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working on expansion

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2012-10-17 08:34:42 -07:00
parent 3a837037d4
commit 8459401b6e
7 changed files with 198 additions and 212 deletions
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59
lib/pdr_context.cpp
View file

@ -1303,9 +1303,6 @@ namespace pdr {
else {
m_model_generalizers.push_back(alloc(model_evaluation_generalizer, *this, m));
}
if (m_params.get_bool(":use-farkas-model", false)) {
m_model_generalizers.push_back(alloc(model_farkas_generalizer, *this));
}
if (m_params.get_bool(":use-precondition-generalizer", false)) {
m_model_generalizers.push_back(alloc(model_precond_generalizer, *this));
}
@ -1689,32 +1686,60 @@ namespace pdr {
Goal is to find phi0(x0), phi1(x1) such that:
phi(x) & phi0(x0) & phi1(x1) => psi(x0, x1, x)
phi(x) & phi0(x0) & phi1(x1) => psi(x0, x1, x)
or at least (ignoring psi alltogether):
phi(x) & phi0(x0) & phi1(x1) => T(x0, x1, x)
Strategy:
- perform cheap existential quantifier elimination on
exists x . T(x0,x1,x) & phi(x)
(e.g., destructive equality resolution)
- Extract literals from T & phi using ternary simulation with M.
- resulting formula is Phi.
- perform cheap existential quantifier elimination on
Phi <- exists x . Phi(x0,x1,x)
(e.g., destructive equality resolution)
- Sub-strategy 1: rename remaining x to fresh variables.
- Sub-strategy 2: replace remaining x to M(x).
- For each literal L in result:
- if L is x0 pure, add L to L0
- if L is x1 pure, add L to L1
- if L mixes x0, x1, add x1 = M(x1) to L1, add L(x1 |-> M(x1)) to L0
- Create sub-goals for L0 and L1.
- pull equalities that use
*/
void context::create_children2(model_node& n, expr* psi) {
SASSERT(n.level() > 0);
pred_transformer& pt = n.pt();
model_core const& M = n.model();
datalog::rule const& r = n.pt().find_rule(M);
expr* T = n.pt().get_transition(r);
datalog::rule const& r = pt.find_rule(M);
expr* T = pt.get_transition(r);
expr* phi = n.state();
expr_ref_vector Ts(m);
datalog::flatten_and(T, Ts);
ternary_model_evaluator tmev(m);
expr_ref_vector mdl(m);
ptr_vector<expr> forms;
forms.push_back(T);
forms.push_back(phi);
datalog::flatten_and(psi, mdl);
expr_ref_vector Phi = tmev.minimize_literals(forms, mdl);
ptr_vector<func_decl> preds;
n.pt().find_predecessors(r, preds);
n.pt().remove_predecessors(Ts);
pt.find_predecessors(r, preds);
pt.remove_predecessors(Phi);
expr_ref_vector vars(m);
unsigned sig_size = pt.head()->get_arity();
for (unsigned i = 0; i < sig_size; ++i) {
vars.push_back(m.mk_const(m_pm.o2n(pt.sig(i), 0)));
}
// TBD: reduce_vars(vars, Phi);
// TBD ...
TRACE("pdr", m_search.display(tout););

6
lib/pdr_context.h
View file

@ -70,10 +70,10 @@ namespace pdr {
ptr_vector<datalog::rule> m_rules; // rules used to derive transformer
prop_solver m_solver; // solver context
vector<expr_ref_vector> m_levels; // level formulas
expr_ref_vector m_invariants; // properties that are invariant.
obj_map<expr, unsigned> m_prop2level; // map property to level where it occurs.
expr_ref_vector m_invariants; // properties that are invariant.
obj_map<expr, unsigned> m_prop2level; // map property to level where it occurs.
obj_map<expr, datalog::rule const*> m_tag2rule; // map tag predicate to rule.
rule2expr m_rule2tag; // map rule to predicate tag.
rule2expr m_rule2tag; // map rule to predicate tag.
qinst_map m_rule2qinst; // map tag to quantifier instantiation.
rule2inst m_rule2inst; // map rules to instantiations of indices
rule2expr m_rule2transition; // map rules to transition

