convert_expr_to_smt.cpp

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// Author: Diffblue Ltd.
#include <util/arith_tools.h>
#include <util/bitvector_expr.h>
#include <util/byte_operators.h>
#include <util/c_types.h>
#include <util/config.h>
#include <util/expr.h>
#include <util/expr_cast.h>
#include <util/expr_util.h>
#include <util/floatbv_expr.h>
#include <util/mathematical_expr.h>
#include <util/pointer_expr.h>
#include <util/pointer_predicates.h>
#include <util/range.h>
#include <util/std_expr.h>
#include <util/string_constant.h>
 
#include <solvers/prop/literal_expr.h>
#include <solvers/smt2_incremental/convert_expr_to_smt.h>
#include <solvers/smt2_incremental/theories/smt_array_theory.h>
#include <solvers/smt2_incremental/theories/smt_bit_vector_theory.h>
#include <solvers/smt2_incremental/theories/smt_core_theory.h>
 
#include <algorithm>
#include <functional>
#include <numeric>
#include <stack>
 
using sub_expression_mapt = std::unordered_map<exprt, smt_termt, irep_hash>;
 
template <typename factoryt>
static smt_termt convert_multiary_operator_to_terms(
  const multi_ary_exprt &expr,
  const sub_expression_mapt &converted,
  const factoryt &factory)
{
  PRECONDITION(expr.operands().size() >= 2);
  const auto operand_terms =
    make_range(expr.operands()).map([&](const exprt &expr) {
      return converted.at(expr);
    });
  return std::accumulate(
    ++operand_terms.begin(),
    operand_terms.end(),
    *operand_terms.begin(),
    factory);
}
 
template <typename target_typet>
static bool operands_are_of_type(const exprt &expr)
{
  return std::all_of(
    expr.operands().cbegin(), expr.operands().cend(), [](const exprt &operand) {
      return can_cast_type<target_typet>(operand.type());
    });
}
 
static smt_sortt convert_type_to_smt_sort(const bool_typet &type)
{
  return smt_bool_sortt{};
}
 
static smt_sortt convert_type_to_smt_sort(const bitvector_typet &type)
{
  return smt_bit_vector_sortt{type.get_width()};
}
 
static smt_sortt convert_type_to_smt_sort(const array_typet &type)
{
  return smt_array_sortt{
    convert_type_to_smt_sort(type.index_type()),
    convert_type_to_smt_sort(type.element_type())};
}
 
smt_sortt convert_type_to_smt_sort(const typet &type)
{
  if(const auto bool_type = type_try_dynamic_cast<bool_typet>(type))
  {
    return convert_type_to_smt_sort(*bool_type);
  }
  if(const auto bitvector_type = type_try_dynamic_cast<bitvector_typet>(type))
  {
    return convert_type_to_smt_sort(*bitvector_type);
  }
  if(const auto array_type = type_try_dynamic_cast<array_typet>(type))
  {
    return convert_type_to_smt_sort(*array_type);
  }
  UNIMPLEMENTED_FEATURE("Generation of SMT formula for type: " + type.pretty());
}
 
static smt_termt convert_expr_to_smt(const symbol_exprt &symbol_expr)
{
  return smt_identifier_termt{symbol_expr.get_identifier(),
                              convert_type_to_smt_sort(symbol_expr.type())};
}
 
static smt_termt convert_expr_to_smt(
  const nondet_symbol_exprt &nondet_symbol,
  const sub_expression_mapt &converted)
{
  // A nondet_symbol is a reference to an unconstrained function. This function
  // will already have been added as a dependency.
  return smt_identifier_termt{
    nondet_symbol.get_identifier(),
    convert_type_to_smt_sort(nondet_symbol.type())};
}
 
static smt_termt make_not_zero(const smt_termt &input, const typet &source_type)
{
  if(input.get_sort().cast<smt_bool_sortt>())
    return input;
  if(const auto bit_vector_sort = input.get_sort().cast<smt_bit_vector_sortt>())
  {
    return smt_core_theoryt::distinct(
      input, smt_bit_vector_constant_termt{0, *bit_vector_sort});
  }
  UNREACHABLE;
}
 
static smt_termt convert_c_bool_cast(
  const smt_termt &from_term,
  const typet &from_type,
  const bitvector_typet &to_type)
{
  const std::size_t c_bool_width = to_type.get_width();
  return smt_core_theoryt::if_then_else(
    make_not_zero(from_term, from_type),
    smt_bit_vector_constant_termt{1, c_bool_width},
    smt_bit_vector_constant_termt{0, c_bool_width});
}
 
static std::function<std::function<smt_termt(smt_termt)>(std::size_t)>
extension_for_type(const typet &type)
{
  if(can_cast_type<signedbv_typet>(type))
    return smt_bit_vector_theoryt::sign_extend;
  if(can_cast_type<unsignedbv_typet>(type))
    return smt_bit_vector_theoryt::zero_extend;
  if(can_cast_type<bv_typet>(type))
    return smt_bit_vector_theoryt::zero_extend;
  if(can_cast_type<pointer_typet>(type))
    return smt_bit_vector_theoryt::zero_extend;
  UNREACHABLE;
}
 
static smt_termt make_bitvector_resize_cast(
  const smt_termt &from_term,
  const bitvector_typet &from_type,
  const bitvector_typet &to_type)
{
  if(const auto to_fixedbv_type = type_try_dynamic_cast<fixedbv_typet>(to_type))
  {
    UNIMPLEMENTED_FEATURE(
      "Generation of SMT formula for type cast to fixed-point bitvector "
      "type: " +
      to_type.pretty());
  }
  if(const auto to_floatbv_type = type_try_dynamic_cast<floatbv_typet>(to_type))
  {
    UNIMPLEMENTED_FEATURE(
      "Generation of SMT formula for type cast to floating-point bitvector "
      "type: " +
      to_type.pretty());
  }
  const std::size_t from_width = from_type.get_width();
  const std::size_t to_width = to_type.get_width();
  if(to_width == from_width)
    return from_term;
  if(to_width < from_width)
    return smt_bit_vector_theoryt::extract(to_width - 1, 0)(from_term);
  const std::size_t extension_size = to_width - from_width;
  return extension_for_type(from_type)(extension_size)(from_term);
}
 
struct sort_based_cast_to_bit_vector_convertert final
  : public smt_sort_const_downcast_visitort
{
  const smt_termt &from_term;
  const typet &from_type;
  const bitvector_typet &to_type;
  std::optional<smt_termt> result;
 
  sort_based_cast_to_bit_vector_convertert(
    const smt_termt &from_term,
    const typet &from_type,
    const bitvector_typet &to_type)
    : from_term{from_term}, from_type{from_type}, to_type{to_type}
  {
  }
 
  void visit(const smt_bool_sortt &) override
  {
    result = convert_c_bool_cast(
      from_term, from_type, c_bool_typet{to_type.get_width()});
  }
 
  void visit(const smt_bit_vector_sortt &) override
  {
    if(const auto bitvector = type_try_dynamic_cast<bitvector_typet>(from_type))
      result = make_bitvector_resize_cast(from_term, *bitvector, to_type);
    else
      UNIMPLEMENTED_FEATURE(
        "Generation of SMT formula for type cast to bit vector from type: " +
        from_type.pretty());
  }
 
  void visit(const smt_array_sortt &) override
  {
    UNIMPLEMENTED_FEATURE(
      "Generation of SMT formula for type cast to bit vector from type: " +
      from_type.pretty());
  }
};
 
static smt_termt convert_bit_vector_cast(
  const smt_termt &from_term,
  const typet &from_type,
  const bitvector_typet &to_type)
{
  sort_based_cast_to_bit_vector_convertert converter{
    from_term, from_type, to_type};
  from_term.get_sort().accept(converter);
  POSTCONDITION(converter.result);
  return *converter.result;
}
 
