c_typecast.cpp

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/*******************************************************************\
 
Module:
 
Author: Daniel Kroening, kroening@kroening.com
 
\*******************************************************************/
 
#include "c_typecast.h"
 
#include <util/arith_tools.h>
#include <util/c_types.h>
#include <util/config.h>
#include <util/expr_util.h>
#include <util/mathematical_types.h>
#include <util/namespace.h>
#include <util/pointer_expr.h>
#include <util/rational.h>
#include <util/rational_tools.h>
#include <util/simplify_expr.h>
#include <util/std_expr.h>
 
#include "c_qualifiers.h"
 
#include <algorithm>
 
bool c_implicit_typecast(
  exprt &expr,
  const typet &dest_type,
  const namespacet &ns)
{
  c_typecastt c_typecast(ns);
  c_typecast.implicit_typecast(expr, dest_type);
  return !c_typecast.errors.empty();
}
 
bool check_c_implicit_typecast(
  const typet &src_type,
  const typet &dest_type,
  const namespacet &ns)
{
  c_typecastt c_typecast(ns);
  exprt tmp;
  tmp.type()=src_type;
  c_typecast.implicit_typecast(tmp, dest_type);
  return !c_typecast.errors.empty();
}

bool c_implicit_typecast_arithmetic(
  exprt &expr1, exprt &expr2,
  const namespacet &ns)
{
  c_typecastt c_typecast(ns);
  c_typecast.implicit_typecast_arithmetic(expr1, expr2);
  return !c_typecast.errors.empty();
}
 
bool has_a_void_pointer(const typet &type)
{
  if(type.id()==ID_pointer)
  {
    const auto &pointer_type = to_pointer_type(type);
 
    if(pointer_type.base_type().id() == ID_empty)
      return true;
 
    return has_a_void_pointer(pointer_type.base_type());
  }
  else
    return false;
}
 
bool check_c_implicit_typecast(
  const typet &src_type,
  const typet &dest_type)
{
  // check qualifiers
 
  if(
    src_type.id() == ID_pointer && dest_type.id() == ID_pointer &&
    to_pointer_type(src_type).base_type().get_bool(ID_C_constant) &&
    !to_pointer_type(dest_type).base_type().get_bool(ID_C_constant))
  {
    return true;
  }
 
  if(src_type==dest_type)
    return false;
 
  const irep_idt &src_type_id=src_type.id();
 
  if(src_type_id==ID_c_bit_field)
  {
    return check_c_implicit_typecast(
      to_c_bit_field_type(src_type).underlying_type(), dest_type);
  }
 
  if(dest_type.id()==ID_c_bit_field)
  {
    return check_c_implicit_typecast(
      src_type, to_c_bit_field_type(dest_type).underlying_type());
  }
 
