))) else: symtab[s] = int(str(counterexample.eval(z3.Bool(s), True))) innersymtab = self.semchecker.getSymtab(symtab) symtab = [symtab] * len(innersymtab) return innersymtab, symtab
def op(self, instruction: Instruction, stack: Stack, immutable_storage_references: List[ImmutableStorageTracker]): # cases that the timestamp is used in conditional jump if instruction.opcode == "JUMPI": # 检查是否是时间戳与一个固定值进行比较 if utils.is_symbol(stack[-2]): for z3_ref in utils.extract_z3_ref(stack[-2]): if utils.is_z3_constant(z3_ref): # 是一个z3表达式中的常量 continue elif z3.eq(z3_ref, z3.Int("IHs")): # 是时间戳 continue else: for ref in immutable_storage_references: if ref.contains( len(stack) - 2) and utils.is_symbol( ref.storage_value) and utils.in_list( utils.extract_z3_ref( ref.storage_value), z3_ref): break else: # 不是一个不可变Storage变量 break # 是某一个不可变Storage变量 continue else: # 参与比较的所有变量都是常量(除了时间戳本身) self.pop(instruction.input_amount, len(stack)) return not_used_before = not self.used self.use(instruction, len(stack)) if not_used_before and self.used: self.dependency_addr = instruction.addr else: self.pop(instruction.input_amount, len(stack))
def generate_assignments(thresh=2): solver = z3.Solver() # declare the SMT variables for the specific code block_1 = {'b1_1': 'move'} block_1_obj = SMT_Block(block_1, thresh) values = block_1_obj.block_values block_1_vars = [ele.var for ele in block_1_obj.block_z3_vars ] # for the conditional constraints c1 = z3.Int('c1') # 4 (repeat) values.append(z3.Or(c1 == 3, c1 == 4, c1 == 5), ) block_2 = {'b2_1': 'turn_left'} block_2_obj = SMT_Block(block_2, thresh) values.extend(block_2_obj.block_values) block_2_vars = [ele.var for ele in block_2_obj.block_z3_vars ] # for the conditional constraints c2 = z3.Int('c2') # 5 (repeat) values.append(z3.Or(c2 == 4, c2 == 5, c2 == 6), ) block_3 = {'b3_1': 'move'} block_3_obj = SMT_Block(block_3, thresh) values.extend(block_3_obj.block_values) block_3_vars = [ele.var for ele in block_3_obj.block_z3_vars ] # for the conditional constraints # add another block in the beginning of the code block_4 = {'b4_1': 'phi'} block_4_obj = SMT_Block(block_4, thresh) values.extend(block_4_obj.block_values) block_4_vars = [ele.var for ele in block_4_obj.block_z3_vars] # add another block in the end of the code block_5 = {'b5_1': 'phi'} block_5_obj = SMT_Block(block_5, thresh) values.extend(block_5_obj.block_values) block_5_vars = [ele.var for ele in block_5_obj.block_z3_vars] # all block objects block_objs = [ block_1_obj, block_2_obj, block_3_obj, block_4_obj, block_5_obj ] X = [ele.var for ele in block_1_obj.block_z3_vars ] # added the variables for block 1 X.append(c1) # added the conditional variable X.extend([ele.var for ele in block_2_obj.block_z3_vars ]) # added the variables for block 2 X.append(c2) # added the conditional variable X.extend([ele.var for ele in block_3_obj.block_z3_vars ]) # added the variables for block 3 X.extend([ele.var for ele in block_4_obj.block_z3_vars ]) # added the variables for block 4 X.extend([ele.var for ele in block_5_obj.block_z3_vars ]) # added the variables for block 5 constraints = block_1_obj.block_append_constraints + block_1_obj.flip_turns_constraints + block_1_obj.block_elimination_constraints + \ block_2_obj.block_append_constraints + block_2_obj.flip_turns_constraints + block_2_obj.block_elimination_constraints + \ block_3_obj.block_append_constraints + block_3_obj.flip_turns_constraints + block_3_obj.block_elimination_constraints + \ block_4_obj.block_append_constraints + block_4_obj.flip_turns_constraints + block_4_obj.block_elimination_constraints + \ block_5_obj.block_append_constraints + block_5_obj.flip_turns_constraints + block_5_obj.block_elimination_constraints single_block_change_cons = single_block_change(block_objs) constraints.extend(single_block_change_cons) # add the values and the constraints solver.add(values + constraints) # generate all the assignments models = gen_all(solver, X) assignments = [] for model in models: a = [str(model[c1].as_long())] a.extend([ type_to_str[VariableType(model[ele].as_long())] for ele in block_1_vars ]) a.extend([ type_to_str[VariableType(model[ele].as_long())] for ele in block_2_vars ]) a.append(str(model[c2].as_long())) a.extend([ type_to_str[VariableType(model[ele].as_long())] for ele in block_3_vars ]) a.extend([ type_to_str[VariableType(model[ele].as_long())] for ele in block_4_vars ]) a.extend([ type_to_str[VariableType(model[ele].as_long())] for ele in block_5_vars ]) assignments.append(a) #print(a) #print('Found #{} SAT values'.format(len(models))) return assignments
def generate_assignments(thresh=2): solver = z3.Solver() # declare the SMT variables for the specific code block_1 = {'b1_1': 'turn_right'} block_1_obj = SMT_Block(block_1, thresh) values = block_1_obj.block_values c1 = z3.Int('c1') # 5 (repeat) values.append(z3.Or(c1 == 4, c1 == 5, c1 == 6), ) block_2 = {'b2_1': 'move'} block_2_obj = SMT_Block(block_2, thresh) values.extend(block_2_obj.block_values) # additional empty block added in the end of the code block_3 = {'b3_1': 'phi'} block_3_obj = SMT_Block(block_3, thresh) values.extend(block_3_obj.block_values) # all block objects block_objs = [block_1_obj, block_2_obj, block_3_obj] X = [ele.var for ele in block_1_obj.block_z3_vars ] # added the variables for block 1 X.append(c1) # added the conditional variable X.extend([ele.var for ele in block_2_obj.block_z3_vars ]) # added the variables for block 2 block_3_vars = [ele.var for ele in block_3_obj.block_z3_vars] X.extend(block_3_vars) # added the variables for block 3 constraints = block_1_obj.block_append_constraints + block_1_obj.flip_turns_constraints + block_1_obj.block_elimination_constraints \ + block_2_obj.block_append_constraints + block_2_obj.flip_turns_constraints + block_2_obj.block_elimination_constraints \ + block_3_obj.block_append_constraints + block_3_obj.flip_turns_constraints + block_3_obj.block_elimination_constraints single_block_change_cons = single_block_change(block_objs) constraints.extend(single_block_change_cons) # add the values and the constraints solver.add(values + constraints) # generate all the assignments models = gen_all(solver, X) assignments = [] for model in models: a = [ type_to_str[VariableType(model[ele].as_long())] for ele in X[:block_1_obj.size] ] a.append(str(model[c1].as_long())) b = [ type_to_str[VariableType(model[ele].as_long())] for ele in X[block_2_obj.size + 1:] ] a.extend(b) c = [ type_to_str[VariableType(model[ele].as_long())] for ele in block_3_vars ] a.extend(c) assignments.append(a) #print(a) #print('Found #{} SAT values'.format(len(models))) return assignments
