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z3/src/smt/theory_special_relations.cpp
Nikolaj Bjorner 8a85cfdb12 fix #5579 -
It is only possible to reach this case when new assertions are created.
2021-09-30 09:32:34 -07:00

1151 lines
42 KiB
C++

/*++
Copyright (c) 2015 Microsoft Corporation
Module Name:
theory_special_relations.cpp
Abstract:
Special Relations theory plugin.
Author:
Nikolaj Bjorner (nbjorner) 2015-9-16
Ashutosh Gupta 2016
Notes:
--*/
#include <fstream>
#include "ast/reg_decl_plugins.h"
#include "ast/datatype_decl_plugin.h"
#include "ast/recfun_decl_plugin.h"
#include "ast/ast_pp.h"
#include "ast/rewriter/recfun_replace.h"
#include "smt/smt_context.h"
#include "smt/theory_arith.h"
#include "smt/theory_special_relations.h"
namespace smt {
func_decl* theory_special_relations::relation::next() {
if (!m_next) {
sort* s = decl()->get_domain(0);
sort* domain[2] = {s, s};
m_next = m.mk_fresh_func_decl("next", "", 2, domain, s);
}
return m_next;
}
void theory_special_relations::relation::push() {
m_scopes.push_back(scope());
scope& s = m_scopes.back();
s.m_asserted_atoms_lim = m_asserted_atoms.size();
s.m_asserted_qhead_old = m_asserted_qhead;
m_graph.push();
m_ufctx.get_trail_stack().push_scope();
}
void theory_special_relations::relation::pop(unsigned num_scopes) {
unsigned new_lvl = m_scopes.size() - num_scopes;
scope& s = m_scopes[new_lvl];
m_asserted_atoms.shrink(s.m_asserted_atoms_lim);
m_asserted_qhead = s.m_asserted_qhead_old;
m_scopes.shrink(new_lvl);
m_graph.pop(num_scopes);
m_ufctx.get_trail_stack().pop_scope(num_scopes);
}
void theory_special_relations::relation::ensure_var(theory_var v) {
while ((unsigned)v > m_uf.mk_var());
if ((unsigned)v >= m_graph.get_num_nodes()) {
m_graph.init_var(v);
}
}
bool theory_special_relations::relation::new_eq_eh(literal l, theory_var v1, theory_var v2) {
ensure_var(v1);
ensure_var(v2);
literal_vector ls;
ls.push_back(l);
return m_graph.add_non_strict_edge(v1, v2, ls) && m_graph.add_non_strict_edge(v2, v1, ls);
}
std::ostream& theory_special_relations::relation::display(theory_special_relations const& th, std::ostream& out) const {
out << mk_pp(m_decl, th.get_manager());
for (unsigned i = 0; i < m_decl->get_num_parameters(); ++i) {
th.get_manager().display(out << " ", m_decl->get_parameter(i));
}
out << ":\n";
m_graph.display(out);
out << "explanation: " << m_explanation << "\n";
m_uf.display(out);
for (atom* ap : m_asserted_atoms) {
th.display_atom(out, *ap);
}
return out;
}
theory_special_relations::theory_special_relations(context& ctx, ast_manager& m):
theory(ctx, m.mk_family_id("specrels")),
m_util(m),
m_can_propagate(false) {
}
theory_special_relations::~theory_special_relations() {
reset_eh();
}
theory * theory_special_relations::mk_fresh(context * new_ctx) {
return alloc(theory_special_relations, *new_ctx, new_ctx->get_manager());
}
/**
\brief for term := next(next(a,b),c) for relation f
assert f(term,c) or term != c
assert f(term,c) or term != next(a,b)
assert f(term,c) or term != b
assert f(term,c) or term != a
*/
void theory_special_relations::internalize_next(func_decl* f, app* term) {
ast_manager& m = get_manager();
func_decl* nxt = term->get_decl();
expr* src = term->get_arg(0);
expr* dst = term->get_arg(1);
expr_ref f_rel(m.mk_app(f, src, dst), m);
ensure_enode(term);
ensure_enode(f_rel);
literal f_lit = ctx.get_literal(f_rel);
src = term;
while (to_app(src)->get_decl() == nxt) {
dst = to_app(src)->get_arg(1);
src = to_app(src)->get_arg(0);
ctx.mk_th_axiom(get_id(), f_lit, ~mk_eq(term, src, false));
ctx.mk_th_axiom(get_id(), f_lit, ~mk_eq(term, dst, false));
}
}
bool theory_special_relations::internalize_term(app * term) {
return false;
}
bool theory_special_relations::internalize_atom(app * atm, bool gate_ctx) {
SASSERT(m_util.is_special_relation(atm));
relation* r = 0;
ast_manager& m = get_manager();