  if(src_type_id==ID_natural)
  {
    if(
      dest_type.id() == ID_bool || dest_type.id() == ID_c_bool ||
      dest_type.id() == ID_integer || dest_type.id() == ID_rational ||
      dest_type.id() == ID_real || dest_type.id() == ID_complex ||
      dest_type.id() == ID_unsignedbv || dest_type.id() == ID_signedbv ||
      dest_type.id() == ID_floatbv || dest_type.id() == ID_complex)
    {
      return false;
    }
  }
  else if(src_type_id==ID_integer)
  {
    if(
      dest_type.id() == ID_bool || dest_type.id() == ID_c_bool ||
      dest_type.id() == ID_natural || dest_type.id() == ID_rational ||
      dest_type.id() == ID_real || dest_type.id() == ID_complex ||
      dest_type.id() == ID_unsignedbv || dest_type.id() == ID_signedbv ||
      dest_type.id() == ID_floatbv || dest_type.id() == ID_fixedbv ||
      dest_type.id() == ID_pointer || dest_type.id() == ID_complex)
    {
      return false;
    }
  }
  else if(src_type_id==ID_real)
  {
    if(dest_type.id()==ID_bool ||
       dest_type.id()==ID_c_bool ||
       dest_type.id()==ID_complex ||
       dest_type.id()==ID_floatbv ||
       dest_type.id()==ID_fixedbv ||
       dest_type.id()==ID_complex)
      return false;
  }
  else if(src_type_id==ID_rational)
  {
    if(
      dest_type.id() == ID_bool || dest_type.id() == ID_c_bool ||
      dest_type.id() == ID_real || dest_type.id() == ID_complex ||
      dest_type.id() == ID_floatbv || dest_type.id() == ID_fixedbv ||
      dest_type.id() == ID_complex)
    {
      return false;
    }
  }
  else if(src_type_id==ID_bool)
  {
    if(
      dest_type.id() == ID_c_bool || dest_type.id() == ID_integer ||
      dest_type.id() == ID_natural || dest_type.id() == ID_rational ||
      dest_type.id() == ID_real || dest_type.id() == ID_unsignedbv ||
      dest_type.id() == ID_signedbv || dest_type.id() == ID_pointer ||
      dest_type.id() == ID_floatbv || dest_type.id() == ID_fixedbv ||
      dest_type.id() == ID_c_enum || dest_type.id() == ID_c_enum_tag ||
      dest_type.id() == ID_complex)
    {
      return false;
    }
  }
  else if(src_type_id==ID_unsignedbv ||
          src_type_id==ID_signedbv ||
          src_type_id==ID_c_enum ||
          src_type_id==ID_c_enum_tag ||
          src_type_id==ID_c_bool)
  {
    if(
      dest_type.id() == ID_unsignedbv || dest_type.id() == ID_bool ||
      dest_type.id() == ID_c_bool || dest_type.id() == ID_integer ||
      dest_type.id() == ID_natural || dest_type.id() == ID_rational ||
      dest_type.id() == ID_real || dest_type.id() == ID_signedbv ||
      dest_type.id() == ID_floatbv || dest_type.id() == ID_fixedbv ||
      dest_type.id() == ID_pointer || dest_type.id() == ID_c_enum ||
      dest_type.id() == ID_c_enum_tag || dest_type.id() == ID_complex)
    {
      return false;
    }
  }
  else if(src_type_id==ID_floatbv ||
          src_type_id==ID_fixedbv)
  {
    if(dest_type.id()==ID_bool ||
       dest_type.id()==ID_c_bool ||
       dest_type.id()==ID_integer ||
       dest_type.id()==ID_real ||
       dest_type.id()==ID_rational ||
       dest_type.id()==ID_signedbv ||
       dest_type.id()==ID_unsignedbv ||
       dest_type.id()==ID_floatbv ||
       dest_type.id()==ID_fixedbv ||
       dest_type.id()==ID_complex)
      return false;
  }
  else if(src_type_id==ID_complex)
  {
    if(dest_type.id()==ID_complex)
    {
      return check_c_implicit_typecast(
        to_complex_type(src_type).subtype(),
        to_complex_type(dest_type).subtype());
    }
    else
    {
      // 6.3.1.7, par 2:
 
      // When a value of complex type is converted to a real type, the
      // imaginary part of the complex value is discarded and the value of the
      // real part is converted according to the conversion rules for the
      // corresponding real type.
 
      return check_c_implicit_typecast(
        to_complex_type(src_type).subtype(), dest_type);
    }
  }
  else if(src_type_id==ID_array ||
          src_type_id==ID_pointer)
  {
    if(dest_type.id()==ID_pointer)
    {
      const irept &dest_subtype = to_pointer_type(dest_type).base_type();
      const irept &src_subtype = to_type_with_subtype(src_type).subtype();
 
      if(src_subtype == dest_subtype)
      {
        return false;
      }
      else if(
        has_a_void_pointer(src_type) || // from void to anything
        has_a_void_pointer(dest_type))  // to void from anything
      {
        return false;
      }
    }
 
    if(
      dest_type.id() == ID_array && to_type_with_subtype(src_type).subtype() ==
                                      to_array_type(dest_type).element_type())
    {
      return false;
    }
 
    if(dest_type.id()==ID_bool ||
       dest_type.id()==ID_c_bool ||
       dest_type.id()==ID_unsignedbv ||
       dest_type.id()==ID_signedbv)
      return false;
  }
  else if(src_type_id==ID_vector)
  {
    if(dest_type.id()==ID_vector)
      return false;
  }
  else if(src_type_id==ID_complex)
  {
    if(dest_type.id()==ID_complex)
    {
      // We convert between complex types if we convert between
      // their component types.
      if(!check_c_implicit_typecast(
           to_complex_type(src_type).subtype(),
           to_complex_type(dest_type).subtype()))
      {
        return false;
      }
    }
  }
 
  return true;
}
 
typet c_typecastt::follow_with_qualifiers(const typet &src_type)
{
  if(
    src_type.id() != ID_struct_tag &&
    src_type.id() != ID_union_tag)
  {
    return src_type;
  }
 
  typet result_type=src_type;
 