def generate_assignments(thresh=2): solver = z3.Solver() # Block 1 block_1 = {'b1_1': 'move'} block_1_obj = SMT_Block(block_1, thresh) values = block_1_obj.block_values block_1_vars = [ele.var for ele in block_1_obj.block_z3_vars ] # for the conditional constraints c1 = z3.Int('c1') # bool_path_left (if_only) values.append(z3.Or(c1 == 8, c1 == 9)) block_2 = {'b2_1': 'turn_left'} block_2_obj = SMT_Block(block_2, thresh) values.extend(block_2_obj.block_values) block_2_vars = [ele.var for ele in block_2_obj.block_z3_vars ] # for the conditional constraints block_3 = {'b3_1': 'phi'} block_3_obj = SMT_Block(block_3, thresh) values.extend(block_3_obj.block_values) block_3_vars = [ele.var for ele in block_3_obj.block_z3_vars ] # for the conditional constraints # all block objects block_objs = [block_1_obj, block_2_obj, block_3_obj] X = [ele.var for ele in block_1_obj.block_z3_vars ] # added the variables for block 1 X.append(c1) # added the conditional variable X.extend([ele.var for ele in block_2_obj.block_z3_vars ]) # added the variables for block 2 X.extend([ele.var for ele in block_3_obj.block_z3_vars ]) # added the variables for block 3 constraints = block_1_obj.block_append_constraints + block_1_obj.flip_turns_constraints + block_1_obj.block_elimination_constraints + \ block_2_obj.block_append_constraints + block_2_obj.flip_turns_constraints + block_2_obj.block_elimination_constraints + \ block_3_obj.block_append_constraints + block_3_obj.flip_turns_constraints + block_3_obj.block_elimination_constraints single_block_change_cons = single_block_change(block_objs) constraints.extend(single_block_change_cons) constraints.extend([ # conditional constraints: if(path_left) z3.Implies(c1 == 8, z3.Or(block_2_vars[0] == 2, block_2_vars[1] == 2, block_2_vars[2] == 2, block_2_vars[3] == 2, block_2_vars[4] == 2, )), z3.Implies(z3.And(c1 == 8, block_2_vars[1] == 2, block_2_vars[0] != 2), z3.And(block_2_vars[0] != 1, block_2_vars[0] != 3 )), z3.Implies(z3.And(c1 == 8, block_2_vars[2] == 2, block_2_vars[0] != 2, block_2_vars[1] != 2), z3.And(block_2_vars[0] != 1, block_2_vars[0] != 3, block_2_vars[1] != 1, block_2_vars[1] != 3)), z3.Implies(z3.And(c1 == 8, block_2_vars[3] == 2, block_2_vars[0] != 2, block_2_vars[1] != 2, block_2_vars[2] != 2), z3.And(block_2_vars[0] != 1, block_2_vars[0] != 3, block_2_vars[1] != 1, \ block_2_vars[1] != 3, block_2_vars[2] != 1, block_2_vars[2] != 3)), z3.Implies(z3.And(c1 == 8, block_2_vars[4] == 2, block_2_vars[0] != 2, block_2_vars[1] != 2, block_2_vars[2] != 2, block_2_vars[3] != 2), z3.And(block_2_vars[0] != 1, block_2_vars[0] != 3, block_2_vars[1] != 1, block_2_vars[1] != 3, block_2_vars[2] != 1, block_2_vars[2] != 3, block_2_vars[3] != 1, block_2_vars[3] != 3)), # conditional constraints: if(path_right) z3.Implies(c1 == 9, z3.Or(block_2_vars[0] == 3, block_2_vars[1] == 3, block_2_vars[2] == 3, block_2_vars[3] == 3, block_2_vars[4] == 3, )), z3.Implies(z3.And(c1 == 9, block_2_vars[1] == 3, block_2_vars[0] != 3, ), z3.And(block_2_vars[0] != 1, block_2_vars[0] != 2)), z3.Implies(z3.And(c1 == 9, block_2_vars[2] == 3, block_2_vars[0] != 3, block_2_vars[1] != 3), z3.And(block_2_vars[0]!= 1, block_2_vars[0] != 2, block_2_vars[1] != 1, block_2_vars[1] != 2)), z3.Implies(z3.And(c1 == 9, block_2_vars[3] == 3, block_2_vars[0] != 3, block_2_vars[1] != 3, block_2_vars[2] != 3), z3.And(block_2_vars[0] != 1, block_2_vars[0] != 2, block_2_vars[1] != 1, block_2_vars[1] != 2, block_2_vars[2] != 1, block_2_vars[2] != 2)), z3.Implies(z3.And(c1 == 9, block_2_vars[4] == 3, block_2_vars[0] != 3, block_2_vars[1] != 3, block_2_vars[2] != 3, block_2_vars[3] != 3 ), z3.And(block_2_vars[0] != 1, block_2_vars[0] != 2, block_2_vars[1] != 1, block_2_vars[1] != 2, block_2_vars[2] != 1, block_2_vars[2] != 2, block_2_vars[3] != 1, block_2_vars[3] != 2)), ]) # add the values and the constraints solver.add(values + constraints) # generate all the assignments models = gen_all(solver, X) assignments = [] for model in models: a = ['repeat_until_goal(bool_goal)'] a.extend([ type_to_str[VariableType(model[ele].as_long())] for ele in X[:block_1_obj.size] ]) a.append(type_to_str[ConditionalType(model[c1].as_long())]) a.extend([ type_to_str[VariableType(model[ele].as_long())] for ele in X[block_1_obj.size + 1:] ]) a.extend([ type_to_str[VariableType(model[ele].as_long())] for ele in block_3_vars ]) assignments.append(a) #print(a) #print('Found #{} SAT values'.format(len(models))) return assignments
def exe_with_path_condition(self, instruction: Instruction, path_condition: list = []) -> PcPointer: self._update_all_ref_tracker(instruction) if instruction.opcode == "SSTORE": # save the value of every referred storage variable before SSTORE bak = {} for ref in self.reentrancy_references: bak[ref] = self._storage[ref.storage_addr] if instruction.opcode == "SSTORE" and self.pre_process: op0 = self._stack[-1] # 在可信条件下进行修改的Storage变量仍然是可信的(immutable) caller = z3.Int("Is") solver = z3.Solver() solver.add(path_condition) if "sat" == str(solver.check()): for storage_addr, storage_value in self._storage.get_storage( ).items(): if not utils.in_list(self.mutable_storage_addresses, storage_addr): # solver.add(caller & 0xffffffffffffffffffff != storage_value & 0xffffffffffffffffffff) mask = 0x000000000000000000000000ffffffffffffffffffffffffffffffffffffffff if utils.is_symbol(storage_value): # solver.add(z3.Int(str("Is") + "&" + str(mask)) != z3.Int(str(storage_value) + "&" + str(mask))) # solver.add(z3.Int(str(mask) + "&" + str("Is")) != z3.Int(str(storage_value) + "&" + str(mask))) # solver.add(z3.Int(str("Is") + "&" + str(mask)) != z3.Int(str(mask) + "&" + str(storage_value))) # solver.add(z3.Int(str(mask) + "&" + str("Is")) != z3.Int(str(mask) + "&" + str(storage_value))) # solver.add(z3.Int(str("Is")) != z3.Int(str(storage_value))) solver.add( z3.Int(str("Is")) != z3.Int(str(storage_value)) ) else: # solver.add(z3.Int(str("Is") + "&" + str(mask)) != storage_value & mask) # solver.add(z3.Int(str(mask) + "&" + str("Is")) != storage_value & mask) solver.add( z3.Int(str("Is")) != storage_value & mask) if "sat" == str(solver.check()): # caller不为任意一个可信storage变量的时候仍然可能进行SSTORE,则说明被修改的storage变量是不可靠的 if not utils.in_list(self.mutable_storage_addresses, op0): self.mutable_storage_addresses.append(op0) pc_pointer = super().exe(instruction) if instruction.opcode == "SSTORE": # check if any referred storage variable is changed after SSTORE # if len(bak) != len(self._storage): # # 如果新增了Storage变量,那么一定是做修改了 # ref.storage_changed = True # if ref.after_used_in_condition: # ref.changed_after_condition = True # if not ref.after_call: # ref.changed_before_call = True # else: # 如果Storage变量的个数没变,那么就检查每一个变量的值有没有改变 for ref, value in bak.items(): if utils.is_symbol(value) is not utils.is_symbol(self._storage[ref.storage_addr]) or \ utils.is_symbol(value) and not eq(simplify(value), simplify(self._storage[ref.storage_addr])) or \ not utils.is_symbol(value) and value != self._storage[ref.storage_addr]: ref.storage_changed = True if ref.after_used_in_condition: ref.changed_after_condition = True if not ref.after_call: ref.changed_before_call = True return pc_pointer
