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improve quantifier elimination for arithmetic

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This update changes the handling of mod and adds support for nested div terms.

Simple use cases that are handled using small results are given below.

```
(declare-const x Int)
(declare-const y Int)
(declare-const z Int)
(assert (exists ((x Int)) (and (<= y (* 10 x)) (<= (* 10 x) z))))
(apply qe2)
(reset)

(declare-const y Int)
(assert (exists ((x Int)) (and (> x 0) (= (div x 41) y))))
(apply qe2)
(reset)

(declare-const y Int)
(assert (exists ((x Int)) (= (mod x 41) y)))
(apply qe2)
(reset)
```

The main idea is to introduce definition rows for mod/div terms.
Elimination of variables under mod/div is defined by rewriting the variable to multiples of the mod/divisior and remainder.

The functionality is disabled in this push.
This commit is contained in:
Nikolaj Bjorner 2022-08-12 10:20:43 -04:00
parent 786280c646
commit 03385bf78d
3 changed files with 1795 additions and 1432 deletions
Download patch file Download diff file Expand all files Collapse all files

2864
src/math/simplex/model_based_opt.cpp
View file

File diff suppressed because it is too large Load diff

38
src/math/simplex/model_based_opt.h
View file

@ -30,7 +30,9 @@ namespace opt {
t_eq, t_eq,
t_lt, t_lt,
t_le, t_le,
t_mod t_divides,
t_mod,
t_div
}; };
@ -57,6 +59,7 @@ namespace opt {
ineq_type m_type; // inequality type ineq_type m_type; // inequality type
rational m_value; // value of m_vars + m_coeff under interpretation of m_var2value. rational m_value; // value of m_vars + m_coeff under interpretation of m_var2value.
bool m_alive; // rows can be marked dead if they have been processed. bool m_alive; // rows can be marked dead if they have been processed.
unsigned m_id; // variable defined by row (used for mod_t and div_t)
void reset() { m_vars.reset(); m_coeff.reset(); m_value.reset(); } void reset() { m_vars.reset(); m_coeff.reset(); m_value.reset(); }
row& normalize(); row& normalize();
@ -85,9 +88,9 @@ namespace opt {
static const unsigned m_objective_id = 0; static const unsigned m_objective_id = 0;
vector<unsigned_vector> m_var2row_ids; vector<unsigned_vector> m_var2row_ids;
vector<rational> m_var2value; vector<rational> m_var2value;
bool_vector m_var2is_int; bool_vector m_var2is_int;
vector<var> m_new_vars; vector<var> m_new_vars;
unsigned_vector m_lub, m_glb, m_mod; unsigned_vector m_lub, m_glb, m_divides, m_mod, m_div;
unsigned_vector m_above, m_below; unsigned_vector m_above, m_below;
unsigned_vector m_retired_rows; unsigned_vector m_retired_rows;
@ -122,14 +125,18 @@ namespace opt {
void sub(unsigned dst, rational const& c); void sub(unsigned dst, rational const& c);
void del_var(unsigned dst, unsigned x); void set_row(unsigned row_id, vector<var> const& coeffs, rational const& c, rational const& m, ineq_type rel);
void set_row(unsigned row_id, vector<var> const& coeffs, rational const& c, rational const& m, ineq_type rel); void add_lower_bound(unsigned x, rational const& lo);
void add_upper_bound(unsigned x, rational const& hi);
void add_constraint(vector<var> const& coeffs, rational const& c, rational const& m, ineq_type r); void add_constraint(vector<var> const& coeffs, rational const& c, rational const& m, ineq_type r);
void replace_var(unsigned row_id, unsigned x, rational const& A, unsigned y, rational const& B); void replace_var(unsigned row_id, unsigned x, rational const& A, unsigned y, rational const& B);
void replace_var(unsigned row_id, unsigned x, rational const& A, unsigned y, rational const& B, unsigned z);
void replace_var(unsigned row_id, unsigned x, rational const& C); void replace_var(unsigned row_id, unsigned x, rational const& C);
void normalize(unsigned row_id); void normalize(unsigned row_id);
@ -138,7 +145,7 @@ namespace opt {
unsigned new_row(); unsigned new_row();
unsigned copy_row(unsigned row_id); unsigned copy_row(unsigned row_id, unsigned excl = UINT_MAX);
rational n_sign(rational const& b) const; rational n_sign(rational const& b) const;
@ -150,8 +157,12 @@ namespace opt {
def solve_for(unsigned row_id, unsigned x, bool compute_def); def solve_for(unsigned row_id, unsigned x, bool compute_def);
def solve_mod(unsigned x, unsigned_vector const& mod_rows, bool compute_def); def solve_divides(unsigned x, unsigned_vector const& divide_rows, bool compute_def);
def solve_mod(unsigned x, unsigned_vector const& divide_rows, bool compute_def);
def solve_div(unsigned x, unsigned_vector const& divide_rows, bool compute_def);
bool is_int(unsigned x) const { return m_var2is_int[x]; } bool is_int(unsigned x) const { return m_var2is_int[x]; }
void retire_row(unsigned row_id); void retire_row(unsigned row_id);
@ -173,6 +184,17 @@ namespace opt {
// add a divisibility constraint. The row should divide m. // add a divisibility constraint. The row should divide m.
