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z3-z3-4.12.6.src.smt.theory_char.cpp Maven / Gradle / Ivy
/*++
Copyright (c) 2011 Microsoft Corporation
Module Name:
seq_char.cpp
Abstract:
Solver for characters
Author:
Nikolaj Bjorner (nbjorner) 2020-5-16
--*/
#include "ast/ast_ll_pp.h"
#include "ast/bv_decl_plugin.h"
#include "smt/theory_char.h"
#include "smt/smt_context.h"
#include "smt/smt_model_generator.h"
namespace smt {
theory_char::theory_char(context& ctx):
theory(ctx, ctx.get_manager().mk_family_id("char")),
seq(m),
m_bb(m, ctx.get_fparams())
{
m_bits2char = symbol("bits2char");
}
struct theory_char::reset_bits : public trail {
theory_char& s;
unsigned idx;
reset_bits(theory_char& s, unsigned idx):
s(s),
idx(idx)
{}
void undo() override {
s.m_bits[idx].reset();
s.m_ebits[idx].reset();
}
};
bool theory_char::has_bits(theory_var v) const {
return (m_bits.size() > (unsigned)v) && !m_bits[v].empty();
}
theory_var theory_char::mk_var(enode* n) {
if (is_attached_to_var(n))
return n->get_th_var(get_id());
theory_var v = theory::mk_var(n);
ctx.attach_th_var(n, this, v);
ctx.mark_as_relevant(n);
return v;
}
bool theory_char::internalize_atom(app * term, bool gate_ctx) {
for (auto arg : *term)
mk_var(ensure_enode(arg));
bool_var bv = ctx.mk_bool_var(term);
ctx.set_var_theory(bv, get_id());
ctx.mark_as_relevant(bv);
if (seq.is_char_le(term))
internalize_le(literal(bv, false), term);
if (seq.is_char_is_digit(term))
internalize_is_digit(literal(bv, false), term);
return true;
}
bool theory_char::internalize_term(app * term) {
for (auto arg : *term)
mk_var(ensure_enode(arg));
enode* e = ctx.e_internalized(term) ? ctx.get_enode(term) : ctx.mk_enode(term, false, m.is_bool(term), true);
theory_var v = mk_var(e);
unsigned c = 0;
if (seq.is_const_char(term, c))
new_const_char(v, c);
expr* n = nullptr;
if (seq.is_char2int(term, n))
new_char2int(v, n);
else if (seq.is_char2bv(term, n))
new_char2bv(term, n);
else if (seq.is_bv2char(term, n))
new_bv2char(v, n);
return true;
}
/**
* Initialize bits associated with theory variable v.
* add also the equality bits2char(char2bit(e, 0),..., char2bit(e, 15)) = e
* to have congruence closure propagate equalities when the bits of two vectors
* end up having the same values. This, together with congruence closure over char2bit
* should ensure that two characters have the same bit-vector assignments if and only
* if they are equal. Nevertheless, the code also checks for these constraints
* independently and adds Ackerman axioms on demand.
