z3-z3-4.13.0.src.tactic.fd_solver.smtfd_solver.cpp Maven / Gradle / Ivy
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/**
F1, F2, .., -> Fa1, Fa2, ...
assert incrementally:
t1 <-> Fa1
t2 <-> Fa2 & t1
....
abstraction replaces subterms that are not bv constants
by atomic formulas or a term of the form:
xor(random_bv, fresh_bv_variable) of enough (24) bits
Then default assignment to the fresh bv variable (to 0)
is hashed to a value that is likely different form other variables
of the same type, so two variables of the same type are then most
likely equal in a model if they have to be.
atoms := list of atomic formulas (including equalities over bit-vectors)
while True:
r = check_sat([t_k])
if r != sat:
return r
M = current model
literals := evaluation of atoms under M
r = check_sat([!t_k] + literals)
if r != unsat:
return unknown
core = rep(some unsat_core excluding !t_k)
if core is SAT modulo A + UF + other theories:
return SAT
optionally apply a step of superposition (reduce congruence and equality diamonds):
let t1 = t2, core1 := core, where t1 in core1
- t1 is uninterpreted constant
core := replace t1 by t2 in core1
- t1 = f(args):
core := replace all occurrences of t1' by t2 in core1 where M(abs(t1)) = M(abs(t1')).
- t1 = select(A,args)?
when is it safe to reduce t1?
for t in subterms(core) where t is f(args):
v1 := M(abs(t))
v_args = M(abs(args))
v2, t2 := table[f][v_args]
if v2 != null and v1 != v2:
lemmas += (args = t2.args => t = t2)
else:
table[f][v_args] := v1, t
for t in subterms((core) where t is select(A, args):
vA := M(abs(A))
v_args = M(abs(args))
v2, args2, t2 := table[vA][v_args]
if v2 != null and v1 != v2:
lemmas += (args1 = args2 => t = t2)
else:
table[vA][v_args] := v1, args, t
for t in subterms(core) where t is store(A, args, b):
vT := M(abs(t))
vA := M(abs(A))
vB := M(abs(b))
v2, args2, t2 := table[vT][v_args]
if v2 != null and vB != v2:
lemmas += (select(t, args) = b)
if v2 = null:
table[vT][v_args] := vB, args, t
for v_args2 |-> v2, args2, t2 in table[vA]:
check table[vT][v_args2] for compatibility with v2
if not compatible:
lemmas += (args2 != args => select(t, args2) = select(A, args2))
for v_args2 |-> v2, args2, t2 in table[tA]:
check table[vA][v_args2] for compatibility with v2
if not compatible:
lemmas += (args2 != args => select(t, args2) = select(A, args2))
for t in subterms(core) where t is (lambda x . M), t is ground:
vT := M(abs(t))
for v_args2 |-> v2, args2, t2 in table[vT]:
v1 := M(abs(M[args2/x]))
if v1 != v2:
lemmas += (select(t2, args2) = M[args2/x])
for t in subterms(core) where t is map(f, A, B, C), t is const:
similar to lambda
for A, B in array_terms(core):
lemmas += (select(A, delta(A,B)) = select(B, delta(A,B)) => A = B)
if AUF solver returned unsat:
add abs(!core) to solver
add abs(lemmas) to solver
Note:
- hint to SMT solver using FD model (add equalities from FD model)
- abstractions for multiplication and other BV operations:
- add ackerman reductions for BV
- commutativity?
- fix most bits using model, blast specialization.
Z = X * Y
X[range] = k1, Y[range] = k2 => Z = (k1++X') * (k2 ++ Y')
- abstract also equality
- add triangle lemmas whenever using equality chaining in lemmas.
- add equality resolution lemmas
For core: v = t & phi(v)
and v = t occurs in several cores
set core := phi(t/v)
- do something about arithmetic?
*/
#include "util/scoped_ptr_vector.h"
#include "util/obj_hashtable.h"
#include "util/obj_pair_hashtable.h"
#include "ast/ast_util.h"
#include "ast/ast_pp.h"
#include "ast/ast_ll_pp.h"
#include "ast/for_each_expr.h"
#include "ast/pb_decl_plugin.h"
#include "ast/rewriter/th_rewriter.h"
#include "ast/rewriter/var_subst.h"
#include "tactic/tactic_exception.h"
#include "tactic/fd_solver/fd_solver.h"
#include "solver/solver.h"
#include "solver/solver_na2as.h"
#include "solver/solver2tactic.h"
namespace smtfd {
struct stats {
unsigned m_num_lemmas;
unsigned m_num_rounds;
unsigned m_num_mbqi;
unsigned m_num_fresh_bool;
stats() { memset(this, 0, sizeof(stats)); }
};
class smtfd_abs {
ast_manager& m;
stats& m_stats;
expr_ref_vector m_abs, m_rep, m_atoms, m_atom_defs; // abstraction and representation maps
array_util m_autil;
bv_util m_butil;
pb_util m_pb;
ptr_vector m_args, m_todo;
unsigned m_nv;
unsigned_vector m_abs_trail, m_rep_trail, m_nv_trail;
unsigned_vector m_abs_lim, m_rep_lim, m_atoms_lim;
random_gen m_rand;
void pop(unsigned n, expr_ref_vector& v, unsigned_vector& trail, unsigned_vector& lim) {
SASSERT(n > 0);
unsigned sz = lim[lim.size() - n];
for (unsigned i = trail.size(); i-- > sz;) {
v[trail[i]] = nullptr;
}
trail.shrink(sz);
lim.shrink(lim.size() - n);
}
expr* try_abs(expr* e) { return m_abs.get(e->get_id(), nullptr); }
expr* try_rep(expr* e) { return m_rep.get(e->get_id(), nullptr); }
expr* fresh_var(expr* t) {
symbol name = is_app(t) ? to_app(t)->get_name() : (is_quantifier(t) ? symbol("Q") : symbol("X"));
if (m.is_bool(t)) {
++m_stats.m_num_fresh_bool;
return m.mk_fresh_const(name, m.mk_bool_sort());
}
else if (m_butil.is_bv(t)) {
return m.mk_fresh_const(name, t->get_sort());
}
else {
++m_nv;
unsigned bw = log2(m_nv) + 1;
if (bw >= 24) {
throw default_exception("number of allowed bits for variables exceeded");
}
unsigned n = (m_rand() << 16) | m_rand();
expr* num = m_butil.mk_numeral(n, bw);
expr* es[2] = { num, m.mk_fresh_const(name, m_butil.mk_sort(bw)) };
expr* e = m_butil.mk_bv_xor(2, es);
return m_butil.mk_concat(e, m_butil.mk_numeral(0, 24 - bw));
}
}
void push_trail(expr_ref_vector& map, unsigned_vector& trail, expr* t, expr* r) {
unsigned idx = t->get_id();
map.reserve(idx + 1);
map.set(idx, r);
trail.push_back(idx);
}
bool is_atom(expr* r) {
if (!m.is_bool(r)) {
return false;
}
if (m.is_eq(r) && !m.is_bool(to_app(r)->get_arg(0))) {
return true;
}
return !is_app(r) || to_app(r)->get_family_id() != m.get_basic_family_id();
}
bool is_uninterp_atom(expr* a) {
return is_app(a) && to_app(a)->get_num_args() == 0 && to_app(a)->get_family_id() == null_family_id;
}
public:
smtfd_abs(ast_manager& m, stats& s):
m(m),
m_stats(s),
m_abs(m),
m_rep(m),
m_atoms(m),
m_atom_defs(m),
m_autil(m),
m_butil(m),
m_pb(m),
m_nv(0)
{
abs(m.mk_true());
abs(m.mk_false());
}
expr_ref_vector const& atoms() {
return m_atoms;
}
expr_ref_vector const& atom_defs() {
return m_atom_defs;
}
void reset_atom_defs() {
m_atom_defs.reset();
}
void push() {
