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plugin work

Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2018-06-11 15:25:20 -07:00 committed by Arie Gurfinkel
parent 5566b5689c
commit 2e616c482b
3 changed files with 358 additions and 0 deletions

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@ -17,6 +17,7 @@ z3_add_component(qe
qe_mbp.cpp
qe_mbi.cpp
qe_sat_tactic.cpp
qe_solve_plugin.cpp
qe_tactic.cpp
qe_term_graph.cpp
qsat.cpp

305
src/qe/qe_solve_plugin.cpp Normal file
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/**
Copyright (c) 2018 Microsoft Corporation
Module Name:
qe_solve.cpp
Abstract:
Light-weight variable solving plugin model for qe-lite and term_graph.
Author:
Nikolaj Bjorner (nbjorner), Arie Gurfinkel 2018-6-8
Revision History:
--*/
#pragma once
#include "ast/arith_decl_plugin.h"
#include "ast/ast_util.h"
#include "ast/ast_pp.h"
#include "qe/qe_solve_plugin.h"
namespace qe {
expr_ref solve_plugin::operator()(expr* lit) {
if (m.is_not(lit, lit))
return solve(lit, false);
else
return solve(lit, true);
}
class arith_solve_plugin : public solve_plugin {
arith_util a;
public:
arith_solve_plugin(ast_manager& m, is_variable_proc& is_var): solve_plugin(m, m.get_family_id("arith"), is_var), a(m) {}
typedef std::pair<bool,expr*> signed_expr;
/**
*\brief
* return r * (sum_{(sign,e) \in exprs} sign * e)
*/
expr_ref mk_term(bool is_int, rational const& r, bool sign, svector<signed_expr> const& exprs) {
expr_ref_vector result(m);
for (auto const& kv : exprs) {
bool sign2 = kv.first;
expr* e = kv.second;
rational r2(r);
if (sign == sign2) {
r2.neg();
}
if (!r2.is_one()) {
result.push_back(a.mk_mul(a.mk_numeral(r2, is_int), e));
}
else {
result.push_back(e);
}
}
return a.mk_add_simplify(result);
}
/**
* \brief return true if lhs = rhs can be solved as v = t, where v is a variable.
*/
bool solve_arith(expr* lhs, expr* rhs, expr_ref& v, expr_ref& t) {
if (!a.is_int(lhs) && !a.is_real(rhs)) {
return false;
}
rational a_val;
bool is_int = a.is_int(lhs);
svector<signed_expr> todo, done;
todo.push_back(std::make_pair(true, lhs));
todo.push_back(std::make_pair(false, rhs));
while (!todo.empty()) {
expr* e = todo.back().second;
bool sign = todo.back().first;
todo.pop_back();
if (a.is_add(e)) {
for (expr* e : *to_app(e)) {
todo.push_back(std::make_pair(sign, e));
}
}
else if (is_invertible_mul(is_int, e, a_val)) {
done.append(todo);
v = e;
a_val = rational(1)/a_val;
t = mk_term(is_int, a_val, sign, done);
TRACE("qe", tout << mk_pp(lhs, m) << " " << mk_pp(rhs, m) << " " << e << " := " << t << "\n";);
return true;
}
else {
done.push_back(std::make_pair(sign, e));
}
}
return false;
}
// can we solve for a variable by ...
bool is_invertible_const(bool is_int, expr* x, rational& a_val) {
expr* y;
if (a.is_uminus(x, y) && is_invertible_const(is_int, y, a_val)) {
a_val.neg();
return true;
}
else if (a.is_numeral(x, a_val) && !a_val.is_zero()) {
if (!is_int || a_val.is_one() || a_val.is_minus_one()) {
return true;
}
}
return false;
}
bool is_invertible_mul(bool is_int, expr*& arg, rational& a_val) {
if (is_variable(arg)) {
a_val = rational(1);
return true;
}
expr* x, *y;
if (a.is_mul(arg, x, y)) {
if (is_variable(x) && is_invertible_const(is_int, y, a_val)) {
arg = x;
return true;
}
if (is_variable(y) && is_invertible_const(is_int, x, a_val)) {
arg = y;
return true;
}
}
return false;
}
expr_ref mk_eq_core (expr *_e1, expr *_e2) {
expr *e1, *e2;
e1 = _e1;
e2 = _e2;
if (a.is_zero(e1)) {
std::swap(e1, e2);
}
// y + -1*x == 0 --> y = x
expr *a0 = 0, *a1 = 0, *x = 0;
if (a.is_zero(e2) && a.is_add(e1, a0, a1)) {
if (a.is_times_minus_one(a1, x)) {
e1 = a0;
e2 = x;
}
else if (a.is_times_minus_one(a0, x)) {
e1 = a1;
e2 = x;
}
}
return expr_ref(m.mk_eq(e1, e2), m);
}
app* mk_le_zero(expr *arg) {
expr *e1, *e2, *e3;
// XXX currently disabled
if (a.is_add(arg, e1, e2)) {
// e1-e2<=0 --> e1<=e2
if (a.is_times_minus_one(e2, e3)) {
return a.mk_le(e1, e3);
}
// -e1+e2<=0 --> e2<=e1
else if (a.is_times_minus_one(e1, e3)) {
return a.mk_le(e2, e3);
}
}
return a.mk_le(arg, mk_zero());
}
app* mk_ge_zero(expr *arg) {
expr *e1, *e2, *e3;
// XXX currently disabled
if (a.is_add(arg, e1, e2)) {
// e1-e2>=0 --> e1>=e2
if (a.is_times_minus_one(e2, e3)) {
return a.mk_ge(e1, e3);
}
// -e1+e2>=0 --> e2>=e1
else if (a.is_times_minus_one(e1, e3)) {
return a.mk_ge(e2, e3);
}
}
return a.mk_ge(arg, mk_zero());
}
bool mk_le_core (expr *arg1, expr * arg2, expr_ref &result) {
// t <= -1 ==> t < 0 ==> ! (t >= 0)
rational n;
if (a.is_int (arg1) && a.is_minus_one (arg2)) {
result = m.mk_not (mk_ge_zero (arg1));
return true;
}
else if (a.is_zero(arg2)) {
result = mk_le_zero(arg1);
return true;
}
else if (a.is_int(arg1) && a.is_numeral(arg2, n) && n < 0) {
// t <= n ==> t < n + 1 ==> ! (t >= n + 1)
result = m.mk_not(a.mk_ge(arg1, a.mk_numeral(n+1, true)));
return true;
}
return false;
}
expr * mk_zero () {
return a.mk_numeral (rational (0), true);
}
bool is_one (expr const * n) const {
rational val;
return a.is_numeral (n, val) && val.is_one ();
}
bool mk_ge_core (expr * arg1, expr * arg2, expr_ref &result) {
// t >= 1 ==> t > 0 ==> ! (t <= 0)
rational n;
if (a.is_int (arg1) && is_one (arg2)) {
result = m.mk_not (mk_le_zero (arg1));
return true;
}
else if (a.is_zero(arg2)) {
result = mk_ge_zero(arg1);
return true;
}
else if (a.is_int(arg1) && a.is_numeral(arg2, n) && n > 0) {
// t >= n ==> t > n - 1 ==> ! (t <= n - 1)
result = m.mk_not(a.mk_le(arg1, a.mk_numeral(n-1, true)));
return true;
}
return false;
}
expr_ref solve(expr* lit, bool is_pos) override {
expr *e1, *e2;
expr_ref res(lit, m);
if (m.is_eq (lit, e1, e2)) {
res = mk_eq_core(e1, e2);
}
else if (a.is_le(lit, e1, e2)) {
mk_le_core(e1, e2, res);
}
else if (a.is_ge(lit, e1, e2)) {
mk_ge_core(e1, e2, res);
}
// restore negation
if (!is_pos) {
res = mk_not(m, res);
}
return res;
}
};
class bv_solve_plugin : public solve_plugin {
public:
bv_solve_plugin(ast_manager& m, is_variable_proc& is_var): solve_plugin(m, m.get_family_id("bv"), is_var) {}
expr_ref solve(expr *atom, bool is_pos) override {
expr_ref res(atom, m);
return is_pos ? res : mk_not(res);
}
};
class dt_solve_plugin : public solve_plugin {
public:
dt_solve_plugin(ast_manager& m, is_variable_proc& is_var): solve_plugin(m, m.get_family_id("dt"), is_var) {}
expr_ref solve(expr *atom, bool is_pos) override {
expr_ref res(atom, m);
return is_pos ? res : mk_not(res);
}
};
class array_solve_plugin : public solve_plugin {
public:
array_solve_plugin(ast_manager& m, is_variable_proc& is_var): solve_plugin(m, m.get_family_id("array"), is_var) {}
expr_ref solve(expr *atom, bool is_pos) override {
expr_ref res(atom, m);
return is_pos ? res : mk_not(res);
}
};
solve_plugin* mk_arith_solve_plugin(ast_manager& m, is_variable_proc& is_var) {
return alloc(arith_solve_plugin, m, is_var);
}
solve_plugin* mk_dt_solve_plugin(ast_manager& m, is_variable_proc& is_var) {
return alloc(dt_solve_plugin, m, is_var);
}
solve_plugin* mk_bv_solve_plugin(ast_manager& m, is_variable_proc& is_var) {
return alloc(bv_solve_plugin, m, is_var);
}
solve_plugin* mk_array_solve_plugin(ast_manager& m, is_variable_proc& is_var) {
return alloc(array_solve_plugin, m, is_var);
}
}

