Example #1
0
def aiger_witness_to_ivy_trace(aiger,witnessfilename,action,stvarset,ext_act,annot,consts,decoder):
    with open(witnessfilename,'r') as f:
        res = f.readline().strip()
        if res != '1':
            badwit()
        tr = None
        aiger.sub.reset()
        lines = []
        for line in f:
            if line.endswith('\n'):
                line = line[:-1]
            lines.append(line)
        print '\nCounterexample follows:'
        print 80*'-'
        current = dict()
        count = 0
        for line in lines:
            if tr:
                print ''
            cols = line.split(' ')
#            iu.dbg('cols')
            if len(cols) != 4:
                badwit()
            pre,inp,out,post = cols
            aiger.sub.step(inp)
            count += 1
            if count == len(lines):
                invar_fail = il.Symbol('invar__fail',il.find_sort('bool'))
                if il.is_true(aiger.get_sym(invar_fail)):
                    break
            # print 'inputs:'
            # for v in aiger.inputs:
            #     if v in decoder:
            #         print '    {} = {}'.format(decoder[v],aiger.get_sym(v))
            print 'path:'
            match_annotation(action,annot,AigerMatchHandler(aiger,decoder,consts,stvarset,current))
            aiger.sub.next()
            post = aiger.sub.latch_vals()  # use this, since file can be wrong!
            stvals = []
            stmap = aiger.get_state(post)                     
#            iu.dbg('stmap')
            current = dict()
            for v in aiger.latches: # last two are used for encoding
                if v in decoder and v.name != '__init':
                    val = stmap[v]
                    if val is not None:
                        stvals.append(il.Equals(decoder[v],val))
                        current[decoder[v]] = val
            print 'state:'
            for stval in stvals:
                print '    {}'.format(stval)
            if not tr:
                tr = IvyMCTrace(stvals) # first transition is initialization
            else:
                tr.add_state(stvals,ext_act) # remainder are exported actions
        print 80*'-'
        if tr is None:
            badwit()
        return tr
Example #2
0
    def __init__(self,inputs,latches,outputs):
#        iu.dbg('inputs')
#        iu.dbg('latches')
#        iu.dbg('outputs')
        inputs = inputs + [il.Symbol('%%bogus%%',il.find_sort('bool'))] # work around abc bug
        self.inputs = inputs
        self.latches = latches
        self.outputs = outputs
        self.gates = []
        self.map = dict()
        self.next_id = 1
        self.values = dict()
        for x in inputs + latches:
            self.map[x] = self.next_id * 2
#            print 'var: {} = {}'.format(x,self.next_id * 2)
            self.next_id += 1
Example #3
0
    def __call__(self, ivy):
        for decl in ivy.decls:
            with ASTContext(decl):
                n = decl.name()
                #                print "decl: {} : {}".format(n,decl.lineno if hasattr(decl,'lineno') else None)
                if n == 'assert': n = '_assert'  # reserved in python!
                if hasattr(self, n):
                    for x in decl.args:
                        getattr(self, n)(x)


from ivy_ast import ASTContext

# ast compilation

ivy_ast.Variable.get_sort = lambda self: ivy_logic.find_sort(self.sort.rep)


def thing(self):
    with ASTContext(self):
        return self.cmpl()


# "roots" are AST objects that bind variables, such as assignment, assume, etc.
# some roots have symbols as args instead of terms (e.g., field assign)
def compile_root_args(self):
    return [(find_symbol(a) if isinstance(a, str) else a.compile())
            for a in self.args]


def other_thing(self):
Example #4
0
def cmpl_sort(sortname):
    return ivy_logic.find_sort(resolve_alias(sortname))
Example #5
0
    def __call__(self,ivy):
        for decl in ivy.decls:
            with ASTContext(decl):
                n = decl.name()
#                print "decl: {} : {}".format(n,decl.lineno if hasattr(decl,'lineno') else None)
                if n == 'assert': n = '_assert' # reserved in python!
                if hasattr(self,n):
                    for x in decl.args:
                        getattr(self,n)(x)

from ivy_ast import ASTContext

# ast compilation


ivy_ast.Variable.get_sort = lambda self: ivy_logic.find_sort(resolve_alias(self.sort.rep))

def thing(self):
    with ASTContext(self):
        return self.cmpl()

