text: /*******************************************************************\
  
  Module:
  
  Author: Daniel Kroening, kroening@kroening.com
  
  \*******************************************************************/
  
  #include "arrays.h"
  
  #include <util/arith_tools.h>
  #include <util/json.h>
  #include <util/message.h>
  #include <util/replace_expr.h>
  #include <util/std_expr.h>
  
  #include <solvers/prop/literal_expr.h>
  #include <solvers/prop/prop.h>
  
  #ifdef DEBUG
  #include <iostream>
  #endif
  
  #include <unordered_set>
  
  arrayst::arrayst(
    const namespacet &_ns,
    propt &_prop,
    message_handlert &_message_handler,
    bool _get_array_constraints)
    : equalityt(_prop, _message_handler),
      ns(_ns),
      log(_message_handler),
      message_handler(_message_handler)
  {
    lazy_arrays = false;        // will be set to true when --refine is used
    incremental_cache = false;  // for incremental solving
    // get_array_constraints is true when --show-array-constraints is used
    get_array_constraints = _get_array_constraints;
  }
  
  void arrayst::record_array_index(const index_exprt &index)
  {
    // we are not allowed to put the index directly in the
    //   entry for the root of the equivalence class
    //   because this map is accessed during building the error trace
    std::size_t number=arrays.number(index.array());
    if(index_map[number].insert(index.index()).second)
      update_indices.insert(number);
  }
  
  literalt arrayst::record_array_equality(
    const equal_exprt &equality)
  {
    const exprt &op0=equality.op0();
    const exprt &op1=equality.op1();
  
    DATA_INVARIANT_WITH_DIAGNOSTICS(
      op0.type() == op1.type(),
      "record_array_equality got equality without matching types",
      irep_pretty_diagnosticst{equality});
  
    DATA_INVARIANT(
      op0.type().id() == ID_array,
      "record_array_equality parameter should be array-typed");
  
    array_equalities.push_back(array_equalityt());
  
    array_equalities.back().f1=op0;
    array_equalities.back().f2=op1;
    array_equalities.back().l=SUB::equality(op0, op1);
  
    arrays.make_union(op0, op1);
    collect_arrays(op0);
    collect_arrays(op1);
  
    return array_equalities.back().l;
  }
  
  void arrayst::collect_indices()
  {
    for(std::size_t i=0; i<arrays.size(); i++)
    {
      collect_indices(arrays[i]);
    }
  }
  
  void arrayst::collect_indices(const exprt &expr)
  {
    if(expr.id()!=ID_index)
    {
      if(expr.id() == ID_array_comprehension)
        array_comprehension_args.insert(
          to_array_comprehension_expr(expr).arg().get_identifier());
  
      forall_operands(op, expr) collect_indices(*op);
    }
    else
    {
      const index_exprt &e = to_index_expr(expr);
  
      if(
        e.index().id() == ID_symbol &&
        array_comprehension_args.count(
          to_symbol_expr(e.index()).get_identifier()) != 0)
      {
        return;
      }
  
      collect_indices(e.index()); // necessary?
  
      const typet &array_op_type = e.array().type();
  
      if(array_op_type.id()==ID_array)
      {
        const array_typet &array_type=
          to_array_type(array_op_type);
  
        if(is_unbounded_array(array_type))
        {
          record_array_index(e);
        }
      }
    }
  }
  
  void arrayst::collect_arrays(const exprt &a)
  {
    const array_typet &array_type = to_array_type(a.type());
  
    if(a.id()==ID_with)
    {
      const with_exprt &with_expr=to_with_expr(a);
  
      DATA_INVARIANT_WITH_DIAGNOSTICS(
        array_type == with_expr.old().type(),
        "collect_arrays got 'with' without matching types",
        irep_pretty_diagnosticst{a});
  
      arrays.make_union(a, with_expr.old());
      collect_arrays(with_expr.old());
  
