template <typename T, typename X> void static_matrix<T, X>::check_consistency() {
std::unordered_map<std::pair<unsigned, unsigned>, T> by_rows;
for (int i = 0; i < m_rows.size(); i++){
for (auto & t : m_rows[i]) {
pair<unsigned, unsigned> p(i, t.m_j);
lean_assert(by_rows.find(p) == by_rows.end());
by_rows[p] = t.get_val();
}
}
std::unordered_map<pair<unsigned, unsigned>, T> by_cols;
for (int i = 0; i < m_columns.size(); i++){
for (auto & t : m_columns[i]) {
pair<unsigned, unsigned> p(t.m_i, i);
lean_assert(by_cols.find(p) == by_cols.end());
by_cols[p] = get_value_of_column_cell(t);
}
}
lean_assert(by_rows.size() == by_cols.size());
for (auto & t : by_rows) {
auto ic = by_cols.find(t.first);
if (ic == by_cols.end()){
std::cout << "rows have pair (" << t.first.first <<"," << t.first.second
<< "), but columns don't " << std::endl;
}
lean_assert(ic != by_cols.end());
lean_assert(t.second == ic->second);
}
}
// Read until the end_str is found, store all characters (not including end_str) in m_buffer.
// Throw a parser exception error_msg if end of file is found before end_str.
void scanner::read_until(char const * end_str, char const * error_msg) {
lean_assert(end_str);
lean_assert(end_str[0]);
m_buffer.clear();
while (true) {
check_not_eof(error_msg);
char c = curr_next();
if (c == end_str[0]) {
m_aux_buffer.clear();
m_aux_buffer += c;
unsigned i = 1;
while (true) {
if (!end_str[i])
return;
check_not_eof(error_msg);
c = curr_next();
if (c != end_str[i]) {
m_buffer += m_aux_buffer;
break;
}
i++;
}
} else {
m_buffer += c;
}
}
}
expr visit_projection(name const & fn, buffer<expr> const & args) {
projection_info const & info = *get_projection_info(env(), fn);
expr major = visit(args[info.m_nparams]);
buffer<bool> rel_fields;
name I_name = *inductive::is_intro_rule(env(), info.m_constructor);
get_constructor_info(info.m_constructor, rel_fields);
lean_assert(info.m_i < rel_fields.size());
lean_assert(rel_fields[info.m_i]); /* We already erased irrelevant information */
/* Adjust projection index by ignoring irrelevant fields */
unsigned j = 0;
for (unsigned i = 0; i < info.m_i; i++) {
if (rel_fields[i])
j++;
}
expr r;
if (has_trivial_structure(I_name, rel_fields)) {
lean_assert(j == 0);
r = major;
} else {
r = mk_app(mk_proj(j), major);
}
/* Add additional arguments */
for (unsigned i = info.m_nparams + 1; i < args.size(); i++)
r = mk_app(r, visit(args[i]));
return r;
}
coercion_elaborator::coercion_elaborator(coercion_info_manager & info, expr const & arg,
list<constraints> const & choices, list<expr> const & coes,
bool use_id):
m_info(info), m_arg(arg), m_id(use_id), m_choices(choices), m_coercions(coes) {
lean_assert(!use_id || length(m_coercions) + 1 == length(m_choices));
lean_assert(use_id || length(m_coercions) == length(m_choices));
}
void get_rec_args(environment const & env, name const & n, buffer<buffer<bool>> & r) {
lean_assert(inductive::is_inductive_decl(env, n));
type_checker tc(env);
name_generator ngen;
declaration ind_decl = env.get(n);
declaration rec_decl = env.get(inductive::get_elim_name(n));
unsigned nparams = *inductive::get_num_params(env, n);
unsigned nminors = *inductive::get_num_minor_premises(env, n);
unsigned ntypeformers = *inductive::get_num_type_formers(env, n);
buffer<expr> rec_args;
to_telescope(ngen, rec_decl.get_type(), rec_args);
buffer<name> typeformer_names;