  // collect qualifiers
  c_qualifierst qualifiers(src_type);
 
  if(
    auto struct_tag_type = type_try_dynamic_cast<struct_tag_typet>(result_type))
  {
    const typet &followed_type = ns.follow_tag(*struct_tag_type);
    result_type = followed_type;
    qualifiers += c_qualifierst(followed_type);
  }
  else if(
    auto union_tag_type = type_try_dynamic_cast<union_tag_typet>(result_type))
  {
    const typet &followed_type = ns.follow_tag(*union_tag_type);
    result_type = followed_type;
    qualifiers += c_qualifierst(followed_type);
  }
 
  qualifiers.write(result_type);
 
  return result_type;
}
 
c_typecastt::c_typet c_typecastt::get_c_type(
  const typet &type) const
{
  if(type.id()==ID_signedbv)
  {
    const std::size_t width = to_bitvector_type(type).get_width();
 
    if(width<=config.ansi_c.char_width)
      return CHAR;
    else if(width<=config.ansi_c.short_int_width)
      return SHORT;
    else if(width<=config.ansi_c.int_width)
      return INT;
    else if(width<=config.ansi_c.long_int_width)
      return LONG;
    else if(width<=config.ansi_c.long_long_int_width)
      return LONGLONG;
    else
      return LARGE_SIGNED_INT;
  }
  else if(type.id()==ID_unsignedbv)
  {
    const std::size_t width = to_bitvector_type(type).get_width();
 
    if(width<=config.ansi_c.char_width)
      return UCHAR;
    else if(width<=config.ansi_c.short_int_width)
      return USHORT;
    else if(width<=config.ansi_c.int_width)
      return UINT;
    else if(width<=config.ansi_c.long_int_width)
      return ULONG;
    else if(width<=config.ansi_c.long_long_int_width)
      return ULONGLONG;
    else
      return LARGE_UNSIGNED_INT;
  }
  else if(type.id()==ID_bool)
    return BOOL;
  else if(type.id()==ID_c_bool)
    return BOOL;
  else if(type.id()==ID_floatbv)
  {
    const std::size_t width = to_bitvector_type(type).get_width();
 
    if(width<=config.ansi_c.single_width)
      return SINGLE;
    else if(width<=config.ansi_c.double_width)
      return DOUBLE;
    else if(width<=config.ansi_c.long_double_width)
      return LONGDOUBLE;
    else if(width<=128)
      return FLOAT128;
  }
  else if(type.id()==ID_fixedbv)
  {
    return FIXEDBV;
  }
  else if(type.id()==ID_pointer)
  {
    if(to_pointer_type(type).base_type().id() == ID_empty)
      return VOIDPTR;
    else
      return PTR;
  }
  else if(type.id()==ID_array)
  {
    return PTR;
  }
  else if(type.id() == ID_c_enum || type.id() == ID_c_enum_tag)
  {
    return INT;
  }
  else if(type.id()==ID_rational)
    return RATIONAL;
  else if(type.id()==ID_real)
    return REAL;
  else if(type.id()==ID_complex)
    return COMPLEX;
  else if(type.id()==ID_c_bit_field)
  {
    const auto &bit_field_type = to_c_bit_field_type(type);
 
    // We take the underlying type, and then apply the number
    // of bits given
    typet underlying_type;
 
    if(bit_field_type.underlying_type().id() == ID_c_enum_tag)
    {
      const auto &followed =
        ns.follow_tag(to_c_enum_tag_type(bit_field_type.underlying_type()));
      if(followed.is_incomplete())
        return INT;
      else
        underlying_type = followed.underlying_type();
    }
    else
      underlying_type = bit_field_type.underlying_type();
 
    const bitvector_typet new_type(
      underlying_type.id(), bit_field_type.get_width());
 
    return get_c_type(new_type);
  }
  else if(type.id() == ID_integer)
    return INTEGER;
  else if(type.id() == ID_natural)
    return NATURAL;
 