m_abs_lim.push_back(m_abs_trail.size());
m_rep_lim.push_back(m_rep_trail.size());
m_atoms_lim.push_back(m_atoms.size());
m_nv_trail.push_back(m_nv);
}
void pop(unsigned n) {
pop(n, m_abs, m_abs_trail, m_abs_lim);
pop(n, m_rep, m_rep_trail, m_rep_lim);
m_atoms.shrink(m_atoms_lim[m_atoms_lim.size() - n]);
m_atoms_lim.shrink(m_atoms_lim.size() - n);
m_nv = m_nv_trail[m_nv_trail.size() - n];
m_nv_trail.shrink(m_nv_trail.size() - n);
}
std::ostream& display(std::ostream& out) {
out << "abs: " << m_atoms.size() << "\n";
for (expr* a : m_atoms) {
out << mk_pp(a, m) << ": ";
out << mk_bounded_pp(rep(a), m, 2) << "\n";
}
return out;
}
expr* abs_assumption(expr* e) {
expr* a = abs(e), *b = nullptr;
if (is_uninterp_atom(a) || (m.is_not(a, b) && is_uninterp_atom(b))) {
return a;
}
expr* f = fresh_var(e);
push_trail(m_abs, m_abs_trail, e, f);
push_trail(m_rep, m_rep_trail, f, e);
m_atoms.push_back(f);
m_atom_defs.push_back(m.mk_iff(f, a));
return f;
}
expr* abs(expr* e) {
expr* r = try_abs(e);
if (r) return r;
m_todo.push_back(e);
family_id bvfid = m_butil.get_fid();
family_id bfid = m.get_basic_family_id();
family_id pbfid = m_pb.get_family_id();
while (!m_todo.empty()) {
expr* t = m_todo.back();
r = try_abs(t);
if (r) {
m_todo.pop_back();
continue;
}
if (is_app(t)) {
app* a = to_app(t);
m_args.reset();
for (expr* arg : *a) {
r = try_abs(arg);
if (r) {
m_args.push_back(r);
}
else {
m_todo.push_back(arg);
}
}
if (m_args.size() != a->get_num_args()) {
continue;
}
family_id fid = a->get_family_id();
if (m.is_eq(a)) {
r = m.mk_eq(m_args.get(0), m_args.get(1));
}
else if (m.is_distinct(a)) {
r = m.mk_distinct(m_args.size(), m_args.data());
}
else if (m.is_ite(a)) {
r = m.mk_ite(m_args.get(0), m_args.get(1), m_args.get(2));
}
else if (bvfid == fid || bfid == fid || pbfid == fid) {
r = m.mk_app(a->get_decl(), m_args.size(), m_args.data());
}
else if (is_uninterp_const(t) && m.is_bool(t)) {
r = t;
}
else if (is_uninterp_const(t) && m_butil.is_bv(t)) {
r = t;
}
else if (m.is_model_value(t)) {
int idx = a->get_parameter(0).get_int();
r = m_butil.mk_numeral(rational(idx), 24);
}
else {
r = fresh_var(t);
}
}
else {
r = fresh_var(t);
}
if (is_atom(r) && !is_uninterp_const(r)) {
expr* rr = fresh_var(r);
m_atom_defs.push_back(m.mk_iff(rr, r));
r = rr;
}
push_trail(m_abs, m_abs_trail, t, r);
push_trail(m_rep, m_rep_trail, r, t);
if (t != r) {
push_trail(m_abs, m_abs_trail, r, r);
}
if (is_atom(r)) {
m_atoms.push_back(r);
}
}
return try_abs(e);
}
expr* rep(expr* e) {
expr* r = try_rep(e);
if (r) return r;
VERIFY(m.is_not(e, r));
r = try_rep(r);
r = m.mk_not(r);
abs(r);
return r;
}
};
struct f_app {
ast* m_f;
app* m_t;
sort* m_s;
unsigned m_val_offset;
};
class theory_plugin;
class plugin_context {
ast_manager& m;
smtfd_abs& m_abs;
expr_ref_vector m_lemmas;
unsigned m_max_lemmas;
th_rewriter m_rewriter;
ptr_vector m_plugins;
model_ref m_model;
public:
plugin_context(smtfd_abs& a, ast_manager& m):
m(m),
m_abs(a),
m_lemmas(m),
m_rewriter(m)
{
}
void set_max_lemmas(unsigned max) {
m_max_lemmas = max;
}
unsigned get_max_lemmas() const { return m_max_lemmas; }
smtfd_abs& get_abs() { return m_abs; }
void add(expr* f, char const* msg) { m_lemmas.push_back(f); TRACE("smtfd", tout << msg << " " << mk_bounded_pp(f, m, 2) << "\n";); }
ast_manager& get_manager() { return m; }
bool at_max() const { return m_lemmas.size() >= m_max_lemmas; }
model& get_model() { return *m_model; }
expr_ref_vector::iterator begin() { return m_lemmas.begin(); }
expr_ref_vector::iterator end() { return m_lemmas.end(); }
unsigned size() const { return m_lemmas.size(); }
bool empty() const { return m_lemmas.empty(); }
void reset_lemmas() { m_lemmas.reset(); }
void add_plugin(theory_plugin* p) { m_plugins.push_back(p); }
expr_ref model_value(expr* t);
expr_ref model_value(sort* s);
bool term_covered(expr* t);
bool sort_covered(sort* s);
void reset(model_ref& mdl);
void rewrite(expr_ref& r) { m_rewriter(r); }
/**
* \brief use propositional model to create a model of uninterpreted functions
*/
void populate_model(model_ref& mdl, expr_ref_vector const& terms);
/**
* \brief check consistency properties that can only be achieved using a global analysis of terms
*/
void global_check(expr_ref_vector const& core);
/**
* \brief add theory axioms that are violdated in the current model
* the round indicator is used to prioritize "cheap" axioms before
* expensive axiom instantiation.
*/
bool add_theory_axioms(expr_ref_vector const& core, unsigned round);
std::ostream& display(std::ostream& out);
};
struct f_app_eq {
theory_plugin& p;
f_app_eq(theory_plugin& p):p(p) {}
bool operator()(f_app const& a, f_app const& b) const;
};
struct f_app_hash {
theory_plugin& p;
f_app_hash(theory_plugin& p):p(p) {}
unsigned operator()(f_app const& a) const;
unsigned operator()(expr* const* args) const { return 14; }
unsigned operator()(expr* const* args, unsigned idx) const { return args[idx]->hash(); }
};
class theory_plugin {
protected:
typedef hashtable table;
ast_manager& m;
smtfd_abs& m_abs;
plugin_context& m_context;
expr_ref_vector m_values;
ast_ref_vector m_pinned;
expr_ref_vector m_args, m_vargs;
f_app_eq m_eq;
f_app_hash m_hash;
scoped_ptr_vector m_tables;
obj_pair_map m_ast2table;
f_app mk_app(ast* f, app* t, sort* s) {
f_app r;
r.m_f = f;
r.m_val_offset = m_values.size();
r.m_t = t;
r.m_s = s;
for (expr* arg : *t) {
m_values.push_back(eval_abs(arg));
}
m_values.push_back(eval_abs(t));
return r;
}
f_app const& insert(f_app const& f) {
return ast2table(f.m_f, f.m_s).insert_if_not_there(f);
}
public:
theory_plugin(plugin_context& context) :
m(context.get_manager()),
m_abs(context.get_abs()),
m_context(context),
m_values(m),
m_pinned(m),
m_args(m),
m_vargs(m),
m_eq(*this),
m_hash(*this)
{
m_context.add_plugin(this);
}
virtual ~theory_plugin() = default;
table& ast2table(ast* f, sort* s) {
unsigned idx = 0;
if (!m_ast2table.find(f, s, idx)) {
idx = m_tables.size();
m_tables.push_back(alloc(table, DEFAULT_HASHTABLE_INITIAL_CAPACITY, m_hash, m_eq));
m_ast2table.insert(f, s, idx);
m_pinned.push_back(f);
}
return *m_tables[idx];
}
expr_ref_vector const& values() const { return m_values; }
ast_manager& get_manager() { return m; }
expr_ref eval_abs(expr* t) { return m_context.get_model()(m_abs.abs(t)); }
bool is_true_abs(expr* t) { return m_context.get_model().is_true(m_abs.abs(t)); }
