#include "ast/ast_pp.h"
#include "ast/ast_ll_pp.h"
#include "ast/pb_decl_plugin.h"
#include "ast/arith_decl_plugin.h"
#include "ast/recfun_decl_plugin.h"
#include "ast/rewriter/rewriter_def.h"
#include "ast/rewriter/expr_safe_replace.h"
#include "ast/ast_util.h"
#include "ast/ast_pp_util.h"
#include "tactic/tactical.h"
#include "params/tactic_params.hpp"
#include "ast/simplifiers/bound_manager.h"
#include "ast/converters/generic_model_converter.h"
class lia2card_tactic : public tactic {
struct bound {
unsigned m_lo;
unsigned m_hi;
expr* m_expr;
bound(unsigned lo, unsigned hi, expr* b):
m_lo(lo), m_hi(hi), m_expr(b) {}
bound(): m_lo(0), m_hi(0), m_expr(nullptr) {}
};
struct lia_rewriter_cfg : public default_rewriter_cfg {
ast_manager& m;
lia2card_tactic& t;
arith_util a;
expr_ref_vector args;
vector<rational> coeffs;
rational coeff;
bool is_pb(expr* x, expr* y, expr_ref_vector& args, vector<rational>& coeffs, rational& coeff) {
args.reset();
coeffs.reset();
coeff.reset();
return
t.get_pb_sum(x, rational::one(), args, coeffs, coeff) &&
t.get_pb_sum(y, -rational::one(), args, coeffs, coeff);
}
bool is_le(expr* x, expr* y, expr_ref& result) {
if (is_pb(x, y, args, coeffs, coeff)) {
result = t.mk_le(coeffs.size(), coeffs.data(), args.data(), -coeff);
return true;
}
else {
return false;
}
}
br_status mk_app_core(func_decl* f, unsigned sz, expr*const* es, expr_ref& result) {
if (is_decl_of(f, a.get_family_id(), OP_LE) && is_le(es[0], es[1], result)) {
}
else if (is_decl_of(f, a.get_family_id(), OP_GE) && is_le(es[1], es[0], result)) {
}
else if (is_decl_of(f, a.get_family_id(), OP_LT) && is_le(es[1], es[0], result)) {
result = m.mk_not(result);
}
else if (is_decl_of(f, a.get_family_id(), OP_GT) && is_le(es[0], es[1], result)) {
result = m.mk_not(result);
}
else if (m.is_eq(f) && is_pb(es[0], es[1], args, coeffs, coeff)) {
result = t.mk_eq(coeffs.size(), coeffs.data(), args.data(), -coeff);
}
else {
return BR_FAILED;
}
TRACE(pbsum, tout << expr_ref(m.mk_app(f, sz, es), m) << " ==>\n" << result << "\n";);
return BR_DONE;
}
bool rewrite_patterns() const { return false; }
bool flat_assoc(func_decl * f) const { return false; }
br_status reduce_app(func_decl * f, unsigned num, expr * const * args, expr_ref & result, proof_ref & result_pr) {
result_pr = nullptr;
return mk_app_core(f, num, args, result);
}
lia_rewriter_cfg(lia2card_tactic& t):m(t.m), t(t), a(m), args(m) {}
};
class lia_rewriter : public rewriter_tpl<lia_rewriter_cfg> {
lia_rewriter_cfg m_cfg;
public:
lia_rewriter(lia2card_tactic& t):
rewriter_tpl<lia_rewriter_cfg>(t.m, false, m_cfg),
m_cfg(t)
{}
};
public:
typedef obj_map<expr, bound> bounds_map;
ast_manager & m;
arith_util a;
lia_rewriter m_rw;
params_ref m_params;
pb_util m_pb;
mutable ptr_vector<expr>* m_todo;
bounds_map m_bounds;
bool m_compile_equality;
unsigned m_max_range = 101;
unsigned m_max_ite_nesting = 1;
ref<generic_model_converter> m_mc;
lia2card_tactic(ast_manager & _m, params_ref const & p):
m(_m),
a(m),
m_rw(*this),
m_pb(m),
m_todo(alloc(ptr_vector<expr>)),
m_compile_equality(true) {
updt_params(p);
}
~lia2card_tactic() override {
dealloc(m_todo);
}
char const* name() const override { return "lia2card"; }
void updt_params(params_ref const & p) override {
m_params.append(p);
tactic_params tp(p);
m_compile_equality = m_params.get_bool("compile_equality", true);
m_max_range = tp.lia2card_max_range();
m_max_ite_nesting = tp.lia2card_max_ite_nesting();
}