void add_divides(vector<var> const& coeffs, rational const& c, rational const& m); void add_divides(vector<var> const& coeffs, rational const& c, rational const& m);
// add sub-expression for modulus
// v = add_mod(coeffs, m) means
// v = coeffs mod m
unsigned add_mod(vector<var> const& coeffs, rational const& c, rational const& m);
// add sub-expression for div
// v = add_div(coeffs, m) means
// v = coeffs div m
unsigned add_div(vector<var> const& coeffs, rational const& c, rational const& m);
// Set the objective function (linear). // Set the objective function (linear).
void set_objective(vector<var> const& coeffs, rational const& c); void set_objective(vector<var> const& coeffs, rational const& c);

325
src/qe/mbp/mbp_arith.cpp
View file

@ -23,7 +23,6 @@ Revision History:
#include "ast/ast_util.h" #include "ast/ast_util.h"
#include "ast/arith_decl_plugin.h" #include "ast/arith_decl_plugin.h"
#include "ast/ast_pp.h" #include "ast/ast_pp.h"
#include "ast/rewriter/th_rewriter.h"
#include "ast/expr_functors.h" #include "ast/expr_functors.h"
#include "ast/rewriter/expr_safe_replace.h" #include "ast/rewriter/expr_safe_replace.h"
#include "math/simplex/model_based_opt.h" #include "math/simplex/model_based_opt.h"
@ -32,13 +31,13 @@ Revision History:
#include "model/model_v2_pp.h" #include "model/model_v2_pp.h"
namespace mbp { namespace mbp {
struct arith_project_plugin::imp { struct arith_project_plugin::imp {
ast_manager& m; ast_manager& m;
arith_util a; arith_util a;
bool m_check_purified { true }; // check that variables are properly pure bool m_check_purified = true; // check that variables are properly pure
bool m_apply_projection { false }; bool m_apply_projection = false;
imp(ast_manager& m) : imp(ast_manager& m) :
@ -48,10 +47,10 @@ namespace mbp {
void insert_mul(expr* x, rational const& v, obj_map<expr, rational>& ts) { void insert_mul(expr* x, rational const& v, obj_map<expr, rational>& ts) {
rational w; rational w;
if (ts.find(x, w)) if (ts.find(x, w))
ts.insert(x, w + v); ts.insert(x, w + v);
else else
ts.insert(x, v); ts.insert(x, v);
} }
@ -65,15 +64,15 @@ namespace mbp {
rational c(0), mul(1); rational c(0), mul(1);
expr_ref t(m); expr_ref t(m);
opt::ineq_type ty = opt::t_le; opt::ineq_type ty = opt::t_le;
expr* e1, *e2; expr* e1, * e2;
DEBUG_CODE(expr_ref val(m); DEBUG_CODE(expr_ref val(m);
eval(lit, val); eval(lit, val);
CTRACE("qe", !m.is_true(val), tout << mk_pp(lit, m) << " := " << val << "\n";); CTRACE("qe", !m.is_true(val), tout << mk_pp(lit, m) << " := " << val << "\n";);
SASSERT(m.limit().is_canceled() || !m.is_false(val));); SASSERT(m.limit().is_canceled() || !m.is_false(val)););
if (!m.inc()) if (!m.inc())
return false; return false;
TRACE("opt", tout << mk_pp(lit, m) << " " << a.is_lt(lit) << " " << a.is_gt(lit) << "\n";); TRACE("opt", tout << mk_pp(lit, m) << " " << a.is_lt(lit) << " " << a.is_gt(lit) << "\n";);
bool is_not = m.is_not(lit, lit); bool is_not = m.is_not(lit, lit);
if (is_not) { if (is_not) {
@ -86,37 +85,35 @@ namespace mbp {
ty = is_not ? opt::t_lt : opt::t_le; ty = is_not ? opt::t_lt : opt::t_le;
} }
else if ((a.is_lt(lit, e1, e2) || a.is_gt(lit, e2, e1))) { else if ((a.is_lt(lit, e1, e2) || a.is_gt(lit, e2, e1))) {
linearize(mbo, eval, mul, e1, c, fmls, ts, tids); linearize(mbo, eval, mul, e1, c, fmls, ts, tids);
