on-restart-benchmarks/lib/flatten.cpp

/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */

/*
 *  Main authors:
 *     Guido Tack <guido.tack@monash.edu>
 */

/* This Source Code Form is subject to the terms of the Mozilla Public
 * License, v. 2.0. If a copy of the MPL was not distributed with this
 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */

#include <minizinc/astexception.hh>
#include <minizinc/astiterator.hh>
#include <minizinc/copy.hh>
#include <minizinc/eval_par.hh>
#include <minizinc/flat_exp.hh>
#include <minizinc/flatten.hh>
#include <minizinc/flatten_internal.hh>
#include <minizinc/hash.hh>
#include <minizinc/optimize.hh>
#include <minizinc/output.hh>

#include <map>
#include <unordered_map>
#include <unordered_set>

namespace MiniZinc {

// Create domain constraints. Return true if successful.
bool create_explicit_domain_constraints(EnvI& envi, VarDecl* vd, Expression* domain) {
  std::vector<Call*> calls;
  Location iloc = Location().introduce();

  if (vd->type().isIntSet()) {
    assert(domain->type().isint() || domain->type().isIntSet());
    IntSetVal* isv = eval_intset(envi, domain);
    calls.push_back(new Call(iloc, constants().ids.set_subset, {vd->id(), new SetLit(iloc, isv)}));
  } else if (domain->type().isbool()) {
    calls.push_back(new Call(iloc, constants().ids.bool_eq, {vd->id(), domain}));
  } else if (domain->type().isBoolSet()) {
    IntSetVal* bsv = eval_boolset(envi, domain);
    assert(bsv->size() == 1);
    if (bsv->min() != bsv->max()) {
      return true;  // Both values are still possible, no change
    }
    calls.push_back(
        new Call(iloc, constants().ids.bool_eq, {vd->id(), constants().boollit(bsv->min() > 0)}));
  } else if (domain->type().isfloat() || domain->type().isFloatSet()) {
    FloatSetVal* fsv = eval_floatset(envi, domain);
    if (fsv->size() == 1) {  // Range based
      if (fsv->min() == fsv->max()) {
        calls.push_back(
            new Call(iloc, constants().ids.float_.eq, {vd->id(), FloatLit::a(fsv->min())}));
      } else {
        FloatSetVal* cfsv;
        if (vd->ti()->domain() != nullptr) {
          cfsv = eval_floatset(envi, vd->ti()->domain());
        } else {
          cfsv = FloatSetVal::a(-FloatVal::infinity(), FloatVal::infinity());
        }
        if (cfsv->min() < fsv->min()) {
          calls.push_back(
              new Call(iloc, constants().ids.float_.le, {FloatLit::a(fsv->min()), vd->id()}));
        }
        if (cfsv->max() > fsv->max()) {
          calls.push_back(
              new Call(iloc, constants().ids.float_.le, {vd->id(), FloatLit::a(fsv->max())}));
        }
      }
    } else {
      calls.push_back(new Call(iloc, constants().ids.set_in, {vd->id(), new SetLit(iloc, fsv)}));
    }
  } else if (domain->type().isint() || domain->type().isIntSet()) {
    IntSetVal* isv = eval_intset(envi, domain);
    if (isv->size() == 1) {  // Range based
      if (isv->min() == isv->max()) {
        calls.push_back(new Call(iloc, constants().ids.int_.eq, {vd->id(), IntLit::a(isv->min())}));
      } else {
        IntSetVal* cisv;
        if (vd->ti()->domain() != nullptr) {
          cisv = eval_intset(envi, vd->ti()->domain());
        } else {
          cisv = IntSetVal::a(-IntVal::infinity(), IntVal::infinity());
        }
        if (cisv->min() < isv->min()) {
          calls.push_back(
              new Call(iloc, constants().ids.int_.le, {IntLit::a(isv->min()), vd->id()}));
        }
        if (cisv->max() > isv->max()) {
          calls.push_back(
              new Call(iloc, constants().ids.int_.le, {vd->id(), IntLit::a(isv->max())}));
        }
      }
    } else {
      calls.push_back(new Call(iloc, constants().ids.set_in, {vd->id(), new SetLit(iloc, isv)}));
    }
  } else {
    return false;
  }

  int counter = 0;
  for (Call* c : calls) {
    CallStackItem csi(envi, IntLit::a(counter++));
    c->ann().add(constants().ann.domain_change_constraint);
    c->type(Type::varbool());
    c->decl(envi.model->matchFn(envi, c, true));
    flat_exp(envi, Ctx(), c, constants().varTrue, constants().varTrue);
  }
  return true;
}

void set_computed_domain(EnvI& envi, VarDecl* vd, Expression* domain, bool is_computed) {
  if (envi.hasReverseMapper(vd->id())) {
    if (!create_explicit_domain_constraints(envi, vd, domain)) {
      std::ostringstream ss;
      ss << "Unable to create domain constraint for reverse mapped variable: " << *vd->id() << " = "
         << *domain << std::endl;
      throw EvalError(envi, domain->loc(), ss.str());
    }
    vd->ti()->domain(domain);
    return;
  }
  if (envi.fopts.recordDomainChanges && !vd->ann().contains(constants().ann.is_defined_var) &&
      !vd->introduced() && !(vd->type().dim() > 0)) {
    if (create_explicit_domain_constraints(envi, vd, domain)) {
      return;
    }
    std::cerr << "Warning: domain change not handled by -g mode: " << *vd->id() << " = " << *domain
              << std::endl;
  }
  vd->ti()->domain(domain);
  vd->ti()->setComputedDomain(is_computed);
}