static smt_termt convert_expr_to_smt(
  const typecast_exprt &cast,
  const sub_expression_mapt &converted)
{
  const auto &from_term = converted.at(cast.op());
  const typet &from_type = cast.op().type();
  const typet &to_type = cast.type();
  if(const auto bool_type = type_try_dynamic_cast<bool_typet>(to_type))
    return make_not_zero(from_term, cast.op().type());
  if(const auto c_bool_type = type_try_dynamic_cast<c_bool_typet>(to_type))
    return convert_c_bool_cast(from_term, from_type, *c_bool_type);
  if(const auto bit_vector = type_try_dynamic_cast<bitvector_typet>(to_type))
    return convert_bit_vector_cast(from_term, from_type, *bit_vector);
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for type cast expression: " + cast.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const floatbv_typecast_exprt &float_cast,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for floating point type cast expression: " +
    float_cast.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const struct_exprt &struct_construction,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for struct construction expression: " +
    struct_construction.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const union_exprt &union_construction,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for union construction expression: " +
    union_construction.pretty());
}
 
struct sort_based_literal_convertert : public smt_sort_const_downcast_visitort
{
  const constant_exprt &member_input;
  std::optional<smt_termt> result;
 
  explicit sort_based_literal_convertert(const constant_exprt &input)
    : member_input{input}
  {
  }
 
  void visit(const smt_bool_sortt &) override
  {
    result = smt_bool_literal_termt{member_input.is_true()};
  }
 
  void visit(const smt_bit_vector_sortt &bit_vector_sort) override
  {
    const auto &width = bit_vector_sort.bit_width();
    // We get the value using a non-signed interpretation, as smt bit vector
    // terms do not carry signedness.
    const auto value = bvrep2integer(member_input.get_value(), width, false);
    result = smt_bit_vector_constant_termt{value, bit_vector_sort};
  }
 
  void visit(const smt_array_sortt &array_sort) override
  {
    UNIMPLEMENTED_FEATURE(
      "Conversion of array SMT literal " + array_sort.pretty());
  }
};
 
static smt_termt convert_expr_to_smt(const constant_exprt &constant_literal)
{
  if(is_null_pointer(constant_literal))
  {
    const size_t bit_width =
      type_checked_cast<pointer_typet>(constant_literal.type()).get_width();
    // An address of 0 encodes an object identifier of 0 for the NULL object
    // and an offset of 0 into the object.
    const auto address = 0;
    return smt_bit_vector_constant_termt{address, bit_width};
  }
  if(constant_literal.type() == integer_typet{})
  {
    // This is converting integer constants into bit vectors for use with
    // bit vector based smt logics. As bit vector widths are not specified for
    // non bit vector types, this chooses a width based on the minimum needed
    // to hold the integer constant value.
    const auto value = numeric_cast_v<mp_integer>(constant_literal);
    return smt_bit_vector_constant_termt{value, address_bits(value + 1)};
  }
  const auto sort = convert_type_to_smt_sort(constant_literal.type());
  sort_based_literal_convertert converter(constant_literal);
  sort.accept(converter);
  return *converter.result;
}
 
static smt_termt convert_expr_to_smt(
  const concatenation_exprt &concatenation,
  const sub_expression_mapt &converted)
{
  if(operands_are_of_type<bitvector_typet>(concatenation))
  {
    return convert_multiary_operator_to_terms(
      concatenation, converted, smt_bit_vector_theoryt::concat);
  }
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for concatenation expression: " +
    concatenation.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const bitand_exprt &bitwise_and_expr,
  const sub_expression_mapt &converted)
{
  if(operands_are_of_type<bitvector_typet>(bitwise_and_expr))
  {
    return convert_multiary_operator_to_terms(
      bitwise_and_expr, converted, smt_bit_vector_theoryt::make_and);
  }
  else
  {
    UNIMPLEMENTED_FEATURE(
      "Generation of SMT formula for bitwise and expression: " +
      bitwise_and_expr.pretty());
  }
}
 
static smt_termt convert_expr_to_smt(
  const bitor_exprt &bitwise_or_expr,
  const sub_expression_mapt &converted)
{
  if(operands_are_of_type<bitvector_typet>(bitwise_or_expr))
  {
    return convert_multiary_operator_to_terms(
      bitwise_or_expr, converted, smt_bit_vector_theoryt::make_or);
  }
  else
  {
    UNIMPLEMENTED_FEATURE(
      "Generation of SMT formula for bitwise or expression: " +
      bitwise_or_expr.pretty());
  }
}
 
static smt_termt convert_expr_to_smt(
  const bitxor_exprt &bitwise_xor,
  const sub_expression_mapt &converted)
{
  if(operands_are_of_type<bitvector_typet>(bitwise_xor))
  {
    return convert_multiary_operator_to_terms(
      bitwise_xor, converted, smt_bit_vector_theoryt::make_xor);
  }
  else
  {
    UNIMPLEMENTED_FEATURE(
      "Generation of SMT formula for bitwise xor expression: " +
      bitwise_xor.pretty());
  }
}
 
static smt_termt convert_expr_to_smt(
  const bitnot_exprt &bitwise_not,
  const sub_expression_mapt &converted)
{
  if(can_cast_type<bitvector_typet>(bitwise_not.op().type()))
  {
    return smt_bit_vector_theoryt::make_not(converted.at(bitwise_not.op()));
  }
  else
  {
    UNIMPLEMENTED_FEATURE(
      "Generation of SMT formula for bitnot_exprt: " + bitwise_not.pretty());
  }
}
 
static smt_termt convert_expr_to_smt(
  const unary_minus_exprt &unary_minus,
  const sub_expression_mapt &converted)
{
  if(can_cast_type<integer_bitvector_typet>(unary_minus.op().type()))
  {
    return smt_bit_vector_theoryt::negate(converted.at(unary_minus.op()));
  }
  else
  {
    UNIMPLEMENTED_FEATURE(
      "Generation of SMT formula for unary minus expression: " +
      unary_minus.pretty());
  }
}
 
static smt_termt convert_expr_to_smt(
  const unary_plus_exprt &unary_plus,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for unary plus expression: " +
    unary_plus.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const sign_exprt &is_negative,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for \"is negative\" expression: " +
    is_negative.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const if_exprt &if_expression,
  const sub_expression_mapt &converted)
{
  return smt_core_theoryt::if_then_else(
    converted.at(if_expression.cond()),
    converted.at(if_expression.true_case()),
    converted.at(if_expression.false_case()));
}
 
static smt_termt convert_expr_to_smt(
  const and_exprt &and_expression,
  const sub_expression_mapt &converted)
{
  return convert_multiary_operator_to_terms(
    and_expression, converted, smt_core_theoryt::make_and);
}
 
static smt_termt convert_expr_to_smt(
  const or_exprt &or_expression,
  const sub_expression_mapt &converted)
{
  return convert_multiary_operator_to_terms(
    or_expression, converted, smt_core_theoryt::make_or);
}
 
static smt_termt convert_expr_to_smt(
  const xor_exprt &xor_expression,
  const sub_expression_mapt &converted)
{
  return convert_multiary_operator_to_terms(
    xor_expression, converted, smt_core_theoryt::make_xor);
}
 
static smt_termt convert_expr_to_smt(
  const implies_exprt &implies,
  const sub_expression_mapt &converted)
{
  return smt_core_theoryt::implies(
    converted.at(implies.op0()), converted.at(implies.op1()));
}
 
static smt_termt convert_expr_to_smt(
  const not_exprt &logical_not,
  const sub_expression_mapt &converted)
{
  return smt_core_theoryt::make_not(converted.at(logical_not.op()));
}
 
