def recur(action,annot,env,pos=None): if isinstance(annot,ia.RenameAnnotation): save = dict() for x,y in annot.map.iteritems(): if x in env: save[x] = env[x] env[x] = env.get(y,y) recur(action,annot.arg,env,pos) env.update(save) return if isinstance(action,ia.Sequence): if pos is None: pos = len(action.args) if pos == 0: assert isinstance(annot,ia.EmptyAnnotation),annot return if not isinstance(annot,ia.ComposeAnnotation): iu.dbg('len(action.args)') iu.dbg('pos') iu.dbg('annot') assert isinstance(annot,ia.ComposeAnnotation) recur(action,annot.args[0],env,pos-1) recur(action.args[pos-1],annot.args[1],env) return if isinstance(action,ia.IfAction): assert isinstance(annot,ia.IteAnnotation),annot rncond = env.get(annot.cond,annot.cond) try: cond = handler.eval(rncond) except KeyError: print '{}skipping conditional'.format(action.lineno) iu.dbg('str_map(env)') iu.dbg('env.get(annot.cond,annot.cond)') return if cond: recur(action.args[1],annot.thenb,env) else: if len(action.args) > 2: recur(action.args[2],annot.elseb,env) return if isinstance(action,ia.ChoiceAction): assert isinstance(annot,ia.IteAnnotation) annots = unite_annot(annot) assert len(annots) == len(action.args) for act,(cond,ann) in reversed(zip(action.args,annots)): if handler.eval(cond): recur(act,ann,env) return assert False,'problem in match_annotation' if isinstance(action,ia.CallAction): callee = im.module.actions[action.args[0].rep] seq = ia.Sequence(*([ia.Sequence() for x in callee.formal_params] + [callee] + [ia.Sequence() for x in callee.formal_returns])) recur(seq,annot,env) return if isinstance(action,ia.LocalAction): recur(action.args[-1],annot,env) return handler.handle(action,env)
def check_fcs_in_state(mod,ag,post,fcs): # iu.dbg('"foo"') history = ag.get_history(post) # iu.dbg('history.actions') gmc = lambda cls, final_cond: itr.small_model_clauses(cls,final_cond,shrink=diagnose.get()) axioms = im.module.background_theory() if opt_trace.get(): clauses = history.post clauses = lut.and_clauses(clauses,axioms) ffcs = filter_fcs(fcs) model = itr.small_model_clauses(clauses,ffcs,shrink=True) if model is not None: # iu.dbg('history.actions') mclauses = lut.and_clauses(*([clauses] + [c.cond() for c in ffcs if c.failed])) vocab = lut.used_symbols_clauses(mclauses) handler = MatchHandler(mclauses,model,vocab) assert all(x is not None for x in history.actions) # work around a bug in ivy_interp actions = [im.module.actions[a] if isinstance(a,str) else a for a in history.actions] # iu.dbg('actions') action = act.Sequence(*actions) act.match_annotation(action,clauses.annot,handler) handler.end() exit(0) else: res = history.satisfy(axioms,gmc,filter_fcs(fcs)) if res is not None and diagnose.get(): show_counterexample(ag,post,res) return not any(fc.failed for fc in fcs)
def check_final_cond(ag, post, final_cond, rels_to_min=[], shrink=False, handler_class=None): history = ag.get_history(post) axioms = im.module.background_theory() clauses = history.post clauses = lut.and_clauses(clauses, axioms) model = slv.get_small_model(clauses, lg.uninterpreted_sorts(), rels_to_min, final_cond=final_cond, shrink=shrink) if model is not None: failed = ([final_cond] if not isinstance(final_cond, list) else [c.cond() for c in ffcs if c.failed]) mclauses = lut.and_clauses(*([clauses] + failed)) vocab = lut.used_symbols_clauses(mclauses) handler = (handler_class(mclauses, model, vocab) if handler_class is not None else Trace(mclauses, model, vocab)) assert all(x is not None for x in history.actions) # work around a bug in ivy_interp actions = [ im.module.actions[a] if isinstance(a, str) else a for a in history.actions ] action = act.Sequence(*actions) act.match_annotation(action, clauses.annot, handler) handler.end() return handler return None
def normal_program_from_module(mod): bindings = [ActionTermBinding(name,old_action_to_new(act)) for name,act in mod.actions.iteritems()] init = iact.Sequence(*[action for actname,action in mod.initializers]) invars = mod.labeled_conjs asms = mod.assumed_invariants calls = sorted(mod.public_actions) return NormalProgram(bindings,init,invars,asms,calls)