/// Output operator for contexts
template <class Char, class Traits>
std::basic_ostream<Char, Traits>& operator<<(std::basic_ostream<Char, Traits>& os, Ctx& ctx) {
  switch (ctx.b) {
    case C_ROOT:
      os << "R";
      break;
    case C_POS:
      os << "+";
      break;
    case C_NEG:
      os << "-";
      break;
    case C_MIX:
      os << "M";
      break;
    default:
      assert(false);
      break;
  }
  switch (ctx.i) {
    case C_ROOT:
      os << "R";
      break;
    case C_POS:
      os << "+";
      break;
    case C_NEG:
      os << "-";
      break;
    case C_MIX:
      os << "M";
      break;
    default:
      assert(false);
      break;
  }
  if (ctx.neg) {
    os << "!";
  }
  return os;
}

BCtx operator+(const BCtx& c) {
  switch (c) {
    case C_ROOT:
    case C_POS:
      return C_POS;
    case C_NEG:
      return C_NEG;
    case C_MIX:
      return C_MIX;
    default:
      assert(false);
      return C_ROOT;
  }
}

BCtx operator-(const BCtx& c) {
  switch (c) {
    case C_ROOT:
    case C_POS:
      return C_NEG;
    case C_NEG:
      return C_POS;
    case C_MIX:
      return C_MIX;
    default:
      assert(false);
      return C_ROOT;
  }
}

/// Check if \a c is non-positive
bool nonpos(const BCtx& c) { return c == C_NEG || c == C_MIX; }
/// Check if \a c is non-negative
bool nonneg(const BCtx& c) { return c == C_ROOT || c == C_POS; }

void dump_ee_b(const std::vector<EE>& ee) {
  for (const auto& i : ee) {
    std::cerr << *i.b() << "\n";
  }
}
void dump_ee_r(const std::vector<EE>& ee) {
  for (const auto& i : ee) {
    std::cerr << *i.r() << "\n";
  }
}

std::tuple<BCtx, bool> ann_to_ctx(VarDecl* vd) {
  if (vd->ann().contains(constants().ctx.root)) {
    return std::make_tuple(C_ROOT, true);
  }
  if (vd->ann().contains(constants().ctx.mix)) {
    return std::make_tuple(C_MIX, true);
  }
  if (vd->ann().contains(constants().ctx.pos)) {
    return std::make_tuple(C_POS, true);
  }
  if (vd->ann().contains(constants().ctx.neg)) {
    return std::make_tuple(C_NEG, true);
  }
  return std::make_tuple(C_MIX, false);
}

void add_ctx_ann(VarDecl* vd, BCtx& c) {
  if (vd != nullptr) {
    Id* ctx_id = nullptr;
    BCtx nc;
    bool annotated;
    std::tie(nc, annotated) = ann_to_ctx(vd);
    // If previously annotated
    if (annotated) {
      // Early exit
      if (nc == c || nc == C_ROOT || (nc == C_MIX && c != C_ROOT)) {
        return;
      }
      // Remove old annotation
      switch (nc) {
        case C_ROOT:
          vd->ann().remove(constants().ctx.root);
          break;
        case C_MIX:
          vd->ann().remove(constants().ctx.mix);
          break;
        case C_POS:
          vd->ann().remove(constants().ctx.pos);
          break;
        case C_NEG:
          vd->ann().remove(constants().ctx.neg);
          break;
        default:
          assert(false);
          break;
      }
      // Determine new context
      if (c == C_ROOT) {
        nc = C_ROOT;
      } else {
        nc = C_MIX;
      }
    } else {
      nc = c;
    }
    switch (nc) {
      case C_ROOT:
        ctx_id = constants().ctx.root;
        break;
      case C_POS:
        ctx_id = constants().ctx.pos;
        break;
      case C_NEG:
        ctx_id = constants().ctx.neg;
        break;
      case C_MIX:
        ctx_id = constants().ctx.mix;
        break;
      default:
        assert(false);
        break;
    }
    vd->addAnnotation(ctx_id);
  }
}

void make_defined_var(VarDecl* vd, Call* c) {
  if (!vd->ann().contains(constants().ann.is_defined_var)) {
    std::vector<Expression*> args(1);
    args[0] = vd->id();
    Call* dv = new Call(Location().introduce(), constants().ann.defines_var, args);
    dv->type(Type::ann());
    vd->addAnnotation(constants().ann.is_defined_var);
    c->addAnnotation(dv);
  }
}

bool is_defines_var_ann(Expression* e) {
  return e->isa<Call>() && e->cast<Call>()->id() == constants().ann.defines_var;
}

/// Check if \a e is NULL or true
bool istrue(EnvI& env, Expression* e) {
  if (e == nullptr) {
    return true;
  }
  if (e->type() == Type::parbool()) {
    if (e->type().cv()) {
      Ctx ctx;
      ctx.b = C_MIX;
      KeepAlive r = flat_cv_exp(env, ctx, e);
      return eval_bool(env, r());
    }
    GCLock lock;
    return eval_bool(env, e);
  }
  return false;
}
/// Check if \a e is non-NULL and false
bool isfalse(EnvI& env, Expression* e) {
  if (e == nullptr) {
    return false;
  }
  if (e->type() == Type::parbool()) {
    if (e->type().cv()) {
      Ctx ctx;
      ctx.b = C_MIX;
      KeepAlive r = flat_cv_exp(env, ctx, e);
      return !eval_bool(env, r());
    }
    GCLock lock;
    return !eval_bool(env, e);
  }
  return false;
}