expr* value_of(f_app const& f) const { return m_values[f.m_val_offset + f.m_t->get_num_args()]; }
bool check_congruence(ast* f, app* t, sort* s) {
f_app f1 = mk_app(f, t, s);
f_app const& f2 = insert(f1);
if (f2.m_val_offset == f1.m_val_offset) {
return true;
}
bool eq = value_of(f1) == value_of(f2);
m_values.shrink(f1.m_val_offset);
return eq;
}
void enforce_congruence(ast* f, app* t, sort* s) {
f_app f1 = mk_app(f, t, s);
f_app const& f2 = insert(f1);
if (f2.m_val_offset == f1.m_val_offset) {
TRACE("smtfd_verbose", tout << "fresh: " << mk_pp(f, m, 2) << "\n";);
return;
}
bool eq = value_of(f1) == value_of(f2);
m_values.shrink(f1.m_val_offset);
if (eq) {
TRACE("smtfd_verbose", tout << "eq: " << " " << mk_bounded_pp(t, m, 2) << " " << mk_bounded_pp(f2.m_t, m, 2) << "\n";);
return;
}
m_args.reset();
SASSERT(t->get_num_args() == f1.m_t->get_num_args());
SASSERT(t->get_num_args() == f2.m_t->get_num_args());
for (unsigned i = 0; i < t->get_num_args(); ++i) {
expr* e1 = f1.m_t->get_arg(i);
expr* e2 = f2.m_t->get_arg(i);
if (e1 != e2) m_args.push_back(m.mk_eq(e1, e2));
}
TRACE("smtfd_verbose", tout << "diff: " << mk_bounded_pp(f1.m_t, m, 2) << " " << mk_bounded_pp(f2.m_t, m, 2) << "\n";);
m_context.add(m.mk_implies(mk_and(m_args), m.mk_eq(f1.m_t, f2.m_t)), __FUNCTION__);
}
std::ostream& display(std::ostream& out) {
for (table* tb : m_tables) {
display(out, *tb);
}
return out;
}
std::ostream& display(std::ostream& out, table& t) {
out << "table\n";
for (auto const& k : t) {
out << "key: " << mk_bounded_pp(k.m_f, m, 2) << "\nterm: " << mk_bounded_pp(k.m_t, m, 2) << "\n";
out << "args:\n";
for (unsigned i = 0; i <= k.m_t->get_num_args(); ++i) {
out << mk_bounded_pp(m_values.get(k.m_val_offset + i), m, 3) << "\n";
}
out << "\n";
}
return out;
}
expr_ref model_value(expr* t) { return m_context.model_value(t); }
expr_ref model_value(sort* s) { return m_context.model_value(s); }
virtual void global_check(expr_ref_vector const& core) {}
virtual void check_term(expr* t, unsigned round) = 0;
virtual expr_ref model_value_core(expr* t) = 0;
virtual expr_ref model_value_core(sort* s) = 0;
virtual bool term_covered(expr* t) = 0;
virtual bool sort_covered(sort* s) = 0;
virtual unsigned max_rounds() = 0;
virtual void populate_model(model_ref& mdl, expr_ref_vector const& terms) {}
virtual void reset() {
m_pinned.reset();
m_tables.reset();
m_ast2table.reset();
m_values.reset();
}
};
void plugin_context::global_check(expr_ref_vector const& core) {
for (theory_plugin* p : m_plugins) {
p->global_check(core);
}
}
bool plugin_context::add_theory_axioms(expr_ref_vector const& core, unsigned round) {
unsigned max_rounds = 0;
for (theory_plugin* p : m_plugins) {
max_rounds = std::max(max_rounds, p->max_rounds());
}
if (max_rounds < round) {
return false;
}
else if (round < max_rounds) {
for (expr* t : subterms::ground(core)) {
for (theory_plugin* p : m_plugins) {
p->check_term(t, round);
}
}
}
else if (round == max_rounds) {
global_check(core);
}
return true;
}
expr_ref plugin_context::model_value(expr* t) {
expr_ref r(get_manager());
for (theory_plugin* p : m_plugins) {
r = p->model_value_core(t);
if (r) break;
}
return r;
}
expr_ref plugin_context::model_value(sort* s) {
expr_ref r(get_manager());
for (theory_plugin* p : m_plugins) {
r = p->model_value_core(s);
if (r) break;
}
return r;
}
void plugin_context::reset(model_ref& mdl) {
m_lemmas.reset();
m_model = mdl;
for (theory_plugin* p : m_plugins) {
p->reset();
}
}
bool plugin_context::sort_covered(sort* s) {
for (theory_plugin* p : m_plugins) {
if (p->sort_covered(s)) return true;
}
return false;
}
bool plugin_context::term_covered(expr* t) {
for (theory_plugin* p : m_plugins) {
if (p->term_covered(t)) return true;
}
return false;
}
std::ostream& plugin_context::display(std::ostream& out) {
for (theory_plugin* p : m_plugins) {
p->display(out);
}
return out;
}
void plugin_context::populate_model(model_ref& mdl, expr_ref_vector const& terms) {
for (theory_plugin* p : m_plugins) {
p->populate_model(mdl, terms);
}
}
bool f_app_eq::operator()(f_app const& a, f_app const& b) const {
if (a.m_f != b.m_f)
return false;
for (unsigned i = 0; i < a.m_t->get_num_args(); ++i) {
if (p.values().get(a.m_val_offset+i) != p.values().get(b.m_val_offset+i))
return false;
if (a.m_t->get_arg(i)->get_sort() != b.m_t->get_arg(i)->get_sort())
return false;
}
return true;
}
unsigned f_app_hash::operator()(f_app const& a) const {
return get_composite_hash(p.values().data() + a.m_val_offset, a.m_t->get_num_args(), *this, *this);
}
class basic_plugin : public theory_plugin {
public:
basic_plugin(plugin_context& context):
theory_plugin(context)
{}
void check_term(expr* t, unsigned round) override { }
bool term_covered(expr* t) override { return is_app(t) && to_app(t)->get_family_id() == m.get_basic_family_id(); }
bool sort_covered(sort* s) override { return m.is_bool(s); }
unsigned max_rounds() override { return 0; }
void populate_model(model_ref& mdl, expr_ref_vector const& terms) override { }
expr_ref model_value_core(expr* t) override { return m.is_bool(t) ? m_context.get_model()(m_abs.abs(t)) : expr_ref(m); }
expr_ref model_value_core(sort* s) override { return m.is_bool(s) ? expr_ref(m.mk_false(), m) : expr_ref(m); }
};
class pb_plugin : public theory_plugin {
pb_util m_pb;
public:
pb_plugin(plugin_context& context):
theory_plugin(context),
m_pb(m)
{}
void check_term(expr* t, unsigned round) override { }
bool term_covered(expr* t) override { return is_app(t) && to_app(t)->get_family_id() == m_pb.get_family_id(); }
bool sort_covered(sort* s) override { return m.is_bool(s); }
unsigned max_rounds() override { return 0; }
void populate_model(model_ref& mdl, expr_ref_vector const& terms) override { }
expr_ref model_value_core(expr* t) override { return expr_ref(m); }
expr_ref model_value_core(sort* s) override { return expr_ref(m); }
};
class bv_plugin : public theory_plugin {
bv_util m_butil;
public:
bv_plugin(plugin_context& context):
theory_plugin(context),
m_butil(m)
{}
void check_term(expr* t, unsigned round) override { }
bool term_covered(expr* t) override { return is_app(t) && to_app(t)->get_family_id() == m_butil.get_family_id(); }
bool sort_covered(sort* s) override { return m_butil.is_bv_sort(s); }
unsigned max_rounds() override { return 0; }
void populate_model(model_ref& mdl, expr_ref_vector const& terms) override { }
