def functions_total_axioms(prog: syntax.Program) -> List[Expr]: res = [] for func in prog.functions(): # TODO: generation of part of the formula duplicated from relaxation_action_def. # TODO: would be best to beef up the expression-generation library names: List[str] = [] params = [] for arg_sort in func.arity: arg_sort_decl = syntax.get_decl_from_sort(arg_sort) name = prog.scope.fresh(arg_sort_decl.name[0].upper(), also_avoid=names) names.append(name) params.append(syntax.SortedVar(name, arg_sort)) ap_func = syntax.Apply(func.name, tuple(syntax.Id(v.name) for v in params)) name = prog.scope.fresh('y', also_avoid=names) ax = syntax.Forall( tuple(params), syntax.Exists((syntax.SortedVar(name, func.sort), ), syntax.Eq(syntax.Id(name), ap_func))) with prog.scope.n_states(1): typechecker.typecheck_expr(prog.scope, ax, syntax.BoolSort) res.append(ax) return res
def as_onestate_formula(self, index: Optional[int] = None) -> Expr: # TODO: move to class State, this shouldn't be here assert self.num_states == 1 or index is not None, \ 'to generate a onestate formula from a multi-state model, ' + \ 'you must specify which state you want' assert index is None or (0 <= index and index < self.num_states) if index is None: index = 0 if index not in self.onestate_formula_cache: prog = syntax.the_program mut_rel_interps = self.rel_interps[index] mut_const_interps = self.const_interps[index] mut_func_interps = self.func_interps[index] vs: List[syntax.SortedVar] = [] ineqs: Dict[SortDecl, List[Expr]] = {} rels: Dict[RelationDecl, List[Expr]] = {} consts: Dict[ConstantDecl, Expr] = {} funcs: Dict[FunctionDecl, List[Expr]] = {} for sort in self.univs: vs.extend(syntax.SortedVar(v, syntax.UninterpretedSort(sort.name)) for v in self.univs[sort]) u = [syntax.Id(v) for v in self.univs[sort]] ineqs[sort] = [syntax.Neq(a, b) for a, b in combinations(u, 2)] for R, l in chain(mut_rel_interps.items(), self.immut_rel_interps.items()): rels[R] = [] for tup, ans in l.items(): e: Expr = ( syntax.AppExpr(R.name, tuple(syntax.Id(col) for col in tup)) if tup else syntax.Id(R.name) ) rels[R].append(e if ans else syntax.Not(e)) for C, c in chain(mut_const_interps.items(), self.immut_const_interps.items()): consts[C] = syntax.Eq(syntax.Id(C.name), syntax.Id(c)) for F, fl in chain(mut_func_interps.items(), self.immut_func_interps.items()): funcs[F] = [ syntax.Eq(syntax.AppExpr(F.name, tuple(syntax.Id(col) for col in tup)), syntax.Id(res)) for tup, res in fl.items() ] # get a fresh variable, avoiding names of universe elements in vs fresh = prog.scope.fresh('x', [v.name for v in vs]) e = syntax.Exists(tuple(vs), syntax.And( *chain(*ineqs.values(), *rels.values(), consts.values(), *funcs.values(), ( syntax.Forall((syntax.SortedVar(fresh, syntax.UninterpretedSort(sort.name)),), syntax.Or(*(syntax.Eq(syntax.Id(fresh), syntax.Id(v)) for v in self.univs[sort]))) for sort in self.univs )))) assert prog.scope is not None with prog.scope.n_states(1): typechecker.typecheck_expr(prog.scope, e, None) self.onestate_formula_cache[index] = e return self.onestate_formula_cache[index]
def consts_exist_axioms(prog: syntax.Program) -> List[Expr]: res = [] for c in prog.constants(): name = prog.scope.fresh('e_%s' % c.name) ax = syntax.Exists((syntax.SortedVar(name, c.sort), ), syntax.Eq(syntax.Id(c.name), syntax.Id(name))) with prog.scope.n_states(1): typechecker.typecheck_expr(prog.scope, ax, syntax.BoolSort) res.append(ax) return res