/// Use bounds from ovd for vd if they are better.
/// Returns true if ovd's bounds are better.
bool update_bounds(EnvI& envi, VarDecl* ovd, VarDecl* vd) {
  bool tighter = false;
  bool fixed = false;
  if ((ovd->ti()->domain() != nullptr) || (ovd->e() != nullptr)) {
    IntVal intval;
    FloatVal doubleval;
    bool boolval;

    if (vd->type().isint()) {
      IntBounds oldbounds = compute_int_bounds(envi, ovd->id());
      IntBounds bounds(0, 0, false);
      if ((vd->ti()->domain() != nullptr) || (vd->e() != nullptr)) {
        bounds = compute_int_bounds(envi, vd->id());
      }

      if (((vd->ti()->domain() != nullptr) || (vd->e() != nullptr)) && bounds.valid &&
          bounds.l.isFinite() && bounds.u.isFinite()) {
        if (oldbounds.valid && oldbounds.l.isFinite() && oldbounds.u.isFinite()) {
          fixed = oldbounds.u == oldbounds.l || bounds.u == bounds.l;
          if (fixed) {
            tighter = true;
            intval = oldbounds.u == oldbounds.l ? oldbounds.u : bounds.l;
            ovd->ti()->domain(new SetLit(ovd->loc(), IntSetVal::a(intval, intval)));
          } else {
            IntSetVal* olddom =
                ovd->ti()->domain() != nullptr ? eval_intset(envi, ovd->ti()->domain()) : nullptr;
            IntSetVal* newdom =
                vd->ti()->domain() != nullptr ? eval_intset(envi, vd->ti()->domain()) : nullptr;

            if (olddom != nullptr) {
              if (newdom == nullptr) {
                tighter = true;
              } else {
                IntSetRanges oisr(olddom);
                IntSetRanges nisr(newdom);
                IntSetRanges nisr_card(newdom);

                Ranges::Inter<IntVal, IntSetRanges, IntSetRanges> inter(oisr, nisr);

                if (Ranges::cardinality(inter) < Ranges::cardinality(nisr_card)) {
                  IntSetRanges oisr_inter(olddom);
                  IntSetRanges nisr_inter(newdom);
                  Ranges::Inter<IntVal, IntSetRanges, IntSetRanges> inter_card(oisr_inter,
                                                                               nisr_inter);
                  tighter = true;
                  ovd->ti()->domain(new SetLit(ovd->loc(), IntSetVal::ai(inter_card)));
                }
              }
            }
          }
        }
      } else {
        if (oldbounds.valid && oldbounds.l.isFinite() && oldbounds.u.isFinite()) {
          tighter = true;
          fixed = oldbounds.u == oldbounds.l;
          if (fixed) {
            intval = oldbounds.u;
            ovd->ti()->domain(new SetLit(ovd->loc(), IntSetVal::a(intval, intval)));
          }
        }
      }
    } else if (vd->type().isfloat()) {
      FloatBounds oldbounds = compute_float_bounds(envi, ovd->id());
      FloatBounds bounds(0.0, 0.0, false);
      if ((vd->ti()->domain() != nullptr) || (vd->e() != nullptr)) {
        bounds = compute_float_bounds(envi, vd->id());
      }
      if (((vd->ti()->domain() != nullptr) || (vd->e() != nullptr)) && bounds.valid) {
        if (oldbounds.valid) {
          fixed = oldbounds.u == oldbounds.l || bounds.u == bounds.l;
          if (fixed) {
            doubleval = oldbounds.u == oldbounds.l ? oldbounds.u : bounds.l;
          }
          tighter = fixed || (oldbounds.u - oldbounds.l < bounds.u - bounds.l);
        }
      } else {
        if (oldbounds.valid) {
          tighter = true;
          fixed = oldbounds.u == oldbounds.l;
          if (fixed) {
            doubleval = oldbounds.u;
          }
        }
      }
    } else if (vd->type().isbool()) {
      if (ovd->ti()->domain() != nullptr) {
        fixed = tighter = true;
        boolval = eval_bool(envi, ovd->ti()->domain());
      } else {
        fixed = tighter = ((ovd->e() != nullptr) && ovd->e()->isa<BoolLit>());
        if (fixed) {
          boolval = ovd->e()->cast<BoolLit>()->v();
        }
      }
    }

    if (tighter) {
      vd->ti()->domain(ovd->ti()->domain());
      if (vd->e() == nullptr && fixed) {
        if (vd->ti()->type().isvarint()) {
          vd->type(Type::parint());
          vd->ti(new TypeInst(vd->loc(), Type::parint()));
          vd->e(IntLit::a(intval));
        } else if (vd->ti()->type().isvarfloat()) {
          vd->type(Type::parfloat());
          vd->ti(new TypeInst(vd->loc(), Type::parfloat()));
          vd->e(FloatLit::a(doubleval));
        } else if (vd->ti()->type().isvarbool()) {
          vd->type(Type::parbool());
          vd->ti(new TypeInst(vd->loc(), Type::parbool()));
          vd->ti()->domain(boolval ? constants().literalTrue : constants().literalFalse);
          vd->e(new BoolLit(vd->loc(), boolval));
        }
      }
    }
  }

  return tighter;
}

std::string get_path(EnvI& env) {
  std::string path;
  std::stringstream ss;
  if (env.dumpPath(ss)) {
    path = ss.str();
  }

  return path;
}

inline Location get_loc(EnvI& env, Expression* e1, Expression* e2) {
  if (e1 != nullptr) {
    return e1->loc().introduce();
  }
  if (e2 != nullptr) {
    return e2->loc().introduce();
  }
  return Location().introduce();
}
inline Id* get_id(EnvI& env, Id* origId) {
  return origId != nullptr ? origId : new Id(Location().introduce(), env.genId(), nullptr);
}