      // make sure this shows as an application
      for(std::size_t i = 1; i < with_expr.operands().size(); i += 2)
      {
        index_exprt index_expr(with_expr.old(), with_expr.operands()[i]);
        record_array_index(index_expr);
      }
    }
    else if(a.id()==ID_update)
    {
      const update_exprt &update_expr=to_update_expr(a);
  
      DATA_INVARIANT_WITH_DIAGNOSTICS(
        array_type == update_expr.old().type(),
        "collect_arrays got 'update' without matching types",
        irep_pretty_diagnosticst{a});
  
      arrays.make_union(a, update_expr.old());
      collect_arrays(update_expr.old());
  
  #if 0
      // make sure this shows as an application
      index_exprt index_expr(update_expr.old(), update_expr.index());
      record_array_index(index_expr);
  #endif
    }
    else if(a.id()==ID_if)
    {
      const if_exprt &if_expr=to_if_expr(a);
  
      DATA_INVARIANT_WITH_DIAGNOSTICS(
        array_type == if_expr.true_case().type(),
        "collect_arrays got if without matching types",
        irep_pretty_diagnosticst{a});
  
      DATA_INVARIANT_WITH_DIAGNOSTICS(
        array_type == if_expr.false_case().type(),
        "collect_arrays got if without matching types",
        irep_pretty_diagnosticst{a});
  
      arrays.make_union(a, if_expr.true_case());
      arrays.make_union(a, if_expr.false_case());
      collect_arrays(if_expr.true_case());
      collect_arrays(if_expr.false_case());
    }
    else if(a.id()==ID_symbol)
    {
    }
    else if(a.id()==ID_nondet_symbol)
    {
    }
    else if(a.id()==ID_member)
    {
      const auto &struct_op = to_member_expr(a).struct_op();
  
      DATA_INVARIANT(
        struct_op.id() == ID_symbol || struct_op.id() == ID_nondet_symbol,
        "unexpected array expression: member with '" + struct_op.id_string() +
          "'");
    }
    else if(a.id()==ID_constant ||
            a.id()==ID_array ||
            a.id()==ID_string_constant)
    {
    }
    else if(a.id()==ID_array_of)
    {
    }
    else if(a.id()==ID_byte_update_little_endian ||
            a.id()==ID_byte_update_big_endian)
    {
      DATA_INVARIANT(
        false,
        "byte_update should be removed before collect_arrays");
    }
    else if(a.id()==ID_typecast)
    {
      const auto &typecast_op = to_typecast_expr(a).op();
  
      // cast between array types?
      DATA_INVARIANT(
        typecast_op.type().id() == ID_array,
        "unexpected array type cast from " + typecast_op.type().id_string());
  
      arrays.make_union(a, typecast_op);
      collect_arrays(typecast_op);
    }
    else if(a.id()==ID_index)
    {
      // nested unbounded arrays
      const auto &array_op = to_index_expr(a).array();
      arrays.make_union(a, array_op);
      collect_arrays(array_op);
    }
    else if(a.id() == ID_array_comprehension)
    {
    }
    else
    {
      DATA_INVARIANT(
        false,
        "unexpected array expression (collect_arrays): '" + a.id_string() + "'");
    }
  }
  
  /// adds array constraints (refine=true...lazily for the refinement loop)
  void arrayst::add_array_constraint(const lazy_constraintt &lazy, bool refine)
  {
    if(lazy_arrays && refine)
    {
      // lazily add the constraint
      if(incremental_cache)
      {
        if(expr_map.find(lazy.lazy) == expr_map.end())
        {
          lazy_array_constraints.push_back(lazy);
          expr_map[lazy.lazy] = true;
        }
      }
      else
      {
        lazy_array_constraints.push_back(lazy);
      }
    }
    else
    {
      // add the constraint eagerly
      prop.l_set_to_true(convert(lazy.lazy));
    }
  }
  
  void arrayst::add_array_constraints()
  {
    collect_indices();
    // at this point all indices should in the index set
  
    // reduce initial index map
    update_index_map(true);
  