expr_ref model_value_core(expr* t) override { return m_butil.is_bv(t) ? m_context.get_model()(m_abs.abs(t)) : expr_ref(m); }
expr_ref model_value_core(sort* s) override { return m_butil.is_bv_sort(s) ? expr_ref(m_butil.mk_numeral(rational(0), s), m) : expr_ref(m); }
};
class uf_plugin : public theory_plugin {
obj_map m_sort2idx;
typedef obj_map val2elem_t;
scoped_ptr_vector m_val2elem;
val2elem_t& get_table(sort* s) {
unsigned idx = 0;
if (!m_sort2idx.find(s, idx)) {
idx = m_val2elem.size();
m_sort2idx.insert(s, idx);
m_val2elem.push_back(alloc(val2elem_t));
}
return *m_val2elem[idx];
}
bool is_uf(expr* t) {
return is_app(t) && to_app(t)->get_family_id() == null_family_id && to_app(t)->get_num_args() > 0;
}
val2elem_t& ensure_table(sort* s) {
val2elem_t& v2e = get_table(s);
if (v2e.empty()) {
v2e.insert(m.mk_true(), nullptr);
}
ptr_vector keys, values;
for (auto const& kv : v2e) {
if (kv.m_value) return v2e;
keys.push_back(kv.m_key);
values.push_back(m.mk_model_value(values.size(), s));
m_pinned.push_back(values.back());
}
m_context.get_model().register_usort(s, values.size(), values.data());
for (unsigned i = 0; i < keys.size(); ++i) {
v2e.insert(keys[i], values[i]);
}
return v2e;
}
public:
uf_plugin(plugin_context& context):
theory_plugin(context)
{}
void check_term(expr* t, unsigned round) override {
sort* s = t->get_sort();
if (round == 0 && is_uf(t)) {
TRACE("smtfd_verbose", tout << "check-term: " << mk_bounded_pp(t, m, 2) << "\n";);
enforce_congruence(to_app(t)->get_decl(), to_app(t), s);
}
else if (round == 1 && sort_covered(s) && m.is_value(t)) {
expr_ref v = eval_abs(t);
val2elem_t& v2e = get_table(s);
expr* e;
if (v2e.find(v, e) && e != t && m.is_value(e)) {
m_context.add(m.mk_not(m.mk_eq(e, t)), __FUNCTION__);
}
else {
m_pinned.push_back(v);
v2e.insert(v, t);
}
}
if (m.is_model_value(t)) {
//std::cout << "model value: " << mk_bounded_pp(t, m, 2) << " " << eval_abs(t) << " " << mk_pp(s, m) << "\n";
}
}
bool term_covered(expr* t) override {
sort* s = t->get_sort();
if (sort_covered(s)) {
val2elem_t& v2e = get_table(s);
expr_ref v = eval_abs(t);
if (!v2e.contains(v)) {
m_pinned.push_back(v);
v2e.insert(v, nullptr);
}
}
check_term(t, 0);
return is_uf(t) || is_uninterp_const(t) || sort_covered(s);
}
bool sort_covered(sort* s) override {
return s->get_family_id() == m.get_user_sort_family_id();
}
void reset() override {
theory_plugin::reset();
for (auto& v2e : m_val2elem) {
v2e->reset();
}
}
unsigned max_rounds() override { return 1; }
void populate_model(model_ref& mdl, expr_ref_vector const& terms) override {
expr_ref_vector args(m);
for (table* tb : m_tables) {
func_interp* fi = nullptr;
func_decl* fn = nullptr;
for (f_app const& f : *tb) {
fn = to_func_decl(f.m_f);
unsigned arity = fn->get_arity();
if (!fi) {
fi = alloc(func_interp, m, arity);
}
args.reset();
for (expr* arg : *f.m_t) {
args.push_back(model_value(arg));
}
expr_ref val = model_value(f.m_t);
TRACE("smtfd_verbose", tout << mk_bounded_pp(f.m_t, m, 2) << " := " << val << "\n";);
fi->insert_new_entry(args.data(), val);
}
mdl->register_decl(fn, fi);
}
for (expr* t : subterms::ground(terms)) {
if (is_uninterp_const(t) && sort_covered(t->get_sort())) {
expr_ref val = model_value(t);
mdl->register_decl(to_app(t)->get_decl(), val);
}
}
}
expr_ref model_value_core(expr* t) override {
sort* s = t->get_sort();
if (sort_covered(s)) {
auto& v2e = ensure_table(s);
return expr_ref(v2e[eval_abs(t)], m);
}
return expr_ref(m);
}
expr_ref model_value_core(sort* s) override {
if (sort_covered(s)) {
auto& v2e = ensure_table(s);
return expr_ref(v2e.begin()->m_value, m);
}
return expr_ref(m);
}
};
class ar_plugin : public theory_plugin {
array_util m_autil;
unsigned_vector m_num_stores;
// count number of equivalent stores
void update_lambda(expr* t) {
if (m_autil.is_store(t)) {
expr_ref tV = eval_abs(t);
inc_lambda(tV);
}
}
unsigned get_lambda(expr* tV) {
unsigned id = tV->get_id();
if (id >= m_num_stores.size()) {
m_num_stores.resize(id + 1, 0);
}
return m_num_stores[id];
}
void inc_lambda(expr* tV) {
unsigned id = tV->get_id();
if (id >= m_num_stores.size()) {
m_num_stores.resize(id + 1, 0);
}
if (0 == m_num_stores[id]++) {
m_pinned.push_back(tV);
}
}
void insert_select(app* t) {
expr* a = t->get_arg(0);
expr_ref vA = eval_abs(a);
check_congruence(vA, t, a->get_sort());
}
void check_select(app* t) {
expr* a = t->get_arg(0);
expr_ref vA = eval_abs(a);
TRACE("smtfd", tout << mk_bounded_pp(t, m, 2) << "\n";);
enforce_congruence(vA, t, a->get_sort());
}
// check that (select(t, t.args) = t.value)
void check_store0(app * t) {
SASSERT(m_autil.is_store(t));
m_args.reset();
m_args.push_back(t);
for (unsigned i = 1; i + 1 < t->get_num_args(); ++i) {
m_args.push_back(t->get_arg(i));
}
app_ref sel(m_autil.mk_select(m_args), m);
expr* stored_value = t->get_arg(t->get_num_args()-1);
expr_ref val1 = eval_abs(sel);
expr_ref val2 = eval_abs(stored_value);
// A[i] = v
if (val1 != val2) {
TRACE("smtfd", tout << "select/store: " << mk_bounded_pp(t, m, 2) << "\n";);
m_context.add(m.mk_eq(sel, stored_value), __FUNCTION__);
m_pinned.push_back(sel);
insert_select(sel);
}
}
// store(A, i, v)[j] = A[i] or i = j
void check_select_store(app * t) {
SASSERT(m_autil.is_select(t));
if (!m_autil.is_store(t->get_arg(0))) {
return;
}
app* store = to_app(t->get_arg(0));
expr* val = store->get_arg(store->get_num_args()-1);
expr* a = store->get_arg(0);
expr_ref_vector eqs(m);
m_args.reset();
m_args.push_back(a);
for (unsigned i = 1; i < t->get_num_args(); ++i) {
expr* arg1 = t->get_arg(i);
expr* arg2 = store->get_arg(i);
m_args.push_back(arg1);
if (arg1 == arg2) {
// skip
}
else if (m.are_distinct(arg1, arg2)) {
eqs.push_back(m.mk_false());
}
else {
eqs.push_back(m.mk_eq(arg1, arg2));
}
}
//if (eqs.empty()) return;
expr_ref eq = mk_and(eqs);
expr_ref eqV = eval_abs(eq);
expr_ref val1 = eval_abs(t);
expr_ref val2 = eval_abs(val);
if (val1 != val2 && !m.is_false(eqV)) {
m_context.add(m.mk_implies(mk_and(eqs), m.mk_eq(t, val)), __FUNCTION__);
}
app_ref sel(m_autil.mk_select(m_args), m);
val2 = eval_abs(sel);
if (val1 != val2 && !m.is_true(eqV)) {
TRACE("smtfd", tout << "select/store: " << mk_bounded_pp(t, m, 2) << "\n";);
m_context.add(m.mk_or(m.mk_eq(sel, t), mk_and(eqs)), __FUNCTION__);
m_pinned.push_back(sel);
insert_select(sel);
}
}
/**
every t and a must agree with select values that
are different from updates in t.
