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z3/lib/dl_mk_simple_joins.cpp
Leonardo de Moura e9eab22e5c Z3 sources 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2012-10-02 11:35:25 -07:00

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/*++
Copyright (c) 2006 Microsoft Corporation
Module Name:
dl_mk_simple_joins.cpp
Abstract:
<abstract>
Author:
Leonardo de Moura (leonardo) 2010-05-20.
Revision History:
--*/
#include<utility>
#include<sstream>
#include<limits>
#include"dl_mk_simple_joins.h"
#include"ast_pp.h"
#include"trace.h"
namespace datalog {
mk_simple_joins::mk_simple_joins(context & ctx):
plugin(1000),
m_context(ctx) {
}
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 \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;
bool m_stratified;
unsigned m_src_stratum;
public:
var_idx_set m_all_nonlocal_vars;
rule_vector m_rules;
pair_info() : m_consumers(0), m_stratified(true), m_src_stratum(0) {}
bool can_be_joined() const {
return m_consumers>0;
}
cost get_cost() const {
/*if(m_instantiated) {
return std::numeric_limits<cost>::min();
}*/
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) {
if(m_rules.empty()) {
m_total_cost = pl.compute_cost(t1, t2);
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_core(r)->get_data().m_value.size()>2) {
m_consumers++;
}
if(m_stratified) {
unsigned head_stratum = pl.get_stratum(r->get_head()->get_decl());
SASSERT(head_stratum>=m_src_stratum);
if(head_stratum==m_src_stratum) {
m_stratified = false;
}
}
idx_set_union(m_all_nonlocal_vars, non_local_vars_normalized);
}
/**
\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) {
TRUSTME( 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();
}
private:
pair_info & operator=(const pair_info &); //to avoid the implicit one
};
typedef std::pair<app*, app*> app_pair;
typedef map<app_pair, pair_info *,
pair_hash<obj_ptr_hash<app>, obj_ptr_hash<app> >, default_eq<app_pair> > cost_map;
typedef map<rule *, ptr_vector<app>, ptr_hash<rule>, ptr_eq<rule> > rule_pred_map;
context & m_context;
ast_manager & m;
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<app> m_interpreted;
rule_pred_map m_rules_content;
rule_ref_vector m_introduced_rules;
ptr_hashtable<rule, ptr_hash<rule>, ptr_eq<rule> > m_modified_rules;
ast_ref_vector m_pinned;
public:
join_planner(context & ctx, rule_set & rs_aux_copy)
: m_context(ctx), m(ctx.get_manager()), m_var_subst(ctx.get_var_subst()),
m_rs_aux_copy(rs_aux_copy),
m_introduced_rules(ctx.get_rule_manager()),
m_pinned(ctx.get_manager())
{
}
~join_planner()
{
cost_map::iterator it = m_costs.begin();
cost_map::iterator end = m_costs.end();
for (; it != end; ++it) {
dealloc(it->m_value);
}
m_costs.reset();
}
private:
void get_normalizer(app * t, unsigned & next_var, expr_ref_vector & result) const {
SASSERT(result.size()>0);
unsigned res_ofs = result.size()-1;
unsigned n=t->get_num_args();
for(unsigned i=0; i<n; i++) {
SASSERT(is_var(t->get_arg(i)));
var * v = to_var(t->get_arg(i));
unsigned var_idx = v->get_idx();
if(result[res_ofs-var_idx]==0) {
result[res_ofs-var_idx]=m.mk_var(next_var, v->get_sort());
next_var++;
}
}
}
void get_normalizer(app * t1, app * t2, expr_ref_vector & result) const {
SASSERT(result.empty());
if(t1->get_num_args()==0 && t2->get_num_args()==0) {
return; //nothing to normalize
}
SASSERT(!t1->is_ground() || !t2->is_ground());
unsigned max_var_idx = 0;
{
var_idx_set orig_var_set;
collect_vars(m, t1, orig_var_set);
collect_vars(m, t2, orig_var_set);
var_idx_set::iterator ovit = orig_var_set.begin();
var_idx_set::iterator ovend = orig_var_set.end();
for(; ovit!=ovend; ++ovit) {
unsigned var_idx = *ovit;
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<expr *>(0));
unsigned next_var = 0;
get_normalizer(t1, next_var, result);
get_normalizer(t2, next_var, result);
}
app_pair get_key(app * t1, app * t2) {
expr_ref_vector norm_subst(m);
get_normalizer(t1, t2, norm_subst);
expr_ref t1n_ref(m);
expr_ref t2n_ref(m);
m_var_subst(t1, norm_subst.size(), norm_subst.c_ptr(), t1n_ref);
m_var_subst(t2, norm_subst.size(), norm_subst.c_ptr(), t2n_ref);
app * t1n = to_app(t1n_ref);
