mirrors/z3
3
0
Fork 0
mirror of https://github.com/Z3Prover/z3 synced 2025-04-08 18:31:49 +00:00
Code Activity
z3/lib/pdr_util.cpp
Leonardo de Moura e9eab22e5c Z3 sources 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2012-10-02 11:35:25 -07:00

842 lines
26 KiB
C++
Raw Blame History

/*++
Copyright (c) 2011 Microsoft Corporation
Module Name:
pdr_util.cpp
Abstract:
Utility functions for PDR.
Author:
Krystof Hoder (t-khoder) 2011-8-19.
Revision History:
Notes:
--*/
#include <sstream>
#include "arith_simplifier_plugin.h"
#include "array_decl_plugin.h"
#include "ast_pp.h"
#include "basic_simplifier_plugin.h"
#include "bv_simplifier_plugin.h"
#include "bool_rewriter.h"
#include "dl_util.h"
#include "for_each_expr.h"
#include "front_end_params.h"
#include "model.h"
#include "model_v2_pp.h"
#include "ref_vector.h"
#include "rewriter.h"
#include "rewriter_def.h"
#include "util.h"
#include "pdr_manager.h"
#include "pdr_prop_solver.h"
#include "pdr_util.h"
#include "arith_decl_plugin.h"
namespace pdr {
unsigned ceil_log2(unsigned u)
{
if (u==0) { return 0; }
unsigned pow2 = next_power_of_two(u);
return get_num_1bits(pow2-1);
}
std::string pp_cube(const ptr_vector<expr>& model, ast_manager& m) {
return pp_cube(model.size(), model.c_ptr(), m);
}
std::string pp_cube(const expr_ref_vector& model, ast_manager& m) {
return pp_cube(model.size(), model.c_ptr(), m);
}
std::string pp_cube(const app_ref_vector& model, ast_manager& m) {
return pp_cube(model.size(), model.c_ptr(), m);
}
std::string pp_cube(const app_vector& model, ast_manager& m) {
return pp_cube(model.size(), model.c_ptr(), m);
}
std::string pp_cube(unsigned sz, app * const * lits, ast_manager& m) {
return pp_cube(sz, reinterpret_cast<expr * const *>(lits), m);
}
std::string pp_cube(unsigned sz, expr * const * lits, ast_manager& m) {
std::stringstream res;
res << "(";
expr * const * end = lits+sz;
for (expr * const * it = lits; it!=end; it++) {
res << mk_pp(*it, m);
if (it+1!=end) {
res << ", ";
}
}
res << ")";
return res.str();
}
/////////////////////////
// model_evaluator_base
//
void model_evaluator_base::minimize_model(ptr_vector<expr> const & formulas, expr_ref_vector & model)
{
ast_manager & m = model.get_manager();
bool has_unknown, has_false;
DEBUG_CODE(
check_model(formulas, model, has_unknown, has_false);
if (has_false) {
std::cout<<"formulas: "<<pdr::pp_cube(formulas, m)<<"\n";
std::cout<<"model: "<<pdr::pp_cube(model, m)<<"\n";
}
SASSERT(!has_false);
);
unsigned i=0;
while(i<model.size()) {
expr_ref removed(m);
removed = model[i].get();
if (i<model.size()-1) {
model[i] = model.back();
}
model.pop_back();
check_model(formulas, model, has_unknown, has_false);
SASSERT(!has_false);
if (has_unknown) {
//if we introduced unknown, we restore the removed element
if (i<model.size()) {
model.push_back(model[i].get());
model[i] = removed;
}
else {
model.push_back(removed);
}
i++;
}
}
}
/////////////////////////////////////
// th_rewriter_model_evaluator_base
//