linearize(mbo, eval, -mul, e2, c, fmls, ts, tids); linearize(mbo, eval, -mul, e2, c, fmls, ts, tids);
ty = is_not ? opt::t_le: opt::t_lt; ty = is_not ? opt::t_le : opt::t_lt;
} }
else if (m.is_eq(lit, e1, e2) && !is_not && is_arith(e1)) { else if (m.is_eq(lit, e1, e2) && !is_not && is_arith(e1)) {
linearize(mbo, eval, mul, e1, c, fmls, ts, tids); linearize(mbo, eval, mul, e1, c, fmls, ts, tids);
linearize(mbo, eval, -mul, e2, c, fmls, ts, tids); linearize(mbo, eval, -mul, e2, c, fmls, ts, tids);
ty = opt::t_eq; ty = opt::t_eq;
} }
else if (m.is_eq(lit, e1, e2) && is_not && is_arith(e1)) { else if (m.is_eq(lit, e1, e2) && is_not && is_arith(e1)) {
rational r1, r2; rational r1, r2;
expr_ref val1 = eval(e1); expr_ref val1 = eval(e1);
expr_ref val2 = eval(e2); expr_ref val2 = eval(e2);
//TRACE("qe", tout << mk_pp(e1, m) << " " << val1 << "\n";);
//TRACE("qe", tout << mk_pp(e2, m) << " " << val2 << "\n";);
if (!a.is_numeral(val1, r1)) return false; if (!a.is_numeral(val1, r1)) return false;
if (!a.is_numeral(val2, r2)) return false; if (!a.is_numeral(val2, r2)) return false;
SASSERT(r1 != r2); SASSERT(r1 != r2);
if (r1 < r2) { if (r1 < r2) {
std::swap(e1, e2); std::swap(e1, e2);
} }
ty = opt::t_lt; ty = opt::t_lt;
linearize(mbo, eval, mul, e1, c, fmls, ts, tids); linearize(mbo, eval, mul, e1, c, fmls, ts, tids);
linearize(mbo, eval, -mul, e2, c, fmls, ts, tids); linearize(mbo, eval, -mul, e2, c, fmls, ts, tids);
} }
else if (m.is_distinct(lit) && !is_not && is_arith(to_app(lit)->get_arg(0))) { else if (m.is_distinct(lit) && !is_not && is_arith(to_app(lit)->get_arg(0))) {
expr_ref val(m); expr_ref val(m);
rational r; rational r;
app* alit = to_app(lit); app* alit = to_app(lit);
vector<std::pair<expr*,rational> > nums; vector<std::pair<expr*, rational> > nums;
for (expr* arg : *alit) { for (expr* arg : *alit) {
val = eval(arg); val = eval(arg);
TRACE("qe", tout << mk_pp(arg, m) << " " << val << "\n";); TRACE("qe", tout << mk_pp(arg, m) << " " << val << "\n";);
@ -125,8 +122,8 @@ namespace mbp {
} }
std::sort(nums.begin(), nums.end(), compare_second()); std::sort(nums.begin(), nums.end(), compare_second());
for (unsigned i = 0; i + 1 < nums.size(); ++i) { for (unsigned i = 0; i + 1 < nums.size(); ++i) {
SASSERT(nums[i].second < nums[i+1].second); SASSERT(nums[i].second < nums[i + 1].second);
expr_ref fml(a.mk_lt(nums[i].first, nums[i+1].first), m); expr_ref fml(a.mk_lt(nums[i].first, nums[i + 1].first), m);
if (!linearize(mbo, eval, fml, fmls, tids)) { if (!linearize(mbo, eval, fml, fmls, tids)) {
return false; return false;
} }
@ -139,14 +136,14 @@ namespace mbp {
map<rational, expr*, rational::hash_proc, rational::eq_proc> values; map<rational, expr*, rational::hash_proc, rational::eq_proc> values;
bool found_eq = false; bool found_eq = false;
for (unsigned i = 0; !found_eq && i < to_app(lit)->get_num_args(); ++i) { for (unsigned i = 0; !found_eq && i < to_app(lit)->get_num_args(); ++i) {
expr* arg1 = to_app(lit)->get_arg(i), *arg2 = nullptr; expr* arg1 = to_app(lit)->get_arg(i), * arg2 = nullptr;
rational r; rational r;
expr_ref val = eval(arg1); expr_ref val = eval(arg1);
TRACE("qe", tout << mk_pp(arg1, m) << " " << val << "\n";); TRACE("qe", tout << mk_pp(arg1, m) << " " << val << "\n";);
if (!a.is_numeral(val, r)) return false; if (!a.is_numeral(val, r)) return false;
if (values.find(r, arg2)) { if (values.find(r, arg2)) {