app * t2n = to_app(t2n_ref);
if(t1n>t2n) {
std::swap(t1n, t2n);
}
m_pinned.push_back(t1n);
m_pinned.push_back(t2n);
/*
IF_VERBOSE(0,
print_renaming(norm_subst, verbose_stream());
display_predicate(m_context, t1, verbose_stream());
display_predicate(m_context, t2, verbose_stream());
display_predicate(m_context, t1n, verbose_stream());
display_predicate(m_context, t2n, verbose_stream()););
*/
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) {
TRACE("dl", tout << mk_pp(t1, m) << " " << mk_pp(t2, m) << "\n";
r->display(m_context, tout); tout << "\n";);
SASSERT(t1!=t2);
cost_map::entry * e = m_costs.insert_if_not_there2(get_key(t1, t2), 0);
pair_info * & ptr_inf = e->get_data().m_value;
if(ptr_inf==0) {
ptr_inf = alloc(pair_info);
}
pair_info & inf = *ptr_inf;
expr_ref_vector normalizer(m);
get_normalizer(t1, t2, normalizer);
unsigned norm_ofs = normalizer.size()-1;
var_idx_set normalized_vars;
var_idx_set::iterator vit = non_local_vars.begin();
var_idx_set::iterator vend = non_local_vars.end();
for(; vit!=vend; ++vit) {
unsigned norm_var = to_var(normalizer.get(norm_ofs-*vit))->get_idx();
normalized_vars.insert(norm_var);
}
inf.add_rule(*this, t1, t2, r, normalized_vars);
}
pair_info & get_pair(app_pair key) const {
cost_map::entry * e = m_costs.find_core(key);
SASSERT(e);
return *e->get_data().m_value;
}
void remove_rule_from_pair(app_pair key, rule * r, unsigned original_len) {
pair_info * ptr = &get_pair(key);
if(ptr->remove_rule(r, original_len)) {
SASSERT(ptr->m_rules.empty());
m_costs.remove(key);
dealloc(ptr);
}
}
void register_rule(rule * r) {
var_counter counter;
counter.count_vars(m, r, 1);
ptr_vector<app> & rule_content =
m_rules_content.insert_if_not_there2(r, ptr_vector<app>())->get_data().m_value;
SASSERT(rule_content.empty());
unsigned pos_tail_size=r->get_positive_tail_size();
for(unsigned i=0; i<pos_tail_size; i++) {
rule_content.push_back(r->get_tail(i));
}
for(unsigned i=0; i<pos_tail_size; i++) {
app * t1 = r->get_tail(i);
var_idx_set t1_vars;
collect_vars(m, t1, t1_vars);
counter.count_vars(m, t1, -1); //temporarily remove t1 variables from counter
for(unsigned j=i+1; j<pos_tail_size; j++) {
app * t2 = r->get_tail(j);
counter.count_vars(m, t2, -1); //temporarily remove t2 variables from counter
var_idx_set scope_vars(t1_vars);
collect_vars(m, t2, scope_vars);
var_idx_set non_local_vars;
counter.collect_positive(non_local_vars);
counter.count_vars(m, t2, 1); //restore t2 variables in counter
set_intersection(non_local_vars, scope_vars);
register_pair(t1, t2, r, non_local_vars);
}
counter.count_vars(m, t1, 1); //restore t1 variables in counter
}
}
bool extract_argument_info(unsigned var_idx, app * t, expr_ref_vector & args,
ptr_vector<sort> & domain) {
unsigned n=t->get_num_args();
for(unsigned i=0; i<n; i++) {
var * v=to_var(t->get_arg(i));
if(v->get_idx()==var_idx) {
args.push_back(v);
domain.push_back(m.get_sort(v));
return true;
}
}
return false;
}
void join_pair(app_pair pair_key) {
app * t1 = pair_key.first;
app * t2 = pair_key.second;
pair_info & inf = get_pair(pair_key);
SASSERT(!inf.m_rules.empty());
var_idx_set & output_vars = inf.m_all_nonlocal_vars;
expr_ref_vector args(m);
ptr_vector<sort> domain;
unsigned arity = output_vars.num_elems();
idx_set::iterator ovit=output_vars.begin();
idx_set::iterator ovend=output_vars.end();
//TODO: improve quadratic complexity
for(;ovit!=ovend;++ovit) {
unsigned var_idx=*ovit;
bool found=extract_argument_info(var_idx, t1, args, domain);
if(!found) {
found=extract_argument_info(var_idx, t2, args, domain);
}
SASSERT(found);
}
SASSERT(args.size()==arity);
SASSERT(domain.size()==arity);
rule * one_parent = inf.m_rules.back();
func_decl* parent_head = one_parent->get_head()->get_decl();
const char * one_parent_name = parent_head->get_name().bare_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.c_str()), symbol("split"),
arity, domain.c_ptr(), parent_head);
app_ref head(m.mk_app(decl, arity, args.c_ptr()), m);
app * tail[] = {t1, t2};
rule * new_rule = m_context.get_rule_manager().mk(head, 2, tail, 0);
//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.