def generate_assignments(thresh=2, id='karel'): solver = z3.Solver() # declare the SMT variables for the specific code # Block 1 block_1 = {'b1_1': 'put_marker'} block_1_obj = SMT_Block(block_1, thresh, id=id) values = block_1_obj.block_values block_1_vars = [ele.var for ele in block_1_obj.block_z3_vars ] # for the conditional constraints c1 = z3.Int('c1') # bool_path_ahead (while) values.append(z3.Or(c1 == 7, c1 == 12)) # bool_path_ahead, bool_no_path_ahead block_2 = { 'b2_1': 'move', 'b2_2': 'turn_left', 'b2_3': 'move', 'b2_4': 'turn_right', 'b2_5': 'put_marker' } block_2_obj = SMT_Block(block_2, thresh, id=id) values.extend(block_2_obj.block_values) block_2_vars = [ele.var for ele in block_2_obj.block_z3_vars ] # for the conditional constraints block_3 = {'b3_1': 'phi'} block_3_obj = SMT_Block(block_3, thresh, id=id) values.extend(block_3_obj.block_values) block_3_vars = [ele.var for ele in block_3_obj.block_z3_vars ] # for the conditional constraints # all block objects block_objs = [block_1_obj, block_2_obj, block_3_obj] X = [c1] X.extend([ele.var for ele in block_1_obj.block_z3_vars ]) # added the variables for block 1 X.extend([ele.var for ele in block_2_obj.block_z3_vars ]) # added the variables for block 2 X.extend([ele.var for ele in block_3_obj.block_z3_vars ]) # added the variables for block 3 constraints = block_1_obj.block_append_constraints + block_1_obj.flip_turns_constraints + block_1_obj.flip_marker_constraints+ \ block_1_obj.block_elimination_constraints + \ block_2_obj.block_append_constraints + block_2_obj.flip_turns_constraints + \ block_2_obj.flip_marker_constraints + block_2_obj.block_elimination_constraints +\ block_3_obj.block_append_constraints + block_3_obj.flip_turns_constraints + \ block_3_obj.flip_marker_constraints + block_3_obj.block_elimination_constraints single_block_change_cons = single_block_change(block_objs) constraints.extend(single_block_change_cons) constraints.extend([ # conditional constraints: while(bool_path_ahead)---while block constraints z3.Implies( c1 == 7, z3.Or( block_2_vars[0] == 1, block_2_vars[1] == 1, block_2_vars[2] == 1, block_2_vars[3] == 1, block_2_vars[4] == 1, block_2_vars[5] == 1, block_2_vars[6] == 1, block_2_vars[7] == 1, block_2_vars[8] == 1, block_2_vars[9] == 1, block_2_vars[10] == 1, block_2_vars[11] == 1, block_2_vars[12] == 1, )), z3.Implies(z3.And(c1 == 7, block_2_vars[1] == 1, block_2_vars[0] != 1), z3.And(block_2_vars[0] != 2, block_2_vars[0] != 3)), z3.Implies( z3.And(c1 == 7, block_2_vars[2] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1), z3.And(block_2_vars[0] != 2, block_2_vars[0] != 3, block_2_vars[1] != 2, block_2_vars[1] != 3)), z3.Implies( z3.And(c1 == 7, block_2_vars[3] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1), z3.And(block_2_vars[0] != 2, block_2_vars[0] != 3, block_2_vars[1] != 2, block_2_vars[1] != 3, block_2_vars[2] != 2, block_2_vars[2] != 3)), z3.Implies( z3.And(c1 == 7, block_2_vars[4] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1, block_2_vars[3] != 1), z3.And(block_2_vars[0] != 2, block_2_vars[0] != 3, block_2_vars[1] != 2, block_2_vars[1] != 3, block_2_vars[2] != 2, block_2_vars[2] != 3, block_2_vars[3] != 2, block_2_vars[3] != 3)), z3.Implies( z3.And(c1 == 7, block_2_vars[5] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1, block_2_vars[3] != 1, block_2_vars[4] != 1), z3.And(block_2_vars[0] != 2, block_2_vars[0] != 3, block_2_vars[1] != 2, block_2_vars[1] != 3, block_2_vars[2] != 2, block_2_vars[2] != 3, block_2_vars[3] != 2, block_2_vars[3] != 3, block_2_vars[4] != 2, block_2_vars[4] != 3)), z3.Implies( z3.And(c1 == 7, block_2_vars[6] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1, block_2_vars[3] != 1, block_2_vars[4] != 1, block_2_vars[5] != 1), z3.And(block_2_vars[0] != 2, block_2_vars[0] != 3, block_2_vars[1] != 2, block_2_vars[1] != 3, block_2_vars[2] != 2, block_2_vars[2] != 3, block_2_vars[3] != 2, block_2_vars[3] != 3, block_2_vars[4] != 2, block_2_vars[4] != 3, block_2_vars[5] != 2, block_2_vars[5] != 3)), z3.Implies( z3.And(c1 == 7, block_2_vars[7] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1, block_2_vars[3] != 1, block_2_vars[4] != 1, block_2_vars[5] != 1, block_2_vars[6] != 1), z3.And(block_2_vars[0] != 2, block_2_vars[0] != 3, block_2_vars[1] != 2, block_2_vars[1] != 3, block_2_vars[2] != 2, block_2_vars[2] != 3, block_2_vars[3] != 2, block_2_vars[3] != 3, block_2_vars[4] != 2, block_2_vars[4] != 3, block_2_vars[5] != 2, block_2_vars[5] != 3, block_2_vars[6] != 2, block_2_vars[6] != 3)), z3.Implies( z3.And(c1 == 7, block_2_vars[8] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1, block_2_vars[3] != 1, block_2_vars[4] != 1, block_2_vars[5] != 1, block_2_vars[6] != 1, block_2_vars[7] != 1), z3.And(block_2_vars[0] != 2, block_2_vars[0] != 3, block_2_vars[1] != 2, block_2_vars[1] != 3, block_2_vars[2] != 2, block_2_vars[2] != 3, block_2_vars[3] != 2, block_2_vars[3] != 3, block_2_vars[4] != 2, block_2_vars[4] != 3, block_2_vars[5] != 2, block_2_vars[5] != 3, block_2_vars[6] != 2, block_2_vars[6] != 3, block_2_vars[7] != 2, block_2_vars[7] != 3)), z3.Implies( z3.And(c1 == 7, block_2_vars[9] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1, block_2_vars[3] != 1, block_2_vars[4] != 1, block_2_vars[5] != 1, block_2_vars[6] != 1, block_2_vars[7] != 1, block_2_vars[8] != 1), z3.And(block_2_vars[0] != 2, block_2_vars[0] != 3, block_2_vars[1] != 2, block_2_vars[1] != 3, block_2_vars[2] != 2, block_2_vars[2] != 3, block_2_vars[3] != 2, block_2_vars[3] != 3, block_2_vars[4] != 2, block_2_vars[4] != 3, block_2_vars[5] != 2, block_2_vars[5] != 3, block_2_vars[6] != 2, block_2_vars[6] != 3, block_2_vars[7] != 2, block_2_vars[7] != 3, block_2_vars[8] != 2, block_2_vars[8] != 3)), z3.Implies( z3.And(c1 == 7, block_2_vars[10] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1, block_2_vars[3] != 1, block_2_vars[4] != 1, block_2_vars[5] != 1, block_2_vars[6] != 1, block_2_vars[7] != 1, block_2_vars[8] != 1, block_2_vars[9] != 1), z3.And(block_2_vars[0] != 2, block_2_vars[0] != 3, block_2_vars[1] != 2, block_2_vars[1] != 3, block_2_vars[2] != 2, block_2_vars[2] != 3, block_2_vars[3] != 2, block_2_vars[3] != 3, block_2_vars[4] != 2, block_2_vars[4] != 3, block_2_vars[5] != 2, block_2_vars[5] != 3, block_2_vars[6] != 2, block_2_vars[6] != 3, block_2_vars[7] != 2, block_2_vars[7] != 3, block_2_vars[8] != 2, block_2_vars[8] != 3, block_2_vars[9] != 2, block_2_vars[9] != 3)), # # ################################################ THRESH = 2 z3.Implies( z3.And(c1 == 