if (!m_relations.find(atm->get_decl(), r)) {
r = alloc(relation, m_util.get_property(atm), atm->get_decl(), m);
m_relations.insert(atm->get_decl(), r);
for (unsigned i = 0; i < m_atoms_lim.size(); ++i) r->push();
}
expr* arg0 = atm->get_arg(0);
expr* arg1 = atm->get_arg(1);
theory_var v0 = mk_var(arg0);
theory_var v1 = mk_var(arg1);
bool_var v = ctx.mk_bool_var(atm);
ctx.set_var_theory(v, get_id());
atom* a = alloc(atom, v, *r, v0, v1);
m_atoms.push_back(a);
TRACE("special_relations", tout << mk_pp(atm, m) << " : bv" << v << " v" << a->v1() << " v" << a->v2() << ' ' << gate_ctx << "\n";);
m_bool_var2atom.insert(v, a);
return true;
}
theory_var theory_special_relations::mk_var(expr* e) {
if (!ctx.e_internalized(e)) {
ctx.internalize(e, false);
}
enode * n = ctx.get_enode(e);
theory_var v = n->get_th_var(get_id());
if (null_theory_var == v) {
v = theory::mk_var(n);
TRACE("special_relations", tout << "v" << v << " := " << mk_pp(e, get_manager()) << "\n";);
ctx.attach_th_var(n, this, v);
}
return v;
}
void theory_special_relations::new_eq_eh(theory_var v1, theory_var v2) {
app* t1 = get_expr(v1);
app* t2 = get_expr(v2);
literal eq = mk_eq(t1, t2, false);
for (auto const& kv : m_relations) {
relation& r = *kv.m_value;
if (!r.new_eq_eh(eq, v1, v2)) {
set_neg_cycle_conflict(r);
break;
}
}
}
final_check_status theory_special_relations::final_check_eh() {
TRACE("special_relations", tout << "\n";);
for (auto const& kv : m_relations) {
lbool r = final_check(*kv.m_value);
switch (r) {
case l_undef:
return FC_GIVEUP;
case l_false:
return FC_CONTINUE;
default:
break;
}
}
bool new_equality = false;
for (auto const& kv : m_relations) {
if (extract_equalities(*kv.m_value)) {
new_equality = true;
}
if (ctx.inconsistent()) {
return FC_CONTINUE;
}
}
if (new_equality) {
return FC_CONTINUE;
}
else {
return FC_DONE;
}
}
lbool theory_special_relations::final_check_lo(relation& r) {
// all constraints are saturated by propagation.
return l_true;
}
enode* theory_special_relations::ensure_enode(expr* e) {
if (!ctx.e_internalized(e)) {
ctx.internalize(e, false);
}
enode* n = ctx.get_enode(e);
ctx.mark_as_relevant(n);
return n;
}
literal theory_special_relations::mk_literal(expr* _e) {
expr_ref e(_e, get_manager());
ensure_enode(e);
return ctx.get_literal(e);
}
theory_var theory_special_relations::mk_var(enode* n) {
if (is_attached_to_var(n)) {
return n->get_th_var(get_id());
}
else {
theory_var v = theory::mk_var(n);
ctx.attach_th_var(n, this, v);
ctx.mark_as_relevant(n);
return v;
}
}
lbool theory_special_relations::final_check_plo(relation& r) {
//
// ensure that !Rxy -> Ryx between connected components
// (where Rzx & Rzy or Rxz & Ryz for some z)
//
lbool res = l_true;
for (unsigned i = 0; res == l_true && i < r.m_asserted_atoms.size(); ++i) {
atom& a = *r.m_asserted_atoms[i];
if (!a.phase() && r.m_uf.find(a.v1()) == r.m_uf.find(a.v2())) {
res = enable(a);
}
}
return res;
}
lbool theory_special_relations::final_check_tc(relation& r) {
//
// Ensure that Rxy -> TC(R)xy
//
func_decl* tcf = r.decl();
func_decl* f = to_func_decl(tcf->get_parameter(0).get_ast());
ast_manager& m = get_manager();
bool new_assertion = false;
graph r_graph;
for (enode* n : ctx.enodes_of(f)) {
literal lit = ctx.enode2literal(n);
if (l_true == ctx.get_assignment(lit)) {
expr* e = ctx.bool_var2expr(lit.var());
expr* arg1 = to_app(e)->get_arg(0);
expr* arg2 = to_app(e)->get_arg(1);
expr_ref tc_app(m.mk_app(tcf, arg1, arg2), m);
enode* tcn = ensure_enode(tc_app);
if (ctx.get_assignment(tcn) != l_true) {
literal consequent = ctx.get_literal(tc_app);
justification* j = ctx.mk_justification(theory_propagation_justification(get_id(), ctx.get_region(), 1, &lit, consequent));
TRACE("special_relations", tout << "propagate: " << tc_app << "\n";);
ctx.assign(consequent, j);
new_assertion = true;
}
else {
theory_var v1 = get_representative(get_th_var(arg1));
