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z3/src/model/model_implicant.cpp
Nikolaj Bjorner 2ff51e9a60 move model_evaluator from pdr to model, call it model_implicant 
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
2013-11-23 21:33:35 +01:00

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/*++
Copyright (c) 2011 Microsoft Corporation
Module Name:
model_implicant.cpp
Abstract:
Facility to extract prime implicant from model.
Author:
Krystof Hoder (t-khoder) 2011-8-19.
Revision History:
Notes:
--*/
#include <sstream>
#include "array_decl_plugin.h"
#include "ast_pp.h"
#include "bool_rewriter.h"
#include "for_each_expr.h"
#include "model.h"
#include "ref_vector.h"
#include "rewriter.h"
#include "rewriter_def.h"
#include "util.h"
#include "model_implicant.h"
#include "arith_decl_plugin.h"
#include "expr_replacer.h"
#include "model_smt2_pp.h"
#include "poly_rewriter.h"
#include "poly_rewriter_def.h"
#include "arith_rewriter.h"
#include "scoped_proof.h"
/////////////////////////
// model_implicant
//
void model_implicant::assign_value(expr* e, expr* val) {
rational r;
if (m.is_true(val)) {
set_true(e);
}
else if (m.is_false(val)) {
set_false(e);
}
else if (m_arith.is_numeral(val, r)) {
set_number(e, r);
}
else if (m.is_value(val)) {
set_value(e, val);
}
else {
IF_VERBOSE(3, verbose_stream() << "Not evaluated " << mk_pp(e, m) << " := " << mk_pp(val, m) << "\n";);
TRACE("pdr", tout << "Variable is not tracked: " << mk_pp(e, m) << " := " << mk_pp(val, m) << "\n";);
set_x(e);
}
}
void model_implicant::setup_model(model_ref& model) {
m_numbers.reset();
m_values.reset();
m_model = model;
rational r;
unsigned sz = model->get_num_constants();
for (unsigned i = 0; i < sz; i++) {
func_decl * d = model->get_constant(i);
expr* val = model->get_const_interp(d);
expr* e = m.mk_const(d);
m_refs.push_back(e);
assign_value(e, val);
}
}
void model_implicant::reset() {
m1.reset();
m2.reset();
m_values.reset();
m_visited.reset();
m_numbers.reset();
m_refs.reset();
m_model = 0;
}
expr_ref_vector model_implicant::minimize_model(ptr_vector<expr> const & formulas, model_ref& mdl) {
setup_model(mdl);
TRACE("pdr_verbose",
tout << "formulas:\n";
for (unsigned i = 0; i < formulas.size(); ++i) tout << mk_pp(formulas[i], m) << "\n";
);
expr_ref_vector model = prune_by_cone_of_influence(formulas);
TRACE("pdr_verbose",
tout << "pruned model:\n";
for (unsigned i = 0; i < model.size(); ++i) tout << mk_pp(model[i].get(), m) << "\n";);
reset();
DEBUG_CODE(
setup_model(mdl);
VERIFY(check_model(formulas));
reset(););
return model;
}
expr_ref_vector model_implicant::minimize_literals(ptr_vector<expr> const& formulas, model_ref& mdl) {
TRACE("pdr",
tout << "formulas:\n";
for (unsigned i = 0; i < formulas.size(); ++i) tout << mk_pp(formulas[i], m) << "\n";
);
expr_ref_vector result(m);
expr_ref tmp(m);
ptr_vector<expr> tocollect;
setup_model(mdl);
collect(formulas, tocollect);
for (unsigned i = 0; i < tocollect.size(); ++i) {
expr* e = tocollect[i];
expr* e1, *e2;
SASSERT(m.is_bool(e));
SASSERT(is_true(e) || is_false(e));
if (is_true(e)) {
result.push_back(e);
}
// hack to break disequalities for arithmetic variables.