7, block_2_vars[11] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1, block_2_vars[3] != 1, block_2_vars[4] != 1, block_2_vars[5] != 1, block_2_vars[6] != 1, block_2_vars[7] != 1, block_2_vars[8] != 1, block_2_vars[9] != 1, block_2_vars[10] != 1), z3.And(block_2_vars[0] != 2, block_2_vars[0] != 3, block_2_vars[1] != 2, block_2_vars[1] != 3, block_2_vars[2] != 2, block_2_vars[2] != 3, block_2_vars[3] != 2, block_2_vars[3] != 3, block_2_vars[4] != 2, block_2_vars[4] != 3, block_2_vars[5] != 2, block_2_vars[5] != 3, block_2_vars[6] != 2, block_2_vars[6] != 3, block_2_vars[7] != 2, block_2_vars[7] != 3, block_2_vars[8] != 2, block_2_vars[8] != 3, block_2_vars[9] != 2, block_2_vars[9] != 3, block_2_vars[10] != 2, block_2_vars[10] != 3)), z3.Implies( z3.And(c1 == 7, block_2_vars[12] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1, block_2_vars[3] != 1, block_2_vars[4] != 1, block_2_vars[5] != 1, block_2_vars[6] != 1, block_2_vars[7] != 1, block_2_vars[8] != 1, block_2_vars[9] != 1, block_2_vars[10] != 1, block_2_vars[11] != 1), z3.And(block_2_vars[0] != 2, block_2_vars[0] != 3, block_2_vars[1] != 2, block_2_vars[1] != 3, block_2_vars[2] != 2, block_2_vars[2] != 3, block_2_vars[3] != 2, block_2_vars[3] != 3, block_2_vars[4] != 2, block_2_vars[4] != 3, block_2_vars[5] != 2, block_2_vars[5] != 3, block_2_vars[6] != 2, block_2_vars[6] != 3, block_2_vars[7] != 2, block_2_vars[7] != 3, block_2_vars[8] != 2, block_2_vars[8] != 3, block_2_vars[9] != 2, block_2_vars[9] != 3, block_2_vars[10] != 2, block_2_vars[10] != 3, block_2_vars[11] != 2, block_2_vars[11] != 3)), # # conditional constraints: while(bool_no_path_ahead)---while block constraints z3.Implies(c1 == 12, block_2_vars[0] != 1), z3.Implies( z3.And(c1 == 12, block_2_vars[1] == 1, block_2_vars[0] != 1), z3.Or(block_2_vars[0] == 2, block_2_vars[0] == 3)), z3.Implies( z3.And(c1 == 12, block_2_vars[2] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1), z3.Or(block_2_vars[0] == 2, block_2_vars[0] == 3, block_2_vars[1] == 2, block_2_vars[1] == 3)), z3.Implies( z3.And(c1 == 12, block_2_vars[3] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1), z3.Or(block_2_vars[0] == 2, block_2_vars[0] == 3, block_2_vars[1] == 2, block_2_vars[1] == 3, block_2_vars[2] == 2, block_2_vars[2] == 3)), z3.Implies( z3.And(c1 == 12, block_2_vars[4] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1, block_2_vars[3] != 1), z3.Or(block_2_vars[0] == 2, block_2_vars[0] == 3, block_2_vars[1] == 2, block_2_vars[1] == 3, block_2_vars[2] == 2, block_2_vars[2] == 3, block_2_vars[3] == 2, block_2_vars[3] == 3)), z3.Implies( z3.And(c1 == 12, block_2_vars[5] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1, block_2_vars[3] != 1, block_2_vars[4] != 1), z3.Or(block_2_vars[0] == 2, block_2_vars[0] == 3, block_2_vars[1] == 2, block_2_vars[1] == 3, block_2_vars[2] == 2, block_2_vars[2] == 3, block_2_vars[3] == 2, block_2_vars[3] == 3, block_2_vars[4] == 2, block_2_vars[4] == 3)), z3.Implies( z3.And(c1 == 12, block_2_vars[6] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1, block_2_vars[3] != 1, block_2_vars[4] != 1, block_2_vars[5] != 1), z3.Or(block_2_vars[0] == 2, block_2_vars[0] == 3, block_2_vars[1] == 2, block_2_vars[1] == 3, block_2_vars[2] == 2, block_2_vars[2] == 3, block_2_vars[3] == 2, block_2_vars[3] == 3, block_2_vars[4] == 2, block_2_vars[4] == 3, block_2_vars[5] == 2, block_2_vars[5] == 3)), z3.Implies( z3.And(c1 == 12, block_2_vars[7] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1, block_2_vars[3] != 1, block_2_vars[4] != 1, block_2_vars[5] != 1, block_2_vars[6] != 1), z3.Or(block_2_vars[0] == 2, block_2_vars[0] == 3, block_2_vars[1] == 2, block_2_vars[1] == 3, block_2_vars[2] == 2, block_2_vars[2] == 3, block_2_vars[3] == 2, block_2_vars[3] == 3, block_2_vars[4] == 2, block_2_vars[4] == 3, block_2_vars[5] == 2, block_2_vars[5] == 3, block_2_vars[6] == 2, block_2_vars[6] == 3)), z3.Implies( z3.And(c1 == 12, block_2_vars[8] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1, block_2_vars[3] != 1, block_2_vars[4] != 1, block_2_vars[5] != 1, block_2_vars[6] != 1, block_2_vars[7] != 1), z3.Or(block_2_vars[0] == 2, block_2_vars[0] == 3, block_2_vars[1] == 2, block_2_vars[1] == 3, block_2_vars[2] == 2, block_2_vars[2] == 3, block_2_vars[3] == 2, block_2_vars[3] == 3, block_2_vars[4] == 2, block_2_vars[4] == 3, block_2_vars[5] == 2, block_2_vars[5] == 3, block_2_vars[6] == 2, block_2_vars[6] == 3, block_2_vars[7] == 2, block_2_vars[7] == 3)), z3.Implies( z3.And(c1 == 12, block_2_vars[9] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1, block_2_vars[3] != 1, block_2_vars[4] != 1, block_2_vars[5] != 1, block_2_vars[6] != 1, block_2_vars[7] != 1, block_2_vars[8] != 1), z3.Or(block_2_vars[0] == 2, block_2_vars[0] == 3, block_2_vars[1] == 2, block_2_vars[1] == 3, block_2_vars[2] == 2, block_2_vars[2] == 3, block_2_vars[3] == 2, block_2_vars[3] == 3, block_2_vars[4] == 2, block_2_vars[4] == 3, block_2_vars[5] == 2, block_2_vars[5] == 3, block_2_vars[6] == 2, block_2_vars[6] == 3, block_2_vars[7] == 2, block_2_vars[7] == 3, block_2_vars[8] == 2, block_2_vars[8] == 3)), z3.Implies( z3.And( c1 == 12, block_2_vars[10] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1, block_2_vars[3] != 1, block_2_vars[4] != 1, block_2_vars[5] != 1, block_2_vars[6] != 1, block_2_vars[7] != 1, block_2_vars[8] != 1, block_2_vars[9] != 1, ), z3.Or( block_2_vars[0] == 2, block_2_vars[0] == 3, block_2_vars[1] == 2, block_2_vars[1] == 3, block_2_vars[2] == 2, block_2_vars[2] == 3, block_2_vars[3] == 2, block_2_vars[3] == 3, block_2_vars[4] == 2, block_2_vars[4] == 3, block_2_vars[5] == 2, block_2_vars[5] == 3, block_2_vars[6] == 2, block_2_vars[6] == 3, block_2_vars[7] == 2, block_2_vars[7] == 3, block_2_vars[8] == 2, block_2_vars[8] == 3, block_2_vars[9] == 2, block_2_vars[9] == 3, )), z3.Implies( z3.And(c1 == 12, block_2_vars[11] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1, block_2_vars[3] != 1, block_2_vars[4] != 1, block_2_vars[5] != 1, block_2_vars[6] != 1, block_2_vars[7] != 1, block_2_vars[8] != 1, block_2_vars[9] != 1, block_2_vars[10] != 1), z3.Or( block_2_vars[0] == 2, block_2_vars[0] == 3, block_2_vars[1] == 2, block_2_vars[1] == 3, block_2_vars[2] == 2, block_2_vars[2] == 3, block_2_vars[3] == 2, block_2_vars[3] == 3, block_2_vars[4] == 2, block_2_vars[4] == 3, block_2_vars[5] == 2, block_2_vars[5] == 3, block_2_vars[6] == 2, block_2_vars[6] == 3, block_2_vars[7] == 2, block_2_vars[7] == 3, block_2_vars[8] == 2, block_2_vars[8] == 3, block_2_vars[9] == 2, block_2_vars[9] == 3, block_2_vars[10] == 2, block_2_vars[10] == 3, )), z3.Implies( z3.And(c1 == 12, block_2_vars[12] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1, block_2_vars[3] != 1, block_2_vars[4] != 1, block_2_vars[5] != 1, block_2_vars[6] != 1, block_2_vars[7] != 