StringLit* get_longest_mzn_path_annotation(EnvI& env, const Expression* e) {
  StringLit* sl = nullptr;

  if (const auto* vd = e->dynamicCast<const VarDecl>()) {
    EnvI::ReversePathMap& reversePathMap = env.getReversePathMap();
    KeepAlive vd_decl_ka(vd->id()->decl());
    auto it = reversePathMap.find(vd_decl_ka);
    if (it != reversePathMap.end()) {
      sl = new StringLit(Location(), it->second);
    }
  } else {
    for (ExpressionSetIter it = e->ann().begin(); it != e->ann().end(); ++it) {
      if (Call* ca = (*it)->dynamicCast<Call>()) {
        if (ca->id() == constants().ann.mzn_path) {
          auto* sl1 = ca->arg(0)->cast<StringLit>();
          if (sl != nullptr) {
            if (sl1->v().size() > sl->v().size()) {
              sl = sl1;
            }
          } else {
            sl = sl1;
          }
        }
      }
    }
  }
  return sl;
}

void add_path_annotation(EnvI& env, Expression* e) {
  if (!(e->type().isAnn() || e->isa<Id>()) && e->type().dim() == 0) {
    GCLock lock;
    Annotation& ann = e->ann();
    if (ann.containsCall(constants().ann.mzn_path)) {
      return;
    }

    EnvI::ReversePathMap& reversePathMap = env.getReversePathMap();

    std::vector<Expression*> path_args(1);
    std::string p;
    KeepAlive e_ka(e);
    auto it = reversePathMap.find(e_ka);
    if (it == reversePathMap.end()) {
      p = get_path(env);
    } else {
      p = it->second;
    }

    if (!p.empty()) {
      path_args[0] = new StringLit(Location(), p);
      Call* path_call = new Call(e->loc(), constants().ann.mzn_path, path_args);
      path_call->type(Type::ann());
      e->addAnnotation(path_call);
    }
  }
}

VarDecl* new_vardecl(EnvI& env, const Ctx& ctx, TypeInst* ti, Id* origId, VarDecl* origVd,
                     Expression* rhs) {
  VarDecl* vd = nullptr;

  // Is this vardecl already in the FlatZinc (for unification)
  bool hasBeenAdded = false;

  // Don't use paths for arrays or annotations
  if (ti->type().dim() == 0 && !ti->type().isAnn()) {
    std::string path = get_path(env);
    if (!path.empty()) {
      EnvI::ReversePathMap& reversePathMap = env.getReversePathMap();
      EnvI::PathMap& pathMap = env.getPathMap();
      auto it = pathMap.find(path);

      if (it != pathMap.end()) {
        auto* ovd = Expression::cast<VarDecl>((it->second.decl)());
        unsigned int ovd_pass = it->second.passNumber;

        if (ovd != nullptr) {
          // If ovd was introduced during the same pass, we can unify
          if (env.currentPassNumber == ovd_pass) {
            vd = ovd;
            if (origId != nullptr) {
              origId->decl(vd);
            }
            hasBeenAdded = true;
          } else {
            vd = new VarDecl(get_loc(env, origVd, rhs), ti, get_id(env, origId));
            hasBeenAdded = false;
            update_bounds(env, ovd, vd);
          }

          // Check whether ovd was unified in a previous pass
          if (ovd->id() != ovd->id()->decl()->id()) {
            // We may not have seen the pointed to decl just yet
            KeepAlive ovd_decl_ka(ovd->id()->decl());
            auto path2It = reversePathMap.find(ovd_decl_ka);
            if (path2It != reversePathMap.end()) {
              std::string path2 = path2It->second;
              EnvI::PathVar vd_tup{vd, env.currentPassNumber};

              pathMap[path] = vd_tup;
              pathMap[path2] = vd_tup;
              KeepAlive vd_ka(vd);
              reversePathMap.insert(vd_ka, path);
            }
          }
        }
      } else {
        // Create new VarDecl and add it to the maps
        vd = new VarDecl(get_loc(env, origVd, rhs), ti, get_id(env, origId));
        hasBeenAdded = false;
        EnvI::PathVar vd_tup{vd, env.currentPassNumber};
        pathMap[path] = vd_tup;
        KeepAlive vd_ka(vd);
        reversePathMap.insert(vd_ka, path);
      }
    }
  }
  if (vd == nullptr) {
    vd = new VarDecl(get_loc(env, origVd, rhs), ti, get_id(env, origId));
    hasBeenAdded = false;
  }

  // If vd has an e() use bind to turn rhs into a constraint
  if (vd->e() != nullptr) {
    if (rhs != nullptr) {
      bind(env, ctx, vd, rhs);
    }
  } else {
    vd->e(rhs);
    if ((rhs != nullptr) && hasBeenAdded) {
      // This variable is being reused, so it won't be added to the model below.
      // Therefore, we need to register that we changed the RHS, in order
      // for the reference counts to be accurate.
      env.voAddExp(vd);
    }
  }
  assert(!vd->type().isbot());
  if ((origVd != nullptr) && (origVd->id()->idn() != -1 || origVd->toplevel())) {
    vd->introduced(origVd->introduced());
  } else {
    vd->introduced(true);
  }

  vd->flat(vd);