class th_rewriter_model_evaluator::expr_rewriter_cfg : public default_rewriter_cfg
{
const obj_map<expr,expr *>& m_assignment;
public:
expr_rewriter_cfg(const obj_map<expr,expr *>& assignment)
: m_assignment(assignment)
{
}
bool get_subst(expr * s, expr * & t, proof * & t_pr) {
return m_assignment.find(s,t);
}
};
void th_rewriter_model_evaluator::setup_assignment(expr_ref_vector const& model, obj_map<expr,expr*>& assignment) {
for (unsigned i = 0; i < model.size(); ++i) {
expr * mlit = model[i]; //model literal
if (is_uninterp(mlit)) {
assignment.insert(mlit, m.mk_true());
}
expr * arg1;
expr * arg2;
if (m.is_not(mlit, arg1)) {
assignment.insert(arg1, m.mk_false());
}
else if (m.is_eq(mlit, arg1, arg2)) {
if (!is_uninterp(arg1)) {
std::swap(arg1, arg2);
}
if (is_uninterp(arg1)) {
assignment.insert(arg1, arg2);
}
else {
assignment.insert(mlit, m.mk_true());
}
}
}
}
void th_rewriter_model_evaluator::check_model(ptr_vector<expr> const & formulas, expr_ref_vector & model,
bool & has_unknown, bool & has_false)
{
obj_map<expr,expr *> assignment;
setup_assignment(model, assignment);
expr_rewriter_cfg r_cfg(assignment);
rewriter_tpl<expr_rewriter_cfg> rwr(m, false, r_cfg);
has_false = false;
has_unknown = false;
for (unsigned i = 0; i < formulas.size(); ++i) {
expr * form = formulas[i];
expr_ref asgn_form(m);
rwr(form, asgn_form);
expr_ref simpl_form(m);
m_rewriter(asgn_form, simpl_form);
if (m.is_false(simpl_form)) {
has_false = true;
}
else if (!m.is_true(simpl_form)) {
IF_VERBOSE(7, verbose_stream() << "formula evaluated as unknown:\noriginal: "
<< mk_pp(form, m) << "\n"
<< "simplified: " << mk_pp(simpl_form,m) << "\n";);
has_unknown = true;
}
}
m_rewriter.reset();
}
//00 -- non-visited
//01 -- X
//10 -- false
//11 -- true
#define UNKNOWN(x) (!m1.is_marked(x) && !m2.is_marked(x))
#define SET_UNKNOWN(x) { TRACE("pdr_verbose", tout << "unknown: " << mk_pp(x,m) << "\n";); m1.reset_mark(x); m2.reset_mark(x); }
#define IS_X(x) (!m1.is_marked(x) && m2.is_marked(x))
#define IS_FALSE(x) (m1.is_marked(x) && !m2.is_marked(x))
#define IS_TRUE(x) (m1.is_marked(x) && m2.is_marked(x))
#define SET_X(x) { SASSERT(UNKNOWN(x)); m2.mark(x); }
#define SET_V(x) { SASSERT(UNKNOWN(x)); m1.mark(x); }
#define SET_FALSE(x) { SASSERT(UNKNOWN(x)); m1.mark(x); }
#define SET_TRUE(x) { SASSERT(UNKNOWN(x)); m1.mark(x); m2.mark(x); }
#define SET_BOOL(x, v) { if (v) { SET_TRUE(x); } else { SET_FALSE(x); } }
#define GET_VALUE(x) m_values.find(x)
#define SET_VALUE(x,y) { SET_V(x); TRACE("pdr_verbose", tout << mk_pp(x,m) << " " << y << "\n";); m_values.insert(x, y); }
void ternary_model_evaluator::add_model(expr* e) {
expr* nlit, *var, *val;
rational r;
// SASSERT(UNKNOWN(e));
if (m.is_eq(e, var, val)) {
if (!is_uninterp(var)) {
std::swap(var, val);
}
if (m.is_true(val) && UNKNOWN(var)) {
SET_TRUE(var);
}
else if (m.is_false(val) && UNKNOWN(var)) {
SET_FALSE(var);
}
else if (m_arith.is_numeral(val, r) && UNKNOWN(var)) {
SET_VALUE(var, r);
}
else {
TRACE("pdr_verbose", tout << "no value for " << mk_pp(val, m) << "\n";);
}
}
