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https://github.com/Z3Prover/z3
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fleshing out reduce-invertible tactic
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
parent
ac014bef94
commit
76417fa3b6
2 changed files with 156 additions and 30 deletions
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@ -43,6 +43,7 @@ z3_add_component(core_tactics
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pb_preprocess_tactic.h
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propagate_values_tactic.h
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reduce_args_tactic.h
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reduce_invertible_tactic.h
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simplify_tactic.h
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solve_eqs_tactic.h
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split_clause_tactic.h
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@ -22,6 +22,7 @@ Notes:
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#include "util/cooperate.h"
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#include "ast/bv_decl_plugin.h"
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#include "ast/ast_pp.h"
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#include "ast/rewriter/expr_safe_replace.h"
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#include "ast/rewriter/rewriter_def.h"
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#include "tactic/tactic.h"
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@ -48,28 +49,29 @@ public:
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void operator()(goal_ref const & g, goal_ref_buffer & result) override {
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TRACE("reduce_invertible", g->display(tout););
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tactic_report report("reduce-invertible", *g);
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m_inverted.reset();
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m_parents.reset();
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collect_parents(g);
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collect_occs occs;
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obj_hashtable<expr> vars;
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generic_model_converter_ref mc;
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//occs(*g, vars);
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occs(*g, vars);
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expr_safe_replace sub(m);
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expr_ref p(m);
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expr_ref p(m), new_v(m);
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for (expr* v : vars) {
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if (is_invertible(v, p, &mc)) {
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sub.insert(v, p);
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if (is_invertible(v, p, new_v, &mc)) {
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mark_inverted(p);
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sub.insert(p, new_v);
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}
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}
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if (sub.empty()) {
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result.push_back(g.get());
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return;
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}
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reduce_q_rw rw(*this);
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unsigned sz = g->size();
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for (unsigned idx = 0; idx < sz; idx++) {
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checkpoint();
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expr* f = g->form(idx);
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expr_ref f_new(m);
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sub(f, f_new);
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rw(f_new, f_new);
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proof_ref new_pr(m);
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if (f == f_new) continue;
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if (g->proofs_enabled()) {
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@ -77,7 +79,8 @@ public:
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new_pr = m.mk_modus_ponens(pr, new_pr);
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}
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g->update(idx, f_new, new_pr, g->dep(idx));
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}
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}
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if (mc) g->add(mc.get());
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result.push_back(g.get());
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g->inc_depth();
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}
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@ -93,6 +96,27 @@ private:
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cooperate("reduce-invertible");
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}
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expr_mark m_inverted;
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void mark_inverted(expr *p) {
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ptr_buffer<expr> todo;
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todo.push_back(p);
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while (!todo.empty()) {
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p = todo.back();
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todo.pop_back();
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if (!m_inverted.is_marked(p)) {
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m_inverted.mark(p, true);
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if (is_app(p)) {
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for (expr* arg : *to_app(p)) {
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todo.push_back(arg);
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}
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}
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else if (is_quantifier(p)) {
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todo.push_back(to_quantifier(p)->get_expr());
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}
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}
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}
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}
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// store up to two parents of expression.
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struct parents {
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parents(): m_p1(nullptr), m_p2(nullptr) {}
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@ -105,8 +129,8 @@ private:
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parent_collector(reduce_invertible_tactic& c):c(c) {}
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void operator()(app* n) {
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for (expr* arg : *n) {
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c.m_parents.reserve(n->get_id() + 1, parents());
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parents& p = c.m_parents[n->get_id()];
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c.m_parents.reserve(arg->get_id() + 1, parents());
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parents& p = c.m_parents[arg->get_id()];
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if (!p.m_p1) p.m_p1 = n; else p.m_p2 = n;
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}
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}
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@ -114,7 +138,6 @@ private:
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};
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void collect_parents(goal_ref const& g) {
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m_parents.reset();
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parent_collector proc(*this);
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expr_fast_mark1 visited;
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unsigned sz = g->size();
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@ -130,17 +153,18 @@ private:
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// TBD: could be made to be recursive, by walking multiple layers of parents.
