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z3-z3-4.12.6.src.muz.rel.dl_mk_simple_joins.cpp Maven / Gradle / Ivy
/*++
Copyright (c) 2006 Microsoft Corporation
Module Name:
dl_mk_simple_joins.cpp
Abstract:
Author:
Krystof Hoder 2010-05-20.
Revision History:
--*/
#include
#include
#include
#include "ast/ast_pp.h"
#include "util/trace.h"
#include "muz/rel/dl_mk_simple_joins.h"
#include "muz/rel/dl_relation_manager.h"
namespace datalog {
mk_simple_joins::mk_simple_joins(context & ctx):
plugin(1000),
m_context(ctx),
rm(ctx.get_rule_manager()) {
}
class join_planner {
typedef float cost;
class pair_info {
cost m_total_cost;
/**
\brief Number of rules longer than two that contain this pair.
This number is being updated by \c add_rule and \c remove_rule. Even though between
adding a rule and removing it, the length of a rule can decrease without this pair
being notified about it, it will surely see the decrease from length 3 to 2 which
the threshold for rule being counted in this counter.
*/
unsigned m_consumers { 0 };
bool m_stratified { true };
unsigned m_src_stratum { 0 };
public:
var_idx_set m_all_nonlocal_vars;
rule_vector m_rules;
pair_info() {}
pair_info & operator=(const pair_info &) = delete;
bool can_be_joined() const {
return m_consumers > 0;
}
cost get_cost() const {
SASSERT(m_consumers > 0);
cost amortized = m_total_cost/m_consumers;
if (m_stratified) {
return amortized * ( (amortized > 0) ? (1/16.0f) : 16.0f);
}
else {
return amortized;
}
}
/**
\brief Add rule \c r among rules interested in current predicate pair.
The \c pl.m_rule_content entry of the rule has to be properly filled in
by the time of a call to this function
*/
void add_rule(join_planner & pl, app * t1, app * t2, rule * r,
const var_idx_set & non_local_vars_normalized,
const var_idx_set & non_local_vars) {
if (m_rules.empty()) {
m_total_cost = pl.compute_cost(t1, t2, non_local_vars);
m_src_stratum = std::max(pl.get_stratum(t1->get_decl()), pl.get_stratum(t2->get_decl()));
}
m_rules.push_back(r);
if (pl.m_rules_content.find(r).size() > 2) {
m_consumers++;
}
if (m_stratified) {
unsigned head_stratum = pl.get_stratum(r->get_decl());
SASSERT(head_stratum >= m_src_stratum);
m_stratified = (head_stratum > m_src_stratum);
}
idx_set_union(m_all_nonlocal_vars, non_local_vars_normalized);
TRACE("dl", tout << "all-nonlocal: " << m_all_nonlocal_vars << "\n";);
}
/**
\brief Remove rule from the pair record. Return true if no rules remain
in the pair, and so it should be removed.
*/
bool remove_rule(rule * r, unsigned original_length) {
VERIFY( remove_from_vector(m_rules, r) );
if (original_length > 2) {
SASSERT(m_consumers > 0);
m_consumers--;
}
SASSERT(!m_rules.empty() || m_consumers == 0);
return m_rules.empty();
}
};
typedef std::pair app_pair;
typedef pair_hash, obj_ptr_hash > app_pair_hash;
typedef map > cost_map;
typedef map, ptr_hash, ptr_eq > rule_pred_map;
typedef ptr_hashtable > rule_hashtable;
context & m_context;
ast_manager & m;
rule_manager & rm;
var_subst & m_var_subst;
rule_set & m_rs_aux_copy; //reference to a rule_set that will allow to ask for stratum levels
cost_map m_costs;
ptr_vector m_interpreted;
rule_pred_map m_rules_content;