else if (m.is_not(e, nlit)) {
SET_FALSE(nlit);
}
else if (m.is_bool(e)) {
SET_TRUE(e);
}
else {
TRACE("pdr_verbose", tout << "no value set of " << mk_pp(e, m) << "\n";);
}
}
void ternary_model_evaluator::del_model(expr* e) {
expr* nlit, *var, *val;
if (m.is_eq(e, var, val)) {
if (!is_uninterp(var)) {
std::swap(var, val);
}
SET_UNKNOWN(var);
m_values.remove(var);
}
else if (m.is_not(e, nlit)) {
SET_UNKNOWN(nlit);
}
else if (m.is_bool(e)) {
SET_UNKNOWN(e);
}
else {
TRACE("pdr_verbose", tout << "no value set of " << mk_pp(e, m) << "\n";);
}
}
void ternary_model_evaluator::setup_model(expr_ref_vector const& model) {
m_values.reset();
for (unsigned i = 0; i < model.size(); ++i) {
expr* e = model[i];
if (UNKNOWN(e)) {
add_model(e);
}
}
m_level1 = m1.get_level();
m_level2 = m2.get_level();
}
void ternary_model_evaluator::minimize_model(ptr_vector<expr> const & formulas, expr_ref_vector & model)
{
setup_model(model);
TRACE("pdr_verbose",
for (unsigned i = 0; i < model.size(); ++i) tout << mk_pp(model[i].get(), m) << "\n";
tout << "formulas\n";
for (unsigned i = 0; i < formulas.size(); ++i) tout << mk_pp(formulas[i], m) << "\n";
);
for (unsigned i = 0; i < model.size(); ) {
expr_ref removed(model[i].get(), m);
if (i + 1 < model.size()) {
model[i] = model.back();
}
model.pop_back();
del_model(removed);
m1.set_level(m_level1);
m2.set_level(m_level2);
bool formulas_hold = check_model(formulas);
m1.set_level(m_level1);
m2.set_level(m_level2);
if (!formulas_hold) {
// if we introduced unknown, we restore the removed element
add_model(removed);
m_level1 = m1.get_level();
m_level2 = m2.get_level();
if (i < model.size()) {
model.push_back(model[i].get());
model[i] = removed;
}
else {
model.push_back(removed);
}
i++;
}
}
m1.reset();
m2.reset();
m_values.reset();
}
bool ternary_model_evaluator::check_model(ptr_vector<expr> const& formulas) {
ptr_vector<expr> todo;
assign_vector_with_casting(todo, formulas);
expr *argCond, *argThen, *argElse, *arg;
rational r, r2;
while(!todo.empty()) {
expr * curr_e = todo.back();
unsigned pre_curr_depth = todo.size()-1;
if (!is_app(curr_e)) {
todo.pop_back();
continue;
}
app * curr = to_app(curr_e);
#define ARG1 curr->get_arg(0)
#define ARG2 curr->get_arg(1)
if (!UNKNOWN(curr)) {
todo.pop_back();
continue;
}
unsigned arity = curr->get_num_args();
if (curr->get_family_id() == m_arith.get_family_id()) {
bool all_set = true, some_x = false;
for (unsigned i = 0; !some_x && i < arity; ++i) {
expr* arg = curr->get_arg(i);
if (UNKNOWN(arg)) {
todo.push_back(arg);
all_set = false;
}
else if (IS_X(arg)) {
some_x = true;
}
}
if (some_x) {
SET_X(curr);
}
else if (!all_set) {
continue;
}
else {
switch(curr->get_decl_kind()) {
case OP_NUM:
VERIFY(m_arith.is_numeral(curr,r));
SET_VALUE(curr, r);
break;
case OP_IRRATIONAL_ALGEBRAIC_NUM:
SET_X(curr);
break;
case OP_LE:
SET_BOOL(curr, GET_VALUE(ARG1) <= GET_VALUE(ARG2));
break;
case OP_GE:
SET_BOOL(curr, GET_VALUE(ARG1) >= GET_VALUE(ARG2));
break;
case OP_LT:
SET_BOOL(curr, GET_VALUE(ARG1) < GET_VALUE(ARG2));