    // add constraints for if, with, array_of, lambda
    std::set<std::size_t> roots_to_process, updated_roots;
    for(std::size_t i=0; i<arrays.size(); i++)
      roots_to_process.insert(arrays.find_number(i));
  
    while(!roots_to_process.empty())
    {
      for(std::size_t i = 0; i < arrays.size(); i++)
      {
        if(roots_to_process.count(arrays.find_number(i)) == 0)
          continue;
  
        // take a copy as arrays may get modified by add_array_constraints
        // in case of nested unbounded arrays
        exprt a = arrays[i];
  
        add_array_constraints(index_map[arrays.find_number(i)], a);
  
        // we have to update before it gets used in the next add_* call
        for(const std::size_t u : update_indices)
          updated_roots.insert(arrays.find_number(u));
        update_index_map(false);
      }
  
      roots_to_process = std::move(updated_roots);
      updated_roots.clear();
    }
  
    // add constraints for equalities
    for(const auto &equality : array_equalities)
    {
      add_array_constraints_equality(
        index_map[arrays.find_number(equality.f1)],
        equality);
  
      // update_index_map should not be necessary here
    }
  
    // add the Ackermann constraints
    add_array_Ackermann_constraints();
  }
  
  void arrayst::add_array_Ackermann_constraints()
  {
    // this is quadratic!
  
  #ifdef DEBUG
    std::cout << "arrays.size(): " << arrays.size() << '\n';
  #endif
  
    // iterate over arrays
    for(std::size_t i=0; i<arrays.size(); i++)
    {
      const index_sett &index_set=index_map[arrays.find_number(i)];
  
  #ifdef DEBUG
      std::cout << "index_set.size(): " << index_set.size() << '\n';
  #endif
  
      // iterate over indices, 2x!
      for(index_sett::const_iterator
          i1=index_set.begin();
          i1!=index_set.end();
          i1++)
        for(index_sett::const_iterator
            i2=i1;
            i2!=index_set.end();
            i2++)
          if(i1!=i2)
          {
            if(i1->is_constant() && i2->is_constant())
              continue;
  
            // index equality
            const equal_exprt indices_equal(
              *i1, typecast_exprt::conditional_cast(*i2, i1->type()));
  
            literalt indices_equal_lit=convert(indices_equal);
  
            if(indices_equal_lit!=const_literal(false))
            {
              const typet &subtype = arrays[i].type().subtype();
              index_exprt index_expr1(arrays[i], *i1, subtype);
  
              index_exprt index_expr2=index_expr1;
              index_expr2.index()=*i2;
  
              equal_exprt values_equal(index_expr1, index_expr2);
  
              // add constraint
              lazy_constraintt lazy(lazy_typet::ARRAY_ACKERMANN,
                implies_exprt(literal_exprt(indices_equal_lit), values_equal));
              add_array_constraint(lazy, true); // added lazily
              array_constraint_count[constraint_typet::ARRAY_ACKERMANN]++;
  
  #if 0 // old code for adding, not significantly faster
              prop.lcnf(!indices_equal_lit, convert(values_equal));
  #endif
            }
          }
    }
  }
  
  /// merge the indices into the root
  void arrayst::update_index_map(std::size_t i)
  {
    if(arrays.is_root_number(i))
      return;
  
    std::size_t root_number=arrays.find_number(i);
    INVARIANT(root_number!=i, "is_root_number incorrect?");
  
    index_sett &root_index_set=index_map[root_number];
    index_sett &index_set=index_map[i];
  
    root_index_set.insert(index_set.begin(), index_set.end());
  }
  
  void arrayst::update_index_map(bool update_all)
  {
    // iterate over non-roots
    // possible reasons why update is needed:
    //  -- there are new equivalence classes in arrays
    //  -- there are new indices for arrays that are not the root
    //     of an equivalence class
    //     (and we cannot do that in record_array_index())
    //  -- equivalence classes have been merged
    if(update_all)
    {
      for(std::size_t i=0; i<arrays.size(); i++)
        update_index_map(i);
    }
    else
    {
      for(const auto &index : update_indices)
        update_index_map(index);
  