static smt_termt convert_expr_to_smt(
  const equal_exprt &equal,
  const sub_expression_mapt &converted)
{
  return smt_core_theoryt::equal(
    converted.at(equal.op0()), converted.at(equal.op1()));
}
 
static smt_termt convert_expr_to_smt(
  const notequal_exprt &not_equal,
  const sub_expression_mapt &converted)
{
  return smt_core_theoryt::distinct(
    converted.at(not_equal.op0()), converted.at(not_equal.op1()));
}
 
static smt_termt convert_expr_to_smt(
  const ieee_float_equal_exprt &float_equal,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for floating point equality expression: " +
    float_equal.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const ieee_float_notequal_exprt &float_not_equal,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for floating point not equal expression: " +
    float_not_equal.pretty());
}
 
template <typename unsigned_factory_typet, typename signed_factory_typet>
static smt_termt convert_relational_to_smt(
  const binary_relation_exprt &binary_relation,
  const unsigned_factory_typet &unsigned_factory,
  const signed_factory_typet &signed_factory,
  const sub_expression_mapt &converted)
{
  PRECONDITION(binary_relation.lhs().type() == binary_relation.rhs().type());
  const auto &lhs = converted.at(binary_relation.lhs());
  const auto &rhs = converted.at(binary_relation.rhs());
  const typet operand_type = binary_relation.lhs().type();
  if(can_cast_type<pointer_typet>(operand_type))
  {
    // The code here is operating under the assumption that the comparison
    // operands have types for which the comparison makes sense.
 
    // We already know this is the case given that we have followed
    // the if statement branch, but including the same check here
    // for consistency (it's cheap).
    const auto lhs_type_is_pointer =
      can_cast_type<pointer_typet>(binary_relation.lhs().type());
    const auto rhs_type_is_pointer =
      can_cast_type<pointer_typet>(binary_relation.rhs().type());
    INVARIANT(
      lhs_type_is_pointer && rhs_type_is_pointer,
      "pointer comparison requires that both operand types are pointers.");
    return unsigned_factory(lhs, rhs);
  }
  else if(lhs.get_sort().cast<smt_bit_vector_sortt>())
  {
    if(can_cast_type<unsignedbv_typet>(operand_type))
      return unsigned_factory(lhs, rhs);
    if(can_cast_type<signedbv_typet>(operand_type))
      return signed_factory(lhs, rhs);
  }
 
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for relational expression: " +
    binary_relation.pretty());
}
 
static std::optional<smt_termt> try_relational_conversion(
  const exprt &expr,
  const sub_expression_mapt &converted)
{
  if(const auto greater_than = expr_try_dynamic_cast<greater_than_exprt>(expr))
  {
    return convert_relational_to_smt(
      *greater_than,
      smt_bit_vector_theoryt::unsigned_greater_than,
      smt_bit_vector_theoryt::signed_greater_than,
      converted);
  }
  if(
    const auto greater_than_or_equal =
      expr_try_dynamic_cast<greater_than_or_equal_exprt>(expr))
  {
    return convert_relational_to_smt(
      *greater_than_or_equal,
      smt_bit_vector_theoryt::unsigned_greater_than_or_equal,
      smt_bit_vector_theoryt::signed_greater_than_or_equal,
      converted);
  }
  if(const auto less_than = expr_try_dynamic_cast<less_than_exprt>(expr))
  {
    return convert_relational_to_smt(
      *less_than,
      smt_bit_vector_theoryt::unsigned_less_than,
      smt_bit_vector_theoryt::signed_less_than,
      converted);
  }
  if(
    const auto less_than_or_equal =
      expr_try_dynamic_cast<less_than_or_equal_exprt>(expr))
  {
    return convert_relational_to_smt(
      *less_than_or_equal,
      smt_bit_vector_theoryt::unsigned_less_than_or_equal,
      smt_bit_vector_theoryt::signed_less_than_or_equal,
      converted);
  }
  return {};
}
 
static smt_termt convert_expr_to_smt(
  const plus_exprt &plus,
  const sub_expression_mapt &converted,
  const type_size_mapt &pointer_sizes)
{
  if(std::all_of(
       plus.operands().cbegin(), plus.operands().cend(), [](exprt operand) {
         return can_cast_type<integer_bitvector_typet>(operand.type());
       }))
  {
    return convert_multiary_operator_to_terms(
      plus, converted, smt_bit_vector_theoryt::add);
  }
  else if(can_cast_type<pointer_typet>(plus.type()))
  {
    INVARIANT(
      plus.operands().size() == 2,
      "We are only handling a binary version of plus when it has a pointer "
      "operand");
 
    exprt pointer;
    exprt scalar;
    for(auto &operand : plus.operands())
    {
      if(can_cast_type<pointer_typet>(operand.type()))
      {
        pointer = operand;
      }
      else
      {
        scalar = operand;
      }
    }
 
    // We need to ensure that we follow this code path only if the expression
    // our assumptions about the structure of the addition expression hold.
    INVARIANT(
      !can_cast_type<pointer_typet>(scalar.type()),
      "An addition expression with both operands being pointers when they are "
      "not dereferenced is malformed");
 
    const pointer_typet pointer_type =
      *type_try_dynamic_cast<pointer_typet>(pointer.type());
    const auto base_type = pointer_type.base_type();
    const auto pointer_size = pointer_sizes.at(base_type);
 
    return smt_bit_vector_theoryt::add(
      converted.at(pointer),
      smt_bit_vector_theoryt::multiply(converted.at(scalar), pointer_size));
  }
  else
  {
    UNIMPLEMENTED_FEATURE(
      "Generation of SMT formula for plus expression: " + plus.pretty());
  }
}
 
static smt_termt convert_expr_to_smt(
  const minus_exprt &minus,
  const sub_expression_mapt &converted,
  const type_size_mapt &pointer_sizes)
{
  const bool both_operands_bitvector =
    can_cast_type<integer_bitvector_typet>(minus.lhs().type()) &&
    can_cast_type<integer_bitvector_typet>(minus.rhs().type());
 
  const bool lhs_is_pointer = can_cast_type<pointer_typet>(minus.lhs().type());
  const bool rhs_is_pointer = can_cast_type<pointer_typet>(minus.rhs().type());
 
  const bool both_operands_pointers = lhs_is_pointer && rhs_is_pointer;
 
  // We don't really handle this - we just compute this to fall
  // into an if-else branch that gives proper error handling information.
  const bool one_operand_pointer = lhs_is_pointer || rhs_is_pointer;
 
  if(both_operands_bitvector)
  {
    return smt_bit_vector_theoryt::subtract(
      converted.at(minus.lhs()), converted.at(minus.rhs()));
  }
  else if(both_operands_pointers)
  {
    const auto lhs_base_type = to_pointer_type(minus.lhs().type()).base_type();
    const auto rhs_base_type = to_pointer_type(minus.rhs().type()).base_type();
    INVARIANT(
      lhs_base_type == rhs_base_type,
      "only pointers of the same object type can be subtracted.");
    return smt_bit_vector_theoryt::signed_divide(
      smt_bit_vector_theoryt::subtract(
        converted.at(minus.lhs()), converted.at(minus.rhs())),
      pointer_sizes.at(lhs_base_type));
  }
  else if(one_operand_pointer)
  {
    // It's semantically void to have an expression `3 - a` where `a`
    // is a pointer.
    INVARIANT(
      lhs_is_pointer,
      "minus expressions of pointer and integer expect lhs to be the pointer");
    const auto lhs_base_type = to_pointer_type(minus.lhs().type()).base_type();
 
    return smt_bit_vector_theoryt::subtract(
      converted.at(minus.lhs()),
      smt_bit_vector_theoryt::multiply(
        converted.at(minus.rhs()), pointer_sizes.at(lhs_base_type)));
  }
  else
  {
    UNIMPLEMENTED_FEATURE(
      "Generation of SMT formula for minus expression: " + minus.pretty());
  }
}
 