ty = opt::t_eq; ty = opt::t_eq;
linearize(mbo, eval, mul, arg1, c, fmls, ts, tids); linearize(mbo, eval, mul, arg1, c, fmls, ts, tids);
linearize(mbo, eval, -mul, arg2, c, fmls, ts, tids); linearize(mbo, eval, -mul, arg2, c, fmls, ts, tids);
found_eq = true; found_eq = true;
} }
@ -169,27 +166,37 @@ namespace mbp {
// //
// convert linear arithmetic term into an inequality for mbo. // convert linear arithmetic term into an inequality for mbo.
// //
void linearize(opt::model_based_opt& mbo, model_evaluator& eval, rational const& mul, expr* t, rational& c, void linearize(opt::model_based_opt& mbo, model_evaluator& eval, rational const& mul, expr* t, rational& c,
expr_ref_vector& fmls, obj_map<expr, rational>& ts, obj_map<expr, unsigned>& tids) { expr_ref_vector& fmls, obj_map<expr, rational>& ts, obj_map<expr, unsigned>& tids) {
expr* t1, *t2, *t3; expr* t1, * t2, * t3;
rational mul1; rational mul1;
expr_ref val(m); expr_ref val(m);
if (a.is_mul(t, t1, t2) && is_numeral(t1, mul1))
linearize(mbo, eval, mul* mul1, t2, c, fmls, ts, tids); auto add_def = [&](expr* t1, rational const& m, vars& coeffs) {
else if (a.is_mul(t, t1, t2) && is_numeral(t2, mul1)) obj_map<expr, rational> ts0;
linearize(mbo, eval, mul* mul1, t1, c, fmls, ts, tids); rational mul0(1), c0(0);
linearize(mbo, eval, mul0, t1, c0, fmls, ts0, tids);
extract_coefficients(mbo, eval, ts0, tids, coeffs);
insert_mul(t, mul, ts);
return c0;
};
if (a.is_mul(t, t1, t2) && is_numeral(t1, mul1))
linearize(mbo, eval, mul * mul1, t2, c, fmls, ts, tids);
else if (a.is_mul(t, t1, t2) && is_numeral(t2, mul1))
linearize(mbo, eval, mul * mul1, t1, c, fmls, ts, tids);
else if (a.is_uminus(t, t1)) else if (a.is_uminus(t, t1))
linearize(mbo, eval, -mul, t1, c, fmls, ts, tids); linearize(mbo, eval, -mul, t1, c, fmls, ts, tids);
else if (a.is_numeral(t, mul1)) else if (a.is_numeral(t, mul1))
c += mul * mul1; c += mul * mul1;
else if (a.is_add(t)) { else if (a.is_add(t)) {
for (expr* arg : *to_app(t)) for (expr* arg : *to_app(t))
linearize(mbo, eval, mul, arg, c, fmls, ts, tids); linearize(mbo, eval, mul, arg, c, fmls, ts, tids);
} }
else if (a.is_sub(t, t1, t2)) { else if (a.is_sub(t, t1, t2)) {
linearize(mbo, eval, mul, t1, c, fmls, ts, tids); linearize(mbo, eval, mul, t1, c, fmls, ts, tids);
linearize(mbo, eval, -mul, t2, c, fmls, ts, tids); linearize(mbo, eval, -mul, t2, c, fmls, ts, tids);
} }
else if (m.is_ite(t, t1, t2, t3)) { else if (m.is_ite(t, t1, t2, t3)) {
val = eval(t1); val = eval(t1);
@ -210,21 +217,30 @@ namespace mbp {
else if (a.is_mod(t, t1, t2) && is_numeral(t2, mul1) && !mul1.is_zero()) { else if (a.is_mod(t, t1, t2) && is_numeral(t2, mul1) && !mul1.is_zero()) {
rational r; rational r;
val = eval(t); val = eval(t);
if (!a.is_numeral(val, r)) { if (!a.is_numeral(val, r))
throw default_exception("mbp evaluation didn't produce an integer"); throw default_exception("mbp evaluation didn't produce an integer");
} c += mul * r;
c += mul*r;
// t1 mod mul1 == r // t1 mod mul1 == r
rational c0(-r), mul0(1);
obj_map<expr, rational> ts0;
linearize(mbo, eval, mul0, t1, c0, fmls, ts0, tids);
vars coeffs; vars coeffs;
extract_coefficients(mbo, eval, ts0, tids, coeffs); rational c0 = add_def(t1, mul1, coeffs);
mbo.add_divides(coeffs, c0, mul1); mbo.add_divides(coeffs, c0 - r, mul1);
} }
else { else if (false && a.is_mod(t, t1, t2) && is_numeral(t2, mul1) && !mul1.is_zero()) {