let t := store(B, i, v)
add axioms of the form:
i = j or A != B or store(B,i,v)[j] = A[j]
where j is in tableA and value equal to some index in tableT
*/
void check_store2(app* t) {
SASSERT(m_autil.is_store(t));
expr* arg = t->get_arg(0);
expr_ref vT = eval_abs(t);
expr_ref vA = eval_abs(arg);
table& tT = ast2table(vT, t->get_sort()); // select table of t
table& tA = ast2table(vA, arg->get_sort()); // select table of arg
if (vT == vA) {
return;
}
m_vargs.reset();
for (unsigned i = 0; i + 1 < t->get_num_args(); ++i) {
m_vargs.push_back(eval_abs(t->get_arg(i)));
}
reconcile_stores(t, vT, tT, vA, tA);
}
//
// T = store(A, i, v)
// T[j] = w: i = j or A[j] = T[j]
// A[j] = w: i = j or T[j] = A[j]
//
void reconcile_stores(app* t, expr* vT, table& tT, expr* vA, table& tA) {
inc_lambda(vT);
for (auto& fA : tA) {
f_app fT;
if (m_context.at_max()) {
break;
}
if (t->get_sort() != fA.m_t->get_arg(0)->get_sort()) {
continue;
}
if (!tT.find(fA, fT) || (value_of(fA) != value_of(fT) && !eq(m_vargs, fA))) {
add_select_store_axiom(t, fA);
}
}
}
void add_select_store_axiom(app* t, f_app& f) {
SASSERT(m_autil.is_store(t));
expr* a = t->get_arg(0);
m_args.reset();
for (expr* arg : *f.m_t) {
m_args.push_back(arg);
}
SASSERT(t->get_sort() == a->get_sort());
TRACE("smtfd", tout << mk_bounded_pp(t, m, 2) << " " << mk_bounded_pp(f.m_t, m, 2) << "\n";);
expr_ref eq = mk_eq_idxs(t, f.m_t);
m_args[0] = t;
expr_ref sel1(m_autil.mk_select(m_args), m);
m_args[0] = a;
expr_ref sel2(m_autil.mk_select(m_args), m);
expr_ref fml(m.mk_or(eq, m.mk_eq(sel1, sel2)), m);
if (!is_true_abs(fml)) {
m_context.add(fml, __FUNCTION__);
}
}
bool same_array_sort(f_app const& fA, f_app const& fT) const {
return fA.m_t->get_arg(0)->get_sort() == fT.m_t->get_arg(0)->get_sort();
}
/**
Enforce M[x] == rewrite(M[x]) for every A[x] such that M = A under current model.
*/
void beta_reduce(expr* t) {
if (m_autil.is_map(t) ||
m_autil.is_const(t) ||
is_lambda(t)) {
expr_ref vT = eval_abs(t);
table& tT = ast2table(vT, t->get_sort());
for (f_app & f : tT) {
if (t->get_sort() != f.m_t->get_arg(0)->get_sort())
continue;
if (m_context.at_max())
break;
m_args.reset();
m_args.append(f.m_t->get_num_args(), f.m_t->get_args());
m_args[0] = t;
expr_ref sel(m_autil.mk_select(m_args), m);
expr_ref selr = sel;
m_context.rewrite(selr);
expr_ref vS = eval_abs(sel);
expr_ref vR = eval_abs(selr);
if (vS != vR) {
m_context.add(m.mk_eq(sel, selr), __FUNCTION__);
}
}
}
}
// arguments, except for array variable are equal.
bool eq(expr_ref_vector const& args, f_app const& f) {
SASSERT(args.size() == f.m_t->get_num_args());
for (unsigned i = args.size(); i-- > 1; ) {
if (args.get(i) != m_values.get(f.m_val_offset + i))
return false;
}
return true;
}
expr_ref mk_eq_idxs(app* t, app* s) {
SASSERT(m_autil.is_store(t));
SASSERT(m_autil.is_select(s));
expr_ref_vector r(m);
for (unsigned i = 1; i < s->get_num_args(); ++i) {
r.push_back(m.mk_eq(t->get_arg(i), s->get_arg(i)));
}
return mk_and(r);
}
bool same_table(table const& t1, table const& t2) {
if (t1.size() != t2.size()) {
return false;
}
for (f_app const& f1 : t1) {
f_app f2;
if (!t2.find(f1, f2) || value_of(f1) != value_of(f2)) {
return false;
}
}
return true;
}
bool same_table(expr* v1, sort* s1, expr* v2, sort* s2) {
return same_table(ast2table(v1, s1), ast2table(v2, s2));
}
void enforce_extensionality(expr* a, expr* b) {
sort* s = a->get_sort();
unsigned arity = get_array_arity(s);
expr_ref_vector args(m);
args.push_back(a);
for (unsigned i = 0; i < arity; ++i) {
args.push_back(m.mk_app(m_autil.mk_array_ext(s, i), a, b));
}
expr_ref a1(m_autil.mk_select(args), m);
args[0] = b;
expr_ref b1(m_autil.mk_select(args), m);
expr_ref ext(m.mk_iff(m.mk_eq(a1, b1), m.mk_eq(a, b)), m);
if (!m.is_true(eval_abs(ext))) {
TRACE("smtfd", tout << mk_bounded_pp(a, m, 2) << " " << mk_bounded_pp(b, m, 2) << "\n";);
m_context.add(ext, __FUNCTION__);
}
}
expr_ref mk_array_value(table& t) {
expr_ref value(m), default_value(m);
SASSERT(!t.empty());
expr_ref_vector args(m);
for (f_app const& f : t) {
SASSERT(m_autil.is_select(f.m_t));
expr_ref v = model_value(f.m_t);
if (!value) {
sort* s = f.m_t->get_arg(0)->get_sort();
default_value = v;
value = m_autil.mk_const_array(s, default_value);
}
else if (v != default_value) {
args.reset();
args.push_back(value);
for (unsigned i = 1; i < f.m_t->get_num_args(); ++i) {
args.push_back(model_value(f.m_t->get_arg(i)));
}
args.push_back(v);
value = m_autil.mk_store(args);
}
}
return value;
}
public:
ar_plugin(plugin_context& context):
theory_plugin(context),
m_autil(m)
{}
void reset() override {
theory_plugin::reset();
m_num_stores.reset();
}
void check_term(expr* t, unsigned round) override {
switch (round) {
case 0:
if (m_autil.is_select(t)) {
insert_select(to_app(t));
}
else if (m_autil.is_store(t)) {
update_lambda(t);
check_store0(to_app(t));
}
break;
case 1:
if (m_autil.is_select(t)) {
check_select(to_app(t));
}
else {
beta_reduce(t);
}
break;
case 2:
if (m_autil.is_store(t)) {
check_store2(to_app(t));
}
else if (m_autil.is_select(t)) {
check_select_store(to_app(t));
}
break;
default:
break;
}
}
bool term_covered(expr* t) override {
// populate congruence table for model building
if (m_autil.is_select(t)) {
expr* a = to_app(t)->get_arg(0);
expr_ref vA = eval_abs(a);
insert(mk_app(vA, to_app(t), a->get_sort()));
}
return
m_autil.is_store(t) ||
m_autil.is_select(t) ||
m_autil.is_map(t) ||
m_autil.is_ext(t) ||
is_lambda(t) ||
m_autil.is_const(t);
}
bool sort_covered(sort* s) override {
if (!m_autil.is_array(s)) {
return false;
}
if (!m_context.sort_covered(get_array_range(s))) {
return false;
}
for (unsigned i = 0; i < get_array_arity(s); ++i) {
if (!m_context.sort_covered(get_array_domain(s, i)))
return false;
}
return true;
}
expr_ref model_value_core(expr* t) override {
if (m_autil.is_array(t)) {
expr_ref vT = eval_abs(t);
table& tb = ast2table(vT, t->get_sort());
if (tb.empty()) {
return model_value_core(t->get_sort());
}
else {
return mk_array_value(tb);
}
}
return expr_ref(m);
}
expr_ref model_value_core(sort* s) override {
if (m_autil.is_array(s)) {
return expr_ref(m_autil.mk_const_array(s, model_value(get_array_range(s))), m);
}
return expr_ref(m);
}
void populate_model(model_ref& mdl, expr_ref_vector const& terms) override {
for (expr* t : subterms::ground(terms)) {
if (is_uninterp_const(t) && m_autil.is_array(t)) {
mdl->register_decl(to_app(t)->get_decl(), model_value_core(t));
}
}
}
unsigned max_rounds() override { return 3; }
void global_check(expr_ref_vector const& core) override {
expr_mark seen;
expr_ref_vector shared(m), sharedvals(m);
for (expr* t : subterms::ground(core)) {
if (!is_app(t)) continue;
app* a = to_app(t);
unsigned offset = 0;
if (m_autil.is_select(t) || m_autil.is_store(t)) {
offset = 1;
}
else if (m_autil.is_map(t)) {
continue;
}
for (unsigned i = a->get_num_args(); i-- > offset; ) {