static smt_termt convert_expr_to_smt(
  const div_exprt &divide,
  const sub_expression_mapt &converted)
{
  const smt_termt &lhs = converted.at(divide.lhs());
  const smt_termt &rhs = converted.at(divide.rhs());
 
  const bool both_operands_bitvector =
    can_cast_type<integer_bitvector_typet>(divide.lhs().type()) &&
    can_cast_type<integer_bitvector_typet>(divide.rhs().type());
 
  const bool both_operands_unsigned =
    can_cast_type<unsignedbv_typet>(divide.lhs().type()) &&
    can_cast_type<unsignedbv_typet>(divide.rhs().type());
 
  if(both_operands_bitvector)
  {
    if(both_operands_unsigned)
    {
      return smt_bit_vector_theoryt::unsigned_divide(lhs, rhs);
    }
    else
    {
      return smt_bit_vector_theoryt::signed_divide(lhs, rhs);
    }
  }
  else
  {
    UNIMPLEMENTED_FEATURE(
      "Generation of SMT formula for divide expression: " + divide.pretty());
  }
}
 
static smt_termt convert_expr_to_smt(
  const ieee_float_op_exprt &float_operation,
  const sub_expression_mapt &converted)
{
  // This case includes the floating point plus, minus, division and
  // multiplication operations.
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for floating point operation expression: " +
    float_operation.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const mod_exprt &truncation_modulo,
  const sub_expression_mapt &converted)
{
  const smt_termt &lhs = converted.at(truncation_modulo.lhs());
  const smt_termt &rhs = converted.at(truncation_modulo.rhs());
 
  const bool both_operands_bitvector =
    can_cast_type<integer_bitvector_typet>(truncation_modulo.lhs().type()) &&
    can_cast_type<integer_bitvector_typet>(truncation_modulo.rhs().type());
 
  const bool both_operands_unsigned =
    can_cast_type<unsignedbv_typet>(truncation_modulo.lhs().type()) &&
    can_cast_type<unsignedbv_typet>(truncation_modulo.rhs().type());
 
  if(both_operands_bitvector)
  {
    if(both_operands_unsigned)
    {
      return smt_bit_vector_theoryt::unsigned_remainder(lhs, rhs);
    }
    else
    {
      return smt_bit_vector_theoryt::signed_remainder(lhs, rhs);
    }
  }
  else
  {
    UNIMPLEMENTED_FEATURE(
      "Generation of SMT formula for remainder (modulus) expression: " +
      truncation_modulo.pretty());
  }
}
 
static smt_termt convert_expr_to_smt(
  const euclidean_mod_exprt &euclidean_modulo,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for euclidean modulo expression: " +
    euclidean_modulo.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const mult_exprt &multiply,
  const sub_expression_mapt &converted)
{
  if(std::all_of(
       multiply.operands().cbegin(),
       multiply.operands().cend(),
       [](exprt operand) {
         return can_cast_type<integer_bitvector_typet>(operand.type());
       }))
  {
    return convert_multiary_operator_to_terms(
      multiply, converted, smt_bit_vector_theoryt::multiply);
  }
  else
  {
    UNIMPLEMENTED_FEATURE(
      "Generation of SMT formula for multiply expression: " +
      multiply.pretty());
  }
}
 
static smt_termt convert_expr_to_smt(
  const address_of_exprt &address_of,
  const sub_expression_mapt &converted,
  const smt_object_mapt &object_map)
{
  const auto type = type_try_dynamic_cast<pointer_typet>(address_of.type());
  INVARIANT(
    type, "Result of the address_of operator should have pointer type.");
  const auto base = find_object_base_expression(address_of);
  const auto object = object_map.find(base);
  INVARIANT(
    object != object_map.end(),
    "Objects should be tracked before converting their address to SMT terms");
  const std::size_t object_id = object->second.unique_id;
  const std::size_t object_bits = config.bv_encoding.object_bits;
  const std::size_t max_objects = std::size_t(1) << object_bits;
  if(object_id >= max_objects)
  {
    throw analysis_exceptiont{
      "too many addressed objects: maximum number of objects is set to 2^n=" +
      std::to_string(max_objects) + " (with n=" + std::to_string(object_bits) +
      "); " +
      "use the `--object-bits n` option to increase the maximum number"};
  }
  const smt_termt object_bit_vector =
    smt_bit_vector_constant_termt{object_id, object_bits};
  INVARIANT(
    type->get_width() > object_bits,
    "Pointer should be wider than object_bits in order to allow for offset "
    "encoding.");
  const size_t offset_bits = type->get_width() - object_bits;
  if(
    const auto symbol =
      expr_try_dynamic_cast<symbol_exprt>(address_of.object()))
  {
    const smt_bit_vector_constant_termt offset{0, offset_bits};
    return smt_bit_vector_theoryt::concat(object_bit_vector, offset);
  }
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for address of expression: " +
    address_of.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const array_of_exprt &array_of,
  const sub_expression_mapt &converted)
{
  // This function is unreachable as the `array_of_exprt` nodes are already
  // fully converted by the incremental decision procedure functions
  // (smt2_incremental_decision_proceduret::define_array_function).
  UNHANDLED_CASE;
}
 
static smt_termt convert_expr_to_smt(
  const array_comprehension_exprt &array_comprehension,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for array comprehension expression: " +
    array_comprehension.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const index_exprt &index_of,
  const sub_expression_mapt &converted)
{
  const smt_termt &array = converted.at(index_of.array());
  const smt_termt &index = converted.at(index_of.index());
  return smt_array_theoryt::select(array, index);
}
 
template <typename factoryt, typename shiftt>
static smt_termt convert_to_smt_shift(
  const factoryt &factory,
  const shiftt &shift,
  const sub_expression_mapt &converted)
{
  const smt_termt &first_operand = converted.at(shift.op0());
  const smt_termt &second_operand = converted.at(shift.op1());
  const auto first_bit_vector_sort =
    first_operand.get_sort().cast<smt_bit_vector_sortt>();
  const auto second_bit_vector_sort =
    second_operand.get_sort().cast<smt_bit_vector_sortt>();
  INVARIANT(
    first_bit_vector_sort && second_bit_vector_sort,
    "Shift expressions are expected to have bit vector operands.");
  INVARIANT(
    shift.type() == shift.op0().type(),
    "Shift expression type must be equals to first operand type.");
  const std::size_t first_width = first_bit_vector_sort->bit_width();
  const std::size_t second_width = second_bit_vector_sort->bit_width();
  if(first_width > second_width)
  {
    return factory(
      first_operand,
      extension_for_type(shift.op1().type())(first_width - second_width)(
        second_operand));
  }
  else if(first_width < second_width)
  {
    const auto result = factory(
      extension_for_type(shift.op0().type())(second_width - first_width)(
        first_operand),
      second_operand);
    return smt_bit_vector_theoryt::extract(first_width - 1, 0)(result);
  }
  else
  {
    return factory(first_operand, second_operand);
  }
}
 
static smt_termt convert_expr_to_smt(
  const shift_exprt &shift,
  const sub_expression_mapt &converted)
{
  // TODO: Dispatch for rotation expressions. A `shift_exprt` can be a rotation.
  if(const auto left_shift = expr_try_dynamic_cast<shl_exprt>(shift))
  {
    return convert_to_smt_shift(
      smt_bit_vector_theoryt::shift_left, *left_shift, converted);
  }
  if(const auto right_logical_shift = expr_try_dynamic_cast<lshr_exprt>(shift))
  {
    return convert_to_smt_shift(
      smt_bit_vector_theoryt::logical_shift_right,
      *right_logical_shift,
      converted);
  }
  if(const auto right_arith_shift = expr_try_dynamic_cast<ashr_exprt>(shift))
  {
    return convert_to_smt_shift(
      smt_bit_vector_theoryt::arithmetic_shift_right,
      *right_arith_shift,
      converted);
  }
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for shift expression: " + shift.pretty());
}
 
