예제 #1
0
 def decompose(self, pre, post, fail=False):
     v = self.get_callee()
     if not isinstance(v, Action):
         return []
     actual_params = self.args[0].args
     actual_returns = self.args[1:]
     vocab = list(symbols_asts(actual_params + actual_returns))
     formals = v.formal_params + v.formal_returns
     premap, pre = hide_state_map(formals, pre)
     postmap, post = hide_state_map(formals, post)
     actual_params = [rename_ast(p, premap) for p in actual_params]
     actual_returns = [rename_ast(p, postmap) for p in actual_returns]
     pre = constrain_state(
         pre,
         And(*
             [Equals(x, y)
              for x, y in zip(actual_params, v.formal_params)]))
     if not fail:
         post = constrain_state(
             post,
             And(*[
                 Equals(x, y)
                 for x, y in zip(actual_returns, v.formal_returns)
             ]))
     ren = dict((x, x.prefix('__hide:')) for x in actual_returns)
     post = (post[0], rename_clauses(post[1], ren), post[2])
     callee = v.clone(v.args)  # drop the formals
     res = [(pre, [callee], post)]
     print "decompose call:"
     print "pre = {}".format(pre)
     print "callee = {}".format(callee)
     print "post = {}".format(post)
     return res
예제 #2
0
 def show_sym(v,decd,val):
     if all(x in inv_env or not my_is_skolem(x) and
            not tr.is_new(x) and x not in env for x in ilu.used_symbols_ast(decd)):
         expr = ilu.rename_ast(decd,inv_env)
         if not (expr in self.current and self.current[expr] == val):
             print '        {} = {}'.format(expr,val)
             self.current[expr] = val
예제 #3
0
    def handle(self,action,env):

        def my_is_skolem(x):
            return tr.is_skolem(x) and x not in self.cnsts

        def show_sym(v,decd,val):
            if all(x in inv_env or not my_is_skolem(x) and
                   not tr.is_new(x) and x not in env for x in ilu.used_symbols_ast(decd)):
                expr = ilu.rename_ast(decd,inv_env)
                if not (expr in self.current and self.current[expr] == val):
                    print '        {} = {}'.format(expr,val)
                    self.current[expr] = val

        if hasattr(action,'lineno'):
#            print '        env: {}'.format('{'+','.join('{}:{}'.format(x,y) for x,y in env.iteritems())+'}')
            inv_env = dict((y,x) for x,y in env.iteritems())
            for v in self.aiger.inputs:
                if v in self.decoder:
                    show_sym(v,self.decoder[v],self.aiger.get_sym(v))
            rn = dict((x,tr.new(x)) for x in self.stvarset)
            for v in self.aiger.latches:
                if v in self.decoder:
                    decd = self.decoder[v]
                    show_sym(v,ilu.rename_ast(decd,rn),self.aiger.get_next_sym(v))

            print '    {}{}'.format(action.lineno,action)
예제 #4
0
파일: ivy_actions.py 프로젝트: JJTRX/ivy
 def decompose(self, pre, post):
     v = self.get_callee()
     if not isinstance(v, Action):
         return []
     actual_params = self.args[0].args
     actual_returns = self.args[1:]
     vocab = list(symbols_asts(actual_params + actual_returns))
     formals = v.formal_params + v.formal_returns
     premap, pre = hide_state_map(formals, pre)
     postmap, post = hide_state_map(formals, post)
     actual_params = [rename_ast(p, premap) for p in actual_params]
     actual_returns = [rename_ast(p, postmap) for p in actual_returns]
     pre = constrain_state(pre, And(*[Equals(x, y) for x, y in zip(actual_params, v.formal_params)]))
     post = constrain_state(post, And(*[Equals(x, y) for x, y in zip(actual_returns, v.formal_returns)]))
     ren = dict((x, x.prefix("__hide:")) for x in actual_returns)
     post = (post[0], rename_clauses(post[1], ren), post[2])
     callee = v.clone(v.args)  # drop the formals
     return [(pre, [callee], post)]
예제 #5
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def prev_expr(stvarset,expr,sort_constants):
    if any(sym in stvarset or tr.is_skolem(sym) and not sym in sort_constants[sym.sort]
           for sym in ilu.symbols_ast(expr)):
        return None
    news = [sym for sym in ilu.used_symbols_ast(expr) if tr.is_new(sym)]
    if news:
        rn = dict((sym,tr.new_of(sym)) for sym in news)
        return ilu.rename_ast(expr,rn)
    return None        
예제 #6
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 def new_state_pairs(self, sym_pairs, env):
     eqns = []
     for sym, renamed_sym in sym_pairs:
         rmap = {renamed_sym: sym}
         # TODO: what if the renamed symbol is not in the model?
         for fmla in self.get_sym_eqs(renamed_sym):
             rfmla = lut.rename_ast(fmla, rmap)
             eqns.append(rfmla)
     self.add_state(eqns)
예제 #7
0
파일: ivy_check.py 프로젝트: hannesm/ivy
 def show_sym(self, sym, renamed_sym):
     if sym in self.renaming and self.renaming[sym] == renamed_sym:
         return
     self.renaming[sym] = renamed_sym
     rmap = {renamed_sym: sym}
     # TODO: what if the renamed symbol is not in the model?
     for fmla in self.eqs[renamed_sym]:
         rfmla = lut.rename_ast(fmla, rmap)
         lhs, rhs = rfmla.args
         if lhs in self.current and self.current[lhs] == rhs:
             continue
         self.current[lhs] = rhs
         print '    {}'.format(rfmla)
예제 #8
0
def action_def_to_str(name,action):
    res = "action {}".format(name)
    if action.formal_params:
        res += params_to_str(action.formal_params)
    if action.formal_returns:
        res += ' returns' + params_to_str(action.formal_returns)
    res += ' = '
    subs = dict()
    for s in action.formal_params + action.formal_returns:
        if s.name.startswith('fml:'):
            subs[s] = s.drop_prefix('fml:')
    action = rename_ast(action,subs)
    if isinstance(action,Sequence):
        res += str(action)
    else:
        res += '{' + str(action) + '}'
    return res
예제 #9
0
파일: ivy_trace.py 프로젝트: hannesm/ivy
 def new_state_pairs(self, sym_pairs, env):
     eqns = []
     for sym, renamed_sym in sym_pairs:
         rmap = {renamed_sym: sym}
         # TODO: what if the renamed symbol is not in the model?
         for fmla in self.eqs[renamed_sym]:
             rfmla = lut.rename_ast(fmla, rmap)
             eqns.append(rfmla)
     clauses = lut.Clauses(eqns)
     state = self.domain.new_state(clauses)
     state.universe = self.model.universes(numerals=True)
     if self.last_action is not None:
         expr = itp.action_app(self.last_action, self.states[-1])
         if self.returned is not None:
             expr.subgraph = self.returned
             self.returned = None
         self.last_action = None
         self.add(state, expr)
     else:
         self.add(state)
예제 #10
0
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