*/
void theory_char::init_bits(theory_var v) {
if (has_bits(v))
return;
expr* e = get_expr(v);
m_bits.reserve(v + 1);
auto& bits = m_bits[v];
while ((unsigned) v >= m_ebits.size())
m_ebits.push_back(expr_ref_vector(m));
ctx.push_trail(reset_bits(*this, v));
auto& ebits = m_ebits[v];
SASSERT(ebits.empty());
bool is_bits2char = seq.is_skolem(e) && to_app(e)->get_decl()->get_parameter(0).get_symbol() == m_bits2char;
if (is_bits2char) {
for (expr* arg : *to_app(e)) {
ebits.push_back(arg);
bits.push_back(literal(ctx.get_bool_var(arg)));
}
}
else {
for (unsigned i = 0; i < seq.num_bits(); ++i)
ebits.push_back(seq.mk_char_bit(e, i));
ctx.internalize(ebits.data(), ebits.size(), true);
for (expr* arg : ebits)
bits.push_back(literal(ctx.get_bool_var(arg)));
for (literal bit : bits)
ctx.mark_as_relevant(bit);
expr_ref bits2char(seq.mk_skolem(m_bits2char, ebits.size(), ebits.data(), e->get_sort()), m);
ctx.mark_as_relevant(bits2char.get());
enode* n1 = ensure_enode(e);
enode* n2 = ensure_enode(bits2char);
justification* j =
ctx.mk_justification(
ext_theory_eq_propagation_justification(get_id(), ctx, n1, n2));
ctx.assign_eq(n1, n2, eq_justification(j));
}
++m_stats.m_num_blast;
}
void theory_char::internalize_le(literal lit, app* term) {
expr* x = nullptr, *y = nullptr;
VERIFY(seq.is_char_le(term, x, y));
theory_var v1 = ctx.get_enode(x)->get_th_var(get_id());
theory_var v2 = ctx.get_enode(y)->get_th_var(get_id());
init_bits(v1);
init_bits(v2);
auto const& b1 = get_ebits(v1);
auto const& b2 = get_ebits(v2);
expr_ref e(m);
m_bb.mk_ule(b1.size(), b1.data(), b2.data(), e);
literal le = mk_literal(e);
ctx.mark_as_relevant(le);
ctx.mk_th_axiom(get_id(), ~lit, le);
ctx.mk_th_axiom(get_id(), lit, ~le);
}
void theory_char::internalize_is_digit(literal lit, app* term) {
expr* x = nullptr;
VERIFY(seq.is_char_is_digit(term, x));
enode* zero = ensure_enode(seq.mk_char('0'));
enode* nine = ensure_enode(seq.mk_char('9'));
theory_var v = ctx.get_enode(x)->get_th_var(get_id());
theory_var z = zero->get_th_var(get_id());
theory_var n = nine->get_th_var(get_id());
init_bits(v);
init_bits(z);
init_bits(n);
auto const& bv = get_ebits(v);
auto const& zv = get_ebits(z);
auto const& nv = get_ebits(n);
expr_ref le1(m), le2(m);
m_bb.mk_ule(bv.size(), zv.data(), bv.data(), le1);
m_bb.mk_ule(bv.size(), bv.data(), nv.data(), le2);
literal lit1 = mk_literal(le1);
literal lit2 = mk_literal(le2);
ctx.mk_th_axiom(get_id(), ~lit, lit1);
ctx.mk_th_axiom(get_id(), ~lit, lit2);
ctx.mk_th_axiom(get_id(), ~lit1, ~lit2, lit);
}
literal_vector const& theory_char::get_bits(theory_var v) {
init_bits(v);
return m_bits[v];
}
expr_ref_vector const& theory_char::get_ebits(theory_var v) {
init_bits(v);
return m_ebits[v];
}
// = on characters
void theory_char::new_eq_eh(theory_var v, theory_var w) {
if (has_bits(v) && has_bits(w)) {
auto& a = get_bits(v);
auto& b = get_bits(w);