expr* arg = a->get_arg(i);
if (m_autil.is_array(arg) && !seen.is_marked(arg)) {
shared.push_back(arg);
seen.mark(arg, true);
}
}
}
for (expr* s : shared) {
sharedvals.push_back(eval_abs(s));
}
for (unsigned i = 0; !m_context.at_max() && i < shared.size(); ++i) {
expr* s1 = shared.get(i);
expr* v1 = sharedvals.get(i);
for (unsigned j = i + 1; !m_context.at_max() && j < shared.size(); ++j) {
expr* s2 = shared.get(j);
expr* v2 = sharedvals.get(j);
if (v1 != v2 && s1->get_sort() == s2->get_sort() && same_table(v1, s1->get_sort(), v2, s2->get_sort())) {
enforce_extensionality(s1, s2);
}
}
}
}
};
class mbqi {
ast_manager& m;
plugin_context& m_context;
obj_hashtable m_enforced;
model_ref m_model;
ref<::solver> m_solver;
obj_pair_map m_val2term;
expr_ref_vector m_val2term_trail;
expr_ref_vector m_fresh_trail;
obj_map*> m_fresh;
scoped_ptr_vector> m_values;
expr* abs(expr* e) { return m_context.get_abs().abs(e); }
expr_ref eval_abs(expr* t) { return (*m_model)(abs(t)); }
void restrict_to_universe(expr * sk, ptr_vector const & universe) {
SASSERT(!universe.empty());
expr_ref_vector eqs(m);
for (expr * e : universe) {
eqs.push_back(m.mk_eq(sk, e));
}
expr_ref fml = mk_or(eqs);
m_solver->assert_expr(fml);
}
void register_value(expr* e) {
sort* s = e->get_sort();
obj_hashtable* values = nullptr;
if (!m_fresh.find(s, values)) {
values = alloc(obj_hashtable);
m_fresh.insert(s, values);
m_values.push_back(values);
}
if (!values->contains(e)) {
for (expr* b : *values) {
m_context.add(m.mk_not(m.mk_eq(e, b)), __FUNCTION__);
}
values->insert(e);
m_fresh_trail.push_back(e);
}
}
// sort -> [ value -> expr ]
// for fixed value return expr
// new fixed value is distinct from other expr
expr_ref replace_model_value(expr* e) {
if (m.is_model_value(e)) {
register_value(e);
expr_ref r(e, m);
return r;
}
if (is_app(e) && to_app(e)->get_num_args() > 0) {
expr_ref_vector args(m);
for (expr* arg : *to_app(e)) {
args.push_back(replace_model_value(arg));
}
return expr_ref(m.mk_app(to_app(e)->get_decl(), args.size(), args.data()), m);
}
return expr_ref(e, m);
}
// !Ex P(x) => !P(t)
// Ax P(x) => P(t)
// l_true: new instance
// l_false: no new instance
// l_undef unresolved
lbool check_forall(quantifier* q) {
expr_ref tmp(m);
unsigned sz = q->get_num_decls();
if (!m_model->eval_expr(q->get_expr(), tmp, true)) {
return l_undef;
}
if (is_forall(q) && m.is_true(tmp)) {
return l_false;
}
if (is_exists(q) && m.is_false(tmp)) {
return l_false;
}
TRACE("smtfd",
tout << mk_pp(q, m) << "\n";
/*tout << *m_model << "\n"; */
tout << "eval: " << tmp << "\n";);
m_solver->push();
expr_ref_vector vars(m), vals(m);
vars.resize(sz, nullptr);
vals.resize(sz, nullptr);
for (unsigned i = 0; i < sz; ++i) {
sort* s = q->get_decl_sort(i);
vars[i] = m.mk_fresh_const(q->get_decl_name(i), s, false);
if (m_model->has_uninterpreted_sort(s)) {
restrict_to_universe(vars.get(i), m_model->get_universe(s));
}
}
var_subst subst(m);
expr_ref body = subst(tmp, vars.size(), vars.data());
if (is_forall(q)) {
body = m.mk_not(body);
}
m_solver->assert_expr(body);
lbool r = m_solver->check_sat(0, nullptr);
model_ref mdl;
TRACE("smtfd", tout << "check: " << r << "\n";);
if (r == l_true) {
expr_ref qq(q->get_expr(), m);
for (expr* t : subterms::ground(qq)) {
init_term(t);
}
m_solver->get_model(mdl);
TRACE("smtfd", tout << *mdl << "\n";);
for (unsigned i = 0; i < sz; ++i) {
app* v = to_app(vars.get(i));
func_decl* f = v->get_decl();
expr_ref val(mdl->get_some_const_interp(f), m);
if (!val) {
r = l_undef;
break;
}
expr* t = nullptr;
if (m_val2term.find(val, v->get_sort(), t)) {
val = t;
}
else {
val = replace_model_value(val);
}
vals[i] = val;
}
}
if (r == l_true) {
body = subst(q->get_expr(), vals.size(), vals.data());
m_context.rewrite(body);
TRACE("smtfd", tout << "vals: " << vals << "\n" << body << "\n";);
if (is_forall(q)) {
body = m.mk_implies(q, body);
}
else {
body = m.mk_implies(body, q);
}
IF_VERBOSE(10, verbose_stream() << body << "\n");
m_context.add(body, __FUNCTION__);
}
m_solver->pop(1);
return r;
}
//
lbool check_exists(quantifier* q) {
if (m_enforced.contains(q)) {
return l_true;
}
expr_ref tmp(m);
expr_ref_vector vars(m);
unsigned sz = q->get_num_decls();
vars.resize(sz, nullptr);
for (unsigned i = 0; i < sz; ++i) {
vars[i] = m.mk_fresh_const(q->get_decl_name(i), q->get_decl_sort(i));
}
var_subst subst(m);
expr_ref body = subst(q->get_expr(), vars.size(), vars.data());
if (is_exists(q)) {
body = m.mk_implies(q, body);
}
else {
body = m.mk_implies(body, q);
}
m_enforced.insert(q);
m_context.add(body, __FUNCTION__);
return l_true;
}
void init_term(expr* t) {
if (!m.is_bool(t) && is_ground(t)) {
expr_ref v = eval_abs(t);
if (!m_val2term.contains(v, t->get_sort())) {
m_val2term.insert(v, t->get_sort(), t);
m_val2term_trail.push_back(v);
}
}
}
public:
mbqi(plugin_context& c):
m(c.get_manager()),
m_context(c),
m_model(nullptr),
m_solver(nullptr),
m_val2term_trail(m),
m_fresh_trail(m)
{}
void set_model(model* mdl) { m_model = mdl; }
ref<::solver> & get_solver() { return m_solver; }
void init_val2term(expr_ref_vector const& fmls, expr_ref_vector const& core) {
m_val2term_trail.reset();
m_val2term.reset();
for (expr* t : subterms::ground(core)) {
init_term(t);
}
for (expr* t : subterms::ground(fmls)) {
init_term(t);
}
}
bool check_quantifiers(expr_ref_vector const& core) {
bool result = true;
IF_VERBOSE(9,
for (expr* c : core) {
verbose_stream() << "core: " << mk_bounded_pp(c, m, 2) << "\n";
});
for (expr* c : core) {
lbool r = l_false;
IF_VERBOSE(10, verbose_stream() << "core: " << mk_bounded_pp(c, m, 2) << "\n");
if (is_forall(c)) {
r = check_forall(to_quantifier(c));
}
else if (is_exists(c)) {
r = check_exists(to_quantifier(c));
}
else if (m.is_not(c, c)) {
if (is_forall(c)) {
r = check_exists(to_quantifier(c));
}
else if (is_exists(c)) {
r = check_forall(to_quantifier(c));
}
}
if (r == l_undef) {
result = false;
}
}
return result;
}
};
class solver : public solver_na2as {
stats m_stats;
ast_manager& m;
mutable smtfd_abs m_abs;
unsigned m_indent;
plugin_context m_context;
uf_plugin m_uf;
ar_plugin m_ar;
bv_plugin m_bv;
basic_plugin m_bs;
pb_plugin m_pb;
ref<::solver> m_fd_sat_solver;
ref<::solver> m_fd_core_solver;
mbqi m_mbqi;
expr_ref_vector m_assertions;
unsigned_vector m_assertions_lim;
unsigned m_assertions_qhead;
expr_ref_vector m_axioms;
unsigned_vector m_axioms_lim;
expr_ref_vector m_toggles;
unsigned_vector m_toggles_lim;
model_ref m_model;
std::string m_reason_unknown;
void set_delay_simplify() {
params_ref p;
p.set_uint("simplify.delay", 10000);
m_fd_sat_solver->updt_params(p);
m_fd_core_solver->updt_params(p);
}
expr* add_toggle(expr* toggle) {
m_toggles.push_back(abs(toggle));
return toggle;
}
bool is_toggle(expr* e) {
return m_toggles.contains(e);
}
void indent() {
for (unsigned i = 0; i < m_indent; ++i) verbose_stream() << " ";