// v = t1 mod mul1
vars coeffs;
rational c0 = add_def(t1, mul1, coeffs);
unsigned v = mbo.add_mod(coeffs, c0, mul1);
tids.insert(t, v);
}
else if (false && a.is_idiv(t, t1, t2) && is_numeral(t2, mul1) && mul1 > 0) {
// v = t1 div mul1
vars coeffs;
rational c0 = add_def(t1, mul1, coeffs);
unsigned v = mbo.add_div(coeffs, c0, mul1);
tids.insert(t, v);
}
else
insert_mul(t, mul, ts); insert_mul(t, mul, ts);
}
} }
bool is_numeral(expr* t, rational& r) { bool is_numeral(expr* t, rational& r) {
@ -232,8 +248,8 @@ namespace mbp {
} }
struct compare_second { struct compare_second {
bool operator()(std::pair<expr*, rational> const& a, bool operator()(std::pair<expr*, rational> const& a,
std::pair<expr*, rational> const& b) const { std::pair<expr*, rational> const& b) const {
return a.second < b.second; return a.second < b.second;
} }
}; };
@ -243,14 +259,14 @@ namespace mbp {
} }
rational n_sign(rational const& b) { rational n_sign(rational const& b) {
return rational(b.is_pos()?-1:1); return rational(b.is_pos() ? -1 : 1);
} }
bool operator()(model& model, app* v, app_ref_vector& vars, expr_ref_vector& lits) { bool operator()(model& model, app* v, app_ref_vector& vars, expr_ref_vector& lits) {
app_ref_vector vs(m); app_ref_vector vs(m);
vs.push_back(v); vs.push_back(v);
vector<def> defs; vector<def> defs;
return project(model, vs, lits, defs, false) && vs.empty(); return project(model, vs, lits, defs, false) && vs.empty();
} }
typedef opt::model_based_opt::var var; typedef opt::model_based_opt::var var;
@ -267,10 +283,10 @@ namespace mbp {
bool project(model& model, app_ref_vector& vars, expr_ref_vector& fmls, vector<def>& result, bool compute_def) { bool project(model& model, app_ref_vector& vars, expr_ref_vector& fmls, vector<def>& result, bool compute_def) {
bool has_arith = false; bool has_arith = false;
for (expr* v : vars) for (expr* v : vars)
has_arith |= is_arith(v); has_arith |= is_arith(v);
if (!has_arith) if (!has_arith)
return true; return true;
model_evaluator eval(model); model_evaluator eval(model);
TRACE("qe", tout << model;); TRACE("qe", tout << model;);
eval.set_model_completion(true); eval.set_model_completion(true);
@ -281,7 +297,7 @@ namespace mbp {
expr_ref_vector pinned(m); expr_ref_vector pinned(m);
unsigned j = 0; unsigned j = 0;
TRACE("qe", tout << "vars: " << vars << "\n"; TRACE("qe", tout << "vars: " << vars << "\n";
for (expr* f : fmls) tout << mk_pp(f, m) << " := " << model(f) << "\n";); for (expr* f : fmls) tout << mk_pp(f, m) << " := " << model(f) << "\n";);
for (unsigned i = 0; i < fmls.size(); ++i) { for (unsigned i = 0; i < fmls.size(); ++i) {
expr* fml = fmls.get(i); expr* fml = fmls.get(i);
if (!linearize(mbo, eval, fml, fmls, tids)) { if (!linearize(mbo, eval, fml, fmls, tids)) {
@ -294,8 +310,8 @@ namespace mbp {
} }
fmls.shrink(j); fmls.shrink(j);
TRACE("qe", tout << "formulas\n" << fmls << "\n"; TRACE("qe", tout << "formulas\n" << fmls << "\n";
for (auto const& [e, id] : tids) for (auto const& [e, id] : tids)
tout << mk_pp(e, m) << " -> " << id << "\n";); tout << mk_pp(e, m) << " -> " << id << "\n";);
// fmls holds residue, // fmls holds residue,
// mbo holds linear inequalities that are in scope // mbo holds linear inequalities that are in scope
@ -306,7 +322,7 @@ namespace mbp {
// return those to fmls. // return those to fmls.