else if (m.is_eq(e, e1, e2) && m_arith.is_int_real(e1)) {
if (get_number(e1) < get_number(e2)) {
result.push_back(m_arith.mk_lt(e1,e2));
}
else {
result.push_back(m_arith.mk_lt(e2,e1));
}
}
else {
result.push_back(m.mk_not(e));
}
}
reset();
TRACE("pdr",
tout << "minimized model:\n";
for (unsigned i = 0; i < result.size(); ++i) tout << mk_pp(result[i].get(), m) << "\n";
);
return result;
}
void model_implicant::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 (args[0] == args[1]) {
SASSERT(v);
// no-op
}
else if (m.is_bool(args[0])) {
todo.append(sz, args);
}
else {
tocollect.push_back(e);
}
break;
case OP_DISTINCT:
tocollect.push_back(e);
break;
case OP_ITE:
if (args[1] == args[2]) {
tocollect.push_back(args[1]);
}
else if (is_true(args[1]) && is_true(args[2])) {
todo.append(2, args+1);
}
else if (is_false(args[1]) && is_false(args[2])) {
todo.append(2, args+1);
}
else if (is_true(args[0])) {
todo.append(2, args);
}
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 {
IF_VERBOSE(0, verbose_stream() << "Term not handled " << mk_pp(e, m) << "\n";);
UNREACHABLE();
}
}
else {
todo.append(sz, args);
}
break;
default:
IF_VERBOSE(0, verbose_stream() << "Term not handled " << mk_pp(e, m) << "\n";);
UNREACHABLE();
}
}
else {
tocollect.push_back(e);
}
}
void model_implicant::collect(ptr_vector<expr> const& formulas, ptr_vector<expr>& tocollect) {
ptr_vector<expr> todo;
todo.append(formulas);
m_visited.reset();
VERIFY(check_model(formulas));
while (!todo.empty()) {
app* e = to_app(todo.back());
todo.pop_back();
if (!m_visited.is_marked(e)) {
process_formula(e, todo, tocollect);
m_visited.mark(e, true);
}
}
m_visited.reset();
}
expr_ref_vector model_implicant::prune_by_cone_of_influence(ptr_vector<expr> const & formulas) {
ptr_vector<expr> tocollect;
collect(formulas, tocollect);
m1.reset();
m2.reset();
for (unsigned i = 0; i < tocollect.size(); ++i) {
TRACE("pdr_verbose", tout << "collect: " << mk_pp(tocollect[i], m) << "\n";);
for_each_expr(*this, m_visited, tocollect[i]);
}
unsigned sz = m_model->get_num_constants();
expr_ref e(m), eq(m), val(m);
expr_ref_vector model(m);
for (unsigned i = 0; i < sz; i++) {
e = m.mk_const(m_model->get_constant(i));
if (m_visited.is_marked(e)) {
val = eval(m_model, e);
eq = m.mk_eq(e, val);
model.push_back(eq);
}
}
m_visited.reset();
TRACE("pdr", tout << sz << " ==> " << model.size() << "\n";);
return model;
}
void model_implicant::eval_arith(app* e) {
rational r, r2;
#define ARG1 e->get_arg(0)
#define ARG2 e->get_arg(1)
unsigned arity = e->get_num_args();
for (unsigned i = 0; i < arity; ++i) {
expr* arg = e->get_arg(i);
if (is_x(arg)) {
set_x(e);
return;
}
SASSERT(!is_unknown(arg));
}
switch(e->get_decl_kind()) {
case OP_NUM:
VERIFY(m_arith.is_numeral(e, r));
set_number(e, r);
break;
case OP_IRRATIONAL_ALGEBRAIC_NUM:
set_x(e);
break;
case OP_LE:
set_bool(e, get_number(ARG1) <= get_number(ARG2));
break;
case OP_GE:
set_bool(e, get_number(ARG1) >= get_number(ARG2));
break;
case OP_LT:
set_bool(e, get_number(ARG1) < get_number(ARG2));
break;
case OP_GT:
set_bool(e, get_number(ARG1) > get_number(ARG2));
break;
case OP_ADD:
r = rational::zero();
for (unsigned i = 0; i < arity; ++i) {
r += get_number(e->get_arg(i));
}
set_number(e, r);
break;
case OP_SUB:
r = get_number(e->get_arg(0));
for (unsigned i = 1; i < arity; ++i) {
r -= get_number(e->get_arg(i));
}
set_number(e, r);
break;
case OP_UMINUS:
SASSERT(arity == 1);
set_number(e, get_number(e->get_arg(0)));
break;
case OP_MUL:
r = rational::one();
for (unsigned i = 0; i < arity; ++i) {
r *= get_number(e->get_arg(i));
}
set_number(e, r);
break;
case OP_DIV:
SASSERT(arity == 2);
r = get_number(ARG2);
if (r.is_zero()) {
set_x(e);
}
else {
set_number(e, get_number(ARG1) / r);
}
break;
case OP_IDIV:
SASSERT(arity == 2);
r = get_number(ARG2);
if (r.is_zero()) {
set_x(e);
}
else {
set_number(e, div(get_number(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_number(ARG2);
if (r.is_zero()) {
set_x(e);
}
else {
r2 = mod(get_number(ARG1), r);
if (r.is_neg()) r2.neg();
set_number(e, r2);
}
break;
case OP_MOD:
SASSERT(arity == 2);
r = get_number(ARG2);
if (r.is_zero()) {
set_x(e);
}
else {
set_number(e, mod(get_number(ARG1), r));
}
break;
case OP_TO_REAL:
SASSERT(arity == 1);
set_number(e, get_number(ARG1));
break;
case OP_TO_INT:
SASSERT(arity == 1);
set_number(e, floor(get_number(ARG1)));
break;
case OP_IS_INT:
SASSERT(arity == 1);
set_bool(e, get_number(ARG1).is_int());
break;
case OP_POWER:
set_x(e);
break;
default:
IF_VERBOSE(0, verbose_stream() << "Term not handled " << mk_pp(e, m) << "\n";);
UNREACHABLE();
break;
}
}
void model_implicant::inherit_value(expr* e, expr* v) {
expr* w;
SASSERT(!is_unknown(v));
SASSERT(m.get_sort(e) == m.get_sort(v));
if (is_x(v)) {
set_x(e);
}
else if (m.is_bool(e)) {
SASSERT(m.is_bool(v));
if (is_true(v)) set_true(e);
else if (is_false(v)) set_false(e);
else {
TRACE("pdr", tout << "not inherited:\n" << mk_pp(e, m) << "\n" << mk_pp(v, m) << "\n";);
set_x(e);
}
}
else if (m_arith.is_int_real(e)) {
set_number(e, get_number(v));
}
else if (m.is_value(v)) {
set_value(e, v);
}
else if (m_values.find(v, w)) {
set_value(e, w);
}
else {
TRACE("pdr", tout << "not inherited:\n" << mk_pp(e, m) << "\n" << mk_pp(v, m) << "\n";);
set_x(e);
}
}
void model_implicant::eval_exprs(expr_ref_vector& es) {
model_ref mr(m_model);
for (unsigned j = 0; j < es.size(); ++j) {
if (m_array.is_as_array(es[j].get())) {
es[j] = eval(mr, es[j].get());
}
}
}
bool model_implicant::extract_array_func_interp(expr* a, vector<expr_ref_vector>& stores, expr_ref& else_case) {
SASSERT(m_array.is_array(a));
TRACE("pdr", tout << mk_pp(a, m) << "\n";);
while (m_array.is_store(a)) {
expr_ref_vector store(m);
store.append(to_app(a)->get_num_args()-1, to_app(a)->get_args()+1);
eval_exprs(store);
stores.push_back(store);
a = to_app(a)->get_arg(0);
}
if (m_array.is_const(a)) {
else_case = to_app(a)->get_arg(0);
return true;
}
while (m_array.is_as_array(a)) {