  return OTHER;
}
 
void c_typecastt::implicit_typecast_arithmetic(
  exprt &expr,
  c_typet c_type)
{
  typet new_type;
 
  switch(c_type)
  {
  case PTR:
    if(expr.type().id() == ID_array)
    {
      new_type = pointer_type(to_array_type(expr.type()).element_type());
      break;
    }
    return;
 
  case BOOL:       UNREACHABLE; // should always be promoted to int
  case CHAR:       UNREACHABLE; // should always be promoted to int
  case UCHAR:      UNREACHABLE; // should always be promoted to int
  case SHORT:      UNREACHABLE; // should always be promoted to int
  case USHORT:     UNREACHABLE; // should always be promoted to int
  case INT:        new_type=signed_int_type(); break;
  case UINT:       new_type=unsigned_int_type(); break;
  case LONG:       new_type=signed_long_int_type(); break;
  case ULONG:      new_type=unsigned_long_int_type(); break;
  case LONGLONG:   new_type=signed_long_long_int_type(); break;
  case ULONGLONG:  new_type=unsigned_long_long_int_type(); break;
  case SINGLE:     new_type=float_type(); break;
  case DOUBLE:     new_type=double_type(); break;
  case LONGDOUBLE: new_type=long_double_type(); break;
  // NOLINTNEXTLINE(whitespace/line_length)
  case FLOAT128:   new_type=ieee_float_spect::quadruple_precision().to_type(); break;
  case RATIONAL:   new_type=rational_typet(); break;
  case REAL:       new_type=real_typet(); break;
  case INTEGER:    new_type=integer_typet(); break;
  case NATURAL:
    new_type = natural_typet();
    break;
  case COMPLEX:
  case OTHER:
  case VOIDPTR:
  case FIXEDBV:
  case LARGE_UNSIGNED_INT:
  case LARGE_SIGNED_INT:
    return; // do nothing
  }
 
  if(new_type != expr.type())
    do_typecast(expr, new_type);
}
 
c_typecastt::c_typet c_typecastt::minimum_promotion(
  const typet &type) const
{
  c_typet c_type=get_c_type(type);
 
  // 6.3.1.1, par 2
 
  // "If an int can represent all values of the original type, the
  // value is converted to an int; otherwise, it is converted to
  // an unsigned int."
 
  c_typet max_type=std::max(c_type, INT); // minimum promotion
 
  // The second case can arise if we promote any unsigned type
  // that is as large as unsigned int. In this case the promotion configuration
  // via the enum is actually wrong, and we need to fix this up.
  if(
    config.ansi_c.short_int_width == config.ansi_c.int_width &&
    c_type == USHORT)
    max_type=UINT;
  else if(
    config.ansi_c.char_width == config.ansi_c.int_width && c_type == UCHAR)
    max_type=UINT;
 
  if(max_type==UINT &&
     type.id()==ID_c_bit_field &&
     to_c_bit_field_type(type).get_width()<config.ansi_c.int_width)
    max_type=INT;
 
  return max_type;
}
 
void c_typecastt::implicit_typecast_arithmetic(exprt &expr)
{
  c_typet c_type=minimum_promotion(expr.type());
  implicit_typecast_arithmetic(expr, c_type);
}
 
void c_typecastt::implicit_typecast(
  exprt &expr,
  const typet &type)
{
  typet src_type=follow_with_qualifiers(expr.type()),
        dest_type=follow_with_qualifiers(type);
 
  typet type_qual=type;
  c_qualifierst qualifiers(dest_type);
  qualifiers.write(type_qual);
 
  implicit_typecast_followed(expr, src_type, type_qual, dest_type);
}
 
void c_typecastt::implicit_typecast_followed(
  exprt &expr,
  const typet &src_type,
  const typet &orig_dest_type,
  const typet &dest_type)
{
  // do transparent union
  if(dest_type.id()==ID_union &&
     dest_type.get_bool(ID_C_transparent_union) &&
     src_type.id()!=ID_union)
  {
    // The argument corresponding to a transparent union type can be of any
    // type in the union; no explicit cast is required.
 
