示例#1
0
 def check_node(self, n):
     x = var_to_skolem('__', Variable('X', n.sort)).suffix(str(n.sort))
     y = var_to_skolem('__', Variable('Y', n.sort)).suffix(str(n.sort))
     #        print "x.sort: {}",format(x.sort)
     self.solver.push()
     s = self.solver
     # if we have a witness we can show node is definite (present in all models)
     wit = get_witness(n)
     #        print "checking: {}".format(n.fmla)
     cube = substitute_clause(n.fmla, {'X': x})
     #        print "cube: {!r}".format(cube)
     #        print wit
     #        if wit != None:
     ##            print "wit: {}, wit.sort: {}, x.sort: {}".format(wit,wit.sort,x.sort)
     res = s_check_cube(s, cube,
                        (Atom(equals, [x, wit]) if wit != None else None))
     ##        print"check cube: %s = %s" % (cube,res)
     #        res = s_check_cube(s,substitute_clause(n.fmla,{'X':x}))
     #        print "status: {}".format(res)
     n.status = res
     s_add(s, cube_to_z3(substitute_clause(n.fmla, {'X': x})))
     s_add(s, cube_to_z3(substitute_clause(n.fmla, {'X': y})))
     s_add(s, cube_to_z3([Literal(0, Atom(equals, [x, y]))]))
     n.summary = s.check() != z3.unsat
     self.solver.pop()
示例#2
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文件: ivy_graph.py 项目: asyaf/ivy
    def check_edge(self,f1,f2,solver):
        x = var_to_skolem('__',Variable('X',self.sorts[0])).suffix(str(self.sorts[0]))
        y = var_to_skolem('__',Variable('Y',self.sorts[1])).suffix(str(self.sorts[1]))
        solver.push()
        s_add(solver,cube_to_z3(substitute_clause(f1,{'X':x})))
        s_add(solver,cube_to_z3(substitute_clause(f2,{'X':y})))
#        print "xsort: {}, ysort: {}".format(x.get_sort(),y.get_sort())
#        print "rel_lit: {}, subs: {}".format(self.rel_lit,substitute_lit(self.rel_lit,{'X':x,'Y':y}))
        res = s_check_cube(solver,[substitute_lit(self.rel_lit,{'X':x,'Y':y})])
        solver.pop()
        return res
示例#3
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文件: ivy_graph.py 项目: asyaf/ivy
    def compile_concepts(self,concepts):
        clauses = self.post.post_step(concepts)
#        print "compile_concepts clauses={}".format(clauses)
        vs = used_variables_in_order_clauses(clauses)
        sksubs = dict((v.rep,var_to_skolem('__',Variable(v.rep,v.sort))) for v in vs)
        clauses = substitute_clauses(clauses,sksubs)
#        print "clauses: {}".format(clauses)
        return clauses
示例#4
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 def compile_concepts(self, concepts):
     clauses = self.post.post_step(concepts)
     #        print "compile_concepts clauses={}".format(clauses)
     vs = used_variables_in_order_clauses(clauses)
     sksubs = dict(
         (v.rep, var_to_skolem('__', Variable(v.rep, v.sort))) for v in vs)
     clauses = substitute_clauses(clauses, sksubs)
     #        print "clauses: {}".format(clauses)
     return clauses
示例#5
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 def check_edge(self, f1, f2, solver):
     x = var_to_skolem('__',
                       Variable('X',
                                self.sorts[0])).suffix(str(self.sorts[0]))
     y = var_to_skolem('__',
                       Variable('Y',
                                self.sorts[1])).suffix(str(self.sorts[1]))
     solver.push()
     s_add(solver, cube_to_z3(substitute_clause(f1, {'X': x})))
     s_add(solver, cube_to_z3(substitute_clause(f2, {'X': y})))
     #        print "xsort: {}, ysort: {}".format(x.get_sort(),y.get_sort())
     #        print "rel_lit: {}, subs: {}".format(self.rel_lit,substitute_lit(self.rel_lit,{'X':x,'Y':y}))
     res = s_check_cube(solver,
                        [substitute_lit(self.rel_lit, {
                            'X': x,
                            'Y': y
                        })])
     solver.pop()
     return res
示例#6