1
lib/pdr_dl_interface.cpp
View file

@ -202,7 +202,6 @@ void dl_interface::collect_params(param_descrs& p) {
p.insert(":inline-proofs", CPK_BOOL, "PDR: (default true) run PDR with proof mode turned on and extract Farkas coefficients directly (instead of creating a separate proof object when extracting coefficients)");
p.insert(":flexible-trace", CPK_BOOL, "PDR: (default false) allow PDR generate long counter-examples by extending candidate trace within search area");
p.insert(":unfold-rules", CPK_UINT, "PDR: (default 0) unfold rules statically using iterative squarring");
PRIVATE_PARAMS(p.insert(":use-farkas-model", CPK_BOOL, "PDR: (default false) enable using Farkas generalization through model propagation"););
PRIVATE_PARAMS(p.insert(":use-precondition-generalizer", CPK_BOOL, "PDR: (default false) enable generalizations from weakest pre-conditions"););
PRIVATE_PARAMS(p.insert(":use-multicore-generalizer", CPK_BOOL, "PDR: (default false) extract multiple cores for blocking states"););
PRIVATE_PARAMS(p.insert(":use-inductive-generalizer", CPK_BOOL, "PDR: (default true) generalize lemmas using induction strengthening"););

78
lib/pdr_generalizers.cpp
View file

@ -121,10 +121,6 @@ namespace pdr {
TRACE("pdr", tout << "old size: " << old_core_size << " new size: " << core.size() << "\n";);
}
//
// extract multiple cores from unreachable state.
//
void core_multi_generalizer::operator()(model_node& n, expr_ref_vector& core, bool& uses_level) {
UNREACHABLE();
@ -567,78 +563,4 @@ namespace pdr {
uses_level = true;
}
}
//
// cube => n.state() & formula
// so n.state() & cube & ~formula is unsat
// so weaken cube while result is still unsat.
//
void model_farkas_generalizer::operator()(model_node& n, expr_ref_vector& cube) {
ast_manager& m = n.pt().get_manager();
manager& pm = n.pt().get_pdr_manager();
front_end_params& p = m_ctx.get_fparams();
farkas_learner learner(p, m);
expr_ref A0(m), A(m), B(m), state(m);
expr_ref_vector states(m);
A0 = n.pt().get_formulas(n.level(), true);
// extract substitution for next-state variables.
expr_substitution sub(m);
solve_for_next_vars(A0, n, sub);
scoped_ptr<expr_replacer> rep = mk_default_expr_replacer(m);
rep->set_substitution(&sub);
(*rep)(A0);
A0 = m.mk_not(A0);
state = n.state();
(*rep)(state);
datalog::flatten_and(state, states);
ptr_vector<func_decl> preds;
n.pt().find_predecessors(n.model(), preds);
TRACE("pdr", for (unsigned i = 0; i < cube.size(); ++i) tout << mk_pp(cube[i].get(), m) << "\n";);
for (unsigned i = 0; i < preds.size(); ++i) {
pred_transformer& pt = m_ctx.get_pred_transformer(preds[i]);
SASSERT(pt.head() == preds[i]);
expr_ref_vector lemmas(m), o_cube(m), other(m), o_state(m), other_state(m);
pm.partition_o_atoms(cube, o_cube, other, i);
pm.partition_o_atoms(states, o_state, other_state, i);
TRACE("pdr",
tout << "cube:\n";
for (unsigned i = 0; i < cube.size(); ++i) tout << mk_pp(cube[i].get(), m) << "\n";
tout << "o_cube:\n";
for (unsigned i = 0; i < o_cube.size(); ++i) tout << mk_pp(o_cube[i].get(), m) << "\n";
tout << "other:\n";
for (unsigned i = 0; i < other.size(); ++i) tout << mk_pp(other[i].get(), m) << "\n";
tout << "o_state:\n";
for (unsigned i = 0; i < o_state.size(); ++i) tout << mk_pp(o_state[i].get(), m) << "\n";
tout << "other_state:\n";
for (unsigned i = 0; i < other_state.size(); ++i) tout << mk_pp(other_state[i].get(), m) << "\n";
);
A = m.mk_and(A0, pm.mk_and(other), pm.mk_and(other_state));
B = m.mk_and(pm.mk_and(o_cube), pm.mk_and(o_state));
TRACE("pdr",
tout << "A: " << mk_pp(A, m) << "\n";
tout << "B: " << mk_pp(B, m) << "\n";);
if (learner.get_lemma_guesses(A, B, lemmas)) {
cube.append(lemmas);
cube.append(o_state);
TRACE("pdr",
tout << "New lemmas:\n";
for (unsigned i = 0; i < lemmas.size(); ++i) {
tout << mk_pp(lemmas[i].get(), m) << "\n";
}
);
}
}
TRACE("pdr", for (unsigned i = 0; i < cube.size(); ++i) tout << mk_pp(cube[i].get(), m) << "\n";);
}
};