1, block_2_vars[8] != 1, block_2_vars[9] != 1, block_2_vars[10] != 1, block_2_vars[11] != 1), z3.Or( block_2_vars[0] == 2, block_2_vars[0] == 3, block_2_vars[1] == 2, block_2_vars[1] == 3, block_2_vars[2] == 2, block_2_vars[2] == 3, block_2_vars[3] == 2, block_2_vars[3] == 3, block_2_vars[4] == 2, block_2_vars[4] == 3, block_2_vars[5] == 2, block_2_vars[5] == 3, block_2_vars[6] == 2, block_2_vars[6] == 3, block_2_vars[7] == 2, block_2_vars[7] == 3, block_2_vars[8] == 2, block_2_vars[8] == 3, block_2_vars[9] == 2, block_2_vars[9] == 3, block_2_vars[10] == 2, block_2_vars[10] == 3, block_2_vars[11] == 2, block_2_vars[11] == 3, )), ]) # add the values and the constraints solver.add(values + constraints) # generate all the assignments models = gen_all(solver, X) assignments = [] for model in models: a = [ type_to_str[VariableType(model[ele].as_long())] for ele in block_1_vars ] a.append(type_to_str[ConditionalType(model[c1].as_long())]) a.extend([ type_to_str[VariableType(model[ele].as_long())] for ele in block_2_vars ]) a.extend([ type_to_str[VariableType(model[ele].as_long())] for ele in block_3_vars ]) assignments.append(a) #print(a) #print('Found #{} SAT values'.format(len(models))) return assignments
def generate_assignments(thresh = 2, id = 'karel'): # create the initial z3 solver solver = z3.Solver() # declare a block block_1 = {'b1_1': 'put_marker', 'b1_2': 'move', 'b1_3': 'turn_left'} block_1_obj = SMT_Block(block_1, thresh, id =id ) values = block_1_obj.block_values c1 = z3.Int('c1') # 4 (repeat) values.append( z3.Or(c1 == 3, c1 == 4, c1 == 5), ) # declare a block block_2 = {'b2_1': 'phi'} block_2_obj = SMT_Block(block_2, thresh, id=id) values.extend(block_2_obj.block_values) # declare a block block_3 = {'b3_1': 'phi'} block_3_obj = SMT_Block(block_3, thresh, id=id) values.extend(block_3_obj.block_values) block_objs = [block_1_obj, block_2_obj, block_3_obj] # declare the values that each of the variables can take X = [ele.var for ele in block_1_obj.block_z3_vars] X.append(c1) X.extend([ele.var for ele in block_2_obj.block_z3_vars]) X.extend([ele.var for ele in block_3_obj.block_z3_vars]) constraints = block_1_obj.block_append_constraints + block_1_obj.flip_turns_constraints + \ block_1_obj.flip_marker_constraints + block_1_obj.block_elimination_constraints + \ block_2_obj.block_append_constraints + block_2_obj.flip_turns_constraints + \ block_2_obj.flip_marker_constraints + block_2_obj.block_elimination_constraints + \ block_3_obj.block_append_constraints + block_3_obj.flip_turns_constraints + \ block_3_obj.flip_marker_constraints + block_3_obj.block_elimination_constraints single_block_change_cons = single_block_change(block_objs) constraints.extend(single_block_change_cons) # add the values and the constraints solver.add(values + constraints) # generate all the assignments models = gen_all(solver, X) assignments = [] for model in models: a = [str(model[c1].as_long())] a.extend([type_to_str[VariableType(model[ele.var].as_long())] for ele in block_1_obj.block_z3_vars ]) a.extend([type_to_str[VariableType(model[ele.var].as_long())] for ele in block_2_obj.block_z3_vars ]) a.extend([type_to_str[VariableType(model[ele.var].as_long())] for ele in block_3_obj.block_z3_vars ]) assignments.append(a) #print(a) #print('Found #{} SAT values'.format(len(models))) return assignments
def generate_assignments(thresh=2): solver = z3.Solver() # declare the SMT variables for the specific code # Block 1 block_1 = {'b1_1': 'move'} block_1_obj = SMT_Block(block_1, thresh) values = block_1_obj.block_values block_1_vars = [ele.var for ele in block_1_obj.block_z3_vars ] # for the conditional constraints c1 = z3.Int('c1') # bool_path_ahead (if_else) block_2 = {'b2_1': 'turn_left'} block_2_obj = SMT_Block(block_2, thresh) values.extend(block_2_obj.block_values) block_2_vars = [ele.var for ele in block_2_obj.block_z3_vars ] # for the conditional constraints values.append(c1 == 7) # same conditional value block_3 = {'b3_1': 'phi'} block_3_obj = SMT_Block(block_3, thresh) values.extend(block_3_obj.block_values) block_3_vars = [ele.var for ele in block_3_obj.block_z3_vars ] # for the conditional constraints # all block objects block_objs = [block_1_obj, block_2_obj, block_3_obj] X = [c1] X.extend([ele.var for ele in block_1_obj.block_z3_vars ]) # added the variables for block 1 X.extend([ele.var for ele in block_2_obj.block_z3_vars ]) # added the variables for block 2 X.extend([ele.var for ele in block_3_obj.block_z3_vars ]) # added the variables for block 2 constraints = block_1_obj.block_append_constraints + block_1_obj.flip_turns_constraints + block_1_obj.block_elimination_constraints + \ block_2_obj.block_append_constraints + block_2_obj.flip_turns_constraints + block_2_obj.block_elimination_constraints + \ block_3_obj.block_append_constraints + block_3_obj.flip_turns_constraints + block_3_obj.block_elimination_constraints single_block_change_cons = single_block_change(block_objs) constraints.extend(single_block_change_cons) constraints.extend([ # conditional constraints: if_else(bool_path_ahead)---if block constraints z3.Implies( c1 == 7, z3.Or( block_1_vars[0] == 1, block_1_vars[1] == 1, block_1_vars[2] == 1, block_1_vars[3] == 1, block_1_vars[4] == 1, )), z3.Implies(z3.And(c1 == 7, block_1_vars[1] == 1, block_1_vars[0] != 1), z3.And(block_1_vars[0] != 2, block_1_vars[0] != 3)), z3.Implies( z3.And(c1 == 7, block_1_vars[2] == 1, block_1_vars[0] != 1, block_1_vars[1] != 1), z3.And(block_1_vars[0] != 2, block_1_vars[0] != 3, block_1_vars[1] != 2, block_1_vars[1] != 3)), z3.Implies( z3.And(c1 == 7, block_1_vars[3] == 1, block_1_vars[0] != 1, block_1_vars[1] != 1, block_1_vars[2] != 1), z3.And(block_1_vars[0] != 2, block_1_vars[0] != 3, block_1_vars[1] != 2, block_1_vars[1] != 3, block_1_vars[2] != 2, block_1_vars[2] != 3)), z3.Implies( z3.And(c1 == 7, block_1_vars[4] == 1, block_1_vars[0] != 1, block_1_vars[1] != 1, block_1_vars[2] != 1, block_1_vars[3] != 1), z3.And(block_1_vars[0] != 2, block_1_vars[0] != 3, block_1_vars[1] != 2, block_1_vars[1] != 3, block_1_vars[2] != 2, block_1_vars[2] != 3, block_1_vars[3] != 2, block_1_vars[3] != 3)), # else block constraints z3.Implies(c1 == 7, block_2_vars[0] != 1), z3.Implies(z3.And(c1 == 7, block_2_vars[1] == 1, block_2_vars[0] != 1), z3.Or(block_2_vars[0] == 2, block_2_vars[0] == 3)), z3.Implies( z3.And(c1 == 7, block_2_vars[2] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1), z3.Or(block_2_vars[0] == 2, block_2_vars[0] == 3, block_2_vars[1] == 2, block_2_vars[1] == 3)), z3.Implies( z3.And(c1 == 7, block_2_vars[3] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1), z3.Or(block_2_vars[0] == 2, block_2_vars[0] == 3, block_2_vars[1] == 2, block_2_vars[1] == 3, block_2_vars[2] == 2, block_2_vars[2] == 