  // Copy annotations from origVd
  if (origVd != nullptr) {
    for (ExpressionSetIter it = origVd->ann().begin(); it != origVd->ann().end(); ++it) {
      EE ee_ann = flat_exp(env, Ctx(), *it, nullptr, constants().varTrue);
      vd->addAnnotation(ee_ann.r());
    }
  }

  if (!hasBeenAdded) {
    if (FunctionI* fi = env.model->matchRevMap(env, vd->type())) {
      // We need to introduce a reverse mapper
      Call* revmap = new Call(Location().introduce(), fi->id(), {vd->id()});
      revmap->decl(fi);
      revmap->type(Type::varbool());
      env.flatAddItem(new ConstraintI(Location().introduce(), revmap));
    }

    auto* ni = new VarDeclI(Location().introduce(), vd);
    env.flatAddItem(ni);
    EE ee(vd, nullptr);
    env.cseMapInsert(vd->id(), ee);
  }

  return vd;
}

#define MZN_FILL_REIFY_MAP(T, ID) \
  _reifyMap.insert(               \
      std::pair<ASTString, ASTString>(constants().ids.T.ID, constants().ids.T##reif.ID));

EnvI::EnvI(Model* model0, std::ostream& outstream0, std::ostream& errstream0)
    : model(model0),
      originalModel(nullptr),
      output(new Model),
      outstream(outstream0),
      errstream(errstream0),
      currentPassNumber(0),
      finalPassNumber(1),
      maxPathDepth(0),
      ignorePartial(false),
      ignoreUnknownIds(false),
      maxCallStack(0),
      inRedundantConstraint(0),
      inSymmetryBreakingConstraint(0),
      inMaybePartial(0),
      inReverseMapVar(false),
      counters({0, 0, 0, 0}),
      pathUse(0),
      _flat(new Model),
      _failed(false),
      _ids(0),
      _collectVardecls(false) {
  MZN_FILL_REIFY_MAP(int_, lin_eq);
  MZN_FILL_REIFY_MAP(int_, lin_le);
  MZN_FILL_REIFY_MAP(int_, lin_ne);
  MZN_FILL_REIFY_MAP(int_, plus);
  MZN_FILL_REIFY_MAP(int_, minus);
  MZN_FILL_REIFY_MAP(int_, times);
  MZN_FILL_REIFY_MAP(int_, div);
  MZN_FILL_REIFY_MAP(int_, mod);
  MZN_FILL_REIFY_MAP(int_, lt);
  MZN_FILL_REIFY_MAP(int_, le);
  MZN_FILL_REIFY_MAP(int_, gt);
  MZN_FILL_REIFY_MAP(int_, ge);
  MZN_FILL_REIFY_MAP(int_, eq);
  MZN_FILL_REIFY_MAP(int_, ne);
  MZN_FILL_REIFY_MAP(float_, lin_eq);
  MZN_FILL_REIFY_MAP(float_, lin_le);
  MZN_FILL_REIFY_MAP(float_, lin_lt);
  MZN_FILL_REIFY_MAP(float_, lin_ne);
  MZN_FILL_REIFY_MAP(float_, plus);
  MZN_FILL_REIFY_MAP(float_, minus);
  MZN_FILL_REIFY_MAP(float_, times);
  MZN_FILL_REIFY_MAP(float_, div);
  MZN_FILL_REIFY_MAP(float_, mod);
  MZN_FILL_REIFY_MAP(float_, lt);
  MZN_FILL_REIFY_MAP(float_, le);
  MZN_FILL_REIFY_MAP(float_, gt);
  MZN_FILL_REIFY_MAP(float_, ge);
  MZN_FILL_REIFY_MAP(float_, eq);
  MZN_FILL_REIFY_MAP(float_, ne);
  _reifyMap.insert(
      std::pair<ASTString, ASTString>(constants().ids.forall, constants().ids.forallReif));
  _reifyMap.insert(
      std::pair<ASTString, ASTString>(constants().ids.bool_eq, constants().ids.bool_eq_reif));
  _reifyMap.insert(std::pair<ASTString, ASTString>(constants().ids.bool_clause,
                                                   constants().ids.bool_clause_reif));
  _reifyMap.insert(
      std::pair<ASTString, ASTString>(constants().ids.clause, constants().ids.bool_clause_reif));
  _reifyMap.insert({constants().ids.bool_not, constants().ids.bool_not});
}
EnvI::~EnvI() {
  delete _flat;
  delete output;
  delete model;
  delete originalModel;
}
long long int EnvI::genId() { return _ids++; }
void EnvI::cseMapInsert(Expression* e, const EE& ee) {
  if (e->type().isPar() && !e->isa<ArrayLit>()) {
    return;
  }
  KeepAlive ka(e);
  _cseMap.insert(ka, WW(ee.r(), ee.b()));
  Call* c = e->dynamicCast<Call>();
  if (c != nullptr && c->decl() != nullptr &&
      get_annotation(c->decl()->ann(), constants().ann.impure) != nullptr) {
    return;
  }
  if ((c != nullptr) && c->id() == constants().ids.bool_not && c->arg(0)->isa<Id>() &&
      ee.r()->isa<Id>() && ee.b() == constants().boollit(true)) {
    Call* neg_c = new Call(Location().introduce(), c->id(), {ee.r()});
    neg_c->type(c->type());
    neg_c->decl(c->decl());
    KeepAlive neg_ka(neg_c);
    _cseMap.insert(neg_ka, WW(c->arg(0), ee.b()));
  }
}
EnvI::CSEMap::iterator EnvI::cseMapFind(Expression* e) {
  KeepAlive ka(e);
  auto it = _cseMap.find(ka);
  if (it != _cseMap.end()) {
    if (it->second.r() != nullptr) {
      VarDecl* it_vd = it->second.r()->isa<Id>() ? it->second.r()->cast<Id>()->decl()
                                                 : it->second.r()->dynamicCast<VarDecl>();
      if (it_vd != nullptr) {
        int idx = varOccurrences.find(it_vd);
        if (idx == -1 || (*_flat)[idx]->removed()) {
          return _cseMap.end();
        }
      }
    } else {
      return _cseMap.end();
    }
  }
  return it;
}
void EnvI::cseMapRemove(Expression* e) {
  KeepAlive ka(e);
  _cseMap.remove(ka);
}
EnvI::CSEMap::iterator EnvI::cseMapEnd() { return _cseMap.end(); }
void EnvI::dump() {
  struct EED {
    static std::string k(Expression* e) {
      std::ostringstream oss;
      oss << *e;
      return oss.str();
    }
    static std::string d(const WW& ee) {
      std::ostringstream oss;
      oss << *ee.r() << " " << ee.b();
      return oss.str();
    }
  };
  _cseMap.dump<EED>();
}

