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https://github.com/Z3Prover/z3
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Complete euf project with eq and diseq on pure representatives
This commit is contained in:
Arie Gurfinkel
parent
b246389267
commit
535b8893ae
3 changed files with 65 additions and 27 deletions
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@ -33,18 +33,18 @@ Notes:
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Sketch of approach by example:
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A: s <= 2a <= t & f(a) = q
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B: t <= 2b <= s + 1 & f(b) != q
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1. Extract arithmetic consequences of A over shared vocabulary.
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A -> s <= t & (even(t) | s < t)
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A -> s <= t & (even(t) | s < t)
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2a. Send to B, have B solve shared variables with EUF_B.
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epsilon b . B & A_pure
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epsilon b . t <= 2b <= s + 1 & s <= t & (even(t) | s < t)
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= t <= s + 1 & (even(t) | t <= s) & s <= t & (even(t) | s < t)
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= even(t) & t = s
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epsilon b . t <= 2b <= s + 1 & s <= t & (even(t) | s < t)
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= t <= s + 1 & (even(t) | t <= s) & s <= t & (even(t) | s < t)
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= even(t) & t = s
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b := t div 2
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B & A_pure -> B[b/t div 2] = f(t div 2) != q & t <= s + 1
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@ -53,13 +53,13 @@ Notes:
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A & B_pure -> false
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Invoke the ping-pong principle to extract interpolant.
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2b. Solve for shared variables with EUF.
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epsilon a . A
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epsilon a . A
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= a := (s + 1) div 2 & s < t & f((s + 1) div 2) = q
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3b. Send to B. Produces core
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3b. Send to B. Produces core
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s < t & f((s + 1) div 2) = q
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4b Solve again in arithmetic for shared variables with EUF.
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@ -71,7 +71,7 @@ Notes:
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Send to B, produces core (s != t | f(t div 2) != q)
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5b. There is no longer a solution for A. A is unsat.
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--*/
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#include "ast/ast_util.h"
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@ -138,7 +138,7 @@ namespace qe {
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void prop_mbi_plugin::block(expr_ref_vector const& lits) {
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m_solver->assert_expr(mk_not(mk_and(lits)));
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}
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}
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// -------------------------------
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// euf_mbi, TBD
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@ -158,8 +158,8 @@ namespace qe {
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void operator()(expr*) {}
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};
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euf_mbi_plugin::euf_mbi_plugin(solver* s, solver* sNot):
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m(s->get_manager()),
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euf_mbi_plugin::euf_mbi_plugin(solver* s, solver* sNot):
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m(s->get_manager()),
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m_atoms(m),
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m_solver(s),
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m_dual_solver(sNot) {
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@ -205,11 +205,11 @@ namespace qe {
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// use the dual solver to find a 'small' implicant
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m_dual_solver->get_unsat_core(core);
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TRACE("qe", tout << "core: " << core << "\n";);
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// project the implicant onto vars
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// project the implicant onto vars
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tg.set_vars(vars, false);
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tg.add_lits(core);
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lits.reset();
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lits.append(tg.project());
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lits.reset();
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lits.append(tg.project(*mdl));
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TRACE("qe", tout << "project: " << lits << "\n";);
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return mbi_sat;
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case l_undef:
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@ -232,8 +232,8 @@ namespace qe {
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void euf_mbi_plugin::block(expr_ref_vector const& lits) {
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m_solver->assert_expr(mk_not(mk_and(lits)));
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}
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}
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/** --------------------------------------------------------------
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* ping-pong interpolation of Gurfinkel & Vizel
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@ -255,7 +255,7 @@ namespace qe {
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auto* t2 = turn ? &b : &a;
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mbi_result next_res = (*t1)(vars, lits, mdl);
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switch (next_res) {
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case mbi_sat:
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case mbi_sat:
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if (last_res == mbi_sat) {
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itp = nullptr;
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return l_true;
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@ -264,7 +264,7 @@ namespace qe {
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break; // continue
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case mbi_unsat: {
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if (lits.empty()) {
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// TBD, either a => itp and itp => !b
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// TBD, either a => itp and itp => !b
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// or b => itp and itp => !a
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itp = mk_and(itps[!turn]);
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return l_false;
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@ -282,7 +282,7 @@ namespace qe {
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case mbi_augment:
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break;
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case mbi_undef:
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return l_undef;
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return l_undef;