func_decl* f = m_array.get_as_array_func_decl(to_app(a));
func_interp* g = m_model->get_func_interp(f);
unsigned sz = g->num_entries();
unsigned arity = f->get_arity();
for (unsigned i = 0; i < sz; ++i) {
expr_ref_vector store(m);
func_entry const* fe = g->get_entry(i);
store.append(arity, fe->get_args());
store.push_back(fe->get_result());
for (unsigned j = 0; j < store.size(); ++j) {
if (!is_ground(store[j].get())) {
TRACE("pdr", tout << "could not extract array interpretation: " << mk_pp(a, m) << "\n" << mk_pp(store[j].get(), m) << "\n";);
return false;
}
}
eval_exprs(store);
stores.push_back(store);
}
else_case = g->get_else();
if (!else_case) {
TRACE("pdr", tout << "no else case " << mk_pp(a, m) << "\n";);
return false;
}
if (!is_ground(else_case)) {
TRACE("pdr", tout << "non-ground else case " << mk_pp(a, m) << "\n" << mk_pp(else_case, m) << "\n";);
return false;
}
if (m_array.is_as_array(else_case)) {
model_ref mr(m_model);
else_case = eval(mr, else_case);
}
TRACE("pdr", tout << "else case: " << mk_pp(else_case, m) << "\n";);
return true;
}
TRACE("pdr", tout << "no translation: " << mk_pp(a, m) << "\n";);
return false;
}
/**
best effort evaluator of extensional array equality.
*/
void model_implicant::eval_array_eq(app* e, expr* arg1, expr* arg2) {
TRACE("pdr", tout << "array equality: " << mk_pp(e, m) << "\n";);
expr_ref v1(m), v2(m);
m_model->eval(arg1, v1);
m_model->eval(arg2, v2);
if (v1 == v2) {
set_true(e);
return;
}
sort* s = m.get_sort(arg1);
sort* r = get_array_range(s);
// give up evaluating finite domain/range arrays
if (!r->is_infinite() && !r->is_very_big() && !s->is_infinite() && !s->is_very_big()) {
TRACE("pdr", tout << "equality is unknown: " << mk_pp(e, m) << "\n";);
set_x(e);
return;
}
vector<expr_ref_vector> store;
expr_ref else1(m), else2(m);
if (!extract_array_func_interp(v1, store, else1) ||
!extract_array_func_interp(v2, store, else2)) {
TRACE("pdr", tout << "equality is unknown: " << mk_pp(e, m) << "\n";);
set_x(e);
return;
}
if (else1 != else2) {
if (m.is_value(else1) && m.is_value(else2)) {
TRACE("pdr", tout
<< "defaults are different: " << mk_pp(e, m) << " "
<< mk_pp(else1, m) << " " << mk_pp(else2, m) << "\n";);
set_false(e);
}
else if (m_array.is_array(else1)) {
eval_array_eq(e, else1, else2);
}
else {
TRACE("pdr", tout << "equality is unknown: " << mk_pp(e, m) << "\n";);
set_x(e);
}
return;
}
expr_ref s1(m), s2(m), w1(m), w2(m);
expr_ref_vector args1(m), args2(m);
args1.push_back(v1);
args2.push_back(v2);
for (unsigned i = 0; i < store.size(); ++i) {
args1.resize(1);
args2.resize(1);
args1.append(store[i].size()-1, store[i].c_ptr());
args2.append(store[i].size()-1, store[i].c_ptr());
s1 = m_array.mk_select(args1.size(), args1.c_ptr());
s2 = m_array.mk_select(args2.size(), args2.c_ptr());
m_model->eval(s1, w1);
m_model->eval(s2, w2);
if (w1 == w2) {
continue;
}
if (m.is_value(w1) && m.is_value(w2)) {
TRACE("pdr", tout << "Equality evaluation: " << mk_pp(e, m) << "\n";