break;
case OP_GT:
SET_BOOL(curr, GET_VALUE(ARG1) > GET_VALUE(ARG2));
break;
case OP_ADD:
r = rational::zero();
for (unsigned i = 0; i < arity; ++i) {
r += GET_VALUE(curr->get_arg(i));
}
SET_VALUE(curr, r);
break;
case OP_SUB:
r = GET_VALUE(curr->get_arg(0));
for (unsigned i = 1; i < arity; ++i) {
r -= GET_VALUE(curr->get_arg(i));
}
SET_VALUE(curr, r);
break;
case OP_UMINUS:
SASSERT(arity == 1);
SET_VALUE(curr, GET_VALUE(curr->get_arg(0)));
break;
case OP_MUL:
r = rational::one();
for (unsigned i = 0; i < arity; ++i) {
r *= GET_VALUE(curr->get_arg(i));
}
SET_VALUE(curr, r);
break;
case OP_DIV:
SASSERT(arity == 2);
r = GET_VALUE(ARG2);
if (r.is_zero()) {
SET_X(curr);
}
else {
SET_VALUE(curr, GET_VALUE(ARG1) / r);
}
break;
case OP_IDIV:
SASSERT(arity == 2);
r = GET_VALUE(ARG2);
if (r.is_zero()) {
SET_X(curr);
}
else {
SET_VALUE(curr, div(GET_VALUE(ARG1), r));
}
break;
case OP_REM:
// rem(v1,v2) = if v2 >= 0 then mod(v1,v2) else -mod(v1,v2)
SASSERT(arity == 2);
r = GET_VALUE(ARG2);
if (r.is_zero()) {
SET_X(curr);
}
else {
r2 = mod(GET_VALUE(ARG1), r);
if (r.is_neg()) r2.neg();
SET_VALUE(curr, r2);
}
break;
case OP_MOD:
SASSERT(arity == 2);
r = GET_VALUE(ARG2);
if (r.is_zero()) {
SET_X(curr);
}
else {
SET_VALUE(curr, mod(GET_VALUE(ARG1), r));
}
break;
case OP_TO_REAL:
SASSERT(arity == 1);
SET_VALUE(curr, GET_VALUE(ARG1));
break;
case OP_TO_INT:
SASSERT(arity == 1);
SET_VALUE(curr, floor(GET_VALUE(ARG1)));
break;
case OP_IS_INT:
SASSERT(arity == 1);
SET_BOOL(curr, GET_VALUE(ARG1).is_int());
break;
case OP_POWER:
SET_X(curr);
break;
default:
UNREACHABLE();
break;
}
}
}
else if (curr->get_family_id() == m_bv.get_family_id()) {
throw default_exception("PDR engine currently does not support bit-vectors");
}
else if (curr->get_family_id() == m.get_basic_family_id()) {
expr* arg1, *arg2;
if (m.is_and(curr)) {
// we're adding unknowns on the top of the todo stack, if there is none added,
// all arguments were known
bool has_x = false, has_false = false;
for (unsigned j = 0; !has_false && j < arity; ++j) {
expr * arg = curr->get_arg(j);
if (IS_FALSE(arg)) {
has_false = true;
}
else if (IS_X(arg)) {
has_x = true;
}
else if (UNKNOWN(arg)) {
todo.push_back(arg);
}
}
if (has_false) {
SET_FALSE(curr);
}
else {
if (todo.back() != curr) {
continue;
}
else if (has_x) {
SET_X(curr);
}
else {
SET_TRUE(curr);
}
}
}
else if (m.is_or(curr)) {
bool has_x = false, has_true = false;
for (unsigned j = 0; !has_true && j < arity; ++j) {
expr * arg = curr->get_arg(j);
if (IS_TRUE(arg)) {
has_true = true;
}
else if (IS_X(arg)) {
has_x = true;
}
else if (UNKNOWN(arg)) {
todo.push_back(arg);
}
}
if (has_true) {
SET_TRUE(curr);
}
else {
if (todo.back() != curr) {
continue;
}
else if (has_x) {
SET_X(curr);
}
else {
SET_FALSE(curr);
}
}
}
else if (m.is_not(curr, arg)) {
if (UNKNOWN(arg)) {
todo.push_back(arg);
continue;
}
if (IS_TRUE(arg)) {
SET_FALSE(curr);
}
else if (IS_FALSE(arg)) {
SET_TRUE(curr);
}
else {
SASSERT(IS_X(arg));
SET_X(curr);
}
}
else if (m.is_implies(curr, arg1, arg2)) {