expr_ref mk_bounded(expr_ref_vector& axioms, app* x, unsigned lo, unsigned hi) {
expr_ref_vector xs(m);
expr_ref last_v(m);
if (!m_mc) m_mc = alloc(generic_model_converter, m, "lia2card");
if (hi == 0) {
expr* r = a.mk_int(0);
m_mc->add(x->get_decl(), r);
return expr_ref(r, m);
}
if (lo > 0) {
xs.push_back(a.mk_int(lo));
}
for (unsigned i = lo; i < hi; ++i) {
checkpoint();
expr_ref v(m.mk_fresh_const(x->get_decl()->get_name(), m.mk_bool_sort()), m);
if (last_v) axioms.push_back(m.mk_implies(v, last_v));
expr_ref one(a.mk_int(1), m);
expr_ref zero(a.mk_int(0), m);
xs.push_back(m.mk_ite(v, one, zero));
m_mc->hide(v);
last_v = v;
}
expr* r = a.mk_add(xs.size(), xs.data());
m_mc->add(x->get_decl(), r);
return expr_ref(r, m);
}
void checkpoint() {
if (!m.inc()) {
throw tactic_exception(m.limit().get_cancel_msg());
}
}
void operator()(goal_ref const & g, goal_ref_buffer & result) override {
m_bounds.reset();
m_mc.reset();
expr_ref_vector axioms(m);
expr_safe_replace rep(m);
tactic_report report("lia2card", *g);
if (recfun::util(m).has_rec_defs()) {
result.push_back(g.get());
return;
}
bound_manager bounds(m);
for (unsigned i = 0; i < g->size(); ++i)
bounds(g->form(i), g->dep(i), g->pr(i));
for (expr* x : bounds) {
checkpoint();
bool s1 = false, s2 = false;
rational lo, hi;
if (a.is_int(x) &&
is_uninterp_const(x) &&
bounds.has_lower(x, lo, s1) && !s1 && lo.is_unsigned() &&
bounds.has_upper(x, hi, s2) && !s2 && hi.is_unsigned() && hi.get_unsigned() - lo.get_unsigned() <= m_max_range) {
expr_ref b = mk_bounded(axioms, to_app(x), lo.get_unsigned(), hi.get_unsigned());
rep.insert(x, b);
m_bounds.insert(x, bound(lo.get_unsigned(), hi.get_unsigned(), b));
TRACE(pb, tout << "add bound " << lo << " " << hi << ": " << mk_pp(x, m) << "\n";);
}
}
for (unsigned i = 0; !g->inconsistent() && i < g->size(); ++i) {
checkpoint();
expr_ref new_curr(m), tmp(m);
proof_ref pr1(m), pr2(m), new_pr(m);
rep(g->form(i), tmp);
if (g->form(i) != tmp && m.proofs_enabled()) {
pr1 = m.mk_rewrite(g->form(i), tmp);
}
m_rw(tmp, new_curr, pr2);
if (m.proofs_enabled() && tmp != new_curr && !pr2) {
pr2 = m.mk_rewrite(tmp, new_curr);
}
if (m.proofs_enabled() && g->pr(i)) {
new_pr = m.mk_transitivity(pr1, pr2);
new_pr = m.mk_modus_ponens(g->pr(i), new_pr);
}
g->update(i, new_curr, new_pr, g->dep(i));
}
for (expr* a : axioms)
g->assert_expr(a);
if (m_mc) g->add(m_mc.get());
g->inc_depth();
result.push_back(g.get());
m_bounds.reset();
}
expr* mk_le(unsigned sz, rational const* weights, expr* const* args, rational const& w) {
if (sz == 0) {
return w.is_neg()?m.mk_false():m.mk_true();
}
if (sz == 1 && weights[0].is_one() && w >= rational::one()) {
return m.mk_true();
}
if (sz == 1 && weights[0].is_one() && w.is_zero()) {
return m.mk_not(args[0]);
}
if (w.is_neg()) {
DEBUG_CODE(for (unsigned i = 0; i < sz; ++i) SASSERT(weights[i].is_nonneg()); );
return m.mk_false();
}
return m_pb.mk_le(sz, weights, args, w);
}
expr* mk_eq(unsigned sz, rational const* weights, expr* const* args, rational const& w) {
if (w.is_neg()) {
DEBUG_CODE(for (unsigned i = 0; i < sz; ++i) SASSERT(weights[i].is_nonneg()); );
return m.mk_false();
}
if (m_compile_equality) {
return m_pb.mk_eq(sz, weights, args, w);
}
else {
expr_ref ge(mk_ge(sz, weights, args, w), m);
expr_ref le(mk_le(sz, weights, args, w), m);
return m.mk_and(ge, le);
}
}
expr* mk_ge(unsigned sz, rational const* weights, expr* const* args, rational const& w) {
if (sz == 0) {
return w.is_pos() ? m.mk_false() : m.mk_true();
}
if (sz == 1 && weights[0].is_one() && w.is_one()) {