for (unsigned i = nparams; i < nparams + ntypeformers; i++) {
typeformer_names.push_back(mlocal_name(rec_args[i]));
}
lean_assert(typeformer_names.size() == ntypeformers);
r.clear();
// add minor premises
for (unsigned i = nparams + ntypeformers; i < nparams + ntypeformers + nminors; i++) {
r.push_back(buffer<bool>());
buffer<bool> & bv = r.back();
expr minor_type = mlocal_type(rec_args[i]);
buffer<expr> minor_args;
to_telescope(ngen, minor_type, minor_args);
for (expr & minor_arg : minor_args) {
buffer<expr> minor_arg_args;
expr minor_arg_type = to_telescope(tc, mlocal_type(minor_arg), minor_arg_args);
bv.push_back(is_typeformer_app(typeformer_names, minor_arg_type));
}
}
}
expr mk_app(unsigned n, expr const * as) {
lean_assert(n > 1);
unsigned new_n;
unsigned n0 = 0;
expr const & arg0 = as[0];
bool has_mv = std::any_of(as, as + n, [](expr const & c) { return c.has_metavar(); });
// Remark: we represent ((app a b) c) as (app a b c)
if (is_app(arg0)) {
n0 = num_args(arg0);
new_n = n + n0 - 1;
} else {
new_n = n;
}
char * mem = new char[sizeof(expr_app) + new_n*sizeof(expr)];
expr r(new (mem) expr_app(new_n, has_mv));
expr * m_args = to_app(r)->m_args;
unsigned i = 0;
unsigned j = 0;
if (new_n != n) {
for (; i < n0; i++)
new (m_args+i) expr(arg(arg0, i));
j++;
}
for (; i < new_n; ++i, ++j) {
lean_assert(j < n);
new (m_args+i) expr(as[j]);
}
to_app(r)->m_hash = hash_args(new_n, m_args);
return r;
}
void tmp_type_context::update_assignment(level const & u, level const & v) {
unsigned idx = to_meta_idx(u);
lean_assert(idx < m_uassignment.size()); // see comments above
lean_assert(!m_uassignment[idx]);
m_uassignment[idx] = v;
if (!m_scopes.empty())
m_trail.emplace_back(trail_kind::Level, idx);
}
void lar_solver::solve_with_core_solver() {
m_mpq_lar_core_solver.solve();
m_status = m_mpq_lar_core_solver.m_status;
lean_assert(m_status != OPTIMAL || all_constraints_hold());
#ifdef LEAN_DEBUG
lean_assert(!settings().row_feasibility || m_status != INFEASIBLE || the_evidence_is_correct());
#endif
}
mpq lar_solver::find_ratio_of_original_constraint_to_normalized(canonic_left_side * ls, const lar_constraint & constraint) {
lean_assert(ls->m_coeffs.size() > 0);
auto first_pair = ls->m_coeffs[0];
lean_assert(first_pair.first == numeric_traits<mpq>::one());
var_index i = first_pair.second;
auto it = constraint.m_left_side.find(i);
lean_assert(it != constraint.m_left_side.end());
return it->second;
}
void lar_solver::fill_row_of_A(static_matrix<U, V> & A, unsigned i, canonic_left_side * ls) {
for (auto & t : ls->m_coeffs) {
var_index vi = t.second;
unsigned column = get_column_index_from_var_index(vi);
lean_assert(is_valid(column));
A.set(i, column, convert_struct<U, mpq>::convert(t.first));
}
unsigned additional_column = get_column_index_from_var_index(ls->m_additional_var_index);
lean_assert(is_valid(additional_column));
A.set(i, additional_column, - one_of_type<U>());
}
void lar_solver::prepare_core_solver_fields(static_matrix<U, V> & A, std::vector<V> & x,
std::vector<V> & low_bound,
std::vector<V> & upper_bound) {
create_matrix_A(A);
fill_bounds_for_core_solver(low_bound, upper_bound);
if (m_status == INFEASIBLE) {
lean_assert(false); // not implemented
}
resize_and_init_x_with_zeros(x, A.column_count());
lean_assert(m_lar_core_solver_params.m_basis.size() == A.row_count());