void EnvI::flatAddItem(Item* i) {
  assert(_flat);
  if (_failed) {
    return;
  }
  _flat->addItem(i);

  Expression* toAnnotate = nullptr;
  Expression* toAdd = nullptr;
  switch (i->iid()) {
    case Item::II_VD: {
      auto* vd = i->cast<VarDeclI>();
      add_path_annotation(*this, vd->e());
      toAnnotate = vd->e()->e();
      varOccurrences.addIndex(vd, static_cast<int>(_flat->size()) - 1);
      toAdd = vd->e();
      break;
    }
    case Item::II_CON: {
      auto* ci = i->cast<ConstraintI>();

      if (ci->e()->isa<BoolLit>() && !ci->e()->cast<BoolLit>()->v()) {
        fail();
      } else {
        toAnnotate = ci->e();
        add_path_annotation(*this, ci->e());
        toAdd = ci->e();
      }
      break;
    }
    case Item::II_SOL: {
      auto* si = i->cast<SolveI>();
      CollectOccurrencesE ce(varOccurrences, si);
      top_down(ce, si->e());
      for (ExpressionSetIter it = si->ann().begin(); it != si->ann().end(); ++it) {
        top_down(ce, *it);
      }
      break;
    }
    case Item::II_OUT: {
      auto* si = i->cast<OutputI>();
      toAdd = si->e();
      break;
    }
    default:
      break;
  }
  if ((toAnnotate != nullptr) && toAnnotate->isa<Call>()) {
    annotateFromCallStack(toAnnotate);
  }
  if (toAdd != nullptr) {
    CollectOccurrencesE ce(varOccurrences, i);
    top_down(ce, toAdd);
  }
}

void EnvI::annotateFromCallStack(Expression* e) {
  int prev = !idStack.empty() ? idStack.back() : 0;
  bool allCalls = true;
  for (int i = static_cast<int>(callStack.size()) - 1; i >= prev; i--) {
    Expression* ee = callStack[i]->untag();
    if (ee->type().isAnn()) {
      // If we are inside an annotation call, don't annotate it again with
      // anything from outside the call
      break;
    }
    allCalls = allCalls && (i == callStack.size() - 1 || ee->isa<Call>() || ee->isa<BinOp>());
    for (ExpressionSetIter it = ee->ann().begin(); it != ee->ann().end(); ++it) {
      EE ee_ann = flat_exp(*this, Ctx(), *it, nullptr, constants().varTrue);
      if (allCalls || !is_defines_var_ann(ee_ann.r())) {
        e->addAnnotation(ee_ann.r());
      }
    }
  }
}

void EnvI::copyPathMapsAndState(EnvI& env) {
  finalPassNumber = env.finalPassNumber;
  maxPathDepth = env.maxPathDepth;
  currentPassNumber = env.currentPassNumber;
  _filenameSet = env._filenameSet;
  maxPathDepth = env.maxPathDepth;
  _pathMap = env.getPathMap();
  _reversePathMap = env.getReversePathMap();
}

void EnvI::flatRemoveExpr(Expression* e, Item* i) {
  std::vector<VarDecl*> toRemove;
  CollectDecls cd(varOccurrences, toRemove, i);
  top_down(cd, e);

  Model& flat = (*_flat);
  while (!toRemove.empty()) {
    VarDecl* cur = toRemove.back();
    toRemove.pop_back();
    assert(varOccurrences.occurrences(cur) == 0 && CollectDecls::varIsFree(cur));

    auto cur_idx = varOccurrences.idx.find(cur->id());
    if (cur_idx != varOccurrences.idx.end()) {
      auto* vdi = flat[cur_idx->second]->cast<VarDeclI>();

      if (!is_output(vdi->e()) && !vdi->removed()) {
        CollectDecls cd(varOccurrences, toRemove, vdi);
        top_down(cd, vdi->e()->e());
        vdi->remove();
      }
    }
  }
}

void EnvI::flatRemoveItem(ConstraintI* ci) {
  flatRemoveExpr(ci->e(), ci);
  ci->e(constants().literalTrue);
  ci->remove();
}
void EnvI::flatRemoveItem(VarDeclI* vdi) {
  flatRemoveExpr(vdi->e(), vdi);
  vdi->remove();
}