def is_rel_blocking_relax(trns: Trace, idx: int, derived_rel: Tuple[List[Tuple[syntax.SortedVar, str]], Expr]) -> bool: # TODO: probably can obtain the sort from the sortedvar when not using scapy free_vars, derived_relation_formula = derived_rel free_vars_active_clause = syntax.And(*(active_var(v.name, sort_name) for (v, sort_name) in free_vars)) diffing_formula = syntax.Exists([v for (v, _) in free_vars], syntax.And(syntax.Old(syntax.And(free_vars_active_clause, derived_relation_formula)), syntax.And(free_vars_active_clause, syntax.Not(derived_relation_formula)))) with syntax.the_program.scope.two_state(twostate=True): # TODO: what is this doing? probably misusing diffing_formula.resolve(syntax.the_program.scope, syntax.BoolSort) res = trns.eval_double_vocab(diffing_formula, idx) assert isinstance(res, bool) return cast(bool, res)
def is_rel_blocking_relax_step( trns: Trace, idx: int, derived_rel: Tuple[List[Tuple[syntax.SortedVar, str]], Expr] ) -> bool: # TODO: probably can obtain the sort from the sortedvar when not using pickle free_vars, derived_relation_formula = derived_rel free_vars_active_clause = syntax.And(*(active_var(v.name, sort_name) for (v, sort_name) in free_vars)) diffing_formula = syntax.Exists([v for (v, _) in free_vars], syntax.And(syntax.And(free_vars_active_clause, derived_relation_formula), syntax.New(syntax.And(free_vars_active_clause, syntax.Not(derived_relation_formula))))) with syntax.the_program.scope.fresh_stack(): with syntax.the_program.scope.n_states(2): diffing_formula.resolve(syntax.the_program.scope, syntax.BoolSort) res = trns.eval(diffing_formula, idx) assert isinstance(res, bool) return cast(bool, res)
def to_ast(self) -> Expr: e = syntax.And(*(c for _, _, c in self.conjuncts())) vs = self.binder.vs return syntax.Exists(vs, e)
def load_relaxed_trace_from_updr_cex(prog: Program, s: Solver) -> logic.Trace: import xml.dom.minidom # type: ignore collection = xml.dom.minidom.parse( "paxos_derived_trace.xml").documentElement components: List[syntax.TraceComponent] = [] xml_decls = reversed(collection.childNodes) seen_first = False for elm in xml_decls: if isinstance(elm, xml.dom.minidom.Text): # type: ignore continue if elm.tagName == 'state': diagram = parser.parse_expr(elm.childNodes[0].data) typechecker.typecheck_expr(prog.scope, diagram, syntax.BoolSort) assert isinstance( diagram, syntax.QuantifierExpr) and diagram.quant == 'EXISTS' active_clauses = [ relaxed_traces.active_var(v.name, str(v.sort)) for v in diagram.get_vs() ] if not seen_first: # restrict the domain to be subdomain of the diagram's existentials seen_first = True import itertools # type: ignore for sort, vars in itertools.groupby( diagram.get_vs(), lambda v: v.sort): # TODO; need to sort first free_var = syntax.SortedVar( syntax.the_program.scope.fresh("v_%s" % str(sort)), None) # TODO: diagram simplification omits them from the exists somewhere consts = list( filter(lambda c: c.sort == sort, prog.constants())) els: Sequence[Union[syntax.SortedVar, syntax.ConstantDecl]] els = list(vars) els += consts restrict_domain = syntax.Forall( (free_var, ), syntax.Or(*(syntax.Eq(syntax.Id(free_var.name), syntax.Id(v.name)) for v in els))) active_clauses += [restrict_domain] diagram_active = syntax.Exists( diagram.get_vs(), syntax.And(diagram.body, *active_clauses)) typechecker.typecheck_expr(prog.scope, diagram_active, syntax.BoolSort) components.append(syntax.AssertDecl(expr=diagram_active)) elif elm.tagName == 'action': action_name = elm.childNodes[0].data.split()[0] tcall = syntax.TransitionCalls( calls=[syntax.TransitionCall(target=action_name, args=None)]) components.append(syntax.TraceTransitionDecl(transition=tcall)) else: assert False, "unknown xml tagName" trace_decl = syntax.TraceDecl(components=components, sat=True) migrated_trace = bmc_trace( prog, trace_decl, s, lambda s, ks: logic.check_solver(s, ks, minimize=True), log=False) assert migrated_trace is not None import pickle pickle.dump(migrated_trace, open("migrated_trace.p", "wb")) return migrated_trace