theory_var v2 = get_representative(get_th_var(arg2));
r_graph.init_var(v1);
r_graph.init_var(v2);
literal_vector ls;
r_graph.enable_edge(r_graph.add_edge(v1, v2, s_integer(0), ls));
}
}
}
//
// Ensure that TC(R)xy -> Rxz1 Rz1z2 .. Rzky
//
// if not Rxy and no path in graph:
// Introduce next(x,y), such that
// TC(R)(x,y) => R(x,y) or TR(R)(next(x,y),y) & R(x,next(x,y))
//
// next(x,y) is fresh unless R(x,y) is true:
// R(x,y) or x != next(x,y)
// R(x,y) or y != next(x,y)
//
unsigned sz = r.m_asserted_atoms.size();
for (unsigned i = 0; i < sz; ++i) {
atom& a = *r.m_asserted_atoms[i];
if (a.phase()) {
bool_var bv = a.var();
expr* arg1 = get_expr(a.v1());
expr* arg2 = get_expr(a.v2());
// we need reachability in the R graph not R* graph
theory_var r1 = get_representative(a.v1());
theory_var r2 = get_representative(a.v2());
if (r_graph.can_reach(r1, r2)) {
TRACE("special_relations",
tout << a.v1() << ": " << mk_pp(arg1, m) << " -> "
<< a.v2() << ": " << mk_pp(arg2, m) << " is positive reachable\n";
r.m_graph.display(tout);
);
continue;
}
expr_ref f_app(m.mk_app(f, arg1, arg2), m);
ensure_enode(f_app);
literal f_lit = ctx.get_literal(f_app);
switch (ctx.get_assignment(f_lit)) {
case l_true:
SASSERT(new_assertion);
break;
case l_false: {
//
// Add the axioms:
// TC(R)(x,y) => R(x,y) or TC(R)(next(x,y),y)
// TC(R)(x,y) => R(x,y) or R(x,next(x,y))
// R(x,y) or next(x,y) != x
// R(x,y) or next(x,y) != y,
// and recursively on all next subterms of x.
// Add the literal R(next(x,y),y) - set case split preference to true.
//
// TBD: perhaps replace by recursion unfolding similar to theory_rec_fun
//
app_ref next(r.next(arg1, arg2), m);
internalize_next(f, next);
expr_ref a2next(m.mk_app(f, arg1, next), m);
expr_ref next2b(m.mk_app(tcf, next, arg2), m);
expr_ref next_b(m.mk_app(f, next, arg2), m);
ensure_enode(a2next);
ensure_enode(next2b);
ensure_enode(next_b);
literal next2b_l = ctx.get_literal(next2b);
literal a2next_l = ctx.get_literal(a2next);
if (ctx.get_assignment(next2b_l) == l_true && ctx.get_assignment(a2next_l) == l_true) {
break;
}
ctx.mk_th_axiom(get_id(), ~literal(bv), f_lit, a2next_l);
ctx.mk_th_axiom(get_id(), ~literal(bv), f_lit, next2b_l);
expr* nxt = next;
while (r.is_next(nxt)) {
expr* left = to_app(nxt)->get_arg(0);
expr* right = to_app(nxt)->get_arg(1);
ctx.assign(~mk_eq(next, left, false), nullptr);
ctx.assign(~mk_eq(next, right, false), nullptr);
nxt = left;
}
ctx.set_true_first_flag(ctx.get_literal(next_b).var());
new_assertion = true;
break;
}
case l_undef:
ctx.set_true_first_flag(bv);
TRACE("special_relations", tout << f_app << " is undefined\n";);
new_assertion = true;
break;
}
}
}
if (new_assertion) {
TRACE("special_relations", tout << "new assertion\n";);
return l_false;
}
return final_check_po(r);
}
lbool theory_special_relations::final_check_to(relation& r) {
uint_set visited, target;
for (atom* ap : r.m_asserted_atoms) {
atom& a = *ap;
if (a.phase()) {
continue;
}
TRACE("special_relations", tout << a.v1() << " !<= " << a.v2() << "\n";);
target.reset();
theory_var w;
// v1 !<= v2 is asserted
target.insert(a.v1());
if (r.m_graph.reachable(a.v2(), target, visited, w)) {
// we already have v2 <= v1
TRACE("special_relations", tout << "already: " << a.v2() << " <= " << a.v1() << "\n";);
continue;
}
// the nodes visited from v1 become target for v2
if (r.m_graph.reachable(a.v2(), visited, target, w)) {
//
// we have the following:
// v1 <= w
// v2 <= w
// v1 !<= v2
//
// enforce the assertion
//
// v1 <= w & v2 <= w & v1 !<= v2 -> v2 <= v1
//
unsigned timestamp = r.m_graph.get_timestamp();
r.m_explanation.reset();
r.m_graph.find_shortest_reachable_path(a.v1(), w, timestamp, r);
r.m_graph.find_shortest_reachable_path(a.v2(), w, timestamp, r);
TRACE("special_relations", tout << "added edge\n";);
r.m_explanation.push_back(a.explanation());
literal_vector const& lits = r.m_explanation;