rule_ref_vector m_introduced_rules;
bool m_modified_rules;
ast_ref_vector m_pinned;
mutable ptr_vector m_vars;
public:
join_planner(context & ctx, rule_set & rs_aux_copy)
: m_context(ctx),
m(ctx.get_manager()),
rm(ctx.get_rule_manager()),
m_var_subst(ctx.get_var_subst()),
m_rs_aux_copy(rs_aux_copy),
m_introduced_rules(rm),
m_modified_rules(false),
m_pinned(m)
{
}
~join_planner() {
for (auto & kv : m_costs) {
dealloc(kv.m_value);
}
m_costs.reset();
}
private:
void get_normalizer(app * t, unsigned & next_var, var_ref_vector & result) const {
SASSERT(!result.empty());
unsigned res_ofs = result.size()-1;
for (expr* arg : *t) {
unsigned var_idx = to_var(arg)->get_idx();
if (!result.get(res_ofs - var_idx)) {
result[res_ofs - var_idx] = m.mk_var(next_var++, arg->get_sort());
}
}
}
var_ref_vector get_normalizer(app * t1, app * t2) const {
var_ref_vector result(m);
if (t1->get_num_args() == 0 && t2->get_num_args() == 0) {
return result; //nothing to normalize
}
SASSERT(!t1->is_ground() || !t2->is_ground());
unsigned max_var_idx = 0;
var_idx_set& orig_var_set = rm.collect_vars(t1, t2);
for (unsigned var_idx : orig_var_set) {
if (var_idx>max_var_idx) {
max_var_idx = var_idx;
}
}
if (t1->get_decl() != t2->get_decl()) {
if (t1->get_decl()->get_id() < t2->get_decl()->get_id()) {
std::swap(t1, t2);
}
}
else {
int_vector norm1(max_var_idx + 1, -1);
int_vector norm2(max_var_idx + 1, -1);
unsigned n = t1->get_num_args();
SASSERT(n == t2->get_num_args());
for (unsigned i = 0; i < n; ++i) {
//We assume that the mk_simple_joins transformer is applied after mk_filter_rules,
//so the only literals which appear in pairs are the ones that contain only variables.
var * v1 = to_var(t1->get_arg(i));
var * v2 = to_var(t2->get_arg(i));
if (v1->get_sort() != v2->get_sort()) {
//different sorts mean we can distinguish the two terms
if (v1->get_sort()->get_id() < v2->get_sort()->get_id()) {
std::swap(t1, t2);
}
break;
}
unsigned v1_idx = v1->get_idx();
unsigned v2_idx = v2->get_idx();
//since the rules already went through the mk_filter_rules transformer,
//variables must be linear
SASSERT(norm1[v1_idx] == -1);
SASSERT(norm2[v2_idx] == -1);
if (norm2[v1_idx] != norm1[v2_idx]) {
//now we can distinguish the two terms
if (norm2[v1_idx] < norm1[v2_idx]) {
std::swap(t1, t2);
}
break;
}
norm1[v1_idx] = i;
norm2[v2_idx] = i;
}
//if we did not exit the loop prematurely, the two terms are indistinguishable,
//so the order should not matter
}
result.resize(max_var_idx + 1, static_cast(nullptr));
unsigned next_var = 0;
get_normalizer(t1, next_var, result);
get_normalizer(t2, next_var, result);
return result;
}
app_pair get_key(app * t1, app * t2) {
var_ref_vector norm_subst = get_normalizer(t1, t2);
expr_ref t1n_ref = m_var_subst(t1, norm_subst);
expr_ref t2n_ref = m_var_subst(t2, norm_subst);
app * t1n = to_app(t1n_ref);
app * t2n = to_app(t2n_ref);
if (t1n->get_id() > t2n->get_id()) {
std::swap(t1n, t2n);
}
m_pinned.push_back(t1n);
m_pinned.push_back(t2n);
TRACE("dl_verbose", tout << mk_pp(t1, m) << " " << mk_pp(t2, m) << " |-> " << t1n_ref << " " << t2n_ref << "\n";);
return app_pair(t1n, t2n);
}
/**
\brief Add rule \c r among rules interested in predicate pair \c t1, \c t2.