void EnvI::fail(const std::string& msg) {
  if (!_failed) {
    addWarning(std::string("model inconsistency detected") +
               (msg.empty() ? std::string() : (": " + msg)));
    _failed = true;
    for (auto& i : *_flat) {
      i->remove();
    }
    auto* failedConstraint = new ConstraintI(Location().introduce(), constants().literalFalse);
    _flat->addItem(failedConstraint);
    _flat->addItem(SolveI::sat(Location().introduce()));
    for (auto& i : *output) {
      i->remove();
    }
    output->addItem(
        new OutputI(Location().introduce(), new ArrayLit(Location(), std::vector<Expression*>())));
    throw ModelInconsistent(*this, Location().introduce());
  }
}

bool EnvI::failed() const { return _failed; }

unsigned int EnvI::registerEnum(VarDeclI* vdi) {
  auto it = _enumMap.find(vdi);
  unsigned int ret;
  if (it == _enumMap.end()) {
    ret = static_cast<unsigned int>(_enumVarDecls.size());
    _enumVarDecls.push_back(vdi);
    _enumMap.insert(std::make_pair(vdi, ret));
  } else {
    ret = it->second;
  }
  return ret + 1;
}
VarDeclI* EnvI::getEnum(unsigned int i) const {
  assert(i > 0 && i <= _enumVarDecls.size());
  return _enumVarDecls[i - 1];
}
unsigned int EnvI::registerArrayEnum(const std::vector<unsigned int>& arrayEnum) {
  std::ostringstream oss;
  for (unsigned int i : arrayEnum) {
    assert(i <= _enumVarDecls.size());
    oss << i << ".";
  }
  auto it = _arrayEnumMap.find(oss.str());
  unsigned int ret;
  if (it == _arrayEnumMap.end()) {
    ret = static_cast<unsigned int>(_arrayEnumDecls.size());
    _arrayEnumDecls.push_back(arrayEnum);
    _arrayEnumMap.insert(std::make_pair(oss.str(), ret));
  } else {
    ret = it->second;
  }
  return ret + 1;
}
const std::vector<unsigned int>& EnvI::getArrayEnum(unsigned int i) const {
  assert(i > 0 && i <= _arrayEnumDecls.size());
  return _arrayEnumDecls[i - 1];
}
bool EnvI::isSubtype(const Type& t1, const Type& t2, bool strictEnums) const {
  if (!t1.isSubtypeOf(t2, strictEnums)) {
    return false;
  }
  if (strictEnums && t1.dim() == 0 && t2.dim() != 0 && t2.enumId() != 0) {
    // set assigned to an array
    const std::vector<unsigned int>& t2enumIds = getArrayEnum(t2.enumId());
    if (t2enumIds[t2enumIds.size() - 1] != 0 && t1.enumId() != t2enumIds[t2enumIds.size() - 1]) {
      return false;
    }
  }
  if (strictEnums && t1.dim() > 0 && t1.enumId() != t2.enumId()) {
    if (t1.enumId() == 0) {
      return t1.isbot();
    }
    if (t2.enumId() != 0) {
      const std::vector<unsigned int>& t1enumIds = getArrayEnum(t1.enumId());
      const std::vector<unsigned int>& t2enumIds = getArrayEnum(t2.enumId());
      assert(t1enumIds.size() == t2enumIds.size());
      for (unsigned int i = 0; i < t1enumIds.size() - 1; i++) {
        if (t2enumIds[i] != 0 && t1enumIds[i] != t2enumIds[i]) {
          return false;
        }
      }
      if (!t1.isbot() && t2enumIds[t1enumIds.size() - 1] != 0 &&
          t1enumIds[t1enumIds.size() - 1] != t2enumIds[t2enumIds.size() - 1]) {
        return false;
      }
    }
  }
  return true;
}

void EnvI::collectVarDecls(bool b) { _collectVardecls = b; }
void EnvI::voAddExp(VarDecl* vd) {
  if ((vd->e() != nullptr) && vd->e()->isa<Call>() && !vd->e()->type().isAnn()) {
    int prev = !idStack.empty() ? idStack.back() : 0;
    for (int i = static_cast<int>(callStack.size()) - 1; i >= prev; i--) {
      Expression* ee = callStack[i]->untag();
      for (ExpressionSetIter it = ee->ann().begin(); it != ee->ann().end(); ++it) {
        Expression* ann = *it;
        if (ann != constants().ann.add_to_output && ann != constants().ann.rhs_from_assignment) {
          bool needAnnotation = true;
          if (Call* ann_c = ann->dynamicCast<Call>()) {
            if (ann_c->id() == constants().ann.defines_var) {
              // only add defines_var annotation if vd is the defined variable
              if (Id* defined_var = ann_c->arg(0)->dynamicCast<Id>()) {
                if (defined_var->decl() != vd->id()->decl()) {
                  needAnnotation = false;
                }
              }
            }
          }
          if (needAnnotation) {
            EE ee_ann = flat_exp(*this, Ctx(), *it, nullptr, constants().varTrue);
            vd->e()->addAnnotation(ee_ann.r());
          }
        }
      }
    }
  }
  int idx = varOccurrences.find(vd);
  CollectOccurrencesE ce(varOccurrences, (*_flat)[idx]);
  top_down(ce, vd->e());
  if (_collectVardecls) {
    modifiedVarDecls.push_back(idx);
  }
}
Model* EnvI::flat() { return _flat; }
void EnvI::swap() {
  Model* tmp = model;
  model = _flat;
  _flat = tmp;
}
ASTString EnvI::reifyId(const ASTString& id) {
  auto it = _reifyMap.find(id);
  if (it == _reifyMap.end()) {
    std::ostringstream ss;
    ss << id << "_reif";
    return {ss.str()};
  }
  return it->second;
}
#undef MZN_FILL_REIFY_MAP
ASTString EnvI::halfReifyId(const ASTString& id) {
  std::ostringstream ss;
  ss << id << "_imp";
  return {ss.str()};
}