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bool is_invertible(expr* v, expr_ref& new_v, generic_model_converter_ref* mc) {
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expr* p1 = m_parents[v->get_id()].m_p1;
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if (m_parents[v->get_id()].m_p2 || !p1) return false;
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if (m_bv.is_bv_add(p1)) {
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bool is_invertible(expr* v, expr_ref& p, expr_ref& new_v, generic_model_converter_ref* mc) {
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p = m_parents[v->get_id()].m_p1;
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if (m_parents[v->get_id()].m_p2 || !p) return false;
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if (m_inverted.is_marked(p)) return false;
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if (mc && !is_ground(p)) return false;
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if (m_bv.is_bv_add(p)) {
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if (mc) {
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ensure_mc(mc);
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// if we solve for v' := v + t
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// then the value for v is v' - t
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expr_ref def(v, m);
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for (expr* arg : *to_app(p1)) {
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for (expr* arg : *to_app(p)) {
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if (arg != v) def = m_bv.mk_bv_sub(def, arg);
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}
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(*mc)->add(v, def);
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@ -148,23 +172,96 @@ private:
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new_v = v;
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return true;
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}
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if (m_bv.is_bv_mul(p1)) {
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if (m_bv.is_bv_mul(p)) {
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expr_ref rest(m);
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for (expr* arg : *to_app(p)) {
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if (arg != v)
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if (rest)
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rest = m_bv.mk_bv_mul(rest, arg);
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else
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rest = arg;
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}
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if (!rest) return false;
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// if multiplier by odd number, then just return division.
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// if general multiplier, then create case split on
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// divisbility of 2
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// v * t -> if (t & 0x1) v / t (if (!(t & 0x1) && (t & 0x3)) ..
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unsigned sz = m_bv.get_bv_size(p);
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expr_ref bit1(m_bv.mk_numeral(1, 1), m);
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new_v = m_bv.mk_numeral(0, sz);
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for (unsigned i = sz; i-- > 0; ) {
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expr_ref extr_i(m_bv.mk_extract(i, i, rest), m);
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expr_ref cond(m.mk_eq(extr_i, bit1), m);
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expr_ref part(v, m);
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if (i > 0) {
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part = m_bv.mk_concat(m_bv.mk_extract(sz-1, i, v), m_bv.mk_numeral(0, i));
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}
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new_v = m.mk_ite(cond, part, new_v);
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}
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if (mc) {
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ensure_mc(mc);
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// TBD: represent inverse
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}
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return true;
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}
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if (m_bv.is_bv_xor(p1)) {
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if (m_bv.is_bv_xor(p)) {
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if (mc) {
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ensure_mc(mc);
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(*mc)->add(v, p);
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}
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new_v = v;
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return true;
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}
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if (m_bv.is_bv_sub(p)) {
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}
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if (m_bv.is_bv_neg(p)) {
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}
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if (m_bv.is_bv_udivi(p)) {
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}
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// sdivi, sremi, uremi, smodi
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expr* e1 = nullptr, *e2 = nullptr;
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if (m.is_eq(p, e1, e2)) {
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if (mc && m_bv.is_bv(e1)) {
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if (!is_ground(p)) return false;
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ensure_mc(mc);
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new_v = m.mk_fresh_const("eq", m.mk_bool_sort());
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expr* other = (v == e1) ? e2 : e1;
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(*mc)->hide(new_v);
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(*mc)->add(v, m.mk_ite(new_v, other, m_bv.mk_bv_neg(other)));
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return true;
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}
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else if (mc) {
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// diagonal functions for other types depend on theory.