The \c m_rule_content entry of the rule \c r has to be properly filled in
by the time of a call to this function
*/
void register_pair(app * t1, app * t2, rule * r, const var_idx_set & non_local_vars) {
SASSERT (t1 != t2);
pair_info * & ptr_inf = m_costs.insert_if_not_there(get_key(t1, t2), nullptr);
if (ptr_inf == nullptr) {
ptr_inf = alloc(pair_info);
}
pair_info & inf = *ptr_inf;
var_ref_vector normalizer = get_normalizer(t1, t2);
unsigned norm_ofs = normalizer.size()-1;
var_idx_set normalized_vars;
for (auto idx : non_local_vars) {
unsigned norm_var = normalizer.get(norm_ofs - idx)->get_idx();
normalized_vars.insert(norm_var);
}
inf.add_rule(*this, t1, t2, r, normalized_vars, non_local_vars);
TRACE("dl", tout << mk_pp(t1, m) << " " << mk_pp(t2, m) << " ";
tout << non_local_vars << "\n";
r->display(m_context, tout);
if (inf.can_be_joined()) tout << "cost: " << inf.get_cost() << "\n";);
}
void remove_rule_from_pair(app_pair key, rule * r, unsigned original_len) {
pair_info * ptr = nullptr;
if (m_costs.find(key, ptr) && ptr && ptr->remove_rule(r, original_len)) {
SASSERT(ptr->m_rules.empty());
m_costs.remove(key);
dealloc(ptr);
}
}
void register_rule(rule * r) {
rule_counter counter;
counter.count_rule_vars(r, 1);
TRACE("dl", tout << "counter: "; for (auto const& kv: counter) tout << kv.m_key << ": " << kv.m_value << " "; tout << "\n";);
ptr_vector & rule_content = m_rules_content.insert_if_not_there(r, ptr_vector());
SASSERT(rule_content.empty());
TRACE("dl", r->display(m_context, tout << "register "););
unsigned pos_tail_size = r->get_positive_tail_size();
for (unsigned i = 0; i < pos_tail_size; i++) {
app* t = r->get_tail(i);
if (!rule_content.contains(t))
rule_content.push_back(t);
else
m_modified_rules = true;
}
pos_tail_size = rule_content.size();
for (unsigned i = 0; i+1 < pos_tail_size; i++) {
app * t1 = rule_content[i];
var_idx_set t1_vars = rm.collect_vars(t1);
counter.count_vars(t1, -1); //temporarily remove t1 variables from counter
for (unsigned j = i+1; j < pos_tail_size; j++) {
app * t2 = rule_content[j];
SASSERT(t1 != t2);
counter.count_vars(t2, -1); //temporarily remove t2 variables from counter
var_idx_set t2_vars = rm.collect_vars(t2);
t2_vars |= t1_vars;
var_idx_set non_local_vars;
counter.collect_positive(non_local_vars);
counter.count_vars(t2, 1); //restore t2 variables in counter
set_intersection(non_local_vars, t2_vars);
TRACE("dl", tout << "non-local vars: " << non_local_vars << "\n";);
register_pair(t1, t2, r, non_local_vars);
}
counter.count_vars(t1, 1); //restore t1 variables in counter
}
}
bool extract_argument_info(unsigned var_idx, app * t, expr_ref_vector & args,
ptr_vector & domain) {
for (expr* arg : *t) {
var * v = to_var(arg);
if (v->get_idx() == var_idx) {
args.push_back(v);
domain.push_back(v->get_sort());
return true;
}
}
return false;
}
void join_pair(app_pair pair_key) {
app * t1 = pair_key.first;
app * t2 = pair_key.second;
pair_info & inf = *m_costs[pair_key];
SASSERT(!inf.m_rules.empty());
var_idx_set const & output_vars = inf.m_all_nonlocal_vars;
expr_ref_vector args(m);
ptr_vector domain;
unsigned arity = output_vars.num_elems();
for (unsigned var_idx : output_vars) {
bool found = extract_argument_info(var_idx, t1, args, domain);
if (!found) {
found = extract_argument_info(var_idx, t2, args, domain);
}
SASSERT(found);
}
TRACE("dl",
tout << mk_pp(t1, m) << " " << mk_pp(t2, m) << " arity: " << arity << "\n";
tout << "output: " << output_vars << "\n";
tout << "args: " << args << "\n";);
SASSERT(args.size() == arity);
SASSERT(domain.size() == arity);
rule * one_parent = inf.m_rules.back();
func_decl* parent_head = one_parent->get_decl();
std::string one_parent_name = parent_head->get_name().str();
std::string parent_name;
if (inf.m_rules.size() > 1) {
parent_name = one_parent_name + std::string("_and_") + to_string(inf.m_rules.size()-1);
}
else {
parent_name = one_parent_name;
}
func_decl * decl = m_context.mk_fresh_head_predicate(
symbol(parent_name), symbol("split"),
arity, domain.data(), parent_head);
app_ref head(m.mk_app(decl, arity, args.data()), m);
app * tail[] = { t1, t2 };
rule * new_rule = rm.mk(head, 2, tail, nullptr);
//TODO: update accounting so that it can handle multiple parents
new_rule->set_accounting_parent_object(m_context, one_parent);
m_introduced_rules.push_back(new_rule);
//here we copy the inf.m_rules vector because inf.m_rules will get changed
//in the iteration. Also we use hashtable instead of vector because we do
//not want to process one rule twice.