if (IS_FALSE(arg1) || IS_TRUE(arg2)) {
SET_TRUE(curr);
}
else if (UNKNOWN(arg1) || UNKNOWN(arg2)) {
if (UNKNOWN(arg1)) { todo.push_back(arg1); }
if (UNKNOWN(arg2)) { todo.push_back(arg2); }
continue;
}
else if (IS_TRUE(arg1) && IS_FALSE(arg2)) {
SET_FALSE(curr);
}
else {
SASSERT(IS_X(arg1) || IS_X(arg2));
SET_X(curr);
}
}
else if (m.is_iff(curr, arg1, arg2) ||
(m.is_eq(curr, arg1, arg2) && m.is_bool(arg1))) {
if (IS_X(arg1) || IS_X(arg2)) {
SET_X(curr);
}
else if (UNKNOWN(arg1) || UNKNOWN(arg2)) {
if (UNKNOWN(arg1)) { todo.push_back(arg1); }
if (UNKNOWN(arg2)) { todo.push_back(arg2); }
continue;
}
else {
bool val = IS_TRUE(arg1)==IS_TRUE(arg2);
SASSERT(val == (IS_FALSE(arg1)==IS_FALSE(arg2)));
if (val) {
SET_TRUE(curr);
}
else {
SET_FALSE(curr);
}
}
}
else if (m.is_ite(curr, argCond, argThen, argElse) && m.is_bool(argThen)) {
if (IS_TRUE(argCond)) {
if (IS_TRUE(argThen)) { SET_TRUE(curr); }
else if (IS_FALSE(argThen)) { SET_FALSE(curr); }
else if (IS_X(argThen)) { SET_X(curr); }
else {
todo.push_back(argThen);
continue;
}
}
else if (IS_FALSE(argCond)) {
if (IS_TRUE(argElse)) { SET_TRUE(curr); }
else if (IS_FALSE(argElse)) { SET_FALSE(curr); }
else if (IS_X(argElse)) { SET_X(curr); }
else {
todo.push_back(argElse);
continue;
}
}
else if (IS_TRUE(argThen) && IS_TRUE(argElse)) {
SET_TRUE(curr);
}
else if (IS_FALSE(argThen) && IS_FALSE(argElse)) {
SET_FALSE(curr);
}
else if (IS_X(argCond) && (IS_X(argThen) || IS_X(argElse)) ) {
SET_X(curr);
} else if (UNKNOWN(argCond) || UNKNOWN(argThen) || UNKNOWN(argElse)) {
if (UNKNOWN(argCond)) { todo.push_back(argCond); }
if (UNKNOWN(argThen)) { todo.push_back(argThen); }
if (UNKNOWN(argElse)) { todo.push_back(argElse); }
continue;
}
else {
SASSERT(IS_X(argCond));
SASSERT((IS_TRUE(argThen) && IS_FALSE(argElse)) ||
(IS_FALSE(argThen) && IS_TRUE(argElse)));
SET_X(curr);
}
}
else if (m.is_true(curr)) {
SET_TRUE(curr);
}
else if (m.is_false(curr)) {
SET_FALSE(curr);
}
else if (m.is_eq(curr, arg1, arg2) && arg1 == arg2) {
SET_TRUE(curr);
}
else if (m.is_eq(curr, arg1, arg2)) {
if (UNKNOWN(arg1)) {
todo.push_back(arg1);
}
if (UNKNOWN(arg2)) {
todo.push_back(arg2);
}
if (curr != todo.back()) {
continue;
}
if (IS_X(arg1) || IS_X(arg2)) {
SET_X(curr);
}
else {
SET_BOOL(curr, GET_VALUE(arg1) == GET_VALUE(arg2));
}
}
else if (m.is_ite(curr, argCond, argThen, argElse) && m_arith.is_int_real(argThen)) {
if (IS_TRUE(argCond) || (argThen == argElse)) {
if (UNKNOWN(argThen)) {
todo.push_back(argThen);
continue;
}
if (IS_X(argThen)) {
SET_X(curr);
}
else {
SET_VALUE(curr, GET_VALUE(argThen));
}
}
else if (IS_FALSE(argCond)) {
if (UNKNOWN(argElse)) {
todo.push_back(argElse);
continue;
}
if (IS_X(argElse)) {
SET_X(curr);
}
else {
SET_VALUE(curr, GET_VALUE(argElse));
}
}
else if (UNKNOWN(argCond)) {
todo.push_back(argCond);
continue;
}
else {
SET_X(curr);
}
}
else {
UNREACHABLE();
}
}
else {
TRACE("pdr_verbse", tout << "Not evaluated " << mk_pp(curr, m) << "\n";);
SET_X(curr);
}
IF_VERBOSE(35,verbose_stream() << "assigned "<<mk_pp(curr_e,m)