def init_method(): asserts = [ia.AssertAction(im.module.init_cond.to_formula())] for a in im.module.axioms: asserts.append(ia.AssertAction(a)) res = ia.Sequence(*asserts) res.formal_params = [] res.formal_returns = [] return res
def env_action(bindings): racts = [] for b in bindings: name = b.name act = b.action ract = iact.Sequence(act.stmt,iact.ReturnAction()) ract.formal_params = act.inputs ract.formal_returns = act.outputs ract.label = name[4:] if name.startswith('ext:') else name racts.append(ract) action = iact.EnvAction(*racts) return action
def check_fcs_in_state(mod, ag, post, fcs): # iu.dbg('"foo"') history = ag.get_history(post) # iu.dbg('history.actions') gmc = lambda cls, final_cond: itr.small_model_clauses( cls, final_cond, shrink=diagnose.get()) axioms = im.module.background_theory() if opt_trace.get() or diagnose.get(): clauses = history.post clauses = lut.and_clauses(clauses, axioms) ffcs = filter_fcs(fcs) model = itr.small_model_clauses(clauses, ffcs, shrink=True) if model is not None: # iu.dbg('history.actions') failed = [c for c in ffcs if c.failed] mclauses = lut.and_clauses(*([clauses] + [c.cond() for c in failed])) vocab = lut.used_symbols_clauses(mclauses) # handler = MatchHandler(mclauses,model,vocab) if opt_trace.get() else ivy_trace.Trace(mclauses,model,vocab) handler = ivy_trace.Trace(mclauses, model, vocab) thing = failed[-1].get_annot() if thing is None: assert all(x is not None for x in history.actions) # work around a bug in ivy_interp actions = [ im.module.actions[a] if isinstance(a, str) else a for a in history.actions ] action = act.Sequence(*actions) annot = clauses.annot else: action, annot = thing act.match_annotation(action, annot, handler) handler.end() ff = failed[0] handler.is_cti = (lut.formula_to_clauses(ff.lf.formula) if isinstance(ff, ConjChecker) else None) if not opt_trace.get(): gui_art(handler) else: print str(handler) exit(0) else: res = history.satisfy(axioms, gmc, filter_fcs(fcs)) if res is not None and diagnose.get(): show_counterexample(ag, post, res) return not any(fc.failed for fc in fcs)
def add_initial_state(self, ic=None, abstractor=None): if ic == None: ic = im.init_cond s = self.domain.new_state(ic) if self.domain.initializers: action = ivy_actions.Sequence( *[a for n, a in self.domain.initializers]) s = action_app(action, s) with AC(self, no_add=True): with EvalContext(check=False): s2 = eval_state(s) s2.expr = s self.add(s2) else: s2 = self.domain.new_state(ic) self.add(s2, s) if abstractor: abstractor(s2)
def check_final_cond(ag, post, final_cond, rels_to_min=[], shrink=False, handler_class=None): history = ag.get_history(post) axioms = im.module.background_theory() clauses = history.post clauses = lut.and_clauses(clauses, axioms) assert all(x is not None for x in history.actions) # work around a bug in ivy_interp actions = [ im.module.actions[a] if isinstance(a, str) else a for a in history.actions ] action = act.Sequence(*actions) return check_vc(clauses, action, final_cond, rels_to_min, shrink, handler_class)
def summarize_action(action): res = ia.Sequence() res.lineno = action.lineno res.formal_params = action.formal_params res.formal_returns = action.formal_returns return res
def to_aiger(mod,ext_act): erf = il.Symbol('err_flag',il.find_sort('bool')) errconds = [] add_err_flag_mod(mod,erf,errconds) # we use a special state variable __init to indicate the initial state ext_acts = [mod.actions[x] for x in sorted(mod.public_actions)] ext_act = ia.EnvAction(*ext_acts) init_var = il.Symbol('__init',il.find_sort('bool')) init = add_err_flag(ia.Sequence(*([a for n,a in mod.initializers]+[ia.AssignAction(init_var,il.And())])),erf,errconds) action = ia.Sequence(ia.AssignAction(erf,il.Or()),ia.IfAction(init_var,ext_act,init)) # get the invariant to be proved, replacing free variables with # skolems. First, we apply any proof tactics. pc = ivy_proof.ProofChecker(mod.axioms,mod.definitions,mod.schemata) pmap = dict((lf.id,p) for lf,p in mod.proofs) conjs = [] for lf in mod.labeled_conjs: if lf.id in pmap: proof = pmap[lf.id] subgoals = pc.admit_proposition(lf,proof) conjs.extend(subgoals) else: conjs.append(lf) invariant = il.And(*[il.drop_universals(lf.formula) for lf in conjs]) # iu.dbg('invariant') skolemizer = lambda v: ilu.var_to_skolem('__',il.Variable(v.rep,v.sort)) vs = ilu.used_variables_in_order_ast(invariant) sksubs = dict((v.rep,skolemizer(v)) for v in vs) invariant = ilu.substitute_ast(invariant,sksubs) invar_syms = ilu.used_symbols_ast(invariant) # compute the transition relation stvars,trans,error = action.update(mod,None) # print 'action : {}'.format(action) # print 'annotation: {}'.format(trans.annot) annot = trans.annot # match_annotation(action,annot,MatchHandler()) indhyps = [il.close_formula(il.Implies(init_var,lf.formula)) for lf in mod.labeled_conjs] # trans = ilu.and_clauses(trans,indhyps) # save the original symbols for trace orig_syms = ilu.used_symbols_clauses(trans) orig_syms.update(ilu.used_symbols_ast(invariant)) # TODO: get the axioms (or maybe only the ground ones?) # axioms = mod.background_theory() # rn = dict((sym,tr.new(sym)) for sym in stvars) # next_axioms = ilu.rename_clauses(axioms,rn) # return ilu.and_clauses(axioms,next_axioms) funs = set() for df in trans.defs: funs.update(ilu.used_symbols_ast(df.args[1])) for fmla in trans.fmlas: funs.update(ilu.used_symbols_ast(fmla)) # funs = ilu.used_symbols_clauses(trans) funs.update(ilu.used_symbols_ast(invariant)) funs = set(sym for sym in funs if il.is_function_sort(sym.sort)) iu.dbg('[str(fun) for fun in funs]') # Propositionally abstract # step 1: get rid of definitions of non-finite symbols by turning # them into constraints new_defs = [] new_fmlas = [] for df in trans.defs: if len(df.args[0].args) == 0 and is_finite_sort(df.args[0].sort): new_defs.append(df) else: fmla = df.to_constraint() new_fmlas.append(fmla) trans = ilu.Clauses(new_fmlas+trans.fmlas,new_defs) # step 2: get rid of ite's over non-finite sorts, by introducing constraints cnsts = [] new_defs = [elim_ite(df,cnsts) for df in trans.defs] new_fmlas = [elim_ite(fmla,cnsts) for fmla in trans.fmlas] trans = ilu.Clauses(new_fmlas+cnsts,new_defs) # step 3: eliminate quantfiers using finite instantiations from_asserts = il.And(*[il.Equals(x,x) for x in ilu.used_symbols_ast(il.And(*errconds)) if tr.is_skolem(x) and not il.is_function_sort(x.sort)]) iu.dbg('from_asserts') invar_syms.update(ilu.used_symbols_ast(from_asserts)) sort_constants = mine_constants(mod,trans,il.And(invariant,from_asserts)) sort_constants2 = mine_constants2(mod,trans,invariant) print '\ninstantiations:' trans,invariant = Qelim(sort_constants,sort_constants2)(trans,invariant,indhyps) # print 'after qe:' # print 'trans: {}'.format(trans) # print 'invariant: {}'.format(invariant) # step 4: instantiate the axioms using patterns # We have to condition both the transition relation and the # invariant on the axioms, so we define a boolean symbol '__axioms' # to represent the axioms. axs = instantiate_axioms(mod,stvars,trans,invariant,sort_constants,funs) ax_conj = il.And(*axs) ax_var = il.Symbol('__axioms',ax_conj.sort) ax_def = il.Definition(ax_var,ax_conj) invariant = il.Implies(ax_var,invariant) trans = ilu.Clauses(trans.fmlas+[ax_var],trans.defs+[ax_def]) # step 5: eliminate all non-propositional atoms by replacing with fresh booleans # An atom with next-state symbols is converted to a next-state symbol if possible stvarset = set(stvars) prop_abs = dict() # map from atoms to proposition variables global prop_abs_ctr # sigh -- python lameness prop_abs_ctr = 0 # counter for fresh symbols new_stvars = [] # list of fresh symbols # get the propositional abstraction of an atom def new_prop(expr): res = prop_abs.get(expr,None) if res is None: prev = prev_expr(stvarset,expr,sort_constants) if prev is not None: # print 'stvar: old: {} new: {}'.format(prev,expr) pva = new_prop(prev) res = tr.new(pva) new_stvars.append(pva) prop_abs[expr] = res # prevent adding this again to new_stvars else: global prop_abs_ctr res = il.Symbol('__abs[{}]'.format(prop_abs_ctr),expr.sort) # print '{} = {}'.format(res,expr) prop_abs[expr] = res prop_abs_ctr += 1 return res # propositionally abstract an expression global mk_prop_fmlas mk_prop_fmlas = [] def mk_prop_abs(expr): if il.is_quantifier(expr) or len(expr.args) > 0 and any(not is_finite_sort(a.sort) for a in expr.args): return new_prop(expr) return expr.clone(map(mk_prop_abs,expr.args)) # apply propositional abstraction to the transition relation new_defs = map(mk_prop_abs,trans.defs) new_fmlas = [mk_prop_abs(il.close_formula(fmla)) for fmla in trans.fmlas] # find any immutable abstract variables, and give them a next definition def my_is_skolem(x): res = tr.is_skolem(x) and x not in invar_syms return res def is_immutable_expr(expr): res = not any(my_is_skolem(sym) or tr.is_new(sym) or sym in stvarset for sym in ilu.used_symbols_ast(expr)) return res for expr,v in prop_abs.iteritems(): if is_immutable_expr(expr): new_stvars.append(v) print 'new state: {}'.format(expr) new_defs.append(il.Definition(tr.new(v),v)) trans = ilu.Clauses(new_fmlas+mk_prop_fmlas,new_defs) # apply propositional abstraction to the invariant invariant = mk_prop_abs(invariant) # create next-state symbols for atoms in the invariant (is this needed?) rn = dict((sym,tr.new(sym)) for sym in stvars) mk_prop_abs(ilu.rename_ast(invariant,rn)) # this is to pick up state variables from invariant # update the state variables by removing the non-finite ones and adding the fresh state booleans stvars = [sym for sym in stvars if is_finite_sort(sym.sort)] + new_stvars # iu.dbg('trans') # iu.dbg('stvars') # iu.dbg('invariant') # exit(0) # For each state var, create a variable that corresponds to the input of its latch # Also, havoc all the state bits except the init flag at the initial time. This # is needed because in aiger, all latches start at 0! def fix(v): return v.prefix('nondet') def curval(v): return v.prefix('curval') def initchoice(v): return v.prefix('initchoice') stvars_fix_map = dict((tr.new(v),fix(v)) for v in stvars) stvars_fix_map.update((v,curval(v)) for v in stvars if v != init_var) trans = ilu.rename_clauses(trans,stvars_fix_map) # iu.dbg('trans') new_defs = trans.defs + [il.Definition(ilu.sym_inst(tr.new(v)),ilu.sym_inst(fix(v))) for v in stvars] new_defs.extend(il.Definition(curval(v),il.Ite(init_var,v,initchoice(v))) for v in stvars if v != init_var) trans = ilu.Clauses(trans.fmlas,new_defs) # Turn the transition constraint into a definition cnst_var = il.Symbol('__cnst',il.find_sort('bool')) new_defs = list(trans.defs) new_defs.append(il.Definition(tr.new(cnst_var),fix(cnst_var))) new_defs.append(il.Definition(fix(cnst_var),il.Or(cnst_var,il.Not(il.And(*trans.fmlas))))) stvars.append(cnst_var) trans = ilu.Clauses([],new_defs) # Input are all the non-defined symbols. Output indicates invariant is false. # iu.dbg('trans') def_set = set(df.defines() for df in trans.defs) def_set.update(stvars) # iu.dbg('def_set') used = ilu.used_symbols_clauses(trans) used.update(ilu.symbols_ast(invariant)) inputs = [sym for sym in used if sym not in def_set and not il.is_interpreted_symbol(sym)] fail = il.Symbol('__fail',il.find_sort('bool')) outputs = [fail] # iu.dbg('trans') # make an aiger aiger = Encoder(inputs,stvars,outputs) comb_defs = [df for df in trans.defs if not tr.is_new(df.defines())] invar_fail = il.Symbol('invar__fail',il.find_sort('bool')) # make a name for invariant fail cond comb_defs.append(il.Definition(invar_fail,il.Not(invariant))) aiger.deflist(comb_defs) for df in trans.defs: if tr.is_new(df.defines()): aiger.set(tr.new_of(df.defines()),aiger.eval(df.args[1])) miter = il.And(init_var,il.Not(cnst_var),il.Or(invar_fail,il.And(fix(erf),il.Not(fix(cnst_var))))) aiger.set(fail,aiger.eval(miter)) # aiger.sub.debug() # make a decoder for the abstract propositions decoder = dict((y,x) for x,y in prop_abs.iteritems()) for sym in aiger.inputs + aiger.latches: if sym not in decoder and sym in orig_syms: decoder[sym] = sym cnsts = set(sym for syms in sort_constants.values() for sym in syms) return aiger,decoder,annot,cnsts,action,stvarset