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return false;
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}
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else if (is_var(v) && non_singleton_sort(m.get_sort(v))) {
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new_v = m.mk_var(to_var(v)->get_idx(), m.mk_bool_sort());
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return true;
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}
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}
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return false;
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}
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struct reduce_q_cfg : public default_rewriter_cfg {
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bool non_singleton_sort(sort* s) {
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if (m_bv.is_bv_sort(s) && m_bv.get_bv_size(s) > 0) return true;
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if (m.is_bool(s)) return true;
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// TBD: add arithmetic and other relevant theories.
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return false;
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}
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struct reduce_q_rw_cfg : public default_rewriter_cfg {
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ast_manager& m;
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reduce_invertible_tactic& t;
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reduce_q_cfg(reduce_invertible_tactic& t): m(t.m), t(t) {}
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reduce_q_rw_cfg(reduce_invertible_tactic& t): m(t.m), t(t) {}
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bool reduce_quantifier(quantifier * old_q,
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expr * new_body,
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@ -172,30 +269,49 @@ private:
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expr * const * new_no_patterns,
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expr_ref & result,
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proof_ref & result_pr) {
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if (is_lambda(old_q)) return false;
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if (has_quantifiers(new_body)) return false;
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ref_buffer<var, ast_manager> vars(m);
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ptr_buffer<sort> new_sorts;
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unsigned n = old_q->get_num_decls();
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for (unsigned i = 0; i < n; ++i) {
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vars.push_back(m.mk_var(n - i - 1, old_q->get_decl_sort(i)));
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sort* srt = old_q->get_decl_sort(i);
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vars.push_back(m.mk_var(n - i - 1, srt));
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new_sorts.push_back(srt);
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}
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// for each variable, collect parents,
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// ensure they are in uniqe location and not under other quantifiers.
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// if they are invertible, then produce inverting expression.
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//
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expr_safe_replace sub(m);
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t.m_parents.reset();
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t.m_inverted.reset();
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expr_ref p(m), new_v(m);
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{
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t.m_parents.reset();
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expr_ref p(m);
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parent_collector proc(t);
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expr_fast_mark1 visited;
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quick_for_each_expr(proc, visited, new_body);
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for (var* v : vars) {
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if (!occurs_under_nested_q(v, new_body) && t.is_invertible(v, p, nullptr)) {
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sub.insert(v, p);
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}
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}
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bool has_new_var = false;
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for (unsigned i = 0; i < vars.size(); ++i) {
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var* v = vars[i];
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if (!occurs_under_nested_q(v, new_body) && t.is_invertible(v, p, new_v, nullptr)) {
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t.mark_inverted(p);
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sub.insert(p, new_v);
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new_sorts[i] = m.get_sort(new_v);
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has_new_var |= new_v != v;
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}
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}
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if (has_new_var) {
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sub(new_body, result);
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result = m.mk_quantifier(old_q->get_kind(), new_sorts.size(), new_sorts.c_ptr(), old_q->get_decl_names(), result);
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result_pr = nullptr;
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return true;
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}
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if (!sub.empty()) {
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sub(new_body, result);
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result = m.update_quantifier(old_q, old_q->get_num_patterns(), new_patterns, old_q->get_num_no_patterns(), new_no_patterns, result);
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result_pr = nullptr;
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return true;
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}
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@ -203,10 +319,19 @@ private:
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}
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bool occurs_under_nested_q(var* v, expr* body) {
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return !has_quantifiers(body);
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return has_quantifiers(body);
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}
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};
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struct reduce_q_rw : rewriter_tpl<reduce_q_rw_cfg> {
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reduce_q_rw_cfg m_cfg;
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public:
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reduce_q_rw(reduce_invertible_tactic& t):
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rewriter_tpl<reduce_q_rw_cfg>(t.m, false, m_cfg),
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m_cfg(t) {}
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};
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};
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tactic * mk_reduce_invertible_tactic(ast_manager & m, params_ref const &) {
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