return args[0];
}
if (sz == 1 && weights[0].is_one() && w.is_zero()) {
return m.mk_not(args[0]);
}
if (w.is_neg()) {
DEBUG_CODE(for (unsigned i = 0; i < sz; ++i) SASSERT(weights[i].is_nonneg()); );
return m.mk_true();
}
return m_pb.mk_ge(sz, weights, args, w);
}
bool get_pb_sum(expr* x, rational const& mul, expr_ref_vector& args, vector<rational>& coeffs, rational& coeff) {
expr_ref_vector conds(m);
return get_sum(0, x, mul, conds, args, coeffs, coeff);
}
bool get_sum(unsigned nesting, expr* x, rational const& mul, expr_ref_vector& conds, expr_ref_vector& args, vector<rational>& coeffs, rational& coeff) {
checkpoint();
expr *y, *z, *u;
rational r, q;
if (!is_app(x))
return false;
if (nesting > m_max_ite_nesting && !is_numeral(x, r))
return false;
app* f = to_app(x);
bool ok = true;
if (is_numeral(x, r)) {
insert_arg(mul * r, conds, m.mk_true(), args, coeffs, coeff);
}
else if (a.is_add(x)) {
for (unsigned i = 0; ok && i < f->get_num_args(); ++i) {
ok = get_sum(nesting, f->get_arg(i), mul, conds, args, coeffs, coeff);
}
}
else if (a.is_sub(x, y, z)) {
ok = get_sum(nesting, y, mul, conds, args, coeffs, coeff);
ok = ok && get_sum(nesting, z, -mul, conds, args, coeffs, coeff);
}
else if (a.is_uminus(x, y)) {
ok = get_sum(nesting, y, -mul, conds, args, coeffs, coeff);
}
else if (a.is_mul(x, y, z) && is_numeral(y, r)) {
ok = get_sum(nesting, z, r*mul, conds, args, coeffs, coeff);
}
else if (a.is_mul(x, z, y) && is_numeral(y, r)) {
ok = get_sum(nesting, z, r*mul, conds, args, coeffs, coeff);
}
else if (a.is_to_real(x, y)) {
ok = get_sum(nesting, y, mul, conds, args, coeffs, coeff);
}
else if (m.is_ite(x, y, z, u)) {
conds.push_back(y);
ok = get_sum(nesting + 1, z, mul, conds, args, coeffs, coeff);
conds.pop_back();
conds.push_back(m.mk_not(y));
ok &= get_sum(nesting + 1, u, mul, conds, args, coeffs, coeff);
conds.pop_back();
}
else {
TRACE(pb, tout << "Can't handle " << mk_pp(x, m) << "\n";);
ok = false;
}
return ok;
}
expr_ref add_conds(expr_ref_vector& es, expr* e) {
expr_ref result(m);
if (!m.is_true(e)) {
es.push_back(e);
}
result = mk_and(es);
if (!m.is_true(e)) {
es.pop_back();
}
return result;
}
bool is_numeral(expr* e, rational& r) {
if (a.is_uminus(e, e) && is_numeral(e, r)) {
r.neg();
return true;
}
if (a.is_to_real(e, e)) {
return is_numeral(e, r);
}
return a.is_numeral(e, r);
}
void insert_arg(
rational const& p,
expr_ref_vector& conds,
expr* x,
expr_ref_vector& args, vector<rational>& coeffs, rational& coeff) {
expr_ref cond = add_conds(conds, x);
if (m.is_true(cond)) {
coeff += p;
}
else if (p.is_neg()) {
args.push_back(m.mk_not(cond));
coeffs.push_back(-p);
coeff += p;
}
else if (p.is_pos()) {
args.push_back(cond);
coeffs.push_back(p);
}
}
tactic * translate(ast_manager & m) override {
return alloc(lia2card_tactic, m, m_params);
}
void collect_param_descrs(param_descrs & r) override {
r.insert("compile_equality", CPK_BOOL,
"(default:false) compile equalities into pseudo-Boolean equality");
}
void cleanup() override {
ptr_vector<expr>* todo = alloc(ptr_vector<expr>);
std::swap(m_todo, todo);
dealloc(todo);
m_bounds.reset();
}
};
tactic * mk_lia2card_tactic(ast_manager & m, params_ref const & p) {
return clean(alloc(lia2card_tactic, m, p));
}
bool get_pb_sum(expr* term, expr_ref_vector& args, vector<rational>& coeffs, rational& coeff) {
params_ref p;
ast_manager& m = args.get_manager();
lia2card_tactic tac(m, p);
return tac.get_pb_sum(term, rational::one(), args, coeffs, coeff);
}