}
edge(expr const & e, bool fn) {
m_fn = fn;
lean_assert(is_constant(e) || is_local(e));
if (is_constant(e)) {
m_kind = edge_kind::Constant;
m_name = const_name(e);
} else {
lean_assert(is_local(e));
m_kind = edge_kind::Local;
m_name = mlocal_name(e);
}
}
template <typename T, typename X> unsigned static_matrix<T, X>::lowest_row_in_column(unsigned col) {
lean_assert(col < column_count());
column_strip & colstrip = m_columns[col];
lean_assert(colstrip.size() > 0);
unsigned ret = 0;
for (auto & t : colstrip) {
if (t.m_i > ret) {
ret = t.m_i;
}
}
return ret;
}
constraint_index lar_solver::add_constraint(const buffer<std::pair<mpq, var_index>>& left_side, lconstraint_kind kind_par, mpq right_side_par) {
lean_assert(left_side.size() > 0);
constraint_index i = m_available_constr_index++;
lean_assert(m_normalized_constraints.find(i) == m_normalized_constraints.end());
lar_constraint original_constr(left_side, kind_par, right_side_par, i);
canonic_left_side * ls = create_or_fetch_existing_left_side(left_side);
mpq ratio = find_ratio_of_original_constraint_to_normalized(ls, original_constr);
auto kind = ratio.is_neg()? flip_kind(kind_par): kind_par;
mpq right_side = right_side_par / ratio;
lar_normalized_constraint normalized_constraint(ls, ratio, kind, right_side, original_constr);
m_normalized_constraints[i] = normalized_constraint;
return i;
}
template <typename T, typename X> void static_matrix<T, X>::set(unsigned row, unsigned col, T const & val) {
if (numeric_traits<T>::is_zero(val)) return;
lean_assert(row < row_count() && col < column_count());
#ifdef LEAN_DEBUG
pair<unsigned, unsigned> p(row, col);
lean_assert(m_domain.find(p) == m_domain.end());
m_domain.insert(p);
#endif
auto & r = m_rows[row];
unsigned offs_in_cols = m_columns[col].size();
m_columns[col].push_back(make_column_cell(row, r.size(), val));
r.push_back(make_row_cell(col, offs_in_cols, val));
}
void lar_solver::map_left_side_to_A_of_core_solver(canonic_left_side* left_side, unsigned j) {
var_index additional_var = left_side->m_additional_var_index;
lean_assert(valid_index(additional_var));
auto it = m_map_from_var_index_to_column_info_with_cls.find(additional_var);
lean_assert(it != m_map_from_var_index_to_column_info_with_cls.end());
column_info<mpq> & ci = it->second.m_column_info;
lean_assert(!is_valid(ci.get_column_index()));
lean_assert(left_side->size() > 0); // if size is zero we have an empty row
left_side->m_row_index = m_lar_core_solver_params.m_basis.size();
m_lar_core_solver_params.m_basis.push_back(j); // j will be a basis column, so we put it into the basis as well
lean_assert(m_map_from_column_indices_to_var_index.find(j) == m_map_from_column_indices_to_var_index.end());
ci.set_column_index(j);
m_map_from_column_indices_to_var_index[j] = additional_var;
}
void lar_solver::restrict_delta_on_upper_bound(mpq& delta, unsigned j) {
numeric_pair<mpq> & x = m_lar_core_solver_params.m_x[j];
numeric_pair<mpq> & u = m_lar_core_solver_params.m_upper_bounds[j];
mpq & xx = x.x;
mpq & xy = x.y;
mpq & ux = u.x;
if (xx == ux) {
lean_assert(xy <= numeric_traits<mpq>::zero());
} else {
lean_assert(xx < ux);
if (xy <= zero_of_type<mpq>()) return;
delta = std::min(delta, (ux - xx)/ (2 * xy)); // we need to have delta * xy < ux - xx, for the strict case
}
}
void refine_lower(mpq const & q, mpbq & l, mpbq & u) {