      update_indices.clear();
    }
  
  #ifdef DEBUG
    // print index sets
    for(const auto &index_entry : index_map)
      for(const auto &index : index_entry.second)
        std::cout << "Index set (" << index_entry.first << " = "
                  << arrays.find_number(index_entry.first) << " = "
                  << format(arrays[arrays.find_number(index_entry.first)])
                  << "): " << format(index) << '\n';
    std::cout << "-----\n";
  #endif
  }
  
  void arrayst::add_array_constraints_equality(
    const index_sett &index_set,
    const array_equalityt &array_equality)
  {
    // add constraints x=y => x[i]=y[i]
  
    for(const auto &index : index_set)
    {
      const typet &subtype1 = array_equality.f1.type().subtype();
      index_exprt index_expr1(array_equality.f1, index, subtype1);
  
      const typet &subtype2 = array_equality.f2.type().subtype();
      index_exprt index_expr2(array_equality.f2, index, subtype2);
  
      DATA_INVARIANT(
        index_expr1.type()==index_expr2.type(),
        "array elements should all have same type");
  
      array_equalityt equal;
      equal.f1 = index_expr1;
      equal.f2 = index_expr2;
      equal.l = array_equality.l;
      equal_exprt equality_expr(index_expr1, index_expr2);
  
      // add constraint
      // equality constraints are not added lazily
      // convert must be done to guarantee correct update of the index_set
      prop.lcnf(!array_equality.l, convert(equality_expr));
      array_constraint_count[constraint_typet::ARRAY_EQUALITY]++;
    }
  }
  
  void arrayst::add_array_constraints(
    const index_sett &index_set,
    const exprt &expr)
  {
    if(expr.id()==ID_with)
      return add_array_constraints_with(index_set, to_with_expr(expr));
    else if(expr.id()==ID_update)
      return add_array_constraints_update(index_set, to_update_expr(expr));
    else if(expr.id()==ID_if)
      return add_array_constraints_if(index_set, to_if_expr(expr));
    else if(expr.id()==ID_array_of)
      return add_array_constraints_array_of(index_set, to_array_of_expr(expr));
    else if(expr.id() == ID_array)
      return add_array_constraints_array_constant(index_set, to_array_expr(expr));
    else if(expr.id() == ID_array_comprehension)
    {
      return add_array_constraints_comprehension(
        index_set, to_array_comprehension_expr(expr));
    }
    else if(expr.id()==ID_symbol ||
            expr.id()==ID_nondet_symbol ||
            expr.id()==ID_constant ||
            expr.id()=="zero_string" ||
            expr.id()==ID_string_constant)
    {
    }
    else if(
      expr.id() == ID_member &&
      (to_member_expr(expr).struct_op().id() == ID_symbol ||
       to_member_expr(expr).struct_op().id() == ID_nondet_symbol))
    {
    }
    else if(expr.id()==ID_byte_update_little_endian ||
            expr.id()==ID_byte_update_big_endian)
    {
      INVARIANT(false, "byte_update should be removed before arrayst");
    }
    else if(expr.id()==ID_typecast)
    {
      // we got a=(type[])b
      const auto &expr_typecast_op = to_typecast_expr(expr).op();
  
      // add a[i]=b[i]
      for(const auto &index : index_set)
      {
        const typet &subtype = expr.type().subtype();
        index_exprt index_expr1(expr, index, subtype);
        index_exprt index_expr2(expr_typecast_op, index, subtype);
  
        DATA_INVARIANT(
          index_expr1.type()==index_expr2.type(),
          "array elements should all have same type");
  