expr_mark var_mark, fmls_mark; expr_mark var_mark, fmls_mark;
for (app * v : vars) { for (app* v : vars) {
var_mark.mark(v); var_mark.mark(v);
if (is_arith(v) && !tids.contains(v)) { if (is_arith(v) && !tids.contains(v)) {
rational r; rational r;
@ -321,60 +337,70 @@ namespace mbp {
} }
// bail on variables in non-linear sub-terms // bail on variables in non-linear sub-terms
auto is_pure = [&](expr* e) {
expr* x, * y;
rational r;
if (a.is_mod(e, x, y) && a.is_numeral(y))
return true;
if (a.is_idiv(e, x, y) && a.is_numeral(y, r) && r > 0)
return true;
return false;
};
for (auto& kv : tids) { for (auto& kv : tids) {
expr* e = kv.m_key; expr* e = kv.m_key;
if (is_arith(e) && !var_mark.is_marked(e)) if (is_arith(e) && !is_pure(e) && !var_mark.is_marked(e))
mark_rec(fmls_mark, e); mark_rec(fmls_mark, e);
} }
if (m_check_purified) { if (m_check_purified) {
for (expr* fml : fmls) for (expr* fml : fmls)
mark_rec(fmls_mark, fml); mark_rec(fmls_mark, fml);
for (auto& kv : tids) { for (auto& kv : tids) {
expr* e = kv.m_key; expr* e = kv.m_key;
if (!var_mark.is_marked(e)) if (!var_mark.is_marked(e) && !is_pure(e))
mark_rec(fmls_mark, e); mark_rec(fmls_mark, e);
} }
} }
ptr_vector<expr> index2expr; ptr_vector<expr> index2expr;
for (auto& kv : tids) for (auto& kv : tids)
index2expr.setx(kv.m_value, kv.m_key, nullptr); index2expr.setx(kv.m_value, kv.m_key, nullptr);
j = 0; j = 0;
unsigned_vector real_vars; unsigned_vector real_vars;
for (app* v : vars) { for (app* v : vars) {
if (is_arith(v) && !fmls_mark.is_marked(v)) if (is_arith(v) && !fmls_mark.is_marked(v))
real_vars.push_back(tids.find(v)); real_vars.push_back(tids.find(v));
else else
vars[j++] = v; vars[j++] = v;
} }
vars.shrink(j); vars.shrink(j);
TRACE("qe", tout << "remaining vars: " << vars << "\n"; TRACE("qe", tout << "remaining vars: " << vars << "\n";
for (unsigned v : real_vars) tout << "v" << v << " " << mk_pp(index2expr[v], m) << "\n"; for (unsigned v : real_vars) tout << "v" << v << " " << mk_pp(index2expr[v], m) << "\n";
mbo.display(tout);); mbo.display(tout););
vector<opt::model_based_opt::def> defs = mbo.project(real_vars.size(), real_vars.data(), compute_def); vector<opt::model_based_opt::def> defs = mbo.project(real_vars.size(), real_vars.data(), compute_def);
vector<row> rows; vector<row> rows;
mbo.get_live_rows(rows); mbo.get_live_rows(rows);
rows2fmls(rows, index2expr, fmls); rows2fmls(rows, index2expr, fmls);
TRACE("qe", mbo.display(tout << "mbo result\n"); TRACE("qe", mbo.display(tout << "mbo result\n");
for (auto const& d : defs) tout << "def: " << d << "\n"; for (auto const& d : defs) tout << "def: " << d << "\n";
tout << fmls << "\n";); tout << fmls << "\n";);
if (compute_def) if (compute_def)
optdefs2mbpdef(defs, index2expr, real_vars, result); optdefs2mbpdef(defs, index2expr, real_vars, result);
if (m_apply_projection && !apply_projection(eval, result, fmls)) if (m_apply_projection && !apply_projection(eval, result, fmls))
return false; return false;
TRACE("qe", TRACE("qe",
for (auto const& [v, t] : result) for (auto const& [v, t] : result)