static smt_termt convert_array_update_to_smt(
  const with_exprt &with,
  const sub_expression_mapt &converted)
{
  smt_termt array = converted.at(with.old());
  for(auto it = ++with.operands().begin(); it != with.operands().end(); it += 2)
  {
    const smt_termt &index_term = converted.at(it[0]);
    const smt_termt &value_term = converted.at(it[1]);
    array = smt_array_theoryt::store(array, index_term, value_term);
  }
  return array;
}
 
static smt_termt convert_expr_to_smt(
  const with_exprt &with,
  const sub_expression_mapt &converted)
{
  if(can_cast_type<array_typet>(with.type()))
    return convert_array_update_to_smt(with, converted);
  // 'with' expression is also used to update struct fields, but for now we do
  // not support them, so we fail.
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for with expression: " + with.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const update_exprt &update,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for update expression: " + update.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const member_exprt &member_extraction,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for member extraction expression: " +
    member_extraction.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const is_dynamic_object_exprt &is_dynamic_object,
  const sub_expression_mapt &converted,
  const smt_is_dynamic_objectt::make_applicationt &apply_is_dynamic_object)
{
  const smt_termt &pointer = converted.at(is_dynamic_object.address());
  const auto pointer_sort = pointer.get_sort().cast<smt_bit_vector_sortt>();
  INVARIANT(
    pointer_sort, "Pointers should be encoded as bit vector sorted terms.");
  const std::size_t pointer_width = pointer_sort->bit_width();
  return apply_is_dynamic_object(
    std::vector<smt_termt>{smt_bit_vector_theoryt::extract(
      pointer_width - 1,
      pointer_width - config.bv_encoding.object_bits)(pointer)});
}
 
static smt_termt convert_expr_to_smt(
  const is_invalid_pointer_exprt &is_invalid_pointer,
  const smt_object_mapt &object_map,
  const sub_expression_mapt &converted)
{
  const exprt &pointer_expr(to_unary_expr(is_invalid_pointer).op());
  const bitvector_typet *pointer_type =
    type_try_dynamic_cast<bitvector_typet>(pointer_expr.type());
  INVARIANT(pointer_type, "Pointer object should have a bitvector-based type.");
  const std::size_t object_bits = config.bv_encoding.object_bits;
  const std::size_t width = pointer_type->get_width();
  INVARIANT(
    width >= object_bits,
    "Width should be at least as big as the number of object bits.");
 
  const auto extract_op = smt_bit_vector_theoryt::extract(
    width - 1, width - object_bits)(converted.at(pointer_expr));
 
  const auto &invalid_pointer = object_map.at(make_invalid_pointer_expr());
 
  const smt_termt invalid_pointer_address = smt_bit_vector_constant_termt(
    invalid_pointer.unique_id, config.bv_encoding.object_bits);
 
  return smt_core_theoryt::equal(invalid_pointer_address, extract_op);
}
 
static smt_termt convert_expr_to_smt(
  const string_constantt &string_constant,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for string constant expression: " +
    string_constant.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const extractbit_exprt &extract_bit,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for extract bit expression: " +
    extract_bit.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const extractbits_exprt &extract_bits,
  const sub_expression_mapt &converted)
{
  const smt_termt &from = converted.at(extract_bits.src());
  const auto upper_value = numeric_cast<std::size_t>(extract_bits.upper());
  const auto lower_value = numeric_cast<std::size_t>(extract_bits.lower());
  if(upper_value && lower_value)
    return smt_bit_vector_theoryt::extract(*upper_value, *lower_value)(from);
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for extract bits expression: " +
    extract_bits.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const replication_exprt &replication,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for bit vector replication expression: " +
    replication.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const byte_extract_exprt &byte_extraction,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for byte extract expression: " +
    byte_extraction.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const byte_update_exprt &byte_update,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for byte update expression: " +
    byte_update.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const abs_exprt &absolute_value_of,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for absolute value of expression: " +
    absolute_value_of.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const isnan_exprt &is_nan_expr,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for is not a number expression: " +
    is_nan_expr.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const isfinite_exprt &is_finite_expr,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for is finite expression: " +
    is_finite_expr.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const isinf_exprt &is_infinite_expr,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for is infinite expression: " +
    is_infinite_expr.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const isnormal_exprt &is_normal_expr,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for is infinite expression: " +
    is_normal_expr.pretty());
}
 
static smt_termt most_significant_bit_is_set(const smt_termt &input)
{
  const auto bit_vector_sort = input.get_sort().cast<smt_bit_vector_sortt>();
  INVARIANT(
    bit_vector_sort,
    "Most significant bit can only be extracted from bit vector terms.");
  const size_t most_significant_bit_index = bit_vector_sort->bit_width() - 1;
  const auto extract_most_significant_bit = smt_bit_vector_theoryt::extract(
    most_significant_bit_index, most_significant_bit_index);
  return smt_core_theoryt::equal(
    extract_most_significant_bit(input), smt_bit_vector_constant_termt{1, 1});
}
 
