/*++ Copyright (c) 2011 Microsoft Corporation Module Name: rewriter_def.h Abstract: Lean and mean rewriter Author: Leonardo (leonardo) 2011-03-31 Notes: --*/ #include"rewriter.h" #include"ast_smt2_pp.h" template template void rewriter_tpl::process_var(var * v) { if (m_cfg.reduce_var(v, m_r, m_pr)) { result_stack().push_back(m_r); SASSERT(v->get_sort() == m().get_sort(m_r)); if (ProofGen) { result_pr_stack().push_back(m_pr); m_pr = 0; } set_new_child_flag(v); TRACE("rewriter", tout << mk_ismt2_pp(v, m()) << " -> " << m_r << "\n";); m_r = 0; return; } if (!ProofGen) { // bindings are only used when Proof Generation is not enabled. unsigned idx = v->get_idx(); if (idx < m_bindings.size()) { unsigned index = m_bindings.size() - idx - 1; var * r = (var*)(m_bindings[index]); if (r != 0) { SASSERT(v->get_sort() == m().get_sort(r)); if (!is_ground(r) && m_shifts[index] != m_bindings.size()) { unsigned shift_amount = m_bindings.size() - m_shifts[index]; expr_ref tmp(m()); m_shifter(r, shift_amount, tmp); result_stack().push_back(tmp); TRACE("rewriter", tout << "shift: " << shift_amount << " idx: " << idx << " --> " << tmp << "\n"; display_bindings(tout);); } else { result_stack().push_back(r); TRACE("rewriter", tout << idx << " " << mk_ismt2_pp(r, m()) << "\n";); } set_new_child_flag(v); return; } } } result_stack().push_back(v); if (ProofGen) result_pr_stack().push_back(0); // implicit reflexivity } template template void rewriter_tpl::process_const(app * t) { SASSERT(t->get_num_args() == 0); br_status st = m_cfg.reduce_app(t->get_decl(), 0, 0, m_r, m_pr); SASSERT(st != BR_DONE || m().get_sort(m_r) == m().get_sort(t)); SASSERT(st == BR_FAILED || st == BR_DONE); if (st == BR_DONE) { result_stack().push_back(m_r.get()); if (ProofGen) { if (m_pr) result_pr_stack().push_back(m_pr); else result_pr_stack().push_back(m().mk_rewrite(t, m_r)); m_pr = 0; } m_r = 0; set_new_child_flag(t); } else { result_stack().push_back(t); if (ProofGen) result_pr_stack().push_back(0); // implicit reflexivity } } /** \brief visit expression t. Return true if t was rewritten and the result is on the top m_result_stack. We may skip t if: - pre_visit(t) returns false - max_depth == 0 - t is already in the cache Otherwise, return false and add a new frame stack for t with the updated max_depth. */ template template bool rewriter_tpl::visit(expr * t, unsigned max_depth) { TRACE("rewriter_visit", tout << "visiting\n" << mk_ismt2_pp(t, m()) << "\n";); expr * new_t = 0; proof * new_t_pr = 0; if (m_cfg.get_subst(t, new_t, new_t_pr)) { TRACE("rewriter_subst", tout << "subst\n" << mk_ismt2_pp(t, m()) << "\n---->\n" << mk_ismt2_pp(new_t, m()) << "\n";); SASSERT(m().get_sort(t) == m().get_sort(new_t)); result_stack().push_back(new_t); set_new_child_flag(t, new_t); if (ProofGen) result_pr_stack().push_back(new_t_pr); return true; } if (max_depth == 0) { result_stack().push_back(t); if (ProofGen) result_pr_stack().push_back(0); // implicit reflexivity return true; // t is not going to be processed } SASSERT(max_depth > 0); SASSERT(max_depth <= RW_UNBOUNDED_DEPTH); bool c = must_cache(t); if (c) { #if 0 static unsigned checked_cache = 0; checked_cache ++; if (checked_cache % 100000 == 0) std::cerr << "[rewriter] num-cache-checks: " << checked_cache << std::endl; #endif expr * r = get_cached(t); if (r) { SASSERT(m().get_sort(r) == m().get_sort(t)); result_stack().push_back(r); set_new_child_flag(t, r); if (ProofGen) { proof * pr = get_cached_pr(t); result_pr_stack().push_back(pr); } return true; } } if (!pre_visit(t)) { result_stack().push_back(t); if (ProofGen) result_pr_stack().push_back(0); // implicit reflexivity return true; // t is not going to be processed } switch (t->get_kind()) { case AST_APP: if (to_app(t)->get_num_args() == 0) { process_const(to_app(t)); return true; } else { if (max_depth != RW_UNBOUNDED_DEPTH) max_depth--; push_frame(t, c, max_depth); return false; } case AST_VAR: process_var(to_var(t)); return true; case AST_QUANTIFIER: if (max_depth != RW_UNBOUNDED_DEPTH) max_depth--; push_frame(t, c, max_depth); return false; default: UNREACHABLE(); return true; } } template bool rewriter_tpl::constant_fold(app * t, frame & fr) { if (fr.m_i == 1 && m().is_ite(t)) { expr * cond = result_stack()[fr.m_spos].get(); expr* arg = 0; if (m().is_true(cond)) { arg = t->get_arg(1); } else if (m().is_false(cond)) { arg = t->get_arg(2); } if (arg) { result_stack().shrink(fr.m_spos); result_stack().push_back(arg); fr.m_state = REWRITE_BUILTIN; unsigned max_depth = fr.m_max_depth; if (visit(arg, fr.m_max_depth)) { m_r = result_stack().back(); result_stack().pop_back(); result_stack().pop_back(); result_stack().push_back(m_r); cache_result(t, m_r, m_pr, fr.m_cache_result); frame_stack().pop_back(); set_new_child_flag(t); } m_r = 0; return true; } } return false; } template template void rewriter_tpl::process_app(app * t, frame & fr) { SASSERT(t->get_num_args() > 0); SASSERT(!frame_stack().empty()); switch (fr.m_state) { case PROCESS_CHILDREN: { unsigned num_args = t->get_num_args(); while (fr.m_i < num_args) { if (!ProofGen && constant_fold(t, fr)) { return; } expr * arg = t->get_arg(fr.m_i); fr.m_i++; if (!visit(arg, fr.m_max_depth)) return; } func_decl * f = t->get_decl(); // If AC flattening is enabled, f is associative, t is not shared, and there is a previous frame on the stack. if (!ProofGen) { // this optimization is only used when Proof generation is disabled. if (f->is_associative() && t->get_ref_count() <= 1 && frame_stack().size() > 1) { frame & prev_fr = frame_stack()[frame_stack().size() - 2]; if (is_app(prev_fr.m_curr) && to_app(prev_fr.m_curr)->get_decl() == f && prev_fr.m_state == PROCESS_CHILDREN && flat_assoc(f)) { frame_stack().pop_back(); set_new_child_flag(t); return; } } } unsigned new_num_args = result_stack().size() - fr.m_spos; expr * const * new_args = result_stack().c_ptr() + fr.m_spos; app * new_t; if (ProofGen) { elim_reflex_prs(fr.m_spos); unsigned num_prs = result_pr_stack().size() - fr.m_spos; if (num_prs == 0) { new_t = t; m_pr = 0; } else { new_t = m().mk_app(f, new_num_args, new_args); m_pr = m().mk_congruence(t, new_t, num_prs, result_pr_stack().c_ptr() + fr.m_spos); } } br_status st = m_cfg.reduce_app(f, new_num_args, new_args, m_r, m_pr2); SASSERT(st != BR_DONE || m().get_sort(m_r) == m().get_sort(t)); TRACE("reduce_app", tout << mk_ismt2_pp(t, m()) << "\n"; tout << "st: " << st; if (m_r) tout << " --->\n" << mk_ismt2_pp(m_r, m()); tout << "\n";); if (st != BR_FAILED) { result_stack().shrink(fr.m_spos); SASSERT(m().get_sort(m_r) == m().get_sort(t)); result_stack().push_back(m_r); if (ProofGen) { result_pr_stack().shrink(fr.m_spos); if (!m_pr2) m_pr2 = m().mk_rewrite(new_t, m_r); m_pr = m().mk_transitivity(m_pr, m_pr2); m_pr2 = 0; result_pr_stack().push_back(m_pr); } if (st == BR_DONE) { cache_result(t, m_r, m_pr, fr.m_cache_result); frame_stack().pop_back(); set_new_child_flag(t); m_r = 0; if (ProofGen) m_pr = 0; return; } else { fr.m_state = REWRITE_BUILTIN; SASSERT(st == BR_REWRITE1 || st == BR_REWRITE2 || st == BR_REWRITE3 || st == BR_REWRITE_FULL); unsigned max_depth = static_cast(st); SASSERT(0 <= max_depth && max_depth <= RW_UNBOUNDED_DEPTH); SASSERT((st == BR_REWRITE1) == (max_depth == 0)); SASSERT((st == BR_REWRITE2) == (max_depth == 1)); SASSERT((st == BR_REWRITE3) == (max_depth == 2)); SASSERT((st == BR_REWRITE_FULL) == (max_depth == RW_UNBOUNDED_DEPTH)); if (max_depth != RW_UNBOUNDED_DEPTH) max_depth++; if (visit(m_r, max_depth)) { if (ProofGen) { proof_ref pr2(m()), pr1(m()); pr2 = result_pr_stack().back(); result_pr_stack().pop_back(); pr1 = result_pr_stack().back(); result_pr_stack().pop_back(); m_pr = m().mk_transitivity(pr1, pr2); result_pr_stack().push_back(m_pr); } m_r = result_stack().back(); result_stack().pop_back(); result_stack().pop_back(); result_stack().push_back(m_r); cache_result(t, m_r, m_pr, fr.m_cache_result); frame_stack().pop_back(); set_new_child_flag(t); m_r = 0; if (ProofGen) m_pr = 0; return; } else { // frame was created for processing m_r m_r = 0; if (ProofGen) m_pr = 0; return; } } UNREACHABLE(); } // TODO: add rewrite rules support expr * def; proof * def_pr; quantifier * def_q; // When get_macro succeeds, then // we know that: // forall X. f(X) = def[X] // and def_pr is a proof for this quantifier. // // Remark: def_q is only used for proof generation. // It is the quantifier forall X. f(X) = def[X] if (get_macro(f, def, def_q, def_pr)) { SASSERT(!f->is_associative() || !flat_assoc(f)); SASSERT(new_num_args == t->get_num_args()); SASSERT(m().get_sort(def) == m().get_sort(t)); if (is_ground(def)) { m_r = def; if (ProofGen) { SASSERT(def_pr); m_pr = m().mk_transitivity(m_pr, def_pr); } } else { if (ProofGen) { NOT_IMPLEMENTED_YET(); // We do not support the use of bindings in proof generation mode. // Thus we have to apply the subsitution here, and // beta_reducer subst(m()); // subst.set_bindings(new_num_args, new_args); // expr_ref r2(m()); // subst(def, r2); } else { fr.m_state = EXPAND_DEF; TRACE("get_macro", tout << "f: " << f->get_name() << ", def: \n" << mk_ismt2_pp(def, m()) << "\n"; tout << "Args num: " << num_args << "\n"; for (unsigned i = 0; i < num_args; i++) tout << mk_ismt2_pp(new_args[i], m()) << "\n";); unsigned sz = m_bindings.size(); unsigned i = num_args; while (i > 0) { --i; m_bindings.push_back(new_args[i]); // num_args - i - 1]); m_shifts.push_back(sz); } result_stack().push_back(def); TRACE("get_macro", display_bindings(tout);); begin_scope(); m_num_qvars += num_args; //m_num_qvars = 0; m_root = def; push_frame(def, false, RW_UNBOUNDED_DEPTH); return; } } } else { if (ProofGen) { m_r = new_t; } else { if (fr.m_new_child) { m_r = m().mk_app(f, new_num_args, new_args); } else { TRACE("rewriter_reuse", tout << "reusing:\n" << mk_ismt2_pp(t, m()) << "\n";); m_r = t; } } } result_stack().shrink(fr.m_spos); result_stack().push_back(m_r); cache_result(t, m_r, m_pr, fr.m_cache_result); if (ProofGen) { result_pr_stack().shrink(fr.m_spos); result_pr_stack().push_back(m_pr); m_pr = 0; } frame_stack().pop_back(); set_new_child_flag(t, m_r); m_r = 0; return; } case REWRITE_BUILTIN: SASSERT(fr.m_spos + 2 == result_stack().size()); if (ProofGen) { proof_ref pr2(m()), pr1(m()); pr2 = result_pr_stack().back(); result_pr_stack().pop_back(); pr1 = result_pr_stack().back(); result_pr_stack().pop_back(); m_pr = m().mk_transitivity(pr1, pr2); result_pr_stack().push_back(m_pr); } m_r = result_stack().back(); result_stack().pop_back(); result_stack().pop_back(); result_stack().push_back(m_r); cache_result(t, m_r, m_pr, fr.m_cache_result); frame_stack().pop_back(); set_new_child_flag(t); return; case EXPAND_DEF: SASSERT(fr.m_spos + t->get_num_args() + 2 == result_stack().size()); SASSERT(t->get_num_args() <= m_bindings.size()); if (!ProofGen) { expr_ref