7
lib/pdr_generalizers.h
View file

@ -57,13 +57,6 @@ namespace pdr {
virtual void operator()(model_node& n, expr_ref_vector& cube);
};
class model_farkas_generalizer : public model_generalizer {
public:
model_farkas_generalizer(context& ctx) : model_generalizer(ctx) {}
virtual ~model_farkas_generalizer() {}
virtual void operator()(model_node& n, expr_ref_vector& cube);
};
class model_evaluation_generalizer : public model_generalizer {
th_rewriter_model_evaluator m_model_evaluator;
public:

249
lib/pdr_util.cpp
View file

@ -299,6 +299,35 @@ void ternary_model_evaluator::minimize_model(ptr_vector<expr> const & formulas,
m_values.reset();
}
expr_ref_vector ternary_model_evaluator::minimize_literals(ptr_vector<expr> const& formulas, expr_ref_vector const& model) {
setup_model(model);
expr_ref_vector result(m);
ptr_vector<expr> tocollect;
m_visited.reset();
m1.set_level(m_level1);
m2.set_level(m_level2);
VERIFY(check_model(formulas));
collect(formulas, tocollect);
for (unsigned i = 0; i < tocollect.size(); ++i) {
expr* e = tocollect[i];
SASSERT(m.is_bool(e));
SASSERT(is_true(e) || is_false(e));
if (is_true(e)) {
result.push_back(e);
}
else {
result.push_back(m.mk_not(e));
}
}
m_visited.reset();
m1.reset();
m2.reset();
m_values.reset();
return result;
}
void ternary_model_evaluator::prune_by_probing(ptr_vector<expr> const& formulas, expr_ref_vector& model) {
unsigned sz1 = model.size();
@ -335,8 +364,112 @@ void ternary_model_evaluator::prune_by_probing(ptr_vector<expr> const& formulas,
TRACE("pdr", tout << sz1 << " ==> " << model.size() << "\n";);
}
void ternary_model_evaluator::prune_by_cone_of_influence(ptr_vector<expr> const & formulas, expr_ref_vector& model) {
ptr_vector<expr> todo, tocollect;
void ternary_model_evaluator::process_formula(app* e, ptr_vector<expr> todo, ptr_vector<expr>& tocollect) {
SASSERT(m.is_bool(e));
SASSERT(is_true(e) || is_false(e));
unsigned v = is_true(e);
unsigned sz = e->get_num_args();
expr* const* args = e->get_args();
if (e->get_family_id() == m.get_basic_family_id()) {
switch(e->get_decl_kind()) {
case OP_TRUE:
break;
case OP_FALSE:
break;
case OP_EQ:
case OP_IFF:
if (e->get_arg(0) == e->get_arg(1)) {
// no-op
}
else if (!m.is_bool(e->get_arg(0))) {
tocollect.push_back(e);
}
else {
todo.append(sz, args);
}
break;
case OP_DISTINCT:
tocollect.push_back(e);
break;
case OP_ITE:
if (args[1] == args[2]) {
//
}
else if (is_true(args[1]) && is_true(args[2])) {
todo.append(2, args+1);
}
else if (is_false(args[2]) && is_false(args[2])) {
todo.append(2, args+1);
}
else if (is_true(args[0])) {
todo.push_back(args[0]);
todo.push_back(args[1]);
}
else {
SASSERT(is_false(args[0]));
todo.push_back(args[0]);
todo.push_back(args[2]);
}
break;
case OP_AND:
if (v) {
todo.append(sz, args);
}
else {
unsigned i = 0;
for (; !is_false(args[i]) && i < sz; ++i);
if (i == sz) {
fatal_error(1);
}
VERIFY(i < sz);
todo.push_back(args[i]);
}
break;
case OP_OR:
if (v) {
unsigned i = 0;
for (; !is_true(args[i]) && i < sz; ++i);
if (i == sz) {
fatal_error(1);
}
VERIFY(i < sz);
todo.push_back(args[i]);
}
else {
todo.append(sz, args);
}
break;
case OP_XOR:
case OP_NOT:
todo.append(sz, args);
break;
case OP_IMPLIES:
if (v) {
if (is_true(args[1])) {
todo.push_back(args[1]);
}
else if (is_false(args[0])) {
todo.push_back(args[0]);
}
else {
UNREACHABLE();
}
}
else {
todo.append(sz, args);
}
break;
default:
UNREACHABLE();
}
}
else {
tocollect.push_back(e);
}
}