}
void flush_assertions() {
SASSERT(m_assertions_qhead <= m_assertions.size());
unsigned sz = m_assertions.size() - m_assertions_qhead;
if (sz > 0) {
m_assertions.push_back(m_toggles.back());
expr_ref fml(m.mk_and(sz + 1, m_assertions.data() + m_assertions_qhead), m);
m_assertions.pop_back();
expr* toggle = add_toggle(m.mk_fresh_const("toggle", m.mk_bool_sort()));
m_assertions_qhead = m_assertions.size();
TRACE("smtfd", tout << "flush: " << m_assertions_qhead << " " << mk_bounded_pp(fml, m, 3) << "\n";);
fml = abs(fml);
m_fd_sat_solver->assert_expr(fml);
fml = m.mk_not(m.mk_and(toggle, fml));
m_fd_core_solver->assert_expr(fml);
flush_atom_defs();
}
}
lbool check_abs(unsigned num_assumptions, expr * const * assumptions) {
expr_ref_vector asms(m);
init_assumptions(num_assumptions, assumptions, asms);
TRACE("smtfd",
for (unsigned i = 0; i < num_assumptions; ++i) {
tout << mk_bounded_pp(assumptions[i], m, 3) << "\n";
}
display(tout << asms << "\n"););
TRACE("smtfd_verbose", m_fd_sat_solver->display(tout););
lbool r = m_fd_sat_solver->check_sat(asms);
update_reason_unknown(r, m_fd_sat_solver);
set_delay_simplify();
return r;
}
// not necessarily prime
lbool get_prime_implicate(unsigned num_assumptions, expr * const * assumptions, expr_ref_vector& core) {
expr_ref_vector asms(m);
m_fd_sat_solver->get_model(m_model);
m_model->set_model_completion(true);
init_model_assumptions(num_assumptions, assumptions, asms);
TRACE("smtfd", display(tout << asms << "\n" << *m_model << "\n"););
lbool r = m_fd_core_solver->check_sat(asms);
update_reason_unknown(r, m_fd_core_solver);
if (r == l_false) {
m_fd_core_solver->get_unsat_core(core);
TRACE("smtfd", display(tout << core << "\n"););
SASSERT(asms.contains(m_toggles.back()));
SASSERT(core.contains(m_toggles.back()));
core.erase(m_toggles.back());
rep(core);
}
return r;
}
bool add_theory_axioms(expr_ref_vector const& core) {
m_context.reset(m_model);
expr_ref_vector terms(core);
terms.append(m_axioms);
for (unsigned round = 0; !m_context.at_max() && m_context.add_theory_axioms(terms, round); ++round) {}
TRACE("smtfd", m_context.display(tout););
for (expr* f : m_context) {
assert_fd(f);
}
m_stats.m_num_lemmas += m_context.size();
if (m_context.at_max()) {
m_context.set_max_lemmas(3*m_context.get_max_lemmas()/2);
}
return !m_context.empty();
}
lbool is_decided_sat(expr_ref_vector const& core) {
bool has_q = false;
lbool is_decided = l_true;
m_context.reset(m_model);
expr_ref_vector terms(core);
terms.append(m_axioms);
for (expr* t : subterms::ground(core)) {
if (is_forall(t) || is_exists(t)) {
has_q = true;
}
}
for (expr* t : subterms::ground(terms)) {
if (!is_forall(t) && !is_exists(t) && (!m_context.term_covered(t) || !m_context.sort_covered(t->get_sort()))) {
is_decided = l_false;
}
}
m_context.populate_model(m_model, terms);
TRACE("smtfd",
tout << "axioms: " << m_axioms << "\n";
for (expr* a : subterms::ground(terms)) {
expr_ref val0 = (*m_model)(a);
expr_ref val1 = (*m_model)(abs(a));
if (is_ground(a) && val0 != val1 && val0->get_sort() == val1->get_sort()) {
tout << mk_bounded_pp(a, m, 2) << " := " << val0 << " " << val1 << "\n";
}
if (!is_forall(a) && !is_exists(a) && (!m_context.term_covered(a) || !m_context.sort_covered(a->get_sort()))) {
tout << "not covered: " << mk_pp(a, m) << " " << mk_pp(a->get_sort(), m) << " ";
tout << m_context.term_covered(a) << " " << m_context.sort_covered(a->get_sort()) << "\n";
}
}
tout << "has quantifier: " << has_q << "\n" << core << "\n";
tout << *m_model.get() << "\n";
);
DEBUG_CODE(
bool found_bad = false;
for (expr* a : subterms::ground(core)) {
expr_ref val0 = (*m_model)(a);
expr_ref val1 = (*m_model)(abs(a));
if (is_ground(a) && val0 != val1 && val0->get_sort() == val1->get_sort()) {
//std::cout << mk_bounded_pp(a, m, 2) << " := " << val0 << " " << val1 << "\n";
found_bad = true;
}
}
if (found_bad) {
//std::cout << "core: " << core << "\n";
//std::cout << *m_model.get() << "\n";
UNREACHABLE();
});
if (!has_q) {
return is_decided;
}
m_mbqi.set_model(m_model.get());
if (!m_mbqi.get_solver()) {
m_mbqi.get_solver() = alloc(solver, m_indent + 1, m, get_params());
}
m_mbqi.init_val2term(m_assertions, core);
if (!m_mbqi.check_quantifiers(core) && m_context.empty()) {
return l_false;
}
for (expr* f : m_context) {
IF_VERBOSE(10, verbose_stream() << "lemma: " << f->get_id() << ": " << expr_ref(f, m) << "\n");
assert_fd(f);
}
m_stats.m_num_mbqi += m_context.size();
IF_VERBOSE(10, verbose_stream() << "context size: " << m_context.size() << "\n");
return m_context.empty() ? is_decided : l_undef;
}
void init_assumptions(unsigned sz, expr* const* user_asms, expr_ref_vector& asms) {
asms.reset();
for (unsigned i = 0; i < sz; ++i) {
asms.push_back(abs_assumption(user_asms[i]));
}
flush_atom_defs();
}
void init_model_assumptions(unsigned sz, expr* const* user_asms, expr_ref_vector& asms) {
asms.reset();
asms.push_back(m_toggles.back());
for (unsigned i = 0; i < sz; ++i) {
asms.push_back(abs(user_asms[i]));
}
for (expr* a : m_abs.atoms()) {
if (is_toggle(a)) {
}
else if (m_model->is_true(a)) {
//for (expr* t : subterms(expr_ref(a, m))) {
// std::cout << expr_ref(t, m) << " " << (*m_model.get())(t) << "\n";
//}
asms.push_back(a);
}
else {
asms.push_back(m.mk_not(a));
}
}
}
void checkpoint() {
tactic::checkpoint(m);
}
expr* rep(expr* e) { return m_abs.rep(e); }
expr* abs(expr* e) { return m_abs.abs(e); }
expr* abs_assumption(expr* e) { return m_abs.abs_assumption(e); }
expr_ref_vector& rep(expr_ref_vector& v) { for (unsigned i = v.size(); i-- > 0; ) v[i] = rep(v.get(i)); return v; }
expr_ref_vector& abs(expr_ref_vector& v) { for (unsigned i = v.size(); i-- > 0; ) v[i] = abs(v.get(i)); return v; }
void init() {
m_axioms.reset();
if (!m_fd_sat_solver) {
m_fd_sat_solver = mk_fd_solver(m, get_params());
m_fd_core_solver = mk_fd_solver(m, get_params());
}
}
std::ostream& display(std::ostream& out, unsigned n = 0, expr * const * assumptions = nullptr) const override {
if (!m_fd_sat_solver) return out;
// m_fd_sat_solver->display(out);
// out << m_assumptions << "\n";
m_abs.display(out);
return out;
}
void update_reason_unknown(lbool r, ::solver_ref& s) {
if (r == l_undef) m_reason_unknown = s->reason_unknown();
}
public:
solver(unsigned indent, ast_manager& m, params_ref const& p):
solver_na2as(m),
m(m),
m_abs(m, m_stats),
m_indent(indent),
m_context(m_abs, m),
m_uf(m_context),
m_ar(m_context),
m_bv(m_context),
m_bs(m_context),
m_pb(m_context),
m_mbqi(m_context),
m_assertions(m),
m_assertions_qhead(0),
m_axioms(m),
m_toggles(m)
{
updt_params(p);
add_toggle(m.mk_true());
}
::solver* translate(ast_manager& dst_m, params_ref const& p) override {
solver* result = alloc(solver, m_indent, dst_m, p);
if (m_fd_sat_solver) result->m_fd_sat_solver = m_fd_sat_solver->translate(dst_m, p);