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文件: ivy_to_cpp.py 项目: xornand/ivy
def emit_derived(header, impl, df, classname):
    name = df.defines().name
    sort = df.defines().sort
    retval = il.Symbol("ret:val", sort)
    vs = df.args[0].args
    ps = [ilu.var_to_skolem('p:', v) for v in vs]
    mp = dict(zip(vs, ps))
    rhs = ilu.substitute_ast(df.args[1], mp)
    action = ia.AssignAction(retval, rhs)
    action.formal_params = ps
    action.formal_returns = [retval]
    emit_some_action(header, impl, name, action, classname)
示例#7
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文件: ivy_to_cpp.py 项目: jamella/ivy
def emit_derived(header,impl,df,classname):
    name = df.defines().name
    sort = df.defines().sort
    retval = il.Symbol("ret:val",sort)
    vs = df.args[0].args
    ps = [ilu.var_to_skolem('p:',v) for v in vs]
    mp = dict(zip(vs,ps))
    rhs = ilu.substitute_ast(df.args[1],mp)
    action = ia.AssignAction(retval,rhs)
    action.formal_params = ps
    action.formal_returns = [retval]
    emit_some_action(header,impl,name,action,classname)
示例#8
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文件: ivy_graph.py 项目: asyaf/ivy
    def check_node(self,n):
        x = var_to_skolem('__',Variable('X',n.sort)).suffix(str(n.sort))
        y = var_to_skolem('__',Variable('Y',n.sort)).suffix(str(n.sort))
#        print "x.sort: {}",format(x.sort)
        self.solver.push()
        s = self.solver
        # if we have a witness we can show node is definite (present in all models)
        wit = get_witness(n)
#        print "checking: {}".format(n.fmla)
        cube = substitute_clause(n.fmla,{'X':x})
#        print "cube: {!r}".format(cube)
#        print wit
#        if wit != None:
##            print "wit: {}, wit.sort: {}, x.sort: {}".format(wit,wit.sort,x.sort)
        res = s_check_cube(s,cube,(Atom(equals,[x,wit]) if wit != None else None))
##        print"check cube: %s = %s" % (cube,res)
#        res = s_check_cube(s,substitute_clause(n.fmla,{'X':x}))
#        print "status: {}".format(res)
        n.status = res
        s_add(s,cube_to_z3(substitute_clause(n.fmla,{'X':x})))
        s_add(s,cube_to_z3(substitute_clause(n.fmla,{'X':y})))
        s_add(s,cube_to_z3([Literal(0,Atom(equals,[x,y]))]))
        n.summary = s.check() != z3.unsat
        self.solver.pop()
示例#9
0
文件: ivy_graph.py 项目: asyaf/ivy
    def check_edge(self,f1,solver):
        x = var_to_skolem('__',Variable('X',self.sorts[0])).suffix(str(self.sorts[0]))
        solver.push()
        s_add(solver,cube_to_z3(substitute_clause(f1,{'X':x})))
        #  print "xsort: {}, ysort: {}".format(x.get_sort(),y.get_sort())
#        print "rel_lit: {}, subs: {}".format(self.rel_lit,substitute_lit(self.rel_lit,{'X':x,'Y':y}))
        f = self.fmla
        vals = [Constant(Symbol(y,f.sort.rng)) for y in f.sort.rng.defines()]
        status = 'undef'
        for v in vals:
            if s_check_fmla(solver,self.test_lit(x,v).atom) == z3.unsat:
                status = v
                break
        solver.pop()
        return status
示例#10
0
 def check_edge(self, f1, solver):
     x = var_to_skolem('__',
                       Variable('X',
                                self.sorts[0])).suffix(str(self.sorts[0]))
     solver.push()
     s_add(solver, cube_to_z3(substitute_clause(f1, {'X': x})))
     #  print "xsort: {}, ysort: {}".format(x.get_sort(),y.get_sort())
     #        print "rel_lit: {}, subs: {}".format(self.rel_lit,substitute_lit(self.rel_lit,{'X':x,'Y':y}))
     f = self.fmla
     vals = [Constant(Symbol(y, f.sort.rng)) for y in f.sort.rng.defines()]
     status = 'undef'
     for v in vals:
         if s_check_fmla(solver, self.test_lit(x, v).atom) == z3.unsat:
             status = v
             break
     solver.pop()
     return status
示例#11
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