    // GCC docs say:
    //  If the union member type is a pointer, qualifiers like const on the
    //  referenced type must be respected, just as with normal pointer
    //  conversions.
    // But it is accepted, and Clang doesn't even emit a warning (GCC 4.7 does)
    typet src_type_no_const=src_type;
    if(
      src_type.id() == ID_pointer &&
      to_pointer_type(src_type).base_type().get_bool(ID_C_constant))
    {
      to_pointer_type(src_type_no_const).base_type().remove(ID_C_constant);
    }
 
    // Check union members.
    for(const auto &comp : to_union_type(dest_type).components())
    {
      if(!check_c_implicit_typecast(src_type_no_const, comp.type()))
      {
        // build union constructor
        union_exprt union_expr(comp.get_name(), expr, orig_dest_type);
        if(!src_type.full_eq(src_type_no_const))
          do_typecast(union_expr.op(), src_type_no_const);
        expr=union_expr;
        return; // ok
      }
    }
  }
 
  if(dest_type.id()==ID_pointer)
  {
    // special case: 0 == NULL
 
    if(
      simplify_expr(expr, ns) == 0 &&
      (src_type.id() == ID_unsignedbv || src_type.id() == ID_signedbv ||
       src_type.id() == ID_natural || src_type.id() == ID_integer))
    {
      expr = null_pointer_exprt{to_pointer_type(orig_dest_type)};
      return; // ok
    }
 
    if(src_type.id()==ID_pointer ||
       src_type.id()==ID_array)
    {
      // we are quite generous about pointers
 
      const typet &src_sub = to_type_with_subtype(src_type).subtype();
      const typet &dest_sub = to_pointer_type(dest_type).base_type();
 
      if(has_a_void_pointer(src_type) || has_a_void_pointer(dest_type))
      {
        // from/to void is always good
      }
      else if(src_sub.id()==ID_code &&
              dest_sub.id()==ID_code)
      {
        // very generous:
        // between any two function pointers it's ok
      }
      else if(src_sub == dest_sub)
      {
        // ok
      }
      else if((is_number(src_sub) ||
               src_sub.id()==ID_c_enum ||
               src_sub.id()==ID_c_enum_tag) &&
              (is_number(dest_sub) ||
               dest_sub.id()==ID_c_enum ||
               src_sub.id()==ID_c_enum_tag))
      {
        // Also generous: between any to scalar types it's ok.
        // We should probably check the size.
      }
      else if(
        src_sub.id() == ID_array && dest_sub.id() == ID_array &&
        to_array_type(src_sub).element_type() ==
          to_array_type(dest_sub).element_type())
      {
        // we ignore the size of the top-level array
        // in the case of pointers to arrays
      }
      else
        warnings.push_back("incompatible pointer types");
 
      // check qualifiers
 
      if(
        to_type_with_subtype(src_type).subtype().get_bool(ID_C_volatile) &&
        !to_pointer_type(dest_type).base_type().get_bool(ID_C_volatile))
      {
        warnings.push_back("disregarding volatile");
      }
 
      if(src_type==dest_type)
      {
        expr.type()=src_type; // because of qualifiers
      }
      else
        do_typecast(expr, orig_dest_type);
 
      return; // ok
    }
  }
 
  if(check_c_implicit_typecast(src_type, dest_type))
    errors.push_back("implicit conversion not permitted");
  else if(src_type!=dest_type)
    do_typecast(expr, orig_dest_type);
}
 
void c_typecastt::implicit_typecast_arithmetic(
  exprt &expr1,
  exprt &expr2)
{
  const typet &type1 = expr1.type();
  const typet &type2 = expr2.type();
 
  c_typet c_type1=minimum_promotion(type1),
          c_type2=minimum_promotion(type2);
 
  c_typet max_type=std::max(c_type1, c_type2);
 
  if(max_type==LARGE_SIGNED_INT || max_type==LARGE_UNSIGNED_INT)
  {
    // produce type
    typet result_type = (max_type == c_type1) ? type1 : type2;
 
    do_typecast(expr1, result_type);
    do_typecast(expr2, result_type);
 
    return;
  }
  else if(max_type==FIXEDBV)
  {
    typet result_type;
 
    if(c_type1==FIXEDBV && c_type2==FIXEDBV)
    {
      // get bigger of both
      std::size_t width1=to_fixedbv_type(type1).get_width();
      std::size_t width2=to_fixedbv_type(type2).get_width();
      if(width1>=width2)
        result_type=type1;
      else
        result_type=type2;
    }
    else if(c_type1==FIXEDBV)
      result_type=type1;
    else
      result_type=type2;
 