literal _eq = null_literal;
auto eq = [&]() {
if (_eq == null_literal) {
_eq = mk_literal(m.mk_eq(get_expr(v), get_expr(w)));
ctx.mark_as_relevant(_eq);
}
return _eq;
};
for (unsigned i = a.size(); i-- > 0; ) {
lbool v1 = ctx.get_assignment(a[i]);
lbool v2 = ctx.get_assignment(b[i]);
if (v1 != l_undef && v2 != l_undef && v1 != v2) {
enforce_ackerman(v, w);
return;
}
if (v1 == l_true)
ctx.mk_th_axiom(get_id(), ~eq(), ~a[i], b[i]);
if (v1 == l_false)
ctx.mk_th_axiom(get_id(), ~eq(), a[i], ~b[i]);
if (v2 == l_true)
ctx.mk_th_axiom(get_id(), ~eq(), a[i], ~b[i]);
if (v2 == l_false)
ctx.mk_th_axiom(get_id(), ~eq(), ~a[i], b[i]);
}
}
}
// != on characters
void theory_char::new_diseq_eh(theory_var v, theory_var w) {
if (has_bits(v) && has_bits(w)) {
auto& a = get_bits(v);
auto& b = get_bits(w);
for (unsigned i = a.size(); i-- > 0; ) {
lbool v1 = ctx.get_assignment(a[i]);
lbool v2 = ctx.get_assignment(b[i]);
if (v1 == l_undef || v2 == l_undef || v1 != v2)
return;
}
enforce_ackerman(v, w);
}
}
void theory_char::new_const_char(theory_var v, unsigned c) {
auto& bits = get_bits(v);
for (auto b : bits) {
bool bit = (0 != (c & 1));
ctx.assign(bit ? b : ~b, nullptr);
c >>= 1;
}
}
void theory_char::new_char2int(theory_var v, expr* c) {
theory_var w = ctx.get_enode(c)->get_th_var(get_id());
init_bits(w);
auto const& bits = get_ebits(w);
expr_ref_vector sum(m);
unsigned p = 0;
arith_util a(m);
for (auto b : bits) {
sum.push_back(m.mk_ite(b, a.mk_int(1 << p), a.mk_int(0)));
p++;
}
expr_ref sum_bits(a.mk_add(sum), m);
enode* n1 = get_enode(v);
enode* n2 = ensure_enode(sum_bits);
justification* j =
ctx.mk_justification(
ext_theory_eq_propagation_justification(get_id(), ctx, n1, n2));
ctx.assign_eq(n1, n2, eq_justification(j));
}
void theory_char::new_char2bv(expr* b, expr* c) {
theory_var w = ctx.get_enode(c)->get_th_var(get_id());
init_bits(w);
auto const& bits = get_bits(w);
bv_util bv(m);
SASSERT(bits.size() == bv.get_bv_size(b));
unsigned i = 0;
for (auto bit1 : bits) {
auto bit2 = mk_literal(bv.mk_bit2bool(b, i++));
ctx.mk_th_axiom(get_id(), ~bit1, bit2);
ctx.mk_th_axiom(get_id(), bit1, ~bit2);
}
}
void theory_char::new_bv2char(theory_var v, expr* b) {
init_bits(v);
auto const& bits = get_bits(v);
bv_util bv(m);
SASSERT(bits.size() == bv.get_bv_size(b));
unsigned i = 0;
for (auto bit1 : bits) {
auto bit2 = mk_literal(bv.mk_bit2bool(b, i++));
ctx.mk_th_axiom(get_id(), ~bit1, bit2);
ctx.mk_th_axiom(get_id(), bit1, ~bit2);
}
}
/**
* 1. Check that values of classes are unique.
* Check that values within each class is the same.
* Enforce that values are within max_char.
* 2. Assign values to characters that haven't been assigned.
*/
bool theory_char::final_check() {
TRACE("seq", tout << "final check " << get_num_vars() << "\n";);
m_var2value.reset();
m_var2value.resize(get_num_vars(), UINT_MAX);
m_value2var.reset();
// extract the initial set of constants.