lean_assert(l < q && q < u);
lean_assert(!q.get_denominator().is_power_of_two());
mpbq mid;
while (true) {
mid = l + u;
div2(mid);
if (mid < q) {
swap(l, mid);
lean_assert(l < q && q < u);
return;
}
swap(u, mid);
}
}
void lar_solver::fill_bounds_for_core_solver(std::vector<V> & lb, std::vector<V> & ub) {
unsigned n = static_cast<unsigned>(m_map_from_var_index_to_column_info_with_cls.size()); // this is the number of columns
lb.resize(n);
ub.resize(n);
for (auto t : m_set_of_canonic_left_sides) {
auto & ci = get_column_info_from_var_index(t->m_additional_var_index);
unsigned j = ci.get_column_index();
lean_assert(is_valid(j));
lean_assert(j < n);
if (ci.low_bound_is_set())
lb[j] = conversion_helper<V>::get_low_bound(ci);
if (ci.upper_bound_is_set())
ub[j] = conversion_helper<V>::get_upper_bound(ci);
}
}
template <typename T, typename X> void static_matrix<T, X>::forget_last_columns(unsigned how_many_to_forget) {
lean_assert(m_columns.size() >= how_many_to_forget);
unsigned j = column_count() - 1;
for (; how_many_to_forget > 0; how_many_to_forget--) {
remove_last_column(j --);
}
}
expr dsimplify_core_fn::visit_app(expr const & e) {
buffer<expr> args;
bool modified = false;
expr f = get_app_args(e, args);
unsigned i = 0;
if (!m_cfg.m_canonize_instances) {
fun_info info = get_fun_info(m_ctx, f, args.size());
for (param_info const & pinfo : info.get_params_info()) {
lean_assert(i < args.size());
expr new_a;
if (pinfo.is_inst_implicit()) {
new_a = m_defeq_canonizer.canonize(args[i], m_need_restart);
} else {
new_a = visit(args[i]);
}
if (new_a != args[i])
modified = true;
args[i] = new_a;
i++;
}
}
for (; i < args.size(); i++) {
expr new_a = visit(args[i]);
if (new_a != args[i])
modified = true;
args[i] = new_a;
}
if (modified)
return mk_app(f, args);
else
return e;
}
void get_structure_instance_info(expr const & e,
name & struct_name,
optional<expr> & source,
buffer<name> & field_names,
buffer<expr> & field_values) {
lean_assert(is_structure_instance(e));
struct_name = static_cast<structure_instance_macro_cell const*>(macro_def(e).raw())->get_struct();
list<name> const & fns = static_cast<structure_instance_macro_cell const*>(macro_def(e).raw())->get_field_names();
to_buffer(fns, field_names);
unsigned num_fields = field_names.size();
lean_assert(macro_num_args(e) == num_fields || macro_num_args(e) == num_fields+1);
if (num_fields < macro_num_args(e))
source = macro_arg(e, num_fields);
for (unsigned i = 0; i < num_fields; i++)
field_values.push_back(macro_arg(e, i));
}
bool scanner::is_next_digit() {
lean_assert(curr() != EOF);
if (m_spos + 1 < static_cast<int>(m_curr_line.size()))
return std::isdigit(m_curr_line[m_spos+1]);
else
return false;
}
expr replace_visitor::visit_let(expr const & e) {
lean_assert(is_let(e));
expr new_t = visit(let_type(e));
expr new_v = visit(let_value(e));
expr new_b = visit(let_body(e));
return update_let(e, new_t, new_v, new_b);
}
void lar_solver::restrict_delta_on_low_bound_column(mpq& delta, unsigned j) {
numeric_pair<mpq> & x = m_lar_core_solver_params.m_x[j];
numeric_pair<mpq> & l = m_lar_core_solver_params.m_low_bounds[j];
mpq & xx = x.x;
mpq & xy = x.y;
mpq & lx = l.x;
if (xx == lx) {
lean_assert(xy >= numeric_traits<mpq>::zero());
} else {
lean_assert(xx >= lx); // we need lx <= xx + delta*xy, or delta*xy >= lx - xx, or - delta*xy <= xx - ls.