typedef ptr_hashtable<rule, ptr_hash<rule>, default_eq<rule *> > rule_hashtable;
rule_hashtable relevant_rules;
insert_into_set(relevant_rules, inf.m_rules);
rule_hashtable::iterator rit = relevant_rules.begin();
rule_hashtable::iterator rend = relevant_rules.end();
for(; rit!=rend; ++rit) {
apply_binary_rule(*rit, pair_key, head);
}
// SASSERT(!m_costs.contains(pair_key));
}
void replace_edges(rule * r, const ptr_vector<app> & removed_tails,
const ptr_vector<app> & added_tails0, const ptr_vector<app> & rule_content) {
SASSERT(removed_tails.size()>=added_tails0.size());
unsigned len = rule_content.size();
unsigned original_len = len+removed_tails.size()-added_tails0.size();
ptr_vector<app> added_tails(added_tails0); //we need a copy since we'll be modifying it
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(m, 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(m, r->get_tail(i), 1);
}
for(unsigned i=0; i<len; i++) {
counter.count_vars(m, rule_content[i], 1);
}
//add edges that contain added tails
while(!added_tails.empty()) {
app * a_tail = added_tails.back(); //added tail
var_idx_set a_tail_vars;
collect_vars(m, a_tail, a_tail_vars);
counter.count_vars(m, 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(m, o_tail, -1); //temporarily remove o_tail variables from counter
var_idx_set scope_vars(a_tail_vars);
collect_vars(m, o_tail, scope_vars);
var_idx_set non_local_vars;
counter.collect_positive(non_local_vars);
counter.count_vars(m, 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(m, 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<app> & rule_content = m_rules_content.find_core(r)->get_data().m_value;
unsigned len = rule_content.size();
if(len==1) {
return;
}
func_decl * t1_pred = t1->get_decl();
func_decl * t2_pred = t2->get_decl();
ptr_vector<app> removed_tails;
ptr_vector<app> added_tails;
for(unsigned i1=0; i1<len; i1++) {
app * rt1 = rule_content[i1];
if(rt1->get_decl()!=t1_pred) {
continue;
}
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;
}
expr_ref_vector normalizer(m);
get_normalizer(rt1, rt2, normalizer);
expr_ref_vector denormalizer(m);
reverse_renaming(m, normalizer, denormalizer);
expr_ref new_transf(m);
m_var_subst(t_new, denormalizer.size(), denormalizer.c_ptr(), new_transf);
app * new_lit = to_app(new_transf);
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;
}
}
SASSERT(!removed_tails.empty());
SASSERT(!added_tails.empty());
m_modified_rules.insert(r);
replace_edges(r, removed_tails, added_tails, rule_content);
}
cost get_domain_size(func_decl * pred, unsigned arg_index) const {
relation_sort sort = pred->get_domain(arg_index);
return static_cast<cost>(m_context.get_sort_size_estimate(sort));
//unsigned sz;
//if(!m_context.get_sort_size(sort, sz)) {
// sz=UINT_MAX;
//}
//return static_cast<cost>(sz);
}
unsigned get_stratum(func_decl * pred) const {
return m_rs_aux_copy.get_predicate_strat(pred);
}
cost estimate_size(app * t) const {
func_decl * pred = t->get_decl();
unsigned n=pred->get_arity();
if( (m_context.saturation_was_run() && m_context.get_rmanager().try_get_relation(pred))
|| m_context.get_rmanager().is_saturated(pred)) {
SASSERT(m_context.get_rmanager().try_get_relation(pred)); //if it is saturated, it should exist
unsigned rel_size_int = m_context.get_relation(pred).get_size_estimate_rows();
