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/*++
Copyright (c) 2012 Microsoft Corporation
Module Name:
recover_01_tactic.cpp
Abstract:
Recover 01 variables
Search for clauses of the form
p or q or x = 0
~p or q or x = k1
p or ~q or x = k2
~p or ~q or x = k1+k2
Then, replaces
x with k1*y1 + k2*y2
p with y1=1
q with y2=1
where y1 and y2 are fresh 01 variables
Issue #5316:
It is in general unsound to remove clauses.
Example:
v or x = 0
~v or x = 0
v or ~x = 0
~v or ~x = 0
The function introduces the fresh variable 0-1 y for v.
The first two clauses produce the replacement x := 0*y
and substitution (x = 0) |-> y = 1.
After substitution:
y = 1 or ~(y = 1)
~(y = 1) or ~(y = 1)
By retaining clauses that introduced the replacement
the claim is that we ensure soundness. The solution ~(y = 1)
is validated against the original clauses
v or x = 0
~v or x = 0
that are expanded into
y = 1 or (y = 1)
~(y = 1) or (y = 1)
Author:
Leonardo de Moura (leonardo) 2012-02-17.
Revision History:
--*/
#include "tactic/tactical.h"
#include "ast/rewriter/th_rewriter.h"
#include "ast/converters/generic_model_converter.h"
#include "ast/arith_decl_plugin.h"
#include "ast/expr_substitution.h"
#include "util/dec_ref_util.h"
#include "ast/ast_smt2_pp.h"
#include "ast/ast_pp.h"
class recover_01_tactic : public tactic {
struct imp {
typedef obj_map<func_decl, ptr_vector<app> > var2clauses;
ast_manager & m;
var2clauses m_var2clauses;
arith_util m_util;
th_rewriter m_rw;
bool m_produce_models;
unsigned m_cls_max_size;
imp(ast_manager & _m, params_ref const & p):
m(_m),
m_util(m),
m_rw(m, p) {
updt_params_core(p);
}
void updt_params_core(params_ref const & p) {
m_cls_max_size = p.get_uint("recover_01_max_bits", 10);
}
void updt_params(params_ref const & p) {
m_rw.updt_params(p);
updt_params_core(p);
}
bool save_clause(expr * c) {
if (!m.is_or(c))
return false;
func_decl * x = nullptr;
app * cls = to_app(c);
if (cls->get_num_args() <= 1 || cls->get_num_args() >= m_cls_max_size)
return false;
for (expr* lit : *cls) {
expr * lhs, * rhs, * arg;
if (is_uninterp_const(lit)) {
// positive literal
}
else if (m.is_not(lit, arg) && is_uninterp_const(arg)) {
// negative literal
}
else if (x == nullptr && m.is_eq(lit, lhs, rhs)) {
// x = k literal
if (is_uninterp_const(lhs) && m_util.is_numeral(rhs)) {
x = to_app(lhs)->get_decl();
}
else if (is_uninterp_const(rhs) && m_util.is_numeral(lhs)) {
x = to_app(rhs)->get_decl();
}
else {
return false;
}
}
else {
return false;
}
}
if (x != nullptr) {
auto& value = m_var2clauses.insert_if_not_there(x, ptr_vector<app>());
if (value.empty() || value.back()->get_num_args() == cls->get_num_args()) {
value.push_back(cls);
return true;
}
}
return false;
}
// temporary fields used by operator() and process
generic_model_converter * gmc;
expr_substitution * subst;
goal_ref new_goal;
obj_map<expr, expr *> bool2int;
app * find_zero_cls(func_decl * x, ptr_vector<app> & clauses) {
for (app * cls : clauses) {
for (expr* arg : *cls) {
expr * lhs, * rhs;
if (m.is_eq(arg, lhs, rhs)) {
if (is_uninterp_const(lhs) && m_util.is_zero(rhs))
return cls;
if (is_uninterp_const(rhs) && m_util.is_zero(lhs))
return cls;
}
}
}
return nullptr;
}
// Find coeff (the k of literal (x = k)) of clause cls.