static smt_termt convert_expr_to_smt(
  const plus_overflow_exprt &plus_overflow,
  const sub_expression_mapt &converted)
{
  const smt_termt &left = converted.at(plus_overflow.lhs());
  const smt_termt &right = converted.at(plus_overflow.rhs());
  if(operands_are_of_type<unsignedbv_typet>(plus_overflow))
  {
    const auto add_carry_bit = smt_bit_vector_theoryt::zero_extend(1);
    return most_significant_bit_is_set(
      smt_bit_vector_theoryt::add(add_carry_bit(left), add_carry_bit(right)));
  }
  if(operands_are_of_type<signedbv_typet>(plus_overflow))
  {
    // Overflow has occurred if the operands have the same sign and adding them
    // gives a result of the opposite sign.
    const smt_termt msb_left = most_significant_bit_is_set(left);
    const smt_termt msb_right = most_significant_bit_is_set(right);
    return smt_core_theoryt::make_and(
      smt_core_theoryt::equal(msb_left, msb_right),
      smt_core_theoryt::distinct(
        msb_left,
        most_significant_bit_is_set(smt_bit_vector_theoryt::add(left, right))));
  }
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for plus overflow expression: " +
    plus_overflow.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const minus_overflow_exprt &minus_overflow,
  const sub_expression_mapt &converted)
{
  const smt_termt &left = converted.at(minus_overflow.lhs());
  const smt_termt &right = converted.at(minus_overflow.rhs());
  if(operands_are_of_type<unsignedbv_typet>(minus_overflow))
  {
    return smt_bit_vector_theoryt::unsigned_less_than(left, right);
  }
  if(operands_are_of_type<signedbv_typet>(minus_overflow))
  {
    // Overflow has occurred if the operands have the opposing signs and
    // subtracting them gives a result having the same signedness as the
    // right-hand operand. For example the following would be overflow for cases
    // for 8 bit wide bit vectors -
    //   -128 - 1 == 127
    //   127 - (-1) == -128
    const smt_termt msb_left = most_significant_bit_is_set(left);
    const smt_termt msb_right = most_significant_bit_is_set(right);
    return smt_core_theoryt::make_and(
      smt_core_theoryt::distinct(msb_left, msb_right),
      smt_core_theoryt::equal(
        msb_right,
        most_significant_bit_is_set(
          smt_bit_vector_theoryt::subtract(left, right))));
  }
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for minus overflow expression: " +
    minus_overflow.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const mult_overflow_exprt &mult_overflow,
  const sub_expression_mapt &converted)
{
  PRECONDITION(mult_overflow.lhs().type() == mult_overflow.rhs().type());
  const auto &operand_type = mult_overflow.lhs().type();
  const smt_termt &left = converted.at(mult_overflow.lhs());
  const smt_termt &right = converted.at(mult_overflow.rhs());
  if(
    const auto unsigned_type =
      type_try_dynamic_cast<unsignedbv_typet>(operand_type))
  {
    const std::size_t width = unsigned_type->get_width();
    const auto extend = smt_bit_vector_theoryt::zero_extend(width);
    return smt_bit_vector_theoryt::unsigned_greater_than_or_equal(
      smt_bit_vector_theoryt::multiply(extend(left), extend(right)),
      smt_bit_vector_constant_termt{power(2, width), width * 2});
  }
  if(
    const auto signed_type =
      type_try_dynamic_cast<signedbv_typet>(operand_type))
  {
    const smt_termt msb_left = most_significant_bit_is_set(left);
    const smt_termt msb_right = most_significant_bit_is_set(right);
    const std::size_t width = signed_type->get_width();
    const auto extend = smt_bit_vector_theoryt::sign_extend(width);
    const auto multiplication =
      smt_bit_vector_theoryt::multiply(extend(left), extend(right));
    const auto too_large = smt_bit_vector_theoryt::signed_greater_than_or_equal(
      multiplication,
      smt_bit_vector_constant_termt{power(2, width - 1), width * 2});
    const auto too_small = smt_bit_vector_theoryt::signed_less_than(
      multiplication,
      smt_bit_vector_theoryt::negate(
        smt_bit_vector_constant_termt{power(2, width - 1), width * 2}));
    return smt_core_theoryt::if_then_else(
      smt_core_theoryt::equal(msb_left, msb_right), too_large, too_small);
  }
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for multiply overflow expression: " +
    mult_overflow.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const pointer_object_exprt &pointer_object,
  const sub_expression_mapt &converted)
{
  const auto type =
    type_try_dynamic_cast<bitvector_typet>(pointer_object.type());
  INVARIANT(type, "Pointer object should have a bitvector-based type.");
  const auto converted_expr = converted.at(pointer_object.pointer());
  const std::size_t width = type->get_width();
  const std::size_t object_bits = config.bv_encoding.object_bits;
  INVARIANT(
    width >= object_bits,
    "Width should be at least as big as the number of object bits.");
  const std::size_t ext = width - object_bits;
  const auto extract_op = smt_bit_vector_theoryt::extract(
    width - 1, width - object_bits)(converted_expr);
  if(ext > 0)
  {
    return smt_bit_vector_theoryt::zero_extend(ext)(extract_op);
  }
  return extract_op;
}
 
static smt_termt convert_expr_to_smt(
  const pointer_offset_exprt &pointer_offset,
  const sub_expression_mapt &converted)
{
  const auto type =
    type_try_dynamic_cast<bitvector_typet>(pointer_offset.type());
  INVARIANT(type, "Pointer offset should have a bitvector-based type.");
  const auto converted_expr = converted.at(pointer_offset.pointer());
  const std::size_t width = type->get_width();
  std::size_t offset_bits = width - config.bv_encoding.object_bits;
  if(offset_bits > width)
    offset_bits = width;
  const auto extract_op =
    smt_bit_vector_theoryt::extract(offset_bits - 1, 0)(converted_expr);
  if(width > offset_bits)
  {
    return smt_bit_vector_theoryt::sign_extend(width - offset_bits)(extract_op);
  }
  return extract_op;
}
 
static smt_termt convert_expr_to_smt(
  const shl_overflow_exprt &shl_overflow,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for shift left overflow expression: " +
    shl_overflow.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const array_exprt &array_construction,
  const sub_expression_mapt &converted)
{
  // This function is unreachable as the `array_exprt` nodes are already fully
  // converted by the incremental decision procedure functions
  // (smt2_incremental_decision_proceduret::define_array_function).
  UNHANDLED_CASE;
}
 
static smt_termt convert_expr_to_smt(
  const literal_exprt &literal,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for literal expression: " + literal.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const forall_exprt &for_all,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for for all expression: " + for_all.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const exists_exprt &exists,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for exists expression: " + exists.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const vector_exprt &vector,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for vector expression: " + vector.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const object_size_exprt &object_size,
  const sub_expression_mapt &converted,
  const smt_object_sizet::make_applicationt &call_object_size)
{
  const smt_termt &pointer = converted.at(object_size.pointer());
  const auto pointer_sort = pointer.get_sort().cast<smt_bit_vector_sortt>();
  INVARIANT(
    pointer_sort, "Pointers should be encoded as bit vector sorted terms.");
  const std::size_t pointer_width = pointer_sort->bit_width();
  return call_object_size(
    std::vector<smt_termt>{smt_bit_vector_theoryt::extract(
      pointer_width - 1,
      pointer_width - config.bv_encoding.object_bits)(pointer)});
}
 
static smt_termt
convert_expr_to_smt(const let_exprt &let, const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for let expression: " + let.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const bswap_exprt &byte_swap,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for byte swap expression: " +
    byte_swap.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const popcount_exprt &population_count,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for population count expression: " +
    population_count.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const count_leading_zeros_exprt &count_leading_zeros,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for count leading zeros expression: " +
    count_leading_zeros.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const count_trailing_zeros_exprt &count_trailing_zeros,
  const sub_expression_mapt &converted)
{
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for count trailing zeros expression: " +
    count_trailing_zeros.pretty());
}
 
static smt_termt convert_expr_to_smt(
  const prophecy_r_or_w_ok_exprt &prophecy_r_or_w_ok,
  const sub_expression_mapt &converted)
{
  UNREACHABLE_BECAUSE(
    "prophecy_r_or_w_ok expression should have been lowered by the decision "
    "procedure before conversion to smt terms");
}
 
static smt_termt convert_expr_to_smt(
  const prophecy_pointer_in_range_exprt &prophecy_pointer_in_range,
  const sub_expression_mapt &converted)
{
  UNREACHABLE_BECAUSE(
    "prophecy_pointer_in_range expression should have been lowered by the "
    "decision procedure before conversion to smt terms");
}
 