// The right part is not negative. The delta is positive. If xy >= 0 we have the ineqality
// otherwise we need to have delta not greater than - (xx - lx)/xy. We use the 2 coefficient to handle the strict case
if (xy >= zero_of_type<mpq>()) return;
delta = std::min(delta, (lx - xx)/ (2 * xy)); // we need to have delta * xy < xx - lx for the strict case
}
}
expr replace_visitor::visit_macro(expr const & e) {
lean_assert(is_macro(e));
buffer<expr> new_args;
for (unsigned i = 0; i < macro_num_args(e); i++)
new_args.push_back(visit(macro_arg(e, i)));
return update_macro(e, new_args.size(), new_args.data());
}
void display_decimal(std::ostream & out, mpq const & a, unsigned prec) {
mpz n1, d1, v1;
numerator(n1, a);
denominator(d1, a);
if (a.is_neg()) {
out << "-";
n1.neg();
}
v1 = n1 / d1;
out << v1;
n1 = rem(n1, d1);
if (n1.is_zero())
return;
out << ".";
for (unsigned i = 0; i < prec; i++) {
n1 *= 10;
v1 = n1 / d1;
lean_assert(v1 < 10);
out << v1;
n1 = rem(n1, d1);
if (n1.is_zero())
return;
}
out << "?";
}
template <typename T, typename X> void static_matrix<T, X>::copy_column_to_vector (unsigned j, indexed_vector<T> & v) const {
lean_assert(j < m_columns.size());
for (auto & it : m_columns[j]) {
if (!is_zero(it.m_value))
v.set_value(it.m_value, it.m_i);
}
}
void expr_cell::dealloc() {
try {
del_buffer todo;
todo.push_back(this);
while (!todo.empty()) {
expr_cell * it = todo.back();
todo.pop_back();
lean_assert(it->get_rc() == 0);
switch (it->kind()) {
case expr_kind::Var: static_cast<expr_var*>(it)->dealloc(); break;
case expr_kind::Macro: static_cast<expr_macro*>(it)->dealloc(todo); break;
case expr_kind::Meta: static_cast<expr_mlocal*>(it)->dealloc(todo); break;
case expr_kind::Local: static_cast<expr_local*>(it)->dealloc(todo); break;
case expr_kind::Constant: static_cast<expr_const*>(it)->dealloc(); break;
case expr_kind::Sort: static_cast<expr_sort*>(it)->dealloc(); break;
case expr_kind::App: static_cast<expr_app*>(it)->dealloc(todo); break;
case expr_kind::Lambda:
case expr_kind::Pi: static_cast<expr_binding*>(it)->dealloc(todo); break;
case expr_kind::Let: static_cast<expr_let*>(it)->dealloc(todo); break;
}
}
} catch (std::bad_alloc&) {
// We need this catch, because push_back may fail when expanding the buffer.
// In this case, we avoid the crash, and "accept" the memory leak.
}
}
void row_eta_matrix<T, X>::apply_from_right(indexed_vector<T> & w) {
T w_row = w[m_row];
if (numeric_traits<T>::is_zero(w_row)) return;
#ifdef LEAN_DEBUG
// dense_matrix<T> deb(*this);
// auto clone_w = clone_vector<T>(w.m_data, m_dimension);
// deb.apply_from_right(clone_w);
#endif
for (auto & it : m_row_vector.m_data) {
T old_val = w[it.first];
T v = w[it.index()] += w_row * it.second;
if (numeric_traits<T>::is_zero(old_val)) {
w.m_index.push_back(it.index());
} else if (numeric_traits<T>::is_zero(v)) { // it is a very rare case
auto w_it = std::find(w.m_index.begin(), w.m_index.end(), it.index());
lean_assert(w_it != w.m_index.end());
w.m_index.erase(w_it);
}
}
#ifdef LEAN_DEBUG
// lean_assert(vectors_are_equal<T>(clone_w, w.m_data, m_dimension));
// for (unsigned i = 0; i < m_dimension; i++) {
// if (!numeric_traits<T>::is_zero(w.m_data[i])) {
// lean_assert(std::find(w.m_index.begin(), w.m_index.end(), i) != w.m_index.end());
// }
// }
// delete clone_w;
#endif
}