void ternary_model_evaluator::collect(ptr_vector<expr> const& formulas, ptr_vector<expr>& tocollect) {
ptr_vector<expr> todo;
todo.append(formulas);
m_visited.reset();
m1.set_level(m_level1);
@ -347,115 +480,19 @@ void ternary_model_evaluator::prune_by_cone_of_influence(ptr_vector<expr> const
while (!todo.empty()) {
app* e = to_app(todo.back());
todo.pop_back();
if (m_visited.is_marked(e)) {
continue;
if (!m_visited.is_marked(e)) {
process_formula(e, todo, tocollect);
m_visited.mark(e, true);
}
unsigned v = is_true(e);
SASSERT(m.is_bool(e));
SASSERT(is_true(e) || is_false(e));
unsigned sz = e->get_num_args();
expr* const* args = e->get_args();
if (e->get_family_id() == m.get_basic_family_id()) {
switch(e->get_decl_kind()) {
case OP_TRUE:
break;
case OP_FALSE:
break;
case OP_EQ:
case OP_IFF:
if (e->get_arg(0) == e->get_arg(1)) {
// no-op
}
else if (!m.is_bool(e->get_arg(0))) {
tocollect.push_back(e);
}
else {
todo.append(sz, args);
}
break;
case OP_DISTINCT:
tocollect.push_back(e);
break;
case OP_ITE:
if (args[1] == args[2]) {
//
}
else if (is_true(args[1]) && is_true(args[2])) {
todo.append(2, args+1);
}
else if (is_false(args[2]) && is_false(args[2])) {
todo.append(2, args+1);
}
else if (is_true(args[0])) {
todo.push_back(args[0]);
todo.push_back(args[1]);
}
else {
SASSERT(is_false(args[0]));
todo.push_back(args[0]);
todo.push_back(args[2]);
}
break;
case OP_AND:
if (v) {
todo.append(sz, args);
}
else {
unsigned i = 0;
for (; !is_false(args[i]) && i < sz; ++i);
if (i == sz) {
fatal_error(1);
}
VERIFY(i < sz);
todo.push_back(args[i]);
}
break;
case OP_OR:
if (v) {
unsigned i = 0;
for (; !is_true(args[i]) && i < sz; ++i);
if (i == sz) {
fatal_error(1);
}
VERIFY(i < sz);
todo.push_back(args[i]);
}
else {
todo.append(sz, args);
}
break;
case OP_XOR:
case OP_NOT:
todo.append(sz, args);
break;
case OP_IMPLIES:
if (v) {
if (is_true(args[1])) {
todo.push_back(args[1]);
}
else if (is_false(args[0])) {
todo.push_back(args[0]);
}
else {
UNREACHABLE();
}
}
else {
todo.append(sz, args);
}
break;
default:
UNREACHABLE();
}
}
else {
tocollect.push_back(e);
}
m_visited.mark(e, true);
}
m1.set_level(m_level1);
m2.set_level(m_level2);
m_visited.reset();
}
void ternary_model_evaluator::prune_by_cone_of_influence(ptr_vector<expr> const & formulas, expr_ref_vector& model) {
ptr_vector<expr> tocollect;
collect(formulas, tocollect);
for (unsigned i = 0; i < tocollect.size(); ++i) {
for_each_expr(*this, m_visited, tocollect[i]);
}

10
lib/pdr_util.h
View file

@ -214,6 +214,9 @@ class ternary_model_evaluator : public model_evaluator_base {
void del_model(expr* e);
bool get_assignment(expr* e, expr*& var, expr*& val);
void collect(ptr_vector<expr> const& formulas, ptr_vector<expr>& tocollect);
void process_formula(app* e, ptr_vector<expr> todo, ptr_vector<expr>& tocollect);
void prune_by_cone_of_influence(ptr_vector<expr> const & formulas, expr_ref_vector& model);
void prune_by_probing(ptr_vector<expr> const & formulas, expr_ref_vector& model);
@ -246,6 +249,13 @@ public:
ternary_model_evaluator(ast_manager& m) : m(m), m_arith(m), m_bv(m) {}
virtual void minimize_model(ptr_vector<expr> const & formulas, expr_ref_vector & model);
/**
\brief extract literals from formulas that satisfy formulas.
\pre model satisfies formulas
*/
expr_ref_vector minimize_literals(ptr_vector<expr> const & formulas, expr_ref_vector const & model);
// for_each_expr visitor.
void operator()(expr* e) {}
};