if (!r.m_graph.add_non_strict_edge(a.v2(), a.v1(), lits)) {
set_neg_cycle_conflict(r);
return l_false;
}
}
target.reset();
visited.reset();
target.insert(a.v2());
if (r.m_graph.reachable(a.v1(), target, visited, w)) {
// we have v1 <= v2
unsigned timestamp = r.m_graph.get_timestamp();
r.m_explanation.reset();
r.m_graph.find_shortest_reachable_path(a.v1(), w, timestamp, r);
r.m_explanation.push_back(a.explanation());
set_conflict(r);
}
}
return l_true;
}
lbool theory_special_relations::enable(atom& a) {
if (!a.enable()) {
relation& r = a.get_relation();
set_neg_cycle_conflict(r);
return l_false;
}
else {
return l_true;
}
}
void theory_special_relations::set_neg_cycle_conflict(relation& r) {
r.m_explanation.reset();
r.m_graph.traverse_neg_cycle2(false, r);
set_conflict(r);
}
void theory_special_relations::set_conflict(relation& r) {
literal_vector const& lits = r.m_explanation;
TRACE("special_relations", ctx.display_literals_verbose(tout, lits) << "\n";);
vector<parameter> params;
ctx.set_conflict(
ctx.mk_justification(
ext_theory_conflict_justification(
get_id(), ctx.get_region(),
lits.size(), lits.data(), 0, 0, params.size(), params.data())));
}
lbool theory_special_relations::final_check(relation& r) {
lbool res = propagate(r);
if (res != l_true) return res;
switch (r.m_property) {
case sr_lo:
res = final_check_lo(r);
break;
case sr_po:
res = final_check_po(r);
break;
case sr_plo:
res = final_check_plo(r);
break;
case sr_to:
res = final_check_to(r);
break;
case sr_tc:
res = final_check_tc(r);
break;
default:
UNREACHABLE();
res = l_undef;
break;
}
TRACE("special_relations", r.display(*this, tout << res << "\n"););
return res;
}
bool theory_special_relations::extract_equalities(relation& r) {
switch (r.m_property) {
case sr_tc:
return false;
default:
break;
}
bool new_eq = false;
int_vector scc_id;
u_map<unsigned> roots;
ast_manager& m = get_manager();
(void)m;
r.m_graph.compute_zero_edge_scc(scc_id);
int start = ctx.get_random_value();
for (unsigned idx = 0, j = 0; !ctx.inconsistent() && idx < scc_id.size(); ++idx) {
unsigned i = (start + idx) % scc_id.size();
if (scc_id[i] == -1) {
continue;
}
enode* x = get_enode(i);
if (roots.find(scc_id[i], j)) {
enode* y = get_enode(j);
if (x->get_root() != y->get_root()) {
new_eq = true;
unsigned timestamp = r.m_graph.get_timestamp();
r.m_explanation.reset();
r.m_graph.find_shortest_zero_edge_path(i, j, timestamp, r);
r.m_graph.find_shortest_zero_edge_path(j, i, timestamp, r);
literal_vector const& lits = r.m_explanation;
TRACE("special_relations", ctx.display_literals_verbose(tout << mk_pp(x->get_expr(), m) << " = " << mk_pp(y->get_expr(), m) << "\n", lits) << "\n";);
IF_VERBOSE(20, ctx.display_literals_verbose(verbose_stream() << mk_pp(x->get_expr(), m) << " = " << mk_pp(y->get_expr(), m) << "\n", lits) << "\n";);
eq_justification js(ctx.mk_justification(ext_theory_eq_propagation_justification(get_id(), ctx.get_region(), lits.size(), lits.data(), 0, nullptr,
x, y)));
ctx.assign_eq(x, y, js);
}
}
else {
roots.insert(scc_id[i], i);
}
}
return new_eq;
}
/*
\brief Propagation for piecewise linear orders
*/
lbool theory_special_relations::propagate_plo(atom& a) {
lbool res = l_true;
relation& r = a.get_relation();
if (a.phase()) {
r.m_uf.merge(a.v1(), a.v2());
res = enable(a);
}
else if (r.m_uf.find(a.v1()) == r.m_uf.find(a.v2())) {
res = enable(a);
}
return res;
}
lbool theory_special_relations::propagate_po(atom& a) {
lbool res = l_true;
if (a.phase()) {
relation& r = a.get_relation();
r.m_uf.merge(a.v1(), a.v2());
res = enable(a);
}
return res;
}
lbool theory_special_relations::propagate_tc(atom& a) {
if (a.phase()) {
VERIFY(a.enable());
relation& r = a.get_relation();
r.m_uf.merge(a.v1(), a.v2());
}
return l_true;
}
lbool theory_special_relations::final_check_po(relation& r) {
for (atom* ap : r.m_asserted_atoms) {
atom& a = *ap;
if (!a.phase() && r.m_uf.find(a.v1()) == r.m_uf.find(a.v2())) {