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}
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turn = !turn;
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last_res = next_res;
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@ -319,4 +319,3 @@ namespace qe {
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}
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}
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};
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@ -24,6 +24,7 @@ Notes:
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#include "ast/for_each_expr.h"
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#include "ast/occurs.h"
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#include "qe/qe_term_graph.h"
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#include "model/model_evaluator.h"
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namespace qe {
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@ -546,6 +547,7 @@ namespace qe {
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u_map<expr*> m_term2app;
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u_map<expr*> m_root2rep;
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model_ref m_model;
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expr_ref_vector m_pinned; // tracks expr in the maps
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expr* mk_pure(term const& t) {
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@ -565,6 +567,7 @@ namespace qe {
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return pure;
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}
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bool is_better_rep(expr *t1, expr *t2) {
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if (!t2) return t1 != nullptr;
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return m.is_unique_value(t1) && !m.is_unique_value(t2);
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@ -740,20 +743,49 @@ namespace qe {
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return is_uninterp_const(rhs) && !occurs(rhs, lhs);
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}
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/// Add equalities and disequalities for all pure representatives
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/// based on their equivalence in the model
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void model_complete(expr_ref_vector &res) {
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if (!m_model) return;
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obj_map<expr,expr*> val2rep;
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model_evaluator mev(*m_model);
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for (auto &kv : m_root2rep) {
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expr *rep = kv.m_value;
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expr_ref val(m);
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expr *u = nullptr;
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if (!mev.eval(rep, val)) continue;
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if (val2rep.find(val, u)) {
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res.push_back(m.mk_eq(u, rep));
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}
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else {
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val2rep.insert(val, rep);
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}
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}
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ptr_buffer<expr> reps;
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for (auto &kv : val2rep) {
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reps.push_back(kv.m_value);
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}
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res.push_back(m.mk_distinct(reps.size(), reps.c_ptr()));
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}
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public:
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projector(term_graph &tg) : m_tg(tg), m(m_tg.m), m_pinned(m) {}
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void set_model(model &mdl) { m_model = &mdl; }
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void reset() {
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m_tg.reset_marks();
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m_term2app.reset();
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m_root2rep.reset();
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m_pinned.reset();
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m_model.reset();
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}
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expr_ref_vector project() {
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expr_ref_vector res(m);
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purify();
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mk_lits(res);
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mk_pure_equalities(res);
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model_complete(res);
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reset();
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return res;
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}
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@ -780,6 +812,13 @@ namespace qe {
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return p.project();
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}
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expr_ref_vector term_graph::project(model &mdl) {
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m_is_var.reset_solved();
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projector p(*this);
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p.set_model(mdl);
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return p.project();
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}
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expr_ref_vector term_graph::solve() {
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// reset solved vars so that they are not considered pure by projector
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m_is_var.reset_solved();
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@ -23,6 +23,7 @@ Notes:
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#include "util/plugin_manager.h"
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#include "qe/qe_solve_plugin.h"
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#include "qe/qe_vartest.h"
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#include "model/model.h"
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namespace qe {
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@ -85,8 +86,6 @@ namespace qe {
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void display(std::ostream &out);
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bool is_pure_def(expr* atom, expr *& v);
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void solve_for_vars();
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public:
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term_graph(ast_manager &m);
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@ -111,9 +110,10 @@ namespace qe {
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* onto the vocabulary of decls (if exclude is false) or outside the
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* vocabulary of decls (if exclude is true).
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*/
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expr_ref_vector project();
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expr_ref_vector solve();
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expr_ref_vector project();
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expr_ref_vector solve();
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expr_ref_vector project(model &mdl);
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};
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}
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