rule_hashtable processed_rules;
rule_vector rules(inf.m_rules);
for (rule * r : rules) {
if (!processed_rules.contains(r)) {
apply_binary_rule(r, pair_key, head);
processed_rules.insert(r);
}
}
// SASSERT(!m_costs.contains(pair_key));
}
void replace_edges(rule * r, const app_ref_vector & removed_tails,
const app_ref_vector & added_tails0, const ptr_vector & rule_content) {
SASSERT(removed_tails.size() >= added_tails0.size());
unsigned len = rule_content.size();
unsigned original_len = len+removed_tails.size()-added_tails0.size();
app_ref_vector added_tails(added_tails0); //we need a copy since we'll be modifying it
TRACE("dl", tout << added_tails << "\n";);
unsigned rt_sz = removed_tails.size();
//remove edges between removed tails
for (unsigned i = 0; i < rt_sz; i++) {
for (unsigned j = i+1; j < rt_sz; j++) {
app_pair pair_key = get_key(removed_tails[i], removed_tails[j]);
remove_rule_from_pair(pair_key, r, original_len);
}
}
//remove edges between surviving tails and removed tails
for (unsigned i = 0; i < len; i++) {
if (added_tails.contains(rule_content[i])) {
continue;
}
for (unsigned ri = 0; ri < rt_sz; ri++) {
app_pair pair_key = get_key(rule_content[i], removed_tails[ri]);
remove_rule_from_pair(pair_key, r, original_len);
}
}
if (len == 1) {
return;
}
app * head = r->get_head();
var_counter counter;
counter.count_vars(head, 1);
unsigned tail_size = r->get_tail_size();
unsigned pos_tail_size = r->get_positive_tail_size();
for (unsigned i = pos_tail_size; i < tail_size; i++) {
counter.count_vars(r->get_tail(i), 1);
}
for (unsigned i = 0; i < len; i++) {
counter.count_vars(rule_content[i], 1);
}
//add edges that contain added tails
while (!added_tails.empty()) {
app * a_tail = added_tails.back(); //added tail
TRACE("dl", tout << "replace edges " << mk_pp(a_tail, m) << "\n";);
var_idx_set a_tail_vars = rm.collect_vars(a_tail);
counter.count_vars(a_tail, -1); //temporarily remove a_tail variables from counter
for (unsigned i = 0; i < len; i++) {
app * o_tail = rule_content[i]; //other tail
if (added_tails.contains(o_tail)) {
//this avoids adding edges between new tails twice
continue;
}
counter.count_vars(o_tail, -1); //temporarily remove o_tail variables from counter
var_idx_set scope_vars = rm.collect_vars(o_tail);
scope_vars |= a_tail_vars;
var_idx_set non_local_vars;
counter.collect_positive(non_local_vars);
counter.count_vars(o_tail, 1); //restore o_tail variables in counter
set_intersection(non_local_vars, scope_vars);
register_pair(o_tail, a_tail, r, non_local_vars);
}
counter.count_vars(a_tail, 1); //restore t1 variables in counter
added_tails.pop_back();
}
}
void apply_binary_rule(rule * r, app_pair pair_key, app * t_new) {
app * t1 = pair_key.first;
app * t2 = pair_key.second;
ptr_vector & rule_content = m_rules_content.find(r);
unsigned len = rule_content.size();