3)), z3.Implies( z3.And(c1 == 7, block_2_vars[4] == 1, block_2_vars[0] != 1, block_2_vars[1] != 1, block_2_vars[2] != 1, block_2_vars[3] != 1), z3.Or(block_2_vars[0] == 2, block_2_vars[0] == 3, block_2_vars[1] == 2, block_2_vars[1] == 3, block_2_vars[2] == 2, block_2_vars[2] == 3, block_2_vars[3] == 2, block_2_vars[3] == 3)), ]) unequal_blocks_con = block_unequal_constraint(block_1_obj, block_2_obj) constraints.extend(unequal_blocks_con) # add the values and the constraints solver.add(values + constraints) # generate all the assignments models = gen_all(solver, X) assignments = [] for model in models: a = [ 'repeat_until_goal(bool_goal)', type_to_str[ConditionalType(model[c1].as_long())] ] a.extend([ type_to_str[VariableType(model[ele].as_long())] for ele in X[1:block_1_obj.size + 1] ]) a.extend([ type_to_str[VariableType(model[ele].as_long())] for ele in X[block_1_obj.size + 1:block_2_obj.size + block_1_obj.size + 1] ]) a.extend([ type_to_str[VariableType(model[ele].as_long())] for ele in block_3_vars ]) assignments.append(a) #print(a) #print('Found #{} SAT values'.format(len(models))) return assignments
def generate_assignments(thresh=2, id='karel'): solver = z3.Solver() # declare the SMT variables for the specific code # Block 1 c0 = z3.Int('c0') # repeat (8) c1 = z3.Int('c1') # bool_no_marker (if_else) block_1 = {'b1_1': 'put_marker'} block_1_obj = SMT_Block(block_1, thresh, id=id) values = block_1_obj.block_values block_1_vars = [ele.var for ele in block_1_obj.block_z3_vars ] # for the conditional constraints block_2 = {'b2_1': 'pick_marker'} block_2_obj = SMT_Block(block_2, thresh, id=id) values.extend(block_2_obj.block_values) block_2_vars = [ele.var for ele in block_2_obj.block_z3_vars ] # for the conditional constraints values.append(z3.Or(c0 == 7, c0 == 8, c0 == 9)) values.append(z3.Or(c1 == 10, c1 == 11)) # bool_no_marker, bool_marker block_3 = {'b3_1': 'move'} block_3_obj = SMT_Block(block_3, thresh, id=id) values.extend(block_3_obj.block_values) block_3_vars = [ele.var for ele in block_3_obj.block_z3_vars ] # for the conditional constraints block_4 = {'b4_1': 'phi'} block_4_obj = SMT_Block(block_4, thresh, id=id) values.extend(block_4_obj.block_values) block_4_vars = [ele.var for ele in block_4_obj.block_z3_vars ] # for the conditional constraints block_5 = {'b5_1': 'phi'} block_5_obj = SMT_Block(block_5, thresh, id=id) values.extend(block_5_obj.block_values) block_5_vars = [ele.var for ele in block_5_obj.block_z3_vars ] # for the conditional constraints # all block objects block_objs = [ block_1_obj, block_2_obj, block_3_obj, block_4_obj, block_5_obj ] X = [c0, c1] X.extend([ele.var for ele in block_1_obj.block_z3_vars ]) # added the variables for block 1 X.extend([ele.var for ele in block_2_obj.block_z3_vars ]) # added the variables for block 2 X.extend([ele.var for ele in block_3_obj.block_z3_vars ]) # added the variables for block 3 X.extend([ele.var for ele in block_4_obj.block_z3_vars ]) # added the variables for block 4 X.extend([ele.var for ele in block_5_obj.block_z3_vars ]) # added the variables for block 5 constraints = block_1_obj.block_append_constraints + block_1_obj.flip_turns_constraints + block_1_obj.flip_marker_constraints+ \ block_1_obj.block_elimination_constraints + \ block_2_obj.block_append_constraints + block_2_obj.flip_turns_constraints + \ block_2_obj.flip_marker_constraints+block_2_obj.block_elimination_constraints + \ block_3_obj.block_append_constraints + block_3_obj.flip_turns_constraints + \ block_3_obj.flip_marker_constraints+block_3_obj.block_elimination_constraints + \ block_4_obj.block_append_constraints + block_4_obj.flip_turns_constraints + \ block_4_obj.flip_marker_constraints + block_4_obj.block_elimination_constraints + \ block_5_obj.block_append_constraints + block_5_obj.flip_turns_constraints + \ block_5_obj.flip_marker_constraints + block_5_obj.block_elimination_constraints single_block_change_cons = single_block_change(block_objs) constraints.extend(single_block_change_cons) constraints.extend([ # conditional constraints: if_else(bool_no_marker)---if block constraints z3.Implies(c1 == 11, block_1_vars[0] != 4), z3.Implies( z3.And(c1 == 11, block_1_vars[1] == 4, block_1_vars[0] != 4), z3.Or(block_1_vars[0] == 1, block_1_vars[0] == 5)), z3.Implies( z3.And(c1 == 11, block_1_vars[2] == 4, block_1_vars[0] != 4, block_1_vars[1] != 4), z3.Or(block_1_vars[0] == 1, block_1_vars[0] == 5, block_1_vars[1] == 1, block_1_vars[1] == 5)), z3.Implies( z3.And(c1 == 11, block_1_vars[3] == 4, block_1_vars[0] != 4, block_1_vars[1] != 4, block_1_vars[2] != 4), z3.Or(block_1_vars[0] == 1, block_1_vars[0] == 5, block_1_vars[1] == 1, block_1_vars[1] == 5, block_1_vars[2] == 1, block_1_vars[2] == 5)), z3.Implies( z3.And(c1 == 11, block_1_vars[4] == 4, block_1_vars[0] != 4, block_1_vars[1] != 4, block_1_vars[2] != 4, block_1_vars[3] != 4), z3.And(block_1_vars[0] == 1, block_1_vars[0] == 5, block_1_vars[1] == 1, block_1_vars[1] == 5, block_1_vars[2] == 1, block_1_vars[2] == 5, block_1_vars[3] == 1, block_1_vars[3] == 5)), # else block constraints z3.Implies(c1 == 11, block_2_vars[0] != 5), z3.Implies( z3.And(c1 == 11, block_2_vars[1] == 5, block_2_vars[0] != 5), z3.Or(block_2_vars[0] == 1, block_2_vars[0] == 4)), z3.Implies( z3.And(c1 == 11, block_2_vars[2] == 5, block_2_vars[0] != 5, block_2_vars[1] != 5), z3.Or(block_2_vars[0] == 1, block_2_vars[0] == 4, block_2_vars[1] == 1, block_2_vars[1] == 4)), z3.Implies( z3.And(c1 == 11, block_2_vars[3] == 5, block_2_vars[0] != 5, block_2_vars[1] != 5, block_2_vars[2] != 5), z3.Or(block_2_vars[0] == 1, block_2_vars[0] == 4, block_2_vars[1] == 1, block_2_vars[1] == 4, block_2_vars[2] == 1, block_2_vars[2] == 4)), z3.Implies( z3.And(c1 == 11, block_2_vars[4] == 5, block_2_vars[0] != 5, block_2_vars[1] != 5, block_2_vars[2] != 5, block_2_vars[3] != 5), z3.And(block_2_vars[0] == 1, block_2_vars[0] == 4, block_2_vars[1] == 1, block_2_vars[1] == 4, block_2_vars[2] == 1, block_2_vars[2] == 4, block_2_vars[3] == 1, block_2_vars[3] == 4)), # conditional constraints: if_else(bool_marker)---if block constraints z3.Implies(c1 == 10, block_1_vars[0] != 5), z3.Implies( z3.And(c1 == 10, block_1_vars[1] == 5, block_1_vars[0] != 5), z3.Or(block_1_vars[0] == 1, block_1_vars[0] == 4)), z3.Implies( z3.And(c1 == 10, block_1_vars[2] == 5, block_1_vars[0] != 5, block_1_vars[1] != 5), z3.Or(block_1_vars[0] == 1, block_1_vars[0] == 4, block_1_vars[1] == 1, block_1_vars[1] == 4)), z3.Implies( z3.And(c1 == 10, block_1_vars[3] == 5, block_1_vars[0] != 5, block_1_vars[1] != 5, block_1_vars[2] != 5), z3.Or(block_1_vars[0] == 1, block_1_vars[0] == 4, block_1_vars[1] == 1, block_1_vars[1] == 4, block_1_vars[2] == 1, block_1_vars[2] == 4)), z3.Implies( z3.And(c1 == 10, block_1_vars[4] == 5, block_1_vars[0] != 