# "roots" are AST objects that bind variables, such as assignment, assume, etc. 
# some roots have symbols as args instead of terms (e.g., field assign)
def compile_root_args(self):
    return [(find_symbol(a) if isinstance(a,str) else a.compile()) for a in self.args]

def other_thing(self):
    # we have to do sort inference on roots
    if hasattr(self,'sort_infer_root'):
        with top_sort_as_default():
            res = self.clone(compile_root_args(self))
Example #6
0
    def __call__(self,ivy):
        for decl in ivy.decls:
            with ASTContext(decl):
                n = decl.name()
#                print "decl: {} : {}".format(n,decl.lineno if hasattr(decl,'lineno') else None)
                if n == 'assert': n = '_assert' # reserved in python!
                if hasattr(self,n):
                    for x in decl.args:
                        getattr(self,n)(x)

from ivy_ast import ASTContext

# ast compilation


ivy_ast.Variable.get_sort = lambda self: ivy_logic.find_sort(self.sort.rep)

def thing(self):
    with ASTContext(self):
        return self.cmpl()

# "roots" are AST objects that bind variables, such as assignment, assume, etc. 
# some roots have symbols as args instead of terms (e.g., field assign)
def compile_root_args(self):
    return [(find_symbol(a) if isinstance(a,str) else a.compile()) for a in self.args]

def other_thing(self):
    # we have to do sort inference on roots
    if hasattr(self,'sort_infer_root'):
        with top_sort_as_default():
            res = self.clone(compile_root_args(self))
Example #7
0
def cmpl_sort(sortname):
    return ivy_logic.find_sort(resolve_alias(sortname))
Example #8
0
    def __call__(self, ivy):
        for decl in ivy.decls:
            with ASTContext(decl):
                n = decl.name()
                #                print "decl: {} : {}".format(n,decl.lineno if hasattr(decl,'lineno') else None)
                if n == 'assert': n = '_assert'  # reserved in python!
                if hasattr(self, n):
                    for x in decl.args:
                        getattr(self, n)(x)


from ivy_ast import ASTContext

# ast compilation

ivy_ast.Variable.get_sort = lambda self: ivy_logic.find_sort(
    resolve_alias(self.sort.rep))


def thing(self):
    with ASTContext(self):
        return self.cmpl()


# "roots" are AST objects that bind variables, such as assignment, assume, etc.
# some roots have symbols as args instead of terms (e.g., field assign)
def compile_root_args(self):
    return [(find_symbol(a) if isinstance(a, str) else a.compile())
            for a in self.args]


def other_thing(self):
Example #9
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
Example #10
0
class ASTContext(object):
    """ ast compiling context, handles line numbers """
    def __init__(self,ast):
        self.ast = ast
    def __enter__(self):
        return self
    def __exit__(self,exc_type, exc_val, exc_tb):
        if isinstance(exc_val,ivy_logic.Error):
#            assert False
            raise IvyError(self.ast,str(exc_val))
        if exc_type == IvyError and exc_val.lineno == None and hasattr(self.ast,'lineno'):
            exc_val.lineno = self.ast.lineno
        return False # don't block any exceptions

ivy_ast.Variable.get_sort = lambda self: ivy_logic.find_sort(self.sort.rep)

def thing(self):
    with ASTContext(self):
        return self.cmpl()

# "roots" are AST objects that bind variables, such as assignment, assume, etc. 
# some roots have symbols as args instead of terms (e.g., field assign)
def compile_root_args(self):
    return [(find_symbol(a) if isinstance(a,str) else a.compile()) for a in self.args]

def other_thing(self):
    # we have to do sort inference on roots
    if hasattr(self,'sort_infer_root'):
        with top_sort_as_default():
            res = self.clone(compile_root_args(self))