if (len == 1) {
return;
}
TRACE("dl",
tout << "pair: " << mk_pp(t1, m) << " " << mk_pp(t2, m) << "\n";
tout << mk_pp(t_new, m) << "\n";
tout << "all-non-local: " << m_costs[pair_key]->m_all_nonlocal_vars << "\n";
tout << mk_pp(r->get_head(), m) << " :-\n";
for (app* a : rule_content) tout << " " << mk_pp(a, m) << "\n";);
rule_counter counter;
for (app* t : rule_content)
counter.count_vars(t, +1);
counter.count_vars(r->get_head(), +1);
func_decl * t1_pred = t1->get_decl();
func_decl * t2_pred = t2->get_decl();
app_ref_vector removed_tails(m);
app_ref_vector added_tails(m);
for (unsigned i1 = 0; i1 < len; i1++) {
app * rt1 = rule_content[i1];
if (rt1->get_decl() != t1_pred) {
continue;
}
var_idx_set rt1_vars = rm.collect_vars(rt1);
counter.count_vars(rt1, -1);
var_idx_set t1_vars = rm.collect_vars(t1);
unsigned i2start = (t1_pred == t2_pred) ? (i1+1) : 0;
for (unsigned i2 = i2start; i2 < len; i2++) {
app * rt2 = rule_content[i2];
if (i1 == i2 || rt2->get_decl() != t2_pred) {
continue;
}
if (get_key(rt1, rt2) != pair_key) {
continue;
}
var_ref_vector denormalizer(m);
var_ref_vector normalizer = get_normalizer(rt1, rt2);
reverse_renaming(normalizer, denormalizer);
expr_ref new_transf(m);
new_transf = m_var_subst(t_new, denormalizer);
TRACE("dl", tout << mk_pp(rt1, m) << " " << mk_pp(rt2, m) << " -> " << new_transf << "\n";);
counter.count_vars(rt2, -1);
var_idx_set rt2_vars = rm.collect_vars(rt2);
var_idx_set tr_vars = rm.collect_vars(new_transf);
rt2_vars |= rt1_vars;
var_idx_set non_local_vars;
counter.collect_positive(non_local_vars);
set_intersection(non_local_vars, rt2_vars);
counter.count_vars(rt2, +1);
// require that tr_vars contains non_local_vars
TRACE("dl", tout << "non-local : " << non_local_vars << " tr_vars " << tr_vars << " rt12_vars " << rt2_vars << "\n";);
if (!non_local_vars.subset_of(tr_vars)) {
var_ref_vector normalizer2 = get_normalizer(rt2, rt1);
TRACE("dl", tout << normalizer << "\nnorm\n" << normalizer2 << "\n";);
denormalizer.reset();
reverse_renaming(normalizer2, denormalizer);
new_transf = m_var_subst(t_new, denormalizer);
TRACE("dl", tout << mk_pp(rt2, m) << " " << mk_pp(rt1, m) << " -> " << new_transf << "\n";);
SASSERT(non_local_vars.subset_of(rm.collect_vars(new_transf)));
}
app * new_lit = to_app(new_transf);
if (added_tails.contains(new_lit)) {
if (i1 < i2)
std::swap(i1, i2);
if (i1 < rule_content.size())
rule_content[i1] = rule_content.back();
rule_content.pop_back();
if (i2 < rule_content.size())
rule_content[i2] = rule_content.back();
rule_content.pop_back();
len -= 2;
removed_tails.push_back(rt1);
removed_tails.push_back(rt2);
counter.count_vars(new_lit, -1);
}
else {
m_pinned.push_back(new_lit);
rule_content[i1] = new_lit;
rule_content[i2] = rule_content.back();
rule_content.pop_back();
len--; //here the bound of both loops changes!!!