    do_typecast(expr1, result_type);
    do_typecast(expr2, result_type);
 
    return;
  }
  else if(max_type==COMPLEX)
  {
    if(c_type1==COMPLEX && c_type2==COMPLEX)
    {
      // promote to the one with bigger subtype
      if(
        get_c_type(to_complex_type(type1).subtype()) >
        get_c_type(to_complex_type(type2).subtype()))
      {
        do_typecast(expr2, type1);
      }
      else
        do_typecast(expr1, type2);
    }
    else if(c_type1==COMPLEX)
    {
      INVARIANT(c_type2 != COMPLEX, "both types were COMPLEX");
      do_typecast(expr2, to_complex_type(type1).subtype());
      do_typecast(expr2, type1);
    }
    else
    {
      INVARIANT(c_type2 == COMPLEX, "neither type was COMPLEX");
      do_typecast(expr1, to_complex_type(type2).subtype());
      do_typecast(expr1, type2);
    }
 
    return;
  }
  else if(max_type==SINGLE || max_type==DOUBLE ||
          max_type==LONGDOUBLE || max_type==FLOAT128)
  {
    // Special-case optimisation:
    // If we have two non-standard sized floats, don't do implicit type
    // promotion if we can possibly avoid it.
    if(type1==type2)
      return;
  }
  else if(max_type == OTHER)
  {
    errors.push_back("implicit arithmetic conversion not permitted");
    return;
  }
 
  implicit_typecast_arithmetic(expr1, max_type);
  implicit_typecast_arithmetic(expr2, max_type);
}
 
void c_typecastt::do_typecast(exprt &expr, const typet &dest_type)
{
  // special case: array -> pointer is actually
  // something like address_of
 
  const typet &src_type = expr.type();
 
  if(src_type.id()==ID_array)
  {
    // This is the promotion from an array
    // to a pointer to the first element.
    auto error_opt = check_address_can_be_taken(expr.type());
    if(error_opt.has_value())
    {
      errors.push_back(error_opt.value());
      return;
    }
 
    index_exprt index(expr, from_integer(0, c_index_type()));
    expr = typecast_exprt::conditional_cast(address_of_exprt(index), dest_type);
    return;
  }
 
  if(src_type!=dest_type)
  {
    // C booleans are special; we produce the
    // explicit comparison with zero.
    // Note that this requires ieee_float_notequal
    // in case of floating-point numbers.
 
    if(dest_type.get(ID_C_c_type)==ID_bool)
    {
      expr = typecast_exprt(is_not_zero(expr, ns), dest_type);
    }
    else if(dest_type.id()==ID_bool)
    {
      expr=is_not_zero(expr, ns);
    }
    else if(dest_type.id() == ID_rational)
    {
      if(auto div_expr = expr_try_dynamic_cast<div_exprt>(expr))
      {
        auto op1 = numeric_cast<mp_integer>(div_expr->lhs());
        auto op2 = numeric_cast<mp_integer>(div_expr->rhs());
        if(op1.has_value() && op2.has_value())
        {
          rationalt numerator{*op1};
          expr = from_rational(rationalt{*op1} / rationalt{*op2});
          return;
        }
      }
      else if(auto int_const = numeric_cast<mp_integer>(expr))
      {
        expr = from_integer(*int_const, dest_type);
        return;
      }
 
      expr = typecast_exprt(expr, dest_type);
    }
    else
    {
      expr = typecast_exprt(expr, dest_type);
    }
  }
}
 
std::optional<std::string>
c_typecastt::check_address_can_be_taken(const typet &type)
{
  if(type.id() == ID_c_bit_field)
    return std::string("cannot take address of a bit field");
 
  if(type.id() == ID_bool)
    return std::string("cannot take address of a proper Boolean");
 
  if(can_cast_type<bitvector_typet>(type))
  {
    // The width of the bitvector must be a multiple of CHAR_BIT.
    auto width = to_bitvector_type(type).get_width();
    if(width % config.ansi_c.char_width != 0)
    {
      return std::string(
        "bitvector must have width that is a multiple of CHAR_BIT");
    }
    else
      return {};
  }
 
  if(type.id() == ID_array)
    return check_address_can_be_taken(to_array_type(type).element_type());
 
  return {}; // ok
}