// v1 !-> v2
// find v1 -> v3 -> v4 -> v2 path
r.m_explanation.reset();
unsigned timestamp = r.m_graph.get_timestamp();
bool found_path = r.m_graph.find_shortest_reachable_path(a.v1(), a.v2(), timestamp, r);
if (found_path) {
TRACE("special_relations", tout << "check po conflict\n";);
r.m_explanation.push_back(a.explanation());
set_conflict(r);
return l_false;
}
}
}
return l_true;
}
void theory_special_relations::propagate() {
if (m_can_propagate) {
for (auto const& kv : m_relations) {
propagate(*kv.m_value);
}
m_can_propagate = false;
}
}
lbool theory_special_relations::propagate(relation& r) {
lbool res = l_true;
while (res == l_true && r.m_asserted_qhead < r.m_asserted_atoms.size()) {
atom& a = *r.m_asserted_atoms[r.m_asserted_qhead];
switch (r.m_property) {
case sr_lo:
res = enable(a);
break;
case sr_plo:
res = propagate_plo(a);
break;
case sr_po:
res = propagate_po(a);
break;
case sr_tc:
res = propagate_tc(a);
break;
default:
if (a.phase()) {
res = enable(a);
}
break;
}
++r.m_asserted_qhead;
}
return res;
}
void theory_special_relations::reset_eh() {
for (auto const& kv : m_relations) {
dealloc(kv.m_value);
}
m_relations.reset();
del_atoms(0);
}
void theory_special_relations::assign_eh(bool_var v, bool is_true) {
TRACE("special_relations", tout << "assign bv" << v << " " << (is_true?" <- true":" <- false") << "\n";);
atom* a = m_bool_var2atom[v];
a->set_phase(is_true);
a->get_relation().m_asserted_atoms.push_back(a);
m_can_propagate = true;
}
void theory_special_relations::push_scope_eh() {
theory::push_scope_eh();
for (auto const& kv : m_relations) {
kv.m_value->push();
}
m_atoms_lim.push_back(m_atoms.size());
}
void theory_special_relations::pop_scope_eh(unsigned num_scopes) {
for (auto const& kv : m_relations) {
kv.m_value->pop(num_scopes);
}
unsigned new_lvl = m_atoms_lim.size() - num_scopes;
del_atoms(m_atoms_lim[new_lvl]);
m_atoms_lim.shrink(new_lvl);
theory::pop_scope_eh(num_scopes);
}
void theory_special_relations::del_atoms(unsigned old_size) {
atoms::iterator begin = m_atoms.begin() + old_size;
atoms::iterator it = m_atoms.end();
while (it != begin) {
--it;
atom* a = *it;
m_bool_var2atom.erase(a->var());
dealloc(a);
}
m_atoms.shrink(old_size);
}
void theory_special_relations::collect_statistics(::statistics & st) const {
for (auto const& kv : m_relations) {
kv.m_value->m_graph.collect_statistics(st);
}
}
model_value_proc * theory_special_relations::mk_value(enode * n, model_generator & mg) {
UNREACHABLE();
return nullptr;
}
void theory_special_relations::ensure_strict(graph& g) {
unsigned sz = g.get_num_edges();
for (unsigned i = 0; i < sz; ++i) {
if (!g.is_enabled(i)) continue;
if (g.get_weight(i) != s_integer(0)) continue;
dl_var src = g.get_source(i);
dl_var dst = g.get_target(i);
if (get_enode(src)->get_root() == get_enode(dst)->get_root()) continue;
VERIFY(g.add_strict_edge(src, dst, literal_vector()));
}
TRACE("special_relations", g.display(tout););
}
/**
src1 <= i, src2 <= i, src1 != src2 => src1 !<= src2
*/
void theory_special_relations::ensure_tree(graph& g) {
unsigned sz = g.get_num_nodes();
for (unsigned i = 0; i < sz; ++i) {
int_vector const& edges = g.get_in_edges(i);
for (unsigned j = 0; j < edges.size(); ++j) {
edge_id e1 = edges[j];
if (!g.is_enabled(e1)) continue;
SASSERT ((int)i == g.get_target(e1));
dl_var src1 = g.get_source(e1);
for (unsigned k = j + 1; k < edges.size(); ++k) {
edge_id e2 = edges[k];
if (!g.is_enabled(e2)) continue;
dl_var src2 = g.get_source(e2);
if (get_enode(src1)->get_root() != get_enode(src2)->get_root() &&
disconnected(g, src1, src2)) {
VERIFY(g.add_strict_edge(src1, src2, literal_vector()));
}
}
}
}
TRACE("special_relations", g.display(tout););
}
bool theory_special_relations::disconnected(graph const& g, dl_var u, dl_var v) const {
s_integer val_u = g.get_assignment(u);
s_integer val_v = g.get_assignment(v);