<<(IS_TRUE(curr_e) ? "true" : IS_FALSE(curr_e) ? "false" : "unknown") << "\n";);
SASSERT(!UNKNOWN(curr));
todo.shrink(pre_curr_depth);
}
bool has_unknown = false;
for (unsigned i = 0; i < formulas.size(); ++i) {
expr * form = formulas[i];
SASSERT(!UNKNOWN(form));
TRACE("pdr_verbose",
tout << "formula is " << (IS_TRUE(form) ? "true" : IS_FALSE(form) ? "false" : "unknown") << "\n" <<mk_pp(form, m)<< "\n";);
if (IS_FALSE(form)) {
IF_VERBOSE(2, verbose_stream() << "formula false in model: "<<mk_pp(form, m) << "\n";);
UNREACHABLE();
}
if (IS_X(form)) {
has_unknown = true;
}
}
return !has_unknown;
}
func_decl * mk_store(ast_manager& m, sort * arr_sort)
{
family_id array_fid = m.get_family_id(symbol("array"));
unsigned num_params = arr_sort->get_num_parameters();
ptr_vector<sort> domain;
domain.push_back(arr_sort);
//we push params of the array as remaining arguments of the store. The first
//num_params-1 parameters are indices and the last one is the range of the array
for (unsigned i=0; i<num_params; ++i) {
domain.push_back(to_sort(arr_sort->get_parameter(i).get_ast()));
}
return m.mk_func_decl(array_fid, OP_STORE,
arr_sort->get_num_parameters(), arr_sort->get_parameters(),
domain.size(), domain.c_ptr(), arr_sort);
}
void get_as_array_value(const model_core & mdl, expr * arr_e, expr_ref& res) {
ast_manager& m = mdl.get_manager();
array_util pl(m);
SASSERT(pl.is_as_array(arr_e));
app * arr = to_app(arr_e);
unsigned sz = 0;
func_decl_ref f(pl.get_as_array_func_decl(arr), m);
sort * arr_sort = arr->get_decl()->get_range();
func_interp* g = mdl.get_func_interp(f);
res = pl.mk_const_array(arr_sort, g->get_else());
unsigned arity = f->get_arity();
sz = g->num_entries();
if (sz) {
func_decl_ref store_fn(mk_store(m, arr_sort), m);
ptr_vector<expr> store_args;
for (unsigned i = 0; i < sz; ++i) {
const func_entry * fe = g->get_entry(i);
store_args.reset();
store_args.push_back(res);
store_args.append(arity, fe->get_args());
store_args.push_back(fe->get_result());
res = m.mk_app(store_fn, store_args.size(), store_args.c_ptr());
}
}
}
void get_value_from_model(const model_core & mdl, func_decl * f, expr_ref& res) {
SASSERT(f->get_arity()==0);
ast_manager& m = mdl.get_manager();
res = mdl.get_const_interp(f);
array_util pl(m);
if (pl.is_as_array(res)) {
get_as_array_value(mdl, res, res);
}
}
void get_cube_from_model(const model_core & mdl, expr_ref_vector & res, pdr::prop_solver& solver)
{
ast_manager& m = res.get_manager();
res.reset();
unsigned sz = mdl.get_num_constants();
for (unsigned i = 0; i < sz; i++) {
func_decl * d = mdl.get_constant(i);
if (solver.is_aux_symbol(d)) {
continue;
}
SASSERT(d->get_arity()==0);
expr_ref interp(m);
pdr::get_value_from_model(mdl, d, interp);
app_ref constant(m.mk_const(d), m);
app_ref lit(m);
if (m.is_bool(d->get_range())) {
if (m.is_true(interp)) {
lit = constant;
}
else {
SASSERT(m.is_false(interp));
lit = m.mk_not(constant);
}
}
else {
lit = m.mk_eq(constant, interp);
}
res.push_back(lit);
}
}
}
View git blame Copy permalink