// Store in idx the bit-vector representing the literals.
// Example: idx = 101 if cls has three boolean literals p1, p2, p3
// where p1 = ~q1, p2 = q2, p3 = ~q3
// and q1 q2 q3 are the corresponding literals in the
// zero clause.
// Return false, if the boolean literals of cls cannot be matched with the literals
// of zero_cls
bool find_coeff(app * cls, app * zero_cls, unsigned & idx, rational & k) {
unsigned num = zero_cls->get_num_args();
if (cls->get_num_args() != num)
return false;
idx = 0;
unsigned val = 1;
for (unsigned i = 0; i < num; ++i) {
expr * lit = zero_cls->get_arg(i);
if (m.is_eq(lit))
continue;
// search for lit or ~lit in cls
unsigned j;
for (j = 0; j < num; ++j) {
expr * lit2 = cls->get_arg(j);
if (m.is_eq(lit2))
continue;
if (lit2 == lit)
break;
if (m.is_complement(lit2, lit)) {
idx += val;
break;
}
}
if (j == num)
return false; // cls does not contain literal lit
val *= 2;
}
// find k
unsigned i;
for (i = 0; i < num; ++i) {
expr * lhs, * rhs;
if (m.is_eq(cls->get_arg(i), lhs, rhs) && (m_util.is_numeral(lhs, k) || m_util.is_numeral(rhs, k)))
break;
}
if (i == num)
return false;
return true;
}
void mk_ivar(expr * lit, expr_ref & def, bool real_ctx) {
expr * atom;
bool sign;
if (m.is_not(lit, atom)) {
sign = true;
}
else {
atom = lit;
sign = false;
}
SASSERT(is_uninterp_const(atom));
expr * var;
if (!bool2int.find(atom, var)) {
var = m.mk_fresh_const(nullptr, m_util.mk_int());
new_goal->assert_expr(m_util.mk_le(m_util.mk_numeral(rational(0), true), var));
new_goal->assert_expr(m_util.mk_le(var, m_util.mk_numeral(rational(1), true)));
expr * bool_def = m.mk_eq(var, m_util.mk_numeral(rational(1), true));
subst->insert(atom, bool_def);
if (m_produce_models) {
gmc->hide(var);
gmc->add(to_app(atom)->get_decl(), bool_def);
}
m.inc_ref(atom);
m.inc_ref(var);
bool2int.insert(atom, var);
}
expr * norm_var = real_ctx ? m_util.mk_to_real(var) : var;
if (sign)
def = m_util.mk_sub(m_util.mk_numeral(rational(1), !real_ctx), norm_var);
else
def = norm_var;
}
bool process(func_decl * x, ptr_vector<app> & clauses) {
unsigned cls_size = clauses.back()->get_num_args();
unsigned expected_num_clauses = 1 << (cls_size - 1);
if (clauses.size() < expected_num_clauses) // using < instead of != because we tolerate duplicates
return false;
app * zero_cls = find_zero_cls(x, clauses);
if (zero_cls == nullptr)
return false;
buffer<bool> found; // marks which idx were found
buffer<rational> idx2coeff;
found.resize(expected_num_clauses, false);
idx2coeff.resize(expected_num_clauses);
for (app * cls : clauses) {
unsigned idx; rational k;
if (!find_coeff(cls, zero_cls, idx, k))
return false;
SASSERT(idx < expected_num_clauses);
if (found[idx] && k != idx2coeff[idx])
return false;
found[idx] = true;
idx2coeff[idx] = k;
}
unsigned num_bits = cls_size - 1;
// check if idxs are consistent
for (unsigned idx = 0; idx < expected_num_clauses; ++idx) {
if (!found[idx])
return false; // case is missing
rational expected_k;
unsigned idx_aux = idx;
unsigned idx_bit = 1;
for (unsigned j = 0; j < num_bits; ++j) {
if (idx_aux % 2 == 1) {
expected_k += idx2coeff[idx_bit];
}
idx_aux /= 2;
idx_bit *= 2;
}
if (idx2coeff[idx] != expected_k)
return false;
}