        // add constraint
        lazy_constraintt lazy(lazy_typet::ARRAY_TYPECAST,
          equal_exprt(index_expr1, index_expr2));
        add_array_constraint(lazy, false); // added immediately
        array_constraint_count[constraint_typet::ARRAY_TYPECAST]++;
      }
    }
    else if(expr.id()==ID_index)
    {
    }
    else
    {
      DATA_INVARIANT(
        false,
        "unexpected array expression (add_array_constraints): '" +
          expr.id_string() + "'");
    }
  }
  
  void arrayst::add_array_constraints_with(
    const index_sett &index_set,
    const with_exprt &expr)
  {
    // We got x=(y with [i:=v, j:=w, ...]).
    // First add constraints x[i]=v, x[j]=w, ...
    std::unordered_set<exprt, irep_hash> updated_indices;
  
    const exprt::operandst &operands = expr.operands();
    for(std::size_t i = 1; i + 1 < operands.size(); i += 2)
    {
      const exprt &index = operands[i];
      const exprt &value = operands[i + 1];
  
      index_exprt index_expr(expr, index, expr.type().subtype());
  
      DATA_INVARIANT_WITH_DIAGNOSTICS(
        index_expr.type() == value.type(),
        "with-expression operand should match array element type",
        irep_pretty_diagnosticst{expr});
  
      lazy_constraintt lazy(
        lazy_typet::ARRAY_WITH, equal_exprt(index_expr, value));
      add_array_constraint(lazy, false); // added immediately
      array_constraint_count[constraint_typet::ARRAY_WITH]++;
  
      updated_indices.insert(index);
    }
  
    // For all other indices use the existing value, i.e., add constraints
    // x[I]=y[I] for I!=i,j,...
  
    for(auto other_index : index_set)
    {
      if(updated_indices.find(other_index) == updated_indices.end())
      {
        // we first build the guard
        exprt::operandst disjuncts;
        disjuncts.reserve(updated_indices.size());
        for(const auto &index : updated_indices)
        {
          disjuncts.push_back(equal_exprt{
            index, typecast_exprt::conditional_cast(other_index, index.type())});
        }
  
        literalt guard_lit = convert(disjunction(disjuncts));
  
        if(guard_lit!=const_literal(true))
        {
          const typet &subtype = expr.type().subtype();
          index_exprt index_expr1(expr, other_index, subtype);
          index_exprt index_expr2(expr.old(), other_index, subtype);
  
          equal_exprt equality_expr(index_expr1, index_expr2);
  
          // add constraint
          lazy_constraintt lazy(lazy_typet::ARRAY_WITH, or_exprt(equality_expr,
                                  literal_exprt(guard_lit)));
  
          add_array_constraint(lazy, false); // added immediately
          array_constraint_count[constraint_typet::ARRAY_WITH]++;
  
  #if 0 // old code for adding, not significantly faster
          {
            literalt equality_lit=convert(equality_expr);
  
            bvt bv;
            bv.reserve(2);
            bv.push_back(equality_lit);
            bv.push_back(guard_lit);
            prop.lcnf(bv);
          }
  #endif
        }
      }
    }
  }
  
  void arrayst::add_array_constraints_update(
    const index_sett &,
    const update_exprt &)
  {
    // we got x=UPDATE(y, [i], v)
    // add constaint x[i]=v
  
  #if 0
    const exprt &index=expr.where();
    const exprt &value=expr.new_value();
  
    {
      index_exprt index_expr(expr, index, expr.type().subtype());
  
      DATA_INVARIANT_WITH_DIAGNOSTICS(
        index_expr.type()==value.type(),
        "update operand should match array element type",
        irep_pretty_diagnosticst{expr});
  
      set_to_true(equal_exprt(index_expr, value));
    }
  
    // use other array index applications for "else" case
    // add constraint x[I]=y[I] for I!=i
  
    for(auto other_index : index_set)
    {
      if(other_index!=index)
      {
        // we first build the guard
  
        other_index = typecast_exprt::conditional_cast(other_index, index.type());
  
        literalt guard_lit=convert(equal_exprt(index, other_index));
  
        if(guard_lit!=const_literal(true))
        {
          const typet &subtype=expr.type().subtype();
          index_exprt index_expr1(expr, other_index, subtype);
          index_exprt index_expr2(expr.op0(), other_index, subtype);
  
          equal_exprt equality_expr(index_expr1, index_expr2);
  
          literalt equality_lit=convert(equality_expr);
  