if(rel_size_int!=0) {
cost rel_size = static_cast<cost>(rel_size_int);
cost curr_size = rel_size;
for(unsigned i=0; i<n; i++) {
if(!is_var(t->get_arg(i))) {
curr_size /= get_domain_size(pred, i);
}
}
return curr_size;
}
}
cost res = 1;
for(unsigned i=0; i<n; i++) {
if(is_var(t->get_arg(i))) {
res *= get_domain_size(pred, i);
}
}
return res;
}
cost compute_cost(app * t1, app * t2) const {
func_decl * t1_pred = t1->get_decl();
func_decl * t2_pred = t2->get_decl();
cost inters_size = 1;
variable_intersection vi(m_context.get_manager());
vi.populate(t1, t2);
unsigned n = vi.size();
for(unsigned i=0; i<n; i++) {
unsigned arg_index1, arg_index2;
vi.get(i, arg_index1, arg_index2);
inters_size *= get_domain_size(t1_pred, arg_index1);
//joined arguments must have the same domain
SASSERT(get_domain_size(t1_pred, arg_index1)==get_domain_size(t2_pred, arg_index2));
}
cost res = estimate_size(t1)*estimate_size(t2)/(inters_size*inters_size);
//cost res = -inters_size;
/*unsigned t1_strat = get_stratum(t1_pred);
SASSERT(t1_strat<=m_head_stratum);
if(t1_strat<m_head_stratum) {
unsigned t2_strat = get_stratum(t2_pred);
SASSERT(t2_strat<=m_head_stratum);
if(t2_strat<m_head_stratum) {
//the rule of this predicates would depend on predicates
//in lower stratum than the head, which is a good thing, since
//then the rule code will not need to appear in a loop
if(res>0) {
res /= 2;
}
else {
res *= 2;
}
}
}*/
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) {
app_pair best;
bool found = false;
cost best_cost;
cost_map::iterator it = m_costs.begin();
cost_map::iterator end = m_costs.end();
for(; it!=end; ++it) {
app_pair key = it->m_key;
pair_info & inf = *it->m_value;
if(!inf.can_be_joined()) {
continue;
}
cost c = inf.get_cost();
if(!found || c<best_cost) {
found = true;
best_cost = c;
best = key;
}
}
if(!found) {
return false;
}
p=best;
return true;
}
public:
rule_set * run(rule_set const & source) {
unsigned num_rules = source.get_num_rules();
for (unsigned i = 0; i < num_rules; i++) {
register_rule(source.get_rule(i));
}
app_pair selected;
while(pick_best_pair(selected)) {
join_pair(selected);
}
if(m_modified_rules.empty()) {
return 0;
}
rule_set * result = alloc(rule_set, m_context);
rule_pred_map::iterator rcit = m_rules_content.begin();
rule_pred_map::iterator rcend = m_rules_content.end();
for(; rcit!=rcend; ++rcit) {
rule * orig_r = rcit->m_key;
ptr_vector<app> content = rcit->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<app> tail(content);
svector<bool> 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 = m_context.get_rule_manager().mk(orig_r->get_head(), tail.size(), tail.c_ptr(),
negs.c_ptr());
new_rule->set_accounting_parent_object(m_context, orig_r);
result->add_rule(new_rule);
}
while(!m_introduced_rules.empty()) {
result->add_rule(m_introduced_rules.back());
m_introduced_rules.pop_back();
}
return result;
}
};
rule_set * mk_simple_joins::operator()(rule_set const & source, model_converter_ref& mc, proof_converter_ref& pc) {
// TODO mc, pc
rule_set rs_aux_copy(m_context);
rs_aux_copy.add_rules(source);
if(!rs_aux_copy.is_closed()) {
rs_aux_copy.close();
}
join_planner planner(m_context, rs_aux_copy);
return planner.run(source);
}
};
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