if (val_u == val_v)
return u != v;
if (val_u < val_v) {
std::swap(u, v);
std::swap(val_u, val_v);
}
SASSERT(val_u > val_v);
svector<dl_var> todo;
todo.push_back(u);
while (!todo.empty()) {
u = todo.back();
todo.pop_back();
if (u == v) {
return false;
}
SASSERT(g.get_assignment(u) <= val_u);
if (g.get_assignment(u) <= val_v) {
continue;
}
for (edge_id e : g.get_out_edges(u)) {
if (is_strict_neighbour_edge(g, e)) {
todo.push_back(g.get_target(e));
}
}
}
return true;
}
expr_ref theory_special_relations::mk_inj(relation& r, model_generator& mg) {
ast_manager& m = get_manager();
r.push();
ensure_strict(r.m_graph);
func_decl_ref fn(m);
expr_ref result(m);
arith_util arith(m);
sort* const* ty = r.decl()->get_domain();
fn = m.mk_fresh_func_decl("inj", 1, ty, arith.mk_int());
unsigned sz = r.m_graph.get_num_nodes();
func_interp* fi = alloc(func_interp, m, 1);
for (unsigned i = 0; i < sz; ++i) {
s_integer val = r.m_graph.get_assignment(i);
expr* arg = get_expr(i);
fi->insert_new_entry(&arg, arith.mk_numeral(val.to_rational(), true));
}
TRACE("special_relations", r.m_graph.display(tout););
r.pop(1);
fi->set_else(arith.mk_numeral(rational(0), true));
mg.get_model().register_decl(fn, fi);
result = arith.mk_le(m.mk_app(fn,m.mk_var(0, *ty)), m.mk_app(fn, m.mk_var(1, *ty)));
return result;
}
expr_ref theory_special_relations::mk_class(relation& r, model_generator& mg) {
ast_manager& m = get_manager();
expr_ref result(m);
func_decl_ref fn(m);
arith_util arith(m);
func_interp* fi = alloc(func_interp, m, 1);
sort* const* ty = r.decl()->get_domain();
fn = m.mk_fresh_func_decl("class", 1, ty, arith.mk_int());
unsigned sz = r.m_graph.get_num_nodes();
for (unsigned i = 0; i < sz; ++i) {
unsigned val = r.m_uf.find(i);
expr* arg = get_expr(i);
fi->insert_new_entry(&arg, arith.mk_numeral(rational(val), true));
}
fi->set_else(arith.mk_numeral(rational(0), true));
mg.get_model().register_decl(fn, fi);
result = m.mk_eq(m.mk_app(fn, m.mk_var(0, *ty)), m.mk_app(fn, m.mk_var(1, *ty)));
return result;
}
expr_ref theory_special_relations::mk_interval(relation& r, model_generator& mg, unsigned_vector & lo, unsigned_vector& hi) {
graph const& g = r.m_graph;
ast_manager& m = get_manager();
expr_ref result(m);
func_decl_ref lofn(m), hifn(m);
arith_util arith(m);
func_interp* lofi = alloc(func_interp, m, 1);
func_interp* hifi = alloc(func_interp, m, 1);
sort* const* ty = r.decl()->get_domain();
lofn = m.mk_fresh_func_decl("lo", 1, ty, arith.mk_int());
hifn = m.mk_fresh_func_decl("hi", 1, ty, arith.mk_int());
unsigned sz = g.get_num_nodes();
for (unsigned i = 0; i < sz; ++i) {
expr* arg = get_expr(i);
lofi->insert_new_entry(&arg, arith.mk_numeral(rational(lo[i]), true));
hifi->insert_new_entry(&arg, arith.mk_numeral(rational(hi[i]), true));
}
lofi->set_else(arith.mk_numeral(rational(0), true));
hifi->set_else(arith.mk_numeral(rational(0), true));
mg.get_model().register_decl(lofn, lofi);
mg.get_model().register_decl(hifn, hifi);
result = m.mk_and(arith.mk_le(m.mk_app(lofn, m.mk_var(0, *ty)), m.mk_app(lofn, m.mk_var(1, *ty))),
arith.mk_le(m.mk_app(hifn, m.mk_var(1, *ty)), m.mk_app(hifn, m.mk_var(0, *ty))));
return result;
}
void theory_special_relations::init_model_lo(relation& r, model_generator& m) {
expr_ref inj = mk_inj(r, m);
func_interp* fi = alloc(func_interp, get_manager(), 2);
fi->set_else(inj);
m.get_model().register_decl(r.decl(), fi);
}
void theory_special_relations::init_model_plo(relation& r, model_generator& mg) {
expr_ref inj = mk_inj(r, mg);
expr_ref cls = mk_class(r, mg);
func_interp* fi = alloc(func_interp, get_manager(), 2);
fi->set_else(get_manager().mk_and(inj, cls));
mg.get_model().register_decl(r.decl(), fi);
}
/**
\brief model for a partial order,
is a recursive function that evaluates membership in partial order over
a fixed set of edges. It runs in O(e*n^2) where n is the number of vertices and e
number of edges.