5, block_1_vars[1] != 5, block_1_vars[2] != 5, block_1_vars[3] != 5), z3.And(block_1_vars[0] == 1, block_1_vars[0] == 4, block_1_vars[1] == 1, block_1_vars[1] == 4, block_1_vars[2] == 1, block_1_vars[2] == 4, block_1_vars[3] == 1, block_1_vars[3] == 4)), # else block constraints z3.Implies(c1 == 10, block_2_vars[0] != 4), z3.Implies( z3.And(c1 == 10, block_2_vars[1] == 4, block_2_vars[0] != 4), z3.Or(block_2_vars[0] == 1, block_2_vars[0] == 5)), z3.Implies( z3.And(c1 == 10, block_2_vars[2] == 4, block_2_vars[0] != 4, block_2_vars[1] != 4), z3.Or(block_2_vars[0] == 1, block_2_vars[0] == 5, block_2_vars[1] == 1, block_2_vars[1] == 5)), z3.Implies( z3.And(c1 == 10, block_2_vars[3] == 4, block_2_vars[0] != 4, block_2_vars[1] != 4, block_2_vars[2] != 4), z3.Or(block_2_vars[0] == 1, block_2_vars[0] == 5, block_2_vars[1] == 1, block_2_vars[1] == 5, block_2_vars[2] == 1, block_2_vars[2] == 5)), z3.Implies( z3.And(c1 == 10, block_2_vars[4] == 4, block_2_vars[0] != 4, block_2_vars[1] != 4, block_2_vars[2] != 4, block_2_vars[3] != 4), z3.And(block_2_vars[0] == 1, block_2_vars[0] == 5, block_2_vars[1] == 1, block_2_vars[1] == 5, block_2_vars[2] == 1, block_2_vars[2] == 5, block_2_vars[3] == 1, block_2_vars[3] == 5)), ]) unequal_blocks_con = block_unequal_constraint(block_1_obj, block_2_obj) constraints.extend(unequal_blocks_con) # add the values and the constraints solver.add(values + constraints) # generate all the assignments models = gen_all(solver, X) assignments = [] for model in models: a = [ str(model[c0].as_long()), type_to_str[ConditionalType(model[c1].as_long())] ] a.extend([ type_to_str[VariableType(model[ele].as_long())] for ele in block_1_vars ]) a.extend([ type_to_str[VariableType(model[ele].as_long())] for ele in block_2_vars ]) a.extend([ type_to_str[VariableType(model[ele].as_long())] for ele in block_3_vars ]) a.extend([ type_to_str[VariableType(model[ele].as_long())] for ele in block_4_vars ]) a.extend([ type_to_str[VariableType(model[ele].as_long())] for ele in block_5_vars ]) assignments.append(a) #print(a) #print('Found #{} SAT values'.format(len(models))) return assignments
CurrStr = translator.toString(Curr) # SynFunResult = FuncDefine+Curr # Str = translator.toString(SynFunResult) Str = FuncDefineStr[:-1] + ' ' + CurrStr + FuncDefineStr[ -1] # insert Program just before the last bracket ')' Count += 1 # print (Count) print(Str) # if Count % 100 == 1: # print (Count) # print (Str) # raw_input() # print '1' counterexample = checker.check(Str) # print counterexample print(int(str(counterexample.eval(z3.Int('x'), True)))) print(int(str(counterexample.eval(z3.Int('y'), True)))) if (counterexample == None): # No counter-example Ans = Str break # print '2' # print(TryExtend) # raw_input() # BfsQueue+=TryExtend for TE in TryExtend: TE_str = str(TE) if not TE_str in TE_set: BfsQueue.append(TE) TE_set.add(TE_str)
def addOriginSMTConstraints(self): """ Realize to transfer the CCSL constraints into SMT formula. :return: """ cnt = 0 for each in self.newCCSLConstraintList: if each[0] == "<" and len(each) == 3: tick1 = self.tickDict["t_%s" % (each[1])] tick2 = self.tickDict["t_%s" % (each[2])] history1 = self.historyDict["h_%s" % (each[1])] history2 = self.historyDict["h_%s" % (each[2])] x = z3.Int("x") if self.bound > 0: for i in range(1, self.bound + 2): self.solver.add( z3.Implies( history1(i) == history2(i), z3.Not(tick2(i)))) # self.solver.add(z3.ForAll(x, z3.Implies( # z3.And(x >= 1, x <= self.n, history1(x) == history2(x)), # z3.Not(tick2(x))))) else: self.solver.add( z3.ForAll( x, z3.Implies( z3.And(x >= 1, history1(x) == history2(x)), z3.Not(tick2(x))))) elif each[0] == "<" and len(each) == 4: tick1 = self.tickDict["t_%s" % (each[1])] delay = each[2] tick2 = self.tickDict["t_%s" % (each[3])] history1 = self.historyDict["h_%s" % (each[1])] history2 = self.historyDict["h_%s" % (each[3])] x = z3.Int("x") if self.bound > 0: for i in range(1, self.bound + 2): self.solver.add( z3.Implies( history2(i) - history1(i) == delay, z3.Not(tick2(i)))) # self.solver.add(z3.ForAll(x, z3.Implies( # z3.And(x >= 1, x <= self.n, history2(x) - history1(x) == delay), # z3.Not(tick2(x))))) else: self.solver.add( z3.ForAll( x, z3.Implies( z3.And(x >= 1, history2(x) - history1(x) == delay), z3.Not(tick2(x))))) elif each[0] == "≤": history1 = self.historyDict["h_%s" % (each[1])] history2 = self.historyDict["h_%s" % (each[2])] x = z3.Int("x") if self.bound > 0: for i in range(1, self.bound + 2): self.solver.add(history1(i) >= history2(i)) # self.solver.add(z3.ForAll(x, z3.Implies( # z3.And(x >= 1, x <= self.n + 1), # history1(x) >= history2(x)))) else: self.solver.add( z3.ForAll( x, z3.Implies(x >= 1, history1(x) >= history2(x)))) elif each[0] == "⊆": tick1 = self.tickDict["t_%s" % (each[1])] tick2 = self.tickDict["t_%s" % (each[2])] x = z3.Int("x") if self.bound > 0: for i in range(1, self.bound + 1): self.solver.add(z3.Implies(tick1(i), tick2(i))) # self.solver.add(z3.ForAll(x, z3.Implies( # z3.And(x >= 1, x <= self.n, tick1(x)), # tick2(x)))) else: self.solver.add( z3.ForAll( x, z3.Implies(z3.And(x >= 1, tick1(x)), tick2(x)))) elif each[0] == "#": tick1 = self.tickDict["t_%s" % (each[1])] tick2 = self.tickDict["t_%s" % (each[2])] x = z3.Int("x") if self.bound > 0: for i in range(1, self.bound + 1): self.solver.add( z3.Or(z3.Not(tick1(i)), z3.Not(tick2(i)))) # self.solver.add(z3.ForAll(x, z3.Implies( # z3.And(x >= 1, x <= self.n), # z3.Or(z3.Not(tick1(x)), z3.Not(tick2(x)))))) else: self.solver.add( z3.ForAll( x, z3.Implies( x >= 1, z3.Or(z3.Not(tick1(x)), z3.Not(tick2(x)))))) elif each[0] == "+": tick1 = self.tickDict["t_%s" % (each[1])] tick2 = self.tickDict["t_%s" % (each[2])] tick3 = self.tickDict["t_%s" % (each[3])] x = z3.Int("x") if self.bound > 0: for i in range(1, self.bound + 1): self.solver.add(tick1(i) == z3.Or(tick2(i), tick3(i))) # self.solver.add(z3.ForAll(x, z3.Implies( # z3.And(x >= 1, x <= self.n), # tick1(x) == z3.Or(tick2(x), tick3(x))))) else: self.solver.add( z3.ForAll( x, z3.Implies(x >= 1, tick1(x) == z3.Or(tick2(x), tick3(x))))) elif each[0] == "*": tick1 = self.tickDict["t_%s" % (each[1])] tick2 = self.tickDict["t_%s" % (each[2])] tick3 = self.tickDict["t_%s" % (each[3])] x = z3.Int("x") if self.bound > 0: for i in range(1, self.bound + 1): self.solver.add( z3.Implies(tick1(i), z3.And(tick2(i), tick3(i)))) # self.solver.add(z3.ForAll(x, z3.Implies( # z3.And(x >= 1, x <= self.n), # tick1(x) == z3.And(tick2(x), tick3(x))))) else: self.solver.add( z3.ForAll( x, z3.Implies(x >= 1, tick1(x) == z3.And(tick2(x), tick3(x))))) elif each[0] == "∧": history1 = self.historyDict["h_%s" % (each[1])] history2 = self.historyDict["h_%s" % (each[2])] history3 = self.historyDict["h_%s" % (each[3])] x = z3.Int("x") if self.bound > 0: for i in range(1, self.bound + 2): self.solver.add( history1(i) == z3.If( history2(i) >= history3(i), history2(i), history3(i))) # self.solver.add(z3.ForAll(x, z3.Implies( # z3.And(x >= 1, x <= self.n + 1), # history1(x) == z3.If(history2(x) >= history3(x),history2(x),history3(x))))) else: self.solver.add( z3.ForAll( x, z3.Implies( x >= 1, history1(x) == z3.If( history2(x) >= history3(x), history2(x), history3(x))))) elif each[0] == "∨": history1 = self.historyDict["h_%s" % (each[1])] history2 = self.historyDict["h_%s" % (each[2])] history3 = self.historyDict["h_%s" % (each[3])] x = z3.Int("x") if self.bound > 0: for i in range(1, self.bound + 2): self.solver.add( history1(i) == z3.If( history2(i) <= history3(i), history2(i), history3(i))) # self.solver.add(z3.ForAll(x, z3.Implies( # z3.And(x >= 1, x <= self.n + 1), # history1(x) == z3.If(history2(x) <= history3(x), history2(x), history3(x))))) else: self.solver.add( z3.ForAll( x, z3.Implies( x >= 1, history1(x) == z3.If( history2(x) <= history3(x), history2(x), history3(x))))) elif each[0] == "$": history1 = self.historyDict["h_%s" % (each[1])] history2 = self.historyDict["h_%s" % (each[2])] delay = z3.IntVal(int(each[3])) x = z3.Int("x") if self.bound > 0: for i in range(1, self.bound + 2): self.solver.add( history1(i) == z3.If( history2(i) >= delay, history2(i) - delay, 0)) # self.solver.add(z3.ForAll(x, z3.Implies( # z3.And(x >= 1, x <= self.n + 1), # history1(x) == z3.If(history2(x) >= delay,history2(x) - delay,0)))) else: self.solver.add( z3.ForAll( x, z3.Implies( x >= 1, history1(x) == z3.If( history2(x) >= delay, history2(x) - delay, 0)))) elif each[0] == "on": tick1 = self.tickDict["t_%s" % (each[1])] tick2 = self.tickDict["t_%s" % (each[2])] tick3 = self.tickDict["t_%s" % (each[4])] history1 = self.historyDict["h_%s" % (each[1])] history2 = self.historyDict["h_%s" % (each[2])] history3 = self.historyDict["h_%s" % (each[4])] self.addTickStep(each[1]) self.addTickStep(each[2]) self.addTickStep(each[4]) tickStep1 = self.tickStep["s_%s" % (each[1])] tickStep2 = self.tickStep["s_%s" % (each[2])] tickStep3 = self.tickStep["s_%s" % (each[4])] x = z3.Int("x") if self.bound > 0: for i in range(1, int(each[3]) + 1): self.solver.add(z3.Not(tick1(i))) for i in range(int(each[3]) + 1, self.bound + 1): t = [] for j in range(1, i - int(each[3]) + 1): t.append( z3.And( tick2(j), history3(i) - history3(j) == int(each[3]))) self.solver.add(z3.And(tick3(i), z3.Or(t)) == tick1(i)) self.solver.add( z3.ForAll( x, z3.Implies(z3.And(x > 0, x <= self.n + 1), history2(x) >= history1(x)))) self.solver.add( z3.ForAll( x, z3.Implies(z3.And(x > 0, x <= self.n, tick1(x)), tick3(x)))) # self.solver.add( # z3.ForAll(x, z3.Implies( # z3.And(x > 0, x <= history1(self.bound + 1)), # history3(tickStep2(x)) - history3(tickStep1(x)) == int(each[3]) # ))) # for i in range(self.bound + 1): # self.solver.add(history2(i) >= history1(i)) # for i in range(self.bound): # self.solver.add( # z3.Implies( # tick1(i), tick3(i) # ) # ) # for i in range(self.bound + 1): # self.solver.add( # history3(tickStep1(i)) - history3(tickStep2(i)) == int(each[3]) # ) # self.solver.add(z3.ForAll(x, z3.And( # z3.Implies(z3.And(x >= 1, x <= history1(self.bound + 1),tick2(x)), # tick1(tickStep3(history3(x) + int(each[3]))) # )))) else: self.solver.add( z3.ForAll( x, z3.And( z3.Implies(x >= 1, history2(x) >= history1(x))))) self.solver.add( z3.ForAll( x, z3.And( z3.Implies(z3.And(x >= 1, tick1(x)), tick3(x))))) self.solver.add( z3.ForAll( x, z3.And( z3.Implies(x >= 1, (history3(tickStep1(x)) - history3(tickStep2(x)) == int(each[3])))))) elif each[0] == "∝": tick1 = self.tickDict["t_%s" % (each[1])] tick2 = self.tickDict["t_%s" % (each[2])] history1 = self.historyDict["h_%s" % (each[1])] history2 = self.historyDict["h_%s" % (each[2])] x = z3.Int("x") left = tick1(x) if is_number(each[3]): k = z3.Int("k_%s" % (cnt)) self.solver.add(k >= 0, k < int(each[3])) right = z3.And(tick2(x), history2(x) >= 0, (history2(x) + k) % z3.IntVal(each[3]) == 0) cnt += 1 # right = z3.And(tick2(x), history2(x) > 0, (history2(x)) % z3.IntVal(each[3]) == 0) else: period = z3.Int("%s" % each[3]) tmp = self.parameter[each[3]] self.printParameter[each[3]] = period k = z3.Int("k_%s" % (cnt)) self.solver.add(k >= 0, k < period) right = z3.And(tick2(x), history2(x) >= 0, (history2(x) + k) % period == 0) self.solver.add(period >= int(tmp[2])) self.solver.add(period <= int(tmp[3])) cnt += 1 if self.bound > 0: self.solver.add( z3.ForAll( x, z3.And( z3.Implies(z3.And(x >= 1, x <= self.n), left == right)))) else: self.solver.add( z3.ForAll(x, z3.And(z3.Implies(x >= 1, left == right)))) elif each[0] == "☇": tick1 = self.tickDict["t_%s" % (each[1])] tick2 = self.tickDict["t_%s" % (each[2])] tick3 = self.tickDict["t_%s" % (each[3])] history1 = self.historyDict["h_%s" % (each[1])] history2 = self.historyDict["h_%s" % (each[2])] history3 = self.historyDict["h_%s" % (each[3])] self.addTickStep(each[1]) self.addTickStep(each[3]) tickStep1 = self.tickStep["s_%s" % (each[1])] tickStep3 = self.tickStep["s_%s" % (each[3])] x = z3.Int("x") if self.bound > 0: self.solver.add( z3.ForAll( x, z3.Implies( z3.And(x >= 2, x <= history3(self.bound + 1)), tick1(tickStep1(x)) == ( history2(tickStep3(x)) - history2(tickStep3(x - 1)) >= 1)))) else: self.solver.add( z3.ForAll( x, z3.Implies( x >= 2, z3.And( tick1(tickStep1(x)), history2(tickStep3(x)) - history2(tickStep3(x - 1)) >= 1)))) elif each[0] == "==": tick1 = self.tickDict["t_%s" % (each[1])] tick2 = self.tickDict["t_%s" % (each[2])] x = z3.Int("x") if self.bound > 0: self.solver.add( z3.ForAll( x, z3.Implies(z3.And(x >= 1, x <= self.n), tick1(x) == tick2(x)))) else: self.solver.add( z3.ForAll(x, z3.Implies(x >= 1, tick1(x) == tick2(x)))) elif each[0] == "⋈±": tick1 = self.tickDict["t_%s" % (each[1])] tick2 = self.tickDict["t_%s" % (each[2])] history1 = self.historyDict["h_%s" % (each[1])] history2 = self.historyDict["h_%s" % (each[2])] self.addTickStep(each[1]) self.addTickStep(each[2]) tickStep1 = self.tickStep["s_%s" % (each[1])] tickStep2 = self.tickStep["s_%s" % (each[2])] lower = int(each[3]) - int(each[4]) upper = int(each[3]) + int(each[4]) x = z3.Int("x") if self.bound > 0: self.solver.add( z3.ForAll( x, z3.Implies( z3.And(x >= 1, x <= self.bound + 1, tick1(x)), history1(tickStep2(history2(x) + upper)) - history1( tickStep2(history2(x) + lower)) == 1))) self.solver.add( z3.ForAll( x, z3.Implies( z3.And(x >= 2, x <= history1(self.bound + 1)), z3.And( (history2(tickStep1(x)) - history2(tickStep1(x - 1)) >= lower), (history2(tickStep1(x)) - history2(tickStep1(x - 1)) <= upper))))) else: self.solver.add( z3.ForAll( x, z3.Implies( x >= 2, z3.And( (history2(tickStep1(x)) - history2(tickStep1(x - 1)) >= lower), (history2(tickStep1(x)) - history2(tickStep1(x - 1)) <= upper)))))