uint_set values;
unsigned c = 0, d = 0;
for (unsigned v = get_num_vars(); v-- > 0; ) {
expr* e = get_expr(v);
if (seq.is_char(e) && m_var2value[v] == UINT_MAX && get_char_value(v, c)) {
CTRACE("seq_verbose", seq.is_char(e), tout << mk_pp(e, m) << " root: " << get_enode(v)->is_root() << " is_value: " << get_char_value(v, c) << "\n";);
enode* r = get_enode(v)->get_root();
m_value2var.reserve(c + 1, null_theory_var);
theory_var u = m_value2var[c];
if (u != null_theory_var && r != get_enode(u)->get_root()) {
enforce_ackerman(u, v);
return false;
}
if (c > seq.max_char()) {
enforce_value_bound(v);
return false;
}
for (enode* n : *r) {
u = n->get_th_var(get_id());
if (u == null_theory_var)
continue;
if (get_char_value(u, d) && d != c) {
enforce_ackerman(u, v);
return false;
}
m_var2value[u] = c;
}
values.insert(c);
m_value2var[c] = v;
}
}
// assign values to other unassigned nodes
c = 'A';
for (unsigned v = get_num_vars(); v-- > 0; ) {
expr* e = get_expr(v);
if (seq.is_char(e) && m_var2value[v] == UINT_MAX) {
d = c;
while (values.contains(c)) {
c = (c + 1) % seq.max_char();
if (d == c) {
enforce_bits();
return false;
}
}
TRACE("seq", tout << "fresh: " << mk_pp(e, m) << " := " << c << "\n";);
for (enode* n : *get_enode(v))
m_var2value[n->get_th_var(get_id())] = c;
m_value2var.reserve(c + 1, null_theory_var);
m_value2var[c] = v;
values.insert(c);
}
}
return true;
}
void theory_char::enforce_bits() {
TRACE("seq", tout << "enforce bits\n";);
for (unsigned v = get_num_vars(); v-- > 0; ) {
expr* e = get_expr(v);
if (seq.is_char(e) && get_enode(v)->is_root() && !has_bits(v))
init_bits(v);
}
}
void theory_char::enforce_value_bound(theory_var v) {
TRACE("seq", tout << "enforce bound " << v << "\n";);
enode* n = ensure_enode(seq.mk_char(seq.max_char()));
theory_var w = n->get_th_var(get_id());
SASSERT(has_bits(w));
init_bits(v);
auto const& mbits = get_ebits(w);
auto const& bits = get_ebits(v);
expr_ref le(m);
m_bb.mk_ule(bits.size(), bits.data(), mbits.data(), le);
ctx.assign(mk_literal(le), nullptr);
++m_stats.m_num_bounds;
}
void theory_char::enforce_ackerman(theory_var v, theory_var w) {
if (v > w)
std::swap(v, w);
TRACE("seq", tout << "enforce ackerman " << v << " " << w << "\n";);
literal eq = mk_literal(m.mk_eq(get_expr(v), get_expr(w)));
ctx.mark_as_relevant(eq);
literal_vector lits;
init_bits(v);
init_bits(w);
auto& a = get_ebits(v);
auto& b = get_ebits(w);
for (unsigned i = a.size(); i-- > 0; ) {
// eq => a = b
literal beq = mk_eq(a[i], b[i], false);
lits.push_back(~beq);
ctx.mark_as_relevant(beq);
ctx.mk_th_axiom(get_id(), ~eq, beq);
}
// a = b => eq
lits.push_back(eq);
ctx.mk_th_axiom(get_id(), lits.size(), lits.data());
++m_stats.m_num_ackerman;
}
unsigned theory_char::get_char_value(theory_var v) {
return m_var2value[v];
}
bool theory_char::get_char_value(theory_var v, unsigned& c) {
if (!has_bits(v))
return false;
auto const & b = get_bits(v);
c = 0;
unsigned p = 1;
for (literal lit : b) {
if (ctx.get_assignment(lit) == l_true)
c += p;
p *= 2;
}
return true;
}
// a stand-alone theory.
void theory_char::init_model(model_generator & mg) {
m_factory = alloc(char_factory, get_manager(), get_family_id());
mg.register_factory(m_factory);
for (auto val : m_var2value)
if (val != UINT_MAX)
m_factory->register_value(val);
}
model_value_proc * theory_char::mk_value(enode * n, model_generator & mg) {
unsigned ch = get_char_value(n->get_th_var(get_id()));
app* val = seq.str.mk_char(ch);
m_factory->add_trail(val);
return alloc(expr_wrapper_proc, val);
}
void theory_char::collect_statistics(::statistics& st) const {
st.update("seq char ackerman", m_stats.m_num_ackerman);
st.update("seq char bounds", m_stats.m_num_bounds);
st.update("seq char2bit", m_stats.m_num_blast);
}
}