          // add constraint
          bvt bv;
          bv.reserve(2);
          bv.push_back(equality_lit);
          bv.push_back(guard_lit);
          prop.lcnf(bv);
        }
      }
    }
  #endif
  }
  
  void arrayst::add_array_constraints_array_of(
    const index_sett &index_set,
    const array_of_exprt &expr)
  {
    // we got x=array_of[v]
    // get other array index applications
    // and add constraint x[i]=v
  
    for(const auto &index : index_set)
    {
      const typet &subtype = expr.type().subtype();
      index_exprt index_expr(expr, index, subtype);
  
      DATA_INVARIANT(
        index_expr.type() == expr.what().type(),
        "array_of operand type should match array element type");
  
      // add constraint
      lazy_constraintt lazy(
        lazy_typet::ARRAY_OF, equal_exprt(index_expr, expr.what()));
      add_array_constraint(lazy, false); // added immediately
      array_constraint_count[constraint_typet::ARRAY_OF]++;
    }
  }
  
  void arrayst::add_array_constraints_array_constant(
    const index_sett &index_set,
    const array_exprt &expr)
  {
    // we got x = { v, ... } - add constraint x[i] = v
    const exprt::operandst &operands = expr.operands();
  
    for(const auto &index : index_set)
    {
      const typet &subtype = expr.type().subtype();
      const index_exprt index_expr{expr, index, subtype};
  
      if(index.is_constant())
      {
        // We have a constant index - just pick the element at that index from the
        // array constant.
  
        const std::size_t i =
          numeric_cast_v<std::size_t>(to_constant_expr(index));
        // if the access is out of bounds, we leave it unconstrained
        if(i >= operands.size())
          continue;
  
        const exprt v = operands[i];
        DATA_INVARIANT(
          index_expr.type() == v.type(),
          "array operand type should match array element type");
  
        // add constraint
        lazy_constraintt lazy{lazy_typet::ARRAY_CONSTANT,
                              equal_exprt{index_expr, v}};
        add_array_constraint(lazy, false); // added immediately
        array_constraint_count[constraint_typet::ARRAY_CONSTANT]++;
      }
      else
      {
        // We have a non-constant index into an array constant. We need to build a
        // case statement testing the index against all possible values. Whenever
        // neighbouring array elements are the same, we can test the index against
        // the range rather than individual elements. This should be particularly
        // helpful when we have arrays of zeros, as is the case for initializers.
  
        std::vector<std::pair<std::size_t, std::size_t>> ranges;
  
        for(std::size_t i = 0; i < operands.size(); ++i)
        {
          if(ranges.empty() || operands[i] != operands[ranges.back().first])
            ranges.emplace_back(i, i);
          else
            ranges.back().second = i;
        }
  
        for(const auto &range : ranges)
        {
          exprt index_constraint;
  
          if(range.first == range.second)
          {
            index_constraint =
              equal_exprt{index, from_integer(range.first, index.type())};
          }
          else
          {
            index_constraint = and_exprt{
              binary_predicate_exprt{
                from_integer(range.first, index.type()), ID_le, index},
              binary_predicate_exprt{
                index, ID_le, from_integer(range.second, index.type())}};
          }
  
          lazy_constraintt lazy{
            lazy_typet::ARRAY_CONSTANT,
            implies_exprt{index_constraint,
                          equal_exprt{index_expr, operands[range.first]}}};
          add_array_constraint(lazy, true); // added lazily
          array_constraint_count[constraint_typet::ARRAY_CONSTANT]++;
        }
      }
    }
  }
  
  void arrayst::add_array_constraints_comprehension(
    const index_sett &index_set,
    const array_comprehension_exprt &expr)
  {
    // we got x=lambda(i: e)
    // get all other array index applications
    // and add constraints x[j]=e[i/j]
  
    for(const auto &index : index_set)
    {
      index_exprt index_expr{expr, index};
      exprt comprehension_body = expr.body();
      replace_expr(expr.arg(), index, comprehension_body);
  