tout << mk_pp(s1, m) << " |-> " << mk_pp(w1, m) << "\n";
tout << mk_pp(s2, m) << " |-> " << mk_pp(w2, m) << "\n";);
set_false(e);
}
else if (m_array.is_array(w1)) {
eval_array_eq(e, w1, w2);
if (is_true(e)) {
continue;
}
}
else {
TRACE("pdr", tout << "equality is unknown: " << mk_pp(e, m) << "\n";);
set_x(e);
}
return;
}
set_true(e);
}
void model_implicant::eval_eq(app* e, expr* arg1, expr* arg2) {
if (arg1 == arg2) {
set_true(e);
}
else if (m_array.is_array(arg1)) {
eval_array_eq(e, arg1, arg2);
}
else if (is_x(arg1) || is_x(arg2)) {
expr_ref eq(m), vl(m);
eq = m.mk_eq(arg1, arg2);
m_model->eval(eq, vl);
if (m.is_true(vl)) {
set_bool(e, true);
}
else if (m.is_false(vl)) {
set_bool(e, false);
}
else {
TRACE("pdr", tout << "cannot evaluate: " << mk_pp(vl, m) << "\n";);
set_x(e);
}
}
else if (m.is_bool(arg1)) {
bool val = is_true(arg1) == is_true(arg2);
SASSERT(val == (is_false(arg1) == is_false(arg2)));
if (val) {
set_true(e);
}
else {
set_false(e);
}
}
else if (m_arith.is_int_real(arg1)) {
set_bool(e, get_number(arg1) == get_number(arg2));
}
else {
expr* e1 = get_value(arg1);
expr* e2 = get_value(arg2);
if (m.is_value(e1) && m.is_value(e2)) {
set_bool(e, e1 == e2);
}
else if (e1 == e2) {
set_bool(e, true);
}
else {
TRACE("pdr", tout << "not value equal:\n" << mk_pp(e1, m) << "\n" << mk_pp(e2, m) << "\n";);
set_x(e);
}
}
}
void model_implicant::eval_basic(app* e) {
expr* arg1, *arg2;
expr *argCond, *argThen, *argElse, *arg;
bool has_x = false;
unsigned arity = e->get_num_args();
switch(e->get_decl_kind()) {
case OP_AND:
for (unsigned j = 0; j < arity; ++j) {
expr * arg = e->get_arg(j);
if (is_false(arg)) {
set_false(e);
return;
}
else if (is_x(arg)) {
has_x = true;
}
else {
SASSERT(is_true(arg));
}
}
if (has_x) {
set_x(e);
}
else {
set_true(e);
}
break;
case OP_OR:
for (unsigned j = 0; j < arity; ++j) {
expr * arg = e->get_arg(j);
if (is_true(arg)) {
set_true(e);
return;
}
else if (is_x(arg)) {
has_x = true;
}
else {
SASSERT(is_false(arg));
}
}
if (has_x) {
set_x(e);
}
else {
set_false(e);
}
break;
case OP_NOT:
VERIFY(m.is_not(e, arg));
if (is_true(arg)) {
set_false(e);
}
else if (is_false(arg)) {
set_true(e);
}
else {
SASSERT(is_x(arg));
set_x(e);
}
break;
case OP_IMPLIES:
VERIFY(m.is_implies(e, arg1, arg2));
if (is_false(arg1) || is_true(arg2)) {
set_true(e);
}
else if (arg1 == arg2) {
set_true(e);
}
else if (is_true(arg1) && is_false(arg2)) {
set_false(e);
}
else {
SASSERT(is_x(arg1) || is_x(arg2));
set_x(e);
}
break;
case OP_IFF:
VERIFY(m.is_iff(e, arg1, arg2));
eval_eq(e, arg1, arg2);
break;
case OP_ITE:
VERIFY(m.is_ite(e, argCond, argThen, argElse));
if (is_true(argCond)) {
inherit_value(e, argThen);
}
else if (is_false(argCond)) {
inherit_value(e, argElse);
}
else if (argThen == argElse) {
inherit_value(e, argThen);
}
else if (m.is_bool(e)) {
SASSERT(is_x(argCond));
if (is_x(argThen) || is_x(argElse)) {
set_x(e);
}
else if (is_true(argThen) == is_true(argElse)) {
inherit_value(e, argThen);
}
else {
set_x(e);
}
}
else {