expr_ref_buffer def_args(m);
expr_ref def(m);
bool real_ctx = m_util.is_real(x->get_range());
unsigned idx_bit = 1;
for (unsigned i = 0; i < cls_size; ++i) {
expr * lit = zero_cls->get_arg(i);
if (m.is_eq(lit))
continue;
mk_ivar(lit, def, real_ctx);
def_args.push_back(m_util.mk_mul(m_util.mk_numeral(idx2coeff[idx_bit], !real_ctx), def));
idx_bit *= 2;
}
expr * x_def;
if (def_args.size() == 1)
x_def = def_args[0];
else
x_def = m_util.mk_add(def_args);
TRACE(recover_01, tout << x->get_name() << " --> " << mk_ismt2_pp(x_def, m) << "\n";);
subst->insert(m.mk_const(x), x_def);
if (m_produce_models) {
gmc->add(x, x_def);
}
return true;
}
void operator()(goal_ref const & g,
goal_ref_buffer & result) {
fail_if_proof_generation("recover-01", g);
fail_if_unsat_core_generation("recover-01", g);
m_produce_models = g->models_enabled();
result.reset();
tactic_report report("recover-01", *g);
bool saved = false;
new_goal = alloc(goal, *g, true);
SASSERT(new_goal->depth() == g->depth());
SASSERT(new_goal->prec() == g->prec());
new_goal->inc_depth();
for (unsigned i = 0; i < g->size(); ++i) {
expr * f = g->form(i);
if (save_clause(f))
saved = true;
new_goal->assert_expr(f);
}
if (!saved) {
result.push_back(g.get());
return;
}
if (m_produce_models) {
gmc = alloc(generic_model_converter, m, "recover_01");
new_goal->add(gmc);
}
dec_ref_key_values(m, bool2int);
unsigned counter = 0;
bool recovered = false;
expr_substitution _subst(m);
subst = &_subst;
for (auto& kv : m_var2clauses) {
if (process(kv.m_key, kv.m_value)) {
recovered = true;
counter++;
}
else {
for (app* a : kv.m_value) {
new_goal->assert_expr(a);
}
}
}
if (!recovered) {
result.push_back(g.get());
return;
}
report_tactic_progress(":recovered-01-vars", counter);
m_rw.set_substitution(subst);
expr_ref new_curr(m);
proof_ref new_pr(m);
for (unsigned idx = 0; idx < new_goal->size(); ++idx) {
expr * curr = new_goal->form(idx);
m_rw(curr, new_curr);
new_goal->update(idx, new_curr);
}
result.push_back(new_goal.get());
TRACE(recover_01, new_goal->display(tout); if (new_goal->mc()) new_goal->mc()->display(tout););
SASSERT(new_goal->is_well_formed());
}
~imp() {
dec_ref_key_values(m, bool2int);
}
};
imp * m_imp;
params_ref m_params;
public:
recover_01_tactic(ast_manager & m, params_ref const & p):
m_params(p) {
m_imp = alloc(imp, m, p);
}
tactic * translate(ast_manager & m) override {
return alloc(recover_01_tactic, m, m_params);
}
~recover_01_tactic() override {
dealloc(m_imp);
}
char const* name() const override { return "recover_01"; }
void updt_params(params_ref const & p) override {
m_params.append(p);
m_imp->updt_params(m_params);
}
void collect_param_descrs(param_descrs & r) override {
th_rewriter::get_param_descrs(r);
r.insert("recover_01_max_bits", CPK_UINT, "maximum number of bits to consider in a clause.", "10");
}
void operator()(goal_ref const & g,
goal_ref_buffer & result) override {
try {
(*m_imp)(g, result);
}
catch (rewriter_exception & ex) {
throw tactic_exception(ex.what());
}
}
void cleanup() override {
imp * d = alloc(imp, m_imp->m, m_params);
std::swap(d, m_imp);
dealloc(d);
}
};
tactic * mk_recover_01_tactic(ast_manager & m, params_ref const & p) {
return clean(alloc(recover_01_tactic, m, p));
}