mirror of
https://github.com/Z3Prover/z3
synced 2025-11-26 07:29:33 +00:00
93 lines
2.5 KiB
C++
93 lines
2.5 KiB
C++
/*++
|
|
Copyright (c) 2017 Microsoft Corporation
|
|
|
|
Author:
|
|
Lev Nachmanson (levnach)
|
|
Nikolaj Bjorner (nbjorner)
|
|
--*/
|
|
#include "math/lp/nla_basics_lemmas.h"
|
|
#include "math/lp/nla_core.h"
|
|
namespace nla {
|
|
|
|
monotone::monotone(core * c) : common(c) {}
|
|
|
|
void monotone::monotonicity_lemma() {
|
|
for (auto v : c().m_to_refine) {
|
|
if (done()) break;
|
|
monotonicity_lemma(c().emons()[v]);
|
|
}
|
|
}
|
|
|
|
void monotone::monotonicity_lemma(monic const& m) {
|
|
SASSERT(!check_monic(m));
|
|
if (c().mon_has_zero(m.vars()))
|
|
return;
|
|
if (c().has_big_num(m))
|
|
return;
|
|
const rational prod_val = abs(c().product_value(m));
|
|
const rational m_val = abs(var_val(m));
|
|
bool is_lt = m_val < prod_val;
|
|
|
|
// Check if this specific combination should be throttled
|
|
if (c().throttle().insert_new(nla_throttle::MONOTONE_LEMMA, m.var(), is_lt))
|
|
return;
|
|
|
|
if (is_lt)
|
|
monotonicity_lemma_lt(m);
|
|
else if (m_val > prod_val)
|
|
monotonicity_lemma_gt(m);
|
|
}
|
|
|
|
/** \brief enforce the inequality |m| <= product |m[i]| .
|
|
|
|
/\_i |m[i]| <= |val(m[i])| => |m| <= |product_i val(m[i])|
|
|
<=>
|
|
\/_i |m[i]| > |val(m[i])| or |m| <= |product_i val(m[i])|
|
|
|
|
implied by
|
|
m[i] > val(m[i]) for val(m[i]) > 0
|
|
m[i] < val(m[i]) for val(m[i]) < 0
|
|
m >= product m[i] for product m[i] < 0
|
|
m <= product m[i] for product m[i] > 0
|
|
|
|
Example:
|
|
|
|
0 >= x >= -2 & 0 <= y <= 3 => x*y >= -6
|
|
0 >= x >= -2 & 0 <= y <= 3 => x*x*y <= 12
|
|
|
|
*/
|
|
void monotone::monotonicity_lemma_gt(const monic& m) {
|
|
lemma_builder lemma(c(), "monotonicity > ");
|
|
rational product(1);
|
|
for (lpvar j : m.vars()) {
|
|
auto v = c().val(j);
|
|
lemma |= ineq(j, v.is_neg() ? llc::LT : llc::GT, v);
|
|
lemma |= ineq(j, v.is_neg() ? llc::GT : llc::LT, 0);
|
|
product *= v;
|
|
}
|
|
lemma |= ineq(m.var(), product.is_neg() ? llc::GE : llc::LE, product);
|
|
}
|
|
|
|
/** \brief enforce the inequality |m| >= product |m[i]| .
|
|
|
|
/\_i |m[i]| >= |val(m[i])| => |m| >= |product_i val(m[i])|
|
|
<=>
|
|
\/_i |m[i]| < |val(m[i])| or |m| >= |product_i val(m[i])|
|
|
|
|
Example:
|
|
|
|
x <= -2 & y >= 3 => x*y <= -6
|
|
*/
|
|
void monotone::monotonicity_lemma_lt(const monic& m) {
|
|
lemma_builder lemma(c(), "monotonicity <");
|
|
rational product(1);
|
|
for (lpvar j : m.vars()) {
|
|
auto v = c().val(j);
|
|
lemma |= ineq(j, v.is_neg() ? llc::GT : llc::LT, v);
|
|
product *= v;
|
|
}
|
|
lemma |= ineq(m.var(), product.is_neg() ? llc::LE : llc::GE, product);
|
|
}
|
|
|
|
|
|
}
|