      // add constraint
      lazy_constraintt lazy(
        lazy_typet::ARRAY_COMPREHENSION,
        equal_exprt(index_expr, comprehension_body));
  
      add_array_constraint(lazy, false); // added immediately
      array_constraint_count[constraint_typet::ARRAY_COMPREHENSION]++;
    }
  }
  
  void arrayst::add_array_constraints_if(
    const index_sett &index_set,
    const if_exprt &expr)
  {
    // we got x=(c?a:b)
    literalt cond_lit=convert(expr.cond());
  
    // get other array index applications
    // and add c => x[i]=a[i]
    //        !c => x[i]=b[i]
  
    // first do true case
  
    for(const auto &index : index_set)
    {
      const typet subtype = expr.type().subtype();
      index_exprt index_expr1(expr, index, subtype);
      index_exprt index_expr2(expr.true_case(), index, subtype);
  
      // add implication
      lazy_constraintt lazy(lazy_typet::ARRAY_IF,
                              or_exprt(literal_exprt(!cond_lit),
                                equal_exprt(index_expr1, index_expr2)));
      add_array_constraint(lazy, false); // added immediately
      array_constraint_count[constraint_typet::ARRAY_IF]++;
  
  #if 0 // old code for adding, not significantly faster
      prop.lcnf(!cond_lit, convert(equal_exprt(index_expr1, index_expr2)));
  #endif
    }
  
    // now the false case
    for(const auto &index : index_set)
    {
      const typet subtype = expr.type().subtype();
      index_exprt index_expr1(expr, index, subtype);
      index_exprt index_expr2(expr.false_case(), index, subtype);
  
      // add implication
      lazy_constraintt lazy(
        lazy_typet::ARRAY_IF,
        or_exprt(literal_exprt(cond_lit),
        equal_exprt(index_expr1, index_expr2)));
      add_array_constraint(lazy, false); // added immediately
      array_constraint_count[constraint_typet::ARRAY_IF]++;
  
  #if 0 // old code for adding, not significantly faster
      prop.lcnf(cond_lit, convert(equal_exprt(index_expr1, index_expr2)));
  #endif
    }
  }
  
  std::string arrayst::enum_to_string(constraint_typet type)
  {
    switch(type)
    {
    case constraint_typet::ARRAY_ACKERMANN:
      return "arrayAckermann";
    case constraint_typet::ARRAY_WITH:
      return "arrayWith";
    case constraint_typet::ARRAY_IF:
      return "arrayIf";
    case constraint_typet::ARRAY_OF:
      return "arrayOf";
    case constraint_typet::ARRAY_TYPECAST:
      return "arrayTypecast";
    case constraint_typet::ARRAY_CONSTANT:
      return "arrayConstant";
    case constraint_typet::ARRAY_COMPREHENSION:
      return "arrayComprehension";
    case constraint_typet::ARRAY_EQUALITY:
      return "arrayEquality";
    default:
      UNREACHABLE;
    }
  }
  
  void arrayst::display_array_constraint_count()
  {
    json_objectt json_result;
    json_objectt &json_array_theory =
      json_result["arrayConstraints"].make_object();
  
    size_t num_constraints = 0;
  
    array_constraint_countt::iterator it = array_constraint_count.begin();
    while(it != array_constraint_count.end())
    {
      std::string contraint_type_string = enum_to_string(it->first);
      json_array_theory[contraint_type_string] =
        json_numbert(std::to_string(it->second));
  
      num_constraints += it->second;
      it++;
    }
  
    json_result["numOfConstraints"] =
      json_numbert(std::to_string(num_constraints));
    log.status() << ",\n" << json_result;
  }
  