removed_tails.push_back(rt1);
removed_tails.push_back(rt2);
added_tails.push_back(new_lit);
}
// this exits the inner loop, the outer one continues in case there will
// be other matches
break;
}
counter.count_vars(rt1, 1);
}
SASSERT(!removed_tails.empty());
SASSERT(!added_tails.empty());
m_modified_rules = true;
TRACE("dl", tout << "replace rule content\n";);
replace_edges(r, removed_tails, added_tails, rule_content);
}
cost get_domain_size(expr* e) const {
return get_domain_size(e->get_sort());
}
cost get_domain_size(sort* s) const {
return static_cast(m_context.get_sort_size_estimate(s));
}
unsigned get_stratum(func_decl * pred) const {
return m_rs_aux_copy.get_predicate_strat(pred);
}
cost estimate_size(app * t) const {
rel_context_base* rel = m_context.get_rel_context();
if (!rel) {
return cost(1);
}
relation_manager& rm = rel->get_rmanager();
func_decl * pred = t->get_decl();
if ( (m_context.saturation_was_run() && rm.try_get_relation(pred)) || rm.is_saturated(pred)) {
SASSERT(rm.try_get_relation(pred)); //if it is saturated, it should exist
unsigned rel_size_int = rel->get_relation(pred).get_size_estimate_rows();
if (rel_size_int != 0) {
cost curr_size = static_cast(rel_size_int);
for (expr* arg : *t) {
if (!is_var(arg)) {
curr_size /= get_domain_size(arg);
}
}
return curr_size;
}
}
cost res = 1;
for (expr* arg : *t) {
if (is_var(arg))
res *= get_domain_size(arg);
}
return res;
}
cost compute_cost(app * t1, app * t2, const var_idx_set & non_local_vars) const {
cost inters_size = 1;
variable_intersection vi(m_context.get_manager());
vi.populate(t1, t2);
unsigned n = vi.size();
// remove contributions from joined columns.
for (unsigned i = 0; i < n; i++) {
unsigned arg_index1, arg_index2;
vi.get(i, arg_index1, arg_index2);
expr* arg = t1->get_arg(arg_index1);
SASSERT(is_var(arg));
if (non_local_vars.contains(to_var(arg)->get_idx())) {
inters_size *= get_domain_size(arg);
}
// joined arguments must have the same domain
SASSERT(get_domain_size(arg) == get_domain_size(t2->get_arg(arg_index2)));
}
// remove contributions from projected columns.
for (expr* arg : *t1) {
if (is_var(arg) && !non_local_vars.contains(to_var(arg)->get_idx())) {
inters_size *= get_domain_size(arg);
}
}
for (expr* arg : *t2) {
if (is_var(arg) && !non_local_vars.contains(to_var(arg)->get_idx())) {
inters_size *= get_domain_size(arg);
}
}
cost res = (estimate_size(t1) * estimate_size(t2)) / inters_size;
TRACE("report_costs",
display_predicate(m_context, t1, tout);
display_predicate(m_context, t2, tout);
tout << res << "\n";);
return res;
}
bool pick_best_pair(app_pair & p) {
bool found = false;
cost best_cost;
for (auto const& kv : m_costs) {
app_pair key = kv.m_key;
pair_info & inf = *kv.m_value;
if (!inf.can_be_joined()) {
continue;
}
cost c = inf.get_cost();
if (!found || c < best_cost) {
found = true;
best_cost = c;
p = key;
}
}
return found;
}
public:
rule_set * run(rule_set const & source) {
for (rule * r : source) {
register_rule(r);
}
app_pair selected;
while (pick_best_pair(selected)) {
join_pair(selected);
}
if (!m_modified_rules) {
return nullptr;
}
scoped_ptr result = alloc(rule_set, m_context);
for (auto& kv : m_rules_content) {
rule * orig_r = kv.m_key;
ptr_vector const& content = kv.m_value;
SASSERT(content.size() <= 2);
if (content.size() == orig_r->get_positive_tail_size()) {
//rule did not change
result->add_rule(orig_r);
continue;
}
ptr_vector tail(content);
bool_vector negs(tail.size(), false);
unsigned or_len = orig_r->get_tail_size();
for (unsigned i = orig_r->get_positive_tail_size(); i < or_len; i++) {
tail.push_back(orig_r->get_tail(i));
negs.push_back(orig_r->is_neg_tail(i));
}
rule * new_rule = rm.mk(orig_r->get_head(), tail.size(), tail.data(),
negs.data(), orig_r->name());
new_rule->set_accounting_parent_object(m_context, orig_r);
rm.mk_rule_rewrite_proof(*orig_r, *new_rule);
result->add_rule(new_rule);
}
for (rule* r : m_introduced_rules) {
result->add_rule(r);
rm.mk_rule_asserted_proof(*r);
}
m_introduced_rules.reset();
result->inherit_predicates(source);
return result.detach();
}
};
rule_set * mk_simple_joins::operator()(rule_set const & source) {
rule_set rs_aux_copy(m_context);
rs_aux_copy.replace_rules(source);
if (!rs_aux_copy.is_closed()) {
rs_aux_copy.close();
}
join_planner planner(m_context, rs_aux_copy);
return planner.run(source);
}
};