static smt_termt dispatch_expr_to_smt_conversion(
  const exprt &expr,
  const sub_expression_mapt &converted,
  const smt_object_mapt &object_map,
  const type_size_mapt &pointer_sizes,
  const smt_object_sizet::make_applicationt &call_object_size,
  const smt_is_dynamic_objectt::make_applicationt &apply_is_dynamic_object)
{
  if(const auto symbol = expr_try_dynamic_cast<symbol_exprt>(expr))
  {
    return convert_expr_to_smt(*symbol);
  }
  if(const auto nondet = expr_try_dynamic_cast<nondet_symbol_exprt>(expr))
  {
    return convert_expr_to_smt(*nondet, converted);
  }
  if(const auto cast = expr_try_dynamic_cast<typecast_exprt>(expr))
  {
    return convert_expr_to_smt(*cast, converted);
  }
  if(
    const auto float_cast = expr_try_dynamic_cast<floatbv_typecast_exprt>(expr))
  {
    return convert_expr_to_smt(*float_cast, converted);
  }
  if(const auto struct_construction = expr_try_dynamic_cast<struct_exprt>(expr))
  {
    return convert_expr_to_smt(*struct_construction, converted);
  }
  if(const auto union_construction = expr_try_dynamic_cast<union_exprt>(expr))
  {
    return convert_expr_to_smt(*union_construction, converted);
  }
  if(const auto constant_literal = expr_try_dynamic_cast<constant_exprt>(expr))
  {
    return convert_expr_to_smt(*constant_literal);
  }
  if(
    const auto concatenation = expr_try_dynamic_cast<concatenation_exprt>(expr))
  {
    return convert_expr_to_smt(*concatenation, converted);
  }
  if(const auto bitwise_and_expr = expr_try_dynamic_cast<bitand_exprt>(expr))
  {
    return convert_expr_to_smt(*bitwise_and_expr, converted);
  }
  if(const auto bitwise_or_expr = expr_try_dynamic_cast<bitor_exprt>(expr))
  {
    return convert_expr_to_smt(*bitwise_or_expr, converted);
  }
  if(const auto bitwise_xor = expr_try_dynamic_cast<bitxor_exprt>(expr))
  {
    return convert_expr_to_smt(*bitwise_xor, converted);
  }
  if(const auto bitwise_not = expr_try_dynamic_cast<bitnot_exprt>(expr))
  {
    return convert_expr_to_smt(*bitwise_not, converted);
  }
  if(const auto unary_minus = expr_try_dynamic_cast<unary_minus_exprt>(expr))
  {
    return convert_expr_to_smt(*unary_minus, converted);
  }
  if(const auto unary_plus = expr_try_dynamic_cast<unary_plus_exprt>(expr))
  {
    return convert_expr_to_smt(*unary_plus, converted);
  }
  if(const auto is_negative = expr_try_dynamic_cast<sign_exprt>(expr))
  {
    return convert_expr_to_smt(*is_negative, converted);
  }
  if(const auto if_expression = expr_try_dynamic_cast<if_exprt>(expr))
  {
    return convert_expr_to_smt(*if_expression, converted);
  }
  if(const auto and_expression = expr_try_dynamic_cast<and_exprt>(expr))
  {
    return convert_expr_to_smt(*and_expression, converted);
  }
  if(const auto or_expression = expr_try_dynamic_cast<or_exprt>(expr))
  {
    return convert_expr_to_smt(*or_expression, converted);
  }
  if(const auto xor_expression = expr_try_dynamic_cast<xor_exprt>(expr))
  {
    return convert_expr_to_smt(*xor_expression, converted);
  }
  if(const auto implies = expr_try_dynamic_cast<implies_exprt>(expr))
  {
    return convert_expr_to_smt(*implies, converted);
  }
  if(const auto logical_not = expr_try_dynamic_cast<not_exprt>(expr))
  {
    return convert_expr_to_smt(*logical_not, converted);
  }
  if(const auto equal = expr_try_dynamic_cast<equal_exprt>(expr))
  {
    return convert_expr_to_smt(*equal, converted);
  }
  if(const auto not_equal = expr_try_dynamic_cast<notequal_exprt>(expr))
  {
    return convert_expr_to_smt(*not_equal, converted);
  }
  if(
    const auto float_equal =
      expr_try_dynamic_cast<ieee_float_equal_exprt>(expr))
  {
    return convert_expr_to_smt(*float_equal, converted);
  }
  if(
    const auto float_not_equal =
      expr_try_dynamic_cast<ieee_float_notequal_exprt>(expr))
  {
    return convert_expr_to_smt(*float_not_equal, converted);
  }
  if(
    const auto converted_relational =
      try_relational_conversion(expr, converted))
  {
    return *converted_relational;
  }
  if(const auto plus = expr_try_dynamic_cast<plus_exprt>(expr))
  {
    return convert_expr_to_smt(*plus, converted, pointer_sizes);
  }
  if(const auto minus = expr_try_dynamic_cast<minus_exprt>(expr))
  {
    return convert_expr_to_smt(*minus, converted, pointer_sizes);
  }
  if(const auto divide = expr_try_dynamic_cast<div_exprt>(expr))
  {
    return convert_expr_to_smt(*divide, converted);
  }
  if(
    const auto float_operation =
      expr_try_dynamic_cast<ieee_float_op_exprt>(expr))
  {
    return convert_expr_to_smt(*float_operation, converted);
  }
  if(const auto truncation_modulo = expr_try_dynamic_cast<mod_exprt>(expr))
  {
    return convert_expr_to_smt(*truncation_modulo, converted);
  }
  if(
    const auto euclidean_modulo =
      expr_try_dynamic_cast<euclidean_mod_exprt>(expr))
  {
    return convert_expr_to_smt(*euclidean_modulo, converted);
  }
  if(const auto multiply = expr_try_dynamic_cast<mult_exprt>(expr))
  {
    return convert_expr_to_smt(*multiply, converted);
  }
#if 0
  else if(expr.id() == ID_floatbv_rem)
  {
    convert_floatbv_rem(to_binary_expr(expr));
  }
#endif
  if(const auto address_of = expr_try_dynamic_cast<address_of_exprt>(expr))
  {
    return convert_expr_to_smt(*address_of, converted, object_map);
  }
  if(const auto array_of = expr_try_dynamic_cast<array_of_exprt>(expr))
  {
    return convert_expr_to_smt(*array_of, converted);
  }
  if(
    const auto array_comprehension =
      expr_try_dynamic_cast<array_comprehension_exprt>(expr))
  {
    return convert_expr_to_smt(*array_comprehension, converted);
  }
  if(const auto index = expr_try_dynamic_cast<index_exprt>(expr))
  {
    return convert_expr_to_smt(*index, converted);
  }
  if(const auto shift = expr_try_dynamic_cast<shift_exprt>(expr))
  {
    return convert_expr_to_smt(*shift, converted);
  }
  if(const auto with = expr_try_dynamic_cast<with_exprt>(expr))
  {
    return convert_expr_to_smt(*with, converted);
  }
  if(const auto update = expr_try_dynamic_cast<update_exprt>(expr))
  {
    return convert_expr_to_smt(*update, converted);
  }
  if(const auto member_extraction = expr_try_dynamic_cast<member_exprt>(expr))
  {
    return convert_expr_to_smt(*member_extraction, converted);
  }
  else if(
    const auto pointer_offset =
      expr_try_dynamic_cast<pointer_offset_exprt>(expr))
  {
    return convert_expr_to_smt(*pointer_offset, converted);
  }
  else if(
    const auto pointer_object =
      expr_try_dynamic_cast<pointer_object_exprt>(expr))
  {
    return convert_expr_to_smt(*pointer_object, converted);
  }
  if(
    const auto is_dynamic_object =
      expr_try_dynamic_cast<is_dynamic_object_exprt>(expr))
  {
    return convert_expr_to_smt(
      *is_dynamic_object, converted, apply_is_dynamic_object);
  }
  if(
    const auto is_invalid_pointer =
      expr_try_dynamic_cast<is_invalid_pointer_exprt>(expr))
  {
    return convert_expr_to_smt(*is_invalid_pointer, object_map, converted);
  }
  if(const auto string_constant = expr_try_dynamic_cast<string_constantt>(expr))
  {
    return convert_expr_to_smt(*string_constant, converted);
  }
  if(const auto extract_bit = expr_try_dynamic_cast<extractbit_exprt>(expr))
  {
    return convert_expr_to_smt(*extract_bit, converted);
  }
  if(const auto extract_bits = expr_try_dynamic_cast<extractbits_exprt>(expr))
  {
    return convert_expr_to_smt(*extract_bits, converted);
  }
  if(const auto replication = expr_try_dynamic_cast<replication_exprt>(expr))
  {
    return convert_expr_to_smt(*replication, converted);
  }
  if(
    const auto byte_extraction =
      expr_try_dynamic_cast<byte_extract_exprt>(expr))
  {
    return convert_expr_to_smt(*byte_extraction, converted);
  }
  if(const auto byte_update = expr_try_dynamic_cast<byte_update_exprt>(expr))
  {
    return convert_expr_to_smt(*byte_update, converted);
  }
  if(const auto absolute_value_of = expr_try_dynamic_cast<abs_exprt>(expr))
  {
    return convert_expr_to_smt(*absolute_value_of, converted);
  }
  if(const auto is_nan_expr = expr_try_dynamic_cast<isnan_exprt>(expr))
  {
    return convert_expr_to_smt(*is_nan_expr, converted);
  }
  if(const auto is_finite_expr = expr_try_dynamic_cast<isfinite_exprt>(expr))
  {
    return convert_expr_to_smt(*is_finite_expr, converted);
  }
  if(const auto is_infinite_expr = expr_try_dynamic_cast<isinf_exprt>(expr))
  {
    return convert_expr_to_smt(*is_infinite_expr, converted);
  }
  if(const auto is_normal_expr = expr_try_dynamic_cast<isnormal_exprt>(expr))
  {
    return convert_expr_to_smt(*is_normal_expr, converted);
  }
  if(
    const auto plus_overflow = expr_try_dynamic_cast<plus_overflow_exprt>(expr))
  {
    return convert_expr_to_smt(*plus_overflow, converted);
  }
  if(
    const auto minus_overflow =
      expr_try_dynamic_cast<minus_overflow_exprt>(expr))
  {
    return convert_expr_to_smt(*minus_overflow, converted);
  }
  if(
    const auto mult_overflow = expr_try_dynamic_cast<mult_overflow_exprt>(expr))
  {
    return convert_expr_to_smt(*mult_overflow, converted);
  }
  if(const auto shl_overflow = expr_try_dynamic_cast<shl_overflow_exprt>(expr))
  {
    return convert_expr_to_smt(*shl_overflow, converted);
  }
  if(const auto array_construction = expr_try_dynamic_cast<array_exprt>(expr))
  {
    return convert_expr_to_smt(*array_construction, converted);
  }
  if(const auto literal = expr_try_dynamic_cast<literal_exprt>(expr))
  {
    return convert_expr_to_smt(*literal, converted);
  }
  if(const auto for_all = expr_try_dynamic_cast<forall_exprt>(expr))
  {
    return convert_expr_to_smt(*for_all, converted);
  }
  if(const auto exists = expr_try_dynamic_cast<exists_exprt>(expr))
  {
    return convert_expr_to_smt(*exists, converted);
  }
  if(const auto vector = expr_try_dynamic_cast<vector_exprt>(expr))
  {
    return convert_expr_to_smt(*vector, converted);
  }
  if(const auto object_size = expr_try_dynamic_cast<object_size_exprt>(expr))
  {
    return convert_expr_to_smt(*object_size, converted, call_object_size);
  }
  if(const auto let = expr_try_dynamic_cast<let_exprt>(expr))
  {
    return convert_expr_to_smt(*let, converted);
  }
  INVARIANT(
    expr.id() != ID_constraint_select_one,
    "constraint_select_one is not expected in smt conversion: " +
      expr.pretty());
  if(const auto byte_swap = expr_try_dynamic_cast<bswap_exprt>(expr))
  {
    return convert_expr_to_smt(*byte_swap, converted);
  }
  if(const auto population_count = expr_try_dynamic_cast<popcount_exprt>(expr))
  {
    return convert_expr_to_smt(*population_count, converted);
  }
  if(
    const auto count_leading_zeros =
      expr_try_dynamic_cast<count_leading_zeros_exprt>(expr))
  {
    return convert_expr_to_smt(*count_leading_zeros, converted);
  }
  if(
    const auto count_trailing_zeros =
      expr_try_dynamic_cast<count_trailing_zeros_exprt>(expr))
  {
    return convert_expr_to_smt(*count_trailing_zeros, converted);
  }
  if(
    const auto prophecy_r_or_w_ok =
      expr_try_dynamic_cast<prophecy_r_or_w_ok_exprt>(expr))
  {
    return convert_expr_to_smt(*prophecy_r_or_w_ok, converted);
  }
  if(
    const auto prophecy_pointer_in_range =
      expr_try_dynamic_cast<prophecy_pointer_in_range_exprt>(expr))
  {
    return convert_expr_to_smt(*prophecy_pointer_in_range, converted);
  }
 