set_x(e);
}
break;
case OP_TRUE:
set_true(e);
break;
case OP_FALSE:
set_false(e);
break;
case OP_EQ:
VERIFY(m.is_eq(e, arg1, arg2));
eval_eq(e, arg1, arg2);
break;
case OP_DISTINCT: {
vector<rational> values;
for (unsigned i = 0; i < arity; ++i) {
expr* arg = e->get_arg(i);
if (is_x(arg)) {
set_x(e);
return;
}
values.push_back(get_number(arg));
}
std::sort(values.begin(), values.end());
for (unsigned i = 0; i + 1 < values.size(); ++i) {
if (values[i] == values[i+1]) {
set_false(e);
return;
}
}
set_true(e);
break;
}
default:
IF_VERBOSE(0, verbose_stream() << "Term not handled " << mk_pp(e, m) << "\n";);
UNREACHABLE();
}
}
bool model_implicant::check_model(ptr_vector<expr> const& formulas) {
ptr_vector<expr> todo(formulas);
while (!todo.empty()) {
expr * curr_e = todo.back();
if (!is_app(curr_e)) {
todo.pop_back();
continue;
}
app * curr = to_app(curr_e);
if (!is_unknown(curr)) {
todo.pop_back();
continue;
}
unsigned arity = curr->get_num_args();
for (unsigned i = 0; i < arity; ++i) {
if (is_unknown(curr->get_arg(i))) {
todo.push_back(curr->get_arg(i));
}
}
if (todo.back() != curr) {
continue;
}
todo.pop_back();
if (curr->get_family_id() == m_arith.get_family_id()) {
eval_arith(curr);
}
else if (curr->get_family_id() == m.get_basic_family_id()) {
eval_basic(curr);
}
else {
expr_ref vl(m);
m_model->eval(curr, vl);
assign_value(curr, vl);
}
IF_VERBOSE(35,verbose_stream() << "assigned "<<mk_pp(curr_e,m)
<<(is_true(curr_e) ? "true" : is_false(curr_e) ? "false" : "unknown") << "\n";);
SASSERT(!is_unknown(curr));
}
bool has_x = false;
for (unsigned i = 0; i < formulas.size(); ++i) {
expr * form = formulas[i];
SASSERT(!is_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(0, verbose_stream() << "formula false in model: " << mk_pp(form, m) << "\n";);
UNREACHABLE();
}
if (is_x(form)) {
IF_VERBOSE(0, verbose_stream() << "formula undetermined in model: " << mk_pp(form, m) << "\n";);
TRACE("pdr", model_smt2_pp(tout, m, *m_model, 0););
has_x = true;
}
}
return !has_x;
}
expr_ref model_implicant::eval(model_ref& model, func_decl* d) {
SASSERT(d->get_arity() == 0);
expr_ref result(m);
if (m_array.is_array(d->get_range())) {
expr_ref e(m);
e = m.mk_const(d);
result = eval(model, e);
}
else {
result = model->get_const_interp(d);
}
return result;
}
expr_ref model_implicant::eval(model_ref& model, expr* e) {
expr_ref result(m);
m_model = model;
VERIFY(m_model->eval(e, result, true));
if (m_array.is_array(e)) {
vector<expr_ref_vector> stores;
expr_ref_vector args(m);
expr_ref else_case(m);
if (extract_array_func_interp(result, stores, else_case)) {
result = m_array.mk_const_array(m.get_sort(e), else_case);
while (!stores.empty() && stores.back().back() == else_case) {
stores.pop_back();
}
for (unsigned i = stores.size(); i > 0; ) {
--i;
args.resize(1);
args[0] = result;
args.append(stores[i]);
result = m_array.mk_store(args.size(), args.c_ptr());
}
return result;
}
}
return result;
}
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