tmp(m()); unsigned num_args = t->get_num_args(); m_bindings.shrink(m_bindings.size() - num_args); m_shifts.shrink(m_shifts.size() - num_args); m_num_qvars -= num_args; end_scope(); m_r = result_stack().back(); if (!is_ground(m_r)) { m_inv_shifter(m_r, num_args, tmp); m_r = tmp; } result_stack().shrink(fr.m_spos); result_stack().push_back(m_r); cache_result(t, m_r, m_pr, fr.m_cache_result); frame_stack().pop_back(); set_new_child_flag(t); } else { // TODO NOT_IMPLEMENTED_YET(); } return; case REWRITE_RULE: // support for rewriting rules was not implemented yet. NOT_IMPLEMENTED_YET(); break; default: UNREACHABLE(); break; } } template template void rewriter_tpl::process_quantifier(quantifier * q, frame & fr) { SASSERT(fr.m_state == PROCESS_CHILDREN); unsigned num_decls = q->get_num_decls(); if (fr.m_i == 0) { if (!ProofGen) { begin_scope(); m_root = q->get_expr(); unsigned sz = m_bindings.size(); for (unsigned i = 0; i < num_decls; i++) { m_bindings.push_back(0); m_shifts.push_back(sz); } } m_num_qvars += num_decls; } unsigned num_children = rewrite_patterns() ? q->get_num_children() : 1; while (fr.m_i < num_children) { expr * child = q->get_child(fr.m_i); fr.m_i++; if (!visit(child, fr.m_max_depth)) { return; } } SASSERT(fr.m_spos + num_children == result_stack().size()); expr * const * it = result_stack().c_ptr() + fr.m_spos; expr * new_body = *it; expr * const * new_pats; expr * const * new_no_pats; if (rewrite_patterns()) { new_pats = it + 1; new_no_pats = new_pats + q->get_num_patterns(); } else { new_pats = q->get_patterns(); new_no_pats = q->get_no_patterns(); } if (ProofGen) { quantifier * new_q = m().update_quantifier(q, q->get_num_patterns(), new_pats, q->get_num_no_patterns(), new_no_pats, new_body); m_pr = q == new_q ? 0 : m().mk_quant_intro(q, new_q, result_pr_stack().get(fr.m_spos)); m_r = new_q; proof_ref pr2(m()); if (m_cfg.reduce_quantifier(new_q, new_body, new_pats, new_no_pats, m_r, pr2)) { m_pr = m().mk_transitivity(m_pr, pr2); } TRACE("reduce_quantifier_bug", tout << "m_pr is_null: " << (m_pr.get() == 0) << "\n"; if (m_pr) tout << mk_ismt2_pp(m_pr, m()) << "\n";); result_pr_stack().shrink(fr.m_spos); result_pr_stack().push_back(m_pr); } else { expr_ref tmp(m()); if (!m_cfg.reduce_quantifier(q, new_body, new_pats, new_no_pats, m_r, m_pr)) { if (fr.m_new_child) { m_r = m().update_quantifier(q, q->get_num_patterns(), new_pats, q->get_num_no_patterns(), new_no_pats, new_body); } else { TRACE("rewriter_reuse", tout << "reusing:\n" << mk_ismt2_pp(q, m()) << "\n";); m_r = q; } } } result_stack().shrink(fr.m_spos); result_stack().push_back(m_r.get()); SASSERT(m().is_bool(m_r)); if (!ProofGen) { SASSERT(num_decls <= m_bindings.size()); m_bindings.shrink(m_bindings.size() - num_decls); m_shifts.shrink(m_shifts.size() - num_decls); end_scope(); cache_result(q, m_r, m_pr, fr.m_cache_result); } else { cache_result(q, m_r, m_pr, fr.m_cache_result); m_pr = 0; } m_r = 0; frame_stack().pop_back(); set_new_child_flag(q, m_r); } template bool rewriter_tpl::not_rewriting() const { SASSERT(frame_stack().empty()); SASSERT(m_cache == m_cache_stack[0]); return true; } template rewriter_tpl::rewriter_tpl(ast_manager & m, bool proof_gen, Config & cfg): rewriter_core(m, proof_gen), m_cfg(cfg), m_num_steps(0), m_shifter(m), m_inv_shifter(m), m_r(m), m_pr(m), m_pr2(m) { } template rewriter_tpl::~rewriter_tpl() { } template void rewriter_tpl::reset() { m_cfg.reset(); rewriter_core::reset(); m_bindings.reset(); m_shifts.reset(); m_shifter.reset(); m_inv_shifter.reset(); } template void