connected(A, dst, S) =
let (A',S') = next1(a1, b1, A, next1(a2, b2, A, ... S, (nil, S)))
if A' = nil then false else
if member(dst, A') then true else
connected(A', dst, S')
next1(a, b, A, S, (A',S')) =
if member(a, A) and not member(b, S) then (cons(b, A'), cons(b, S')) else (A',S')
*/
void theory_special_relations::init_model_po(relation& r, model_generator& mg, bool is_reflexive) {
ast_manager& m = get_manager();
sort* s = r.m_decl->get_domain(0);
datatype_util dt(m);
recfun::util rf(m);
recfun::decl::plugin& p = rf.get_plugin();
func_decl_ref nil(m), is_nil(m), cons(m), is_cons(m), hd(m), tl(m);
sort_ref listS(dt.mk_list_datatype(s, symbol("List"), cons, is_cons, hd, tl, nil, is_nil), m);
func_decl_ref fst(m), snd(m), pair(m);
expr_ref nilc(m.mk_const(nil), m);
expr* T = m.mk_true();
expr* F = m.mk_false();
func_decl* memf, *nextf, *connectedf;
{
sort* dom[2] = { s, listS };
recfun::promise_def mem = p.ensure_def(symbol("member"), 2, dom, m.mk_bool_sort(), true);
memf = mem.get_def()->get_decl();
var_ref xV(m.mk_var(1, s), m);
var_ref SV(m.mk_var(0, listS), m);
var_ref yV(m), vV(m), wV(m);
expr* x = xV, *S = SV;
expr_ref mem_body(m);
mem_body = m.mk_ite(m.mk_app(is_nil, S),
F,
m.mk_ite(m.mk_eq(m.mk_app(hd, S), x),
T,
m.mk_app(memf, x, m.mk_app(tl, S))));
recfun_replace rep(m);
var* vars[2] = { xV, SV };
p.set_definition(rep, mem, false, 2, vars, mem_body);
}
sort_ref tup(dt.mk_pair_datatype(listS, listS, fst, snd, pair), m);
{
sort* dom[5] = { s, s, listS, listS, tup };
recfun::promise_def nxt = p.ensure_def(symbol("next"), 5, dom, tup, true);
nextf = nxt.get_def()->get_decl();
expr_ref next_body(m);
var_ref aV(m.mk_var(4, s), m);
var_ref bV(m.mk_var(3, s), m);
var_ref AV(m.mk_var(2, listS), m);
var_ref SV(m.mk_var(1, listS), m);
var_ref tupV(m.mk_var(0, tup), m);
expr* a = aV, *b = bV, *A = AV, *S = SV, *t = tupV;
next_body = m.mk_ite(m.mk_and(m.mk_app(memf, a, A), m.mk_not(m.mk_app(memf, b, S))),
m.mk_app(pair, m.mk_app(cons, b, m.mk_app(fst, t)), m.mk_app(cons, b, m.mk_app(snd, t))),
t);
recfun_replace rep(m);
var* vars[5] = { aV, bV, AV, SV, tupV };
p.set_definition(rep, nxt, false, 5, vars, next_body);
}
{
sort* dom[3] = { listS, s, listS };
recfun::promise_def connected = p.ensure_def(symbol("connected"), 3, dom, m.mk_bool_sort(), true);
connectedf = connected.get_def()->get_decl();
var_ref AV(m.mk_var(2, listS), m);
var_ref dstV(m.mk_var(1, s), m);
var_ref SV(m.mk_var(0, listS), m);
expr* A = AV, *dst = dstV, *S = SV;
expr_ref connected_body(m);
connected_body = m.mk_app(pair, nilc.get(), S);
for (atom* ap : r.m_asserted_atoms) {
atom& a = *ap;
if (!a.phase()) continue;
SASSERT(ctx.get_assignment(a.var()) == l_true);
expr* x = get_enode(a.v1())->get_root()->get_expr();
expr* y = get_enode(a.v2())->get_root()->get_expr();
expr* cb = connected_body;
expr* args[5] = { x, y, A, S, cb };
connected_body = m.mk_app(nextf, 5, args);
}
expr_ref Ap(m.mk_app(fst, connected_body.get()), m);
expr_ref Sp(m.mk_app(snd, connected_body.get()), m);
connected_body = m.mk_ite(m.mk_eq(Ap, nilc), F,
m.mk_ite(m.mk_app(memf, dst, Ap), T,
m.mk_app(connectedf, Ap, dst, Sp)));
TRACE("special_relations", tout << connected_body << "\n";);
recfun_replace rep(m);
var* vars[3] = { AV, dstV, SV };
p.set_definition(rep, connected, false, 3, vars, connected_body);
}
{
var_ref xV(m.mk_var(0, s), m);
var_ref yV(m.mk_var(1, s), m);
expr* x = xV, *y = yV;
func_interp* fi = alloc(func_interp, m, 2);
expr_ref consx(m.mk_app(cons, x, nilc), m);
expr_ref pred(m.mk_app(connectedf, consx, y, consx), m);
if (is_reflexive) {
pred = m.mk_or(pred, m.mk_eq(x, y));
}
fi->set_else(pred);
mg.get_model().register_decl(r.decl(), fi);
}
}
/**
\brief map each node to an interval of numbers, such that
the children are proper sub-intervals.
Then the <= relation becomes interval containment.
1. For each vertex, count the number of nodes below it in the transitive closure.
Store the result in num_children.