tout << v << " := " << t << "\n"; tout << v << " := " << t << "\n";
for (auto* f : fmls) for (auto* f : fmls)
tout << mk_pp(f, m) << " := " << eval(f) << "\n"; tout << mk_pp(f, m) << " := " << eval(f) << "\n";
tout << "fmls:" << fmls << "\n";); tout << "fmls:" << fmls << "\n";);
return true; return true;
} }
void optdefs2mbpdef(vector<opt::model_based_opt::def> const& defs, ptr_vector<expr> const& index2expr, unsigned_vector const& real_vars, vector<def>& result) { void optdefs2mbpdef(vector<opt::model_based_opt::def> const& defs, ptr_vector<expr> const& index2expr, unsigned_vector const& real_vars, vector<def>& result) {
SASSERT(defs.size() == real_vars.size()); SASSERT(defs.size() == real_vars.size());
@ -384,31 +410,92 @@ namespace mbp {
bool is_int = a.is_int(x); bool is_int = a.is_int(x);
expr_ref_vector ts(m); expr_ref_vector ts(m);
expr_ref t(m); expr_ref t(m);
for (var const& v : d.m_vars) for (var const& v : d.m_vars)
ts.push_back(var2expr(index2expr, v)); ts.push_back(var2expr(index2expr, v));
if (!d.m_coeff.is_zero()) if (!d.m_coeff.is_zero())
ts.push_back(a.mk_numeral(d.m_coeff, is_int)); ts.push_back(a.mk_numeral(d.m_coeff, is_int));
if (ts.empty()) if (ts.empty())
ts.push_back(a.mk_numeral(rational(0), is_int)); ts.push_back(a.mk_numeral(rational(0), is_int));
t = mk_add(ts); t = mk_add(ts);
if (!d.m_div.is_one() && is_int) if (!d.m_div.is_one() && is_int)
t = a.mk_idiv(t, a.mk_numeral(d.m_div, is_int)); t = a.mk_idiv(t, a.mk_numeral(d.m_div, is_int));
else if (!d.m_div.is_one() && !is_int) else if (!d.m_div.is_one() && !is_int)
t = a.mk_div(t, a.mk_numeral(d.m_div, is_int)); t = a.mk_div(t, a.mk_numeral(d.m_div, is_int));
result.push_back(def(expr_ref(x, m), t)); result.push_back(def(expr_ref(x, m), t));
} }
} }
void rows2fmls(vector<row> const& rows, ptr_vector<expr> const& index2expr, expr_ref_vector& fmls) { expr_ref id2expr(u_map<row> const& def_vars, ptr_vector<expr> const& index2expr, unsigned id) {
for (row const& r : rows) { row r;
expr_ref_vector ts(m); if (def_vars.find(id, r))
expr_ref t(m), s(m), val(m); return row2expr(def_vars, index2expr, r);
if (r.m_vars.empty()) { return expr_ref(index2expr[id], m);
}
expr_ref row2expr(u_map<row> const& def_vars, ptr_vector<expr> const& index2expr, row const& r) {
expr_ref_vector ts(m);
expr_ref t(m);
rational n;
for (var const& v : r.m_vars) {
t = id2expr(def_vars, index2expr, v.m_id);
if (a.is_numeral(t, n) && n == 0)
continue; continue;
else if (a.is_numeral(t, n))
t = a.mk_numeral(v.m_coeff * n, a.is_int(t));
else if (!v.m_coeff.is_one())
t = a.mk_mul(a.mk_numeral(v.m_coeff, a.is_int(t)), t);
ts.push_back(t);
}
switch (r.m_type) {
case opt::t_mod:
if (ts.empty()) {
t = a.mk_int(mod(r.m_coeff, r.m_mod));
return t;
} }
if (r.m_vars.size() == 1 && r.m_vars[0].m_coeff.is_neg() && r.m_type != opt::t_mod) { ts.push_back(a.mk_int(r.m_coeff));
t = mk_add(ts);
t = a.mk_mod(t, a.mk_int(r.m_mod));
return t;
case opt::t_div:
if (ts.empty()) {
t = a.mk_int(div(r.m_coeff, r.m_mod));
return t;
}