def derived_rels_candidates_from_trace(trns: Trace, more_traces: List[Trace], max_conj_size: int, max_free_vars: int) -> List[Tuple[List[syntax.SortedVar],Expr]]: first_relax_idx = first_relax_step_idx(trns) pre_relax_state = trns.as_state(first_relax_idx) post_relax_state = trns.as_state(first_relax_idx + 1) assert pre_relax_state.univs == post_relax_state.univs # relaxed elements relaxed_elements = [] for sort, univ in pre_relax_state.univs.items(): active_rel_name = 'active_' + sort.name # TODO: de-duplicate pre_active_interp = dict_val_from_rel_name(active_rel_name, pre_relax_state.rel_interp) post_active_interp = dict_val_from_rel_name(active_rel_name, post_relax_state.rel_interp) pre_active_elements = [tup[0] for (tup, b) in pre_active_interp if b] post_active_elements = [tup[0] for (tup, b) in post_active_interp if b] assert set(post_active_elements).issubset(set(pre_active_elements)) for relaxed_elem in utils.OrderedSet(pre_active_elements) - set(post_active_elements): relaxed_elements.append((sort, relaxed_elem)) # pre-relaxation step facts concerning at least one relaxed element (other to be found by UPDR) relevant_facts: List[Union[RelationFact,FunctionFact,InequalityFact]] = [] for rel, rintp in pre_relax_state.rel_interp.items(): for rfact in rintp: (elms, polarity) = rfact relation_fact = RelationFact(rel, elms, polarity) if set(relation_fact.involved_elms()) & set(ename for (_, ename) in relaxed_elements): relevant_facts.append(relation_fact) for func, fintp in pre_relax_state.func_interp.items(): for ffact in fintp: (els_params, els_res) = ffact function_fact = FunctionFact(func, els_params, els_res) if set(function_fact.involved_elms()) & set(ename for (_, ename) in relaxed_elements): relevant_facts.append(function_fact) for sort, elm in relaxed_elements: # other inequalities presumably handled by UPDR for other_elm in pre_relax_state.univs[sort]: if other_elm == elm: continue relevant_facts.append(InequalityFact(elm, other_elm)) # facts blocking this specific relaxation step diff_conjunctions = [] candidates_cache: Set[str] = set() for fact_lst in itertools.combinations(relevant_facts, max_conj_size): elements = utils.OrderedSet(itertools.chain.from_iterable(fact.involved_elms() for fact in fact_lst)) relaxed_elements_relevant = [elm for (_, elm) in relaxed_elements if elm in elements] vars_from_elm = dict((elm, syntax.SortedVar(None, syntax.the_program.scope.fresh("v%d" % i), None)) for (i, elm) in enumerate(elements)) parameter_elements = elements - set(relaxed_elements_relevant) if len(parameter_elements) > max_free_vars: continue conjuncts = [fact.as_expr(lambda elm: vars_from_elm[elm].name) for fact in fact_lst] # for elm, var in vars_from_elm.items(): # TODO: make the two loops similar for elm in relaxed_elements_relevant: var = vars_from_elm[elm] sort = pre_relax_state.element_sort(elm) active_element_conj = syntax.Apply('active_%s' % sort.name, [syntax.Id(None, var.name)]) conjuncts.append(active_element_conj) derived_relation_formula = syntax.Exists([vars_from_elm[elm] for (_, elm) in relaxed_elements if elm in vars_from_elm], syntax.And(*conjuncts)) if str(derived_relation_formula) in candidates_cache: continue candidates_cache.add(str(derived_relation_formula)) if closing_qa_cycle(syntax.the_program, [pre_relax_state.element_sort(elm) for elm in parameter_elements], [pre_relax_state.element_sort(elm) for elm in relaxed_elements_relevant]): # adding the derived relation would close a quantifier alternation cycle, discard the candidate continue # if trns.eval_double_vocab(diffing_formula, first_relax_idx): if is_rel_blocking_relax(trns, first_relax_idx, ([(vars_from_elm[elm], pre_relax_state.element_sort(elm).name) for elm in parameter_elements], derived_relation_formula)): # if all(trs.eval_double_vocab(diffing_formula, first_relax_step_idx(trs)) for trs in more_traces): diff_conjunctions.append(([vars_from_elm[elm] for elm in parameter_elements], derived_relation_formula)) return diff_conjunctions