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src/qe/qe_solve_plugin.h Normal file
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/**
Copyright (c) 2018 Microsoft Corporation
Module Name:
qe_solve.h
Abstract:
Light-weight variable solving plugin model for qe-lite and term_graph.
Author:
Nikolaj Bjorner (nbjorner), Arie Gurfinkel 2018-6-8
Revision History:
--*/
#pragma once
#include "ast/ast.h"
#include "util/plugin_manager.h"
#include "qe/qe_vartest.h"
namespace qe {
class solve_plugin {
protected:
ast_manager& m;
family_id m_id;
is_variable_proc& m_is_var;
virtual expr_ref solve(expr* atom, bool is_pos) = 0;
bool is_variable(expr* e) const { return m_is_var(e); }
public:
solve_plugin(ast_manager& m, family_id fid, is_variable_proc& is_var) : m(m), m_id(fid), m_is_var(is_var) {}
virtual ~solve_plugin() {}
family_id get_family_id() const { return m_id; }
/// Process (and potentially augment) a literal
expr_ref operator() (expr *lit);
};
solve_plugin* mk_arith_solve_plugin(ast_manager& m, is_variable_proc& is_var);
solve_plugin* mk_dt_solve_plugin(ast_manager& m, is_variable_proc& is_var);
solve_plugin* mk_bv_solve_plugin(ast_manager& m, is_variable_proc& is_var);
solve_plugin* mk_array_solve_plugin(ast_manager& m, is_variable_proc& is_var);
}