if (m_fd_core_solver) result->m_fd_core_solver = m_fd_core_solver->translate(dst_m, p);
return result;
}
void assert_expr_core(expr* t) override {
m_assertions.push_back(t);
}
void push_core() override {
init();
flush_assertions();
m_abs.push();
m_fd_sat_solver->push();
m_fd_core_solver->push();
m_assertions_lim.push_back(m_assertions.size());
m_axioms_lim.push_back(m_axioms.size());
m_toggles_lim.push_back(m_toggles.size());
}
void pop_core(unsigned n) override {
m_fd_sat_solver->pop(n);
m_fd_core_solver->pop(n);
m_abs.pop(n);
unsigned sz = m_toggles_lim[m_toggles_lim.size() - n];
m_toggles.shrink(sz);
m_toggles_lim.shrink(m_toggles_lim.size() - n);
m_assertions.shrink(m_assertions_lim[m_assertions_lim.size() - n]);
m_assertions_lim.shrink(m_assertions_lim.size() - n);
m_axioms.shrink(m_axioms_lim[m_axioms_lim.size() - n]);
m_axioms_lim.shrink(m_axioms_lim.size() - n);
m_assertions_qhead = m_assertions.size();
}
void flush_atom_defs() {
CTRACE("smtfd", !m_abs.atom_defs().empty(), for (expr* f : m_abs.atom_defs()) tout << mk_bounded_pp(f, m, 4) << "\n";);
for (expr* f : m_abs.atom_defs()) {
m_fd_sat_solver->assert_expr(f);
m_fd_core_solver->assert_expr(f);
// TBD we want these too: m_axioms.push_back(f);
}
m_abs.reset_atom_defs();
}
void assert_fd(expr* fml) {
expr_ref _fml(fml, m);
TRACE("smtfd", tout << mk_bounded_pp(fml, m, 3) << "\n";);
CTRACE("smtfd", m_axioms.contains(fml),
tout << "formula:\n" << _fml << "\n";
tout << "axioms:\n" << m_axioms << "\n";
tout << "assertions:\n" << m_assertions << "\n";);
// if (m_axioms.contains(fml)) return;
SASSERT(!m_axioms.contains(fml));
m_axioms.push_back(fml);
_fml = abs(fml);
TRACE("smtfd", tout << mk_bounded_pp(_fml, m, 3) << "\n";);
m_fd_sat_solver->assert_expr(_fml);
m_fd_core_solver->assert_expr(_fml);
flush_atom_defs();
}
void block_core(expr_ref_vector const& core) {
expr_ref fml(m.mk_not(mk_and(core)), m);
TRACE("smtfd", tout << "block:\n" << mk_bounded_pp(fml, m, 3) << "\n" << mk_bounded_pp(abs(fml), m, 3) << "\n";);
assert_fd(fml);
}
lbool check_sat_core2(unsigned num_assumptions, expr * const * assumptions) override {
init();
flush_assertions();
lbool r = l_undef;
expr_ref_vector core(m), axioms(m);
while (true) {
IF_VERBOSE(1, indent(); verbose_stream() << "(smtfd-check-sat :rounds " << m_stats.m_num_rounds
<< " :lemmas " << m_stats.m_num_lemmas << " :qi " << m_stats.m_num_mbqi << ")\n");
m_stats.m_num_rounds++;
checkpoint();
// phase 1: check sat of abs
r = check_abs(num_assumptions, assumptions);
if (r != l_true) {
break;
}
// phase 2: find prime implicate over FD (abstraction)
r = get_prime_implicate(num_assumptions, assumptions, core);
if (r != l_false) {
break;
}
// phase 3: check if prime implicate is really valid, or add theory lemmas until there is a theory core
r = refine_core(core);
switch (r) {
case l_true:
switch (is_decided_sat(core)) {
case l_true:
return l_true;
case l_undef:
break;
case l_false:
break;
}
break;
case l_false:
block_core(core);
break;
case l_undef:
return r;
}
}
return r;
}
lbool refine_core(expr_ref_vector & core) {
lbool r = l_true;
unsigned round = 0;
m_context.reset(m_model);
while (true) {
expr_ref_vector terms(core);
terms.append(m_axioms);
if (!m_context.add_theory_axioms(terms, round)) {
break;
}
if (m_context.empty()) {
++round;
continue;
}
IF_VERBOSE(1, indent(); verbose_stream() << "(smtfd-round :round " << round << " :lemmas " << m_context.size() << ")\n");
round = 0;
TRACE("smtfd_verbose",
for (expr* f : m_context) tout << "refine " << mk_bounded_pp(f, m, 3) << "\n";
m_context.display(tout););
for (expr* f : m_context) {
assert_fd(f);
}
m_stats.m_num_lemmas += m_context.size();
m_context.reset(m_model);
r = check_abs(core.size(), core.data());
update_reason_unknown(r, m_fd_sat_solver);
switch (r) {
case l_false:
m_fd_sat_solver->get_unsat_core(core);
rep(core);
return r;
case l_true:
m_fd_sat_solver->get_model(m_model);
m_model->set_model_completion(true);
m_context.reset(m_model);
break;
default:
return r;
}
}
// context is satisfiable
SASSERT(r == l_true);
return r;
}
void set_phase(expr* e) override {}
phase* get_phase() override { return nullptr; }
void set_phase(phase* p) override { }
void move_to_front(expr* e) override { }
void updt_params(params_ref const & p) override {
::solver::updt_params(p);
if (m_fd_sat_solver) {
m_fd_sat_solver->updt_params(p);
m_fd_core_solver->updt_params(p);
}
m_context.set_max_lemmas(UINT_MAX); // p.get_uint("max-lemmas", 100));
}
void collect_param_descrs(param_descrs & r) override {
init();
m_fd_sat_solver->collect_param_descrs(r);
r.insert("max-lemmas", CPK_UINT, "maximal number of lemmas per round", "10");
}
void set_produce_models(bool f) override { }
void set_progress_callback(progress_callback * callback) override { }
void collect_statistics(statistics & st) const override {
if (m_fd_sat_solver) {
m_fd_sat_solver->collect_statistics(st);
m_fd_core_solver->collect_statistics(st);
}
st.update("smtfd-num-lemmas", m_stats.m_num_lemmas);
st.update("smtfd-num-rounds", m_stats.m_num_rounds);
st.update("smtfd-num-mbqi", m_stats.m_num_mbqi);
st.update("smtfd-num-fresh-bool", m_stats.m_num_fresh_bool);
}
void get_unsat_core(expr_ref_vector & r) override {
m_fd_sat_solver->get_unsat_core(r);
rep(r);
}
void get_model_core(model_ref & mdl) override {
mdl = m_model;
}
model_converter_ref get_model_converter() const override {
return m_fd_sat_solver->get_model_converter();
}
proof * get_proof_core() override { return nullptr; }
std::string reason_unknown() const override { return m_reason_unknown; }
void set_reason_unknown(char const* msg) override { m_reason_unknown = msg; }
void get_labels(svector & r) override { }
ast_manager& get_manager() const override { return m; }
lbool find_mutexes(expr_ref_vector const& vars, vector& mutexes) override {
return l_undef;
}
expr_ref_vector cube(expr_ref_vector& vars, unsigned backtrack_level) override {
return expr_ref_vector(m);
}
expr* congruence_root(expr* e) override { return e; }
expr* congruence_next(expr* e) override { return e; }
lbool get_consequences_core(expr_ref_vector const& asms, expr_ref_vector const& vars, expr_ref_vector& consequences) override {
return l_undef;
}
void get_levels(ptr_vector const& vars, unsigned_vector& depth) override {
init();
m_fd_sat_solver->get_levels(vars, depth);
}
expr_ref_vector get_trail(unsigned max_level) override {
init();
return m_fd_sat_solver->get_trail(max_level);
}
unsigned get_num_assertions() const override {
return m_assertions.size();
}
expr * get_assertion(unsigned idx) const override {
return m_assertions.get(idx);
}
};
}
solver * mk_smtfd_solver(ast_manager & m, params_ref const & p) {
return alloc(smtfd::solver, 0, m, p);
}
tactic * mk_smtfd_tactic(ast_manager & m, params_ref const & p) {
return mk_solver2tactic(mk_smtfd_solver(m, p));
}
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