2. Identify each root.
3. Process children, assigning unique (and disjoint) intervals.
4. Extract interpretation.
*/
void theory_special_relations::init_model_to(relation& r, model_generator& mg) {
unsigned_vector num_children, lo, hi;
graph const& g = r.m_graph;
r.push();
ensure_strict(r.m_graph);
ensure_tree(r.m_graph);
count_children(g, num_children);
assign_interval(g, num_children, lo, hi);
expr_ref iv = mk_interval(r, mg, lo, hi);
r.pop(1);
func_interp* fi = alloc(func_interp, get_manager(), 2);
fi->set_else(iv);
mg.get_model().register_decl(r.decl(), fi);
}
bool theory_special_relations::is_neighbour_edge(graph const& g, edge_id edge) const {
CTRACE("special_relations_verbose", g.is_enabled(edge),
tout << edge << ": " << g.get_source(edge) << " " << g.get_target(edge) << " ";
tout << (g.get_assignment(g.get_target(edge)) - g.get_assignment(g.get_source(edge))) << "\n";);
return
g.is_enabled(edge) &&
g.get_assignment(g.get_source(edge)) - s_integer(1) == g.get_assignment(g.get_target(edge));
}
bool theory_special_relations::is_strict_neighbour_edge(graph const& g, edge_id e) const {
return is_neighbour_edge(g, e) && g.get_weight(e) != s_integer(0);
}
void theory_special_relations::count_children(graph const& g, unsigned_vector& num_children) {
unsigned sz = g.get_num_nodes();
svector<dl_var> nodes;
num_children.resize(sz, 0);
bool_vector processed(sz, false);
for (unsigned i = 0; i < sz; ++i) nodes.push_back(i);
while (!nodes.empty()) {
dl_var v = nodes.back();
if (processed[v]) {
nodes.pop_back();
continue;
}
unsigned nc = 1;
bool all_p = true;
for (edge_id e : g.get_out_edges(v)) {
if (is_strict_neighbour_edge(g, e)) {
dl_var dst = g.get_target(e);
TRACE("special_relations", tout << v << " -> " << dst << "\n";);
if (!processed[dst]) {
all_p = false;
nodes.push_back(dst);
}
nc += num_children[dst];
}
}
if (all_p) {
nodes.pop_back();
num_children[v] = nc;
processed[v] = true;
}
}
TRACE("special_relations",
for (unsigned i = 0; i < sz; ++i) {
tout << i << ": " << num_children[i] << "\n";
});
}
void theory_special_relations::assign_interval(graph const& g, unsigned_vector const& num_children, unsigned_vector& lo, unsigned_vector& hi) {
svector<dl_var> nodes;
unsigned sz = g.get_num_nodes();
lo.resize(sz, 0);
hi.resize(sz, 0);
unsigned offset = 0;
for (unsigned i = 0; i < sz; ++i) {
bool is_root = true;
int_vector const& edges = g.get_in_edges(i);
for (edge_id e_id : edges) {
is_root &= !g.is_enabled(e_id);
}
if (is_root) {
lo[i] = offset;
hi[i] = offset + num_children[i] - 1;
offset = hi[i] + 1;
nodes.push_back(i);
}
}
while (!nodes.empty()) {
dl_var v = nodes.back();
int_vector const& edges = g.get_out_edges(v);
unsigned l = lo[v];
unsigned h = hi[v];
(void)h;
nodes.pop_back();
for (unsigned i = 0; i < edges.size(); ++i) {
SASSERT(l <= h);
if (is_strict_neighbour_edge(g, edges[i])) {
dl_var dst = g.get_target(edges[i]);
lo[dst] = l;
hi[dst] = l + num_children[dst] - 1;
l = hi[dst] + 1;
nodes.push_back(dst);
}
}
SASSERT(l == h);
}
}
void theory_special_relations::init_model(model_generator & m) {
for (auto const& kv : m_relations) {
switch (kv.m_value->m_property) {
case sr_lo:
init_model_lo(*kv.m_value, m);
break;
case sr_plo:
init_model_plo(*kv.m_value, m);
break;
case sr_to:
init_model_to(*kv.m_value, m);
break;
case sr_po:
init_model_po(*kv.m_value, m, true);
break;
case sr_tc:
init_model_po(*kv.m_value, m, true);
break;
default:
// other 28 combinations of 0x1F
NOT_IMPLEMENTED_YET();
}
}
}
void theory_special_relations::display(std::ostream & out) const {
if (m_relations.empty()) return;
out << "Theory Special Relations\n";
display_var2enode(out);
for (auto const& kv : m_relations) {
kv.m_value->display(*this, out);
}
}
void theory_special_relations::collect_asserted_po_atoms(vector<std::pair<bool_var, bool>>& atoms) const {
for (auto const& kv : m_relations) {
relation& r = *kv.m_value;
if (r.m_property != sr_po) continue;
for (atom* ap : r.m_asserted_atoms) {
atoms.push_back(std::make_pair(ap->var(), ap->phase()));
}
}
}
void theory_special_relations::display_atom(std::ostream & out, atom& a) const {
expr* e = ctx.bool_var2expr(a.var());
out << (a.phase() ? "" : "(not ") << mk_pp(e, get_manager()) << (a.phase() ? "" : ")") << "\n";
}
}