ts.push_back(a.mk_int(r.m_coeff));
t = mk_add(ts);
t = a.mk_idiv(t, a.mk_int(r.m_mod));
return t;
case opt::t_divides:
ts.push_back(a.mk_int(r.m_coeff));
return mk_add(ts);
default:
return mk_add(ts);
}
}
void rows2fmls(vector<row> const& rows, ptr_vector<expr> const& index2expr, expr_ref_vector& fmls) {
u_map<row> def_vars;
for (row const& r : rows) {
if (r.m_type == opt::t_mod)
def_vars.insert(r.m_id, r);
else if (r.m_type == opt::t_div)
def_vars.insert(r.m_id, r);
}
for (row const& r : rows) {
expr_ref t(m), s(m), val(m);
if (r.m_vars.empty())
continue;
if (r.m_type == opt::t_mod)
continue;
if (r.m_type == opt::t_div)
continue;
if (r.m_vars.size() == 1 && r.m_vars[0].m_coeff.is_neg() && r.m_type != opt::t_divides) {
var const& v = r.m_vars[0]; var const& v = r.m_vars[0];
t = index2expr[v.m_id]; t = id2expr(def_vars, index2expr, v.m_id);
if (!v.m_coeff.is_minus_one()) { if (!v.m_coeff.is_minus_one()) {
t = a.mk_mul(a.mk_numeral(-v.m_coeff, a.is_int(t)), t); t = a.mk_mul(a.mk_numeral(-v.m_coeff, a.is_int(t)), t);
} }
@ -422,24 +509,14 @@ namespace mbp {
fmls.push_back(t); fmls.push_back(t);
continue; continue;
} }
for (var const& v : r.m_vars) { t = row2expr(def_vars, index2expr, r);
t = index2expr[v.m_id];
if (!v.m_coeff.is_one()) {
t = a.mk_mul(a.mk_numeral(v.m_coeff, a.is_int(t)), t);
}
ts.push_back(t);
}
t = mk_add(ts);
s = a.mk_numeral(-r.m_coeff, r.m_coeff.is_int() && a.is_int(t)); s = a.mk_numeral(-r.m_coeff, r.m_coeff.is_int() && a.is_int(t));
switch (r.m_type) { switch (r.m_type) {
case opt::t_lt: t = a.mk_lt(t, s); break; case opt::t_lt: t = a.mk_lt(t, s); break;
case opt::t_le: t = a.mk_le(t, s); break; case opt::t_le: t = a.mk_le(t, s); break;
case opt::t_eq: t = a.mk_eq(t, s); break; case opt::t_eq: t = a.mk_eq(t, s); break;
case opt::t_mod: case opt::t_divides:
if (!r.m_coeff.is_zero()) { t = a.mk_eq(a.mk_mod(t, a.mk_int(r.m_mod)), a.mk_int(0));
t = a.mk_sub(t, s);
}
t = a.mk_eq(a.mk_mod(t, a.mk_numeral(r.m_mod, true)), a.mk_int(0));
break; break;
} }
fmls.push_back(t); fmls.push_back(t);
@ -468,11 +545,11 @@ namespace mbp {
SASSERT(validate_model(eval, fmls0)); SASSERT(validate_model(eval, fmls0));
// extract linear constraints // extract linear constraints
for (expr * fml : fmls) { for (expr* fml : fmls) {
linearize(mbo, eval, fml, fmls, tids); linearize(mbo, eval, fml, fmls, tids);
} }
// find optimal value // find optimal value
value = mbo.maximize(); value = mbo.maximize();
@ -543,7 +620,7 @@ namespace mbp {
} }
CTRACE("qe", kv.m_value.is_zero(), tout << mk_pp(v, m) << " has coefficeint 0\n";); CTRACE("qe", kv.m_value.is_zero(), tout << mk_pp(v, m) << " has coefficeint 0\n";);
if (!kv.m_value.is_zero()) { if (!kv.m_value.is_zero()) {
coeffs.push_back(var(id, kv.m_value)); coeffs.push_back(var(id, kv.m_value));
} }
} }
} }
@ -571,7 +648,7 @@ namespace mbp {
}; };
arith_project_plugin::arith_project_plugin(ast_manager& m):project_plugin(m) { arith_project_plugin::arith_project_plugin(ast_manager& m) :project_plugin(m) {
m_imp = alloc(imp, m); m_imp = alloc(imp, m);
} }