  UNIMPLEMENTED_FEATURE(
    "Generation of SMT formula for unknown kind of expression: " +
    expr.pretty());
}
 
#ifndef CPROVER_INVARIANT_DO_NOT_CHECK
template <typename functiont>
struct at_scope_exitt
{
  explicit at_scope_exitt(functiont exit_function)
    : exit_function(exit_function)
  {
  }
  ~at_scope_exitt()
  {
    exit_function();
  }
  functiont exit_function;
};
 
template <typename functiont>
at_scope_exitt<functiont> at_scope_exit(functiont exit_function)
{
  return at_scope_exitt<functiont>(exit_function);
}
#endif
 
exprt lower_address_of_array_index(exprt expr)
{
  expr.visit_pre([](exprt &expr) {
    const auto address_of_expr = expr_try_dynamic_cast<address_of_exprt>(expr);
    if(!address_of_expr)
      return;
    const auto array_index_expr =
      expr_try_dynamic_cast<index_exprt>(address_of_expr->object());
    if(!array_index_expr)
      return;
    expr = plus_exprt{
      address_of_exprt{
        array_index_expr->array(),
        type_checked_cast<pointer_typet>(address_of_expr->type())},
      array_index_expr->index()};
  });
  return expr;
}
 
void filtered_visit_post(
  const exprt &_expr,
  std::function<bool(const exprt &)> filter,
  std::function<void(const exprt &)> visitor)
{
  struct stack_entryt
  {
    const exprt *e;
    bool operands_pushed;
    explicit stack_entryt(const exprt *_e) : e(_e), operands_pushed(false)
    {
    }
  };
 
  std::stack<stack_entryt> stack;
 
  stack.emplace(&_expr);
 
  while(!stack.empty())
  {
    auto &top = stack.top();
    if(top.operands_pushed)
    {
      visitor(*top.e);
      stack.pop();
    }
    else
    {
      // do modification of 'top' before pushing in case 'top' isn't stable
      top.operands_pushed = true;
      if(filter(*top.e))
        for(auto &op : top.e->operands())
          stack.emplace(&op);
    }
  }
}
 
smt_termt convert_expr_to_smt(
  const exprt &expr,
  const smt_object_mapt &object_map,
  const type_size_mapt &pointer_sizes,
  const smt_object_sizet::make_applicationt &object_size,
  const smt_is_dynamic_objectt::make_applicationt &is_dynamic_object)
{
#ifndef CPROVER_INVARIANT_DO_NOT_CHECK
  static bool in_conversion = false;
  INVARIANT(
    !in_conversion,
    "Conversion of expr to smt should be non-recursive. "
    "Re-entrance found in conversion of " +
      expr.pretty(1, 0));
  in_conversion = true;
  const auto end_conversion = at_scope_exit([&]() { in_conversion = false; });
#endif
  sub_expression_mapt sub_expression_map;
  const auto lowered_expr = lower_address_of_array_index(expr);
  filtered_visit_post(
    lowered_expr,
    [](const exprt &expr) {
      // Code values inside "address of" expressions do not need to be converted
      // as the "address of" conversion only depends on the object identifier.
      // Avoiding the conversion side steps a need to convert arbitrary code to
      // SMT terms.
      const auto address_of = expr_try_dynamic_cast<address_of_exprt>(expr);
      if(!address_of)
        return true;
      return !can_cast_type<code_typet>(address_of->object().type());
    },
    [&](const exprt &expr) {
      const auto find_result = sub_expression_map.find(expr);
      if(find_result != sub_expression_map.cend())
        return;
      smt_termt term = dispatch_expr_to_smt_conversion(
        expr,
        sub_expression_map,
        object_map,
        pointer_sizes,
        object_size,
        is_dynamic_object);
      sub_expression_map.emplace_hint(find_result, expr, std::move(term));
    });
  return std::move(sub_expression_map.at(lowered_expr));
}