rewriter_tpl::cleanup() { m_cfg.cleanup(); rewriter_core::cleanup(); m_bindings.finalize(); m_shifter.cleanup(); m_shifts.finalize(); m_inv_shifter.cleanup(); } template void rewriter_tpl::display_bindings(std::ostream& out) { out << "bindings:\n"; for (unsigned i = 0; i < m_bindings.size(); i++) { if (m_bindings[i]) out << i << ": " << mk_ismt2_pp(m_bindings[i], m()) << "\n"; } } template void rewriter_tpl::set_bindings(unsigned num_bindings, expr * const * bindings) { SASSERT(!m_proof_gen); SASSERT(not_rewriting()); m_bindings.reset(); m_shifts.reset(); unsigned i = num_bindings; while (i > 0) { --i; m_bindings.push_back(bindings[i]); m_shifts.push_back(num_bindings); } TRACE("rewriter", display_bindings(tout);); } template void rewriter_tpl::set_inv_bindings(unsigned num_bindings, expr * const * bindings) { SASSERT(!m_proof_gen); SASSERT(not_rewriting()); m_bindings.reset(); m_shifts.reset(); for (unsigned i = 0; i < num_bindings; i++) { m_bindings.push_back(bindings[i]); m_shifts.push_back(num_bindings); } TRACE("rewriter", display_bindings(tout);); } template template void rewriter_tpl::main_loop(expr * t, expr_ref & result, proof_ref & result_pr) { if (m_cancel_check && m().canceled()) { reset(); throw rewriter_exception(m().limit().get_cancel_msg()); } SASSERT(!ProofGen || result_stack().size() == result_pr_stack().size()); SASSERT(not_rewriting()); m_root = t; m_num_qvars = 0; m_num_steps = 0; if (visit(t, RW_UNBOUNDED_DEPTH)) { result = result_stack().back(); result_stack().pop_back(); SASSERT(result_stack().empty()); if (ProofGen) { result_pr = result_pr_stack().back(); result_pr_stack().pop_back(); if (result_pr.get() == 0) result_pr = m().mk_reflexivity(t); SASSERT(result_pr_stack().empty()); } } else { resume_core(result, result_pr); } TRACE("rewriter", tout << mk_ismt2_pp(t, m()) << "\n=>\n" << result << "\n";;); } /** \brief Resume the execution when it was interrupted by cancel() or check_max_steps(). */ template template void rewriter_tpl::resume_core(expr_ref & result, proof_ref & result_pr) { SASSERT(!frame_stack().empty()); while (!frame_stack().empty()) { if (m_cancel_check && m().canceled()) { reset(); throw rewriter_exception(m().limit().get_cancel_msg()); } SASSERT(!ProofGen || result_stack().size() == result_pr_stack().size()); frame & fr = frame_stack().back(); expr * t = fr.m_curr; TRACE("rewriter_step", tout << "step\n" << mk_ismt2_pp(t, m()) << "\n";); m_num_steps++; check_max_steps(); if (first_visit(fr) && fr.m_cache_result) { expr * r = get_cached(t); if (r) { SASSERT(m().get_sort(r) == m().get_sort(t)); result_stack().push_back(r); if (ProofGen) { proof * pr = get_cached_pr(t); result_pr_stack().push_back(pr); } frame_stack().pop_back(); set_new_child_flag(t, r); continue; } } switch (t->get_kind()) { case AST_APP: process_app(to_app(t), fr); break; case AST_QUANTIFIER: process_quantifier(to_quantifier(t), fr); break; case AST_VAR: frame_stack().pop_back(); process_var(to_var(t)); break; default: UNREACHABLE(); break; } } result = result_stack().back(); result_stack().pop_back(); SASSERT(result_stack().empty()); if (ProofGen) { result_pr = result_pr_stack().back(); result_pr_stack().pop_back(); if (result_pr.get() == 0) result_pr = m().mk_reflexivity(m_root); SASSERT(result_pr_stack().empty()); } } template void rewriter_tpl::operator()(expr * t, expr_ref & result, proof_ref & result_pr) { if (m_proof_gen) main_loop(t, result, result_pr); else main_loop(t, result, result_pr); } template void rewriter_tpl::resume(expr_ref & result, proof_ref & result_pr) { if (m_proof_gen) resume_core(result, result_pr); else resume_core(result, result_pr); }