void EnvI::addWarning(const std::string& msg) {
  if (warnings.size() > 20) {
    return;
  }
  if (warnings.size() == 20) {
    warnings.emplace_back("Further warnings have been suppressed.\n");
  } else {
    std::ostringstream oss;
    createErrorStack();
    dumpStack(oss, true);
    warnings.push_back(msg + "\n" + oss.str());
  }
}

void EnvI::createErrorStack() {
  errorStack.clear();
  for (auto i = static_cast<unsigned int>(callStack.size()); (i--) != 0U;) {
    Expression* e = callStack[i]->untag();
    bool isCompIter = callStack[i]->isTagged();
    KeepAlive ka(e);
    errorStack.emplace_back(ka, isCompIter);
  }
}

Call* EnvI::surroundingCall() const {
  if (callStack.size() >= 2) {
    return callStack[callStack.size() - 2]->untag()->dynamicCast<Call>();
  }
  return nullptr;
}

void EnvI::cleanupExceptOutput() {
  cmap.clear();
  _cseMap.clear();
  delete _flat;
  delete model;
  delete originalModel;
  _flat = nullptr;
  model = nullptr;
}

CallStackItem::CallStackItem(EnvI& env0, Expression* e) : env(env0) {
  if (e->isa<VarDecl>()) {
    env.idStack.push_back(static_cast<int>(env.callStack.size()));
  }
  if (e->isa<Call>() && e->cast<Call>()->id() == "redundant_constraint") {
    env.inRedundantConstraint++;
  }
  if (e->isa<Call>() && e->cast<Call>()->id() == "symmetry_breaking_constraint") {
    env.inSymmetryBreakingConstraint++;
  }
  if (e->ann().contains(constants().ann.maybe_partial)) {
    env.inMaybePartial++;
  }
  env.callStack.push_back(e);
  env.maxCallStack = std::max(env.maxCallStack, static_cast<unsigned int>(env.callStack.size()));
}
CallStackItem::CallStackItem(EnvI& env0, Id* ident, IntVal i) : env(env0) {
  Expression* ee = ident->tag();
  env.callStack.push_back(ee);
  env.maxCallStack = std::max(env.maxCallStack, static_cast<unsigned int>(env.callStack.size()));
}
CallStackItem::~CallStackItem() {
  try {
    Expression* e = env.callStack.back()->untag();
    if (e->isa<VarDecl>()) {
      env.idStack.pop_back();
    }
    if (e->isa<Call>() && e->cast<Call>()->id() == "redundant_constraint") {
      env.inRedundantConstraint--;
    }
    if (e->isa<Call>() && e->cast<Call>()->id() == "symmetry_breaking_constraint") {
      env.inSymmetryBreakingConstraint--;
    }
    if (e->ann().contains(constants().ann.maybe_partial)) {
      env.inMaybePartial--;
    }
    env.callStack.pop_back();
  } catch (std::exception&) {
    assert(false);  // Invariant: These Env vector operations will never throw an exception
  }
}

FlatteningError::FlatteningError(EnvI& env, const Location& loc, const std::string& msg)
    : LocationException(env, loc, msg) {}

Env::Env(Model* m, std::ostream& outstream, std::ostream& errstream)
    : _e(new EnvI(m, outstream, errstream)) {}
Env::~Env() { delete _e; }

Model* Env::model() { return _e->model; }
void Env::model(Model* m) { _e->model = m; }
Model* Env::flat() { return _e->flat(); }
void Env::swap() { _e->swap(); }
Model* Env::output() { return _e->output; }

std::ostream& Env::evalOutput(std::ostream& os, std::ostream& log) {
  return _e->evalOutput(os, log);
}
EnvI& Env::envi() { return *_e; }
const EnvI& Env::envi() const { return *_e; }
std::ostream& Env::dumpErrorStack(std::ostream& os) { return _e->dumpStack(os, true); }

bool EnvI::dumpPath(std::ostream& os, bool force) {
  force = force ? force : fopts.collectMznPaths;
  if (callStack.size() > maxPathDepth) {
    if (!force && currentPassNumber >= finalPassNumber - 1) {
      return false;
    }
    maxPathDepth = static_cast<int>(callStack.size());
  }

  auto lastError = static_cast<unsigned int>(callStack.size());

  std::string major_sep = ";";
  std::string minor_sep = "|";
  for (unsigned int i = 0; i < lastError; i++) {
    Expression* e = callStack[i]->untag();
    bool isCompIter = callStack[i]->isTagged();
    Location loc = e->loc();
    auto findFilename = _filenameSet.find(loc.filename());
    if (findFilename == _filenameSet.end()) {
      if (!force && currentPassNumber >= finalPassNumber - 1) {
        return false;
      }
      _filenameSet.insert(loc.filename());
    }

    // If this call is not a dummy StringLit with empty Location (so that deferred compilation
    // doesn't drop the paths)
    if (e->eid() != Expression::E_STRINGLIT || (loc.firstLine() != 0U) ||
        (loc.firstColumn() != 0U) || (loc.lastLine() != 0U) || (loc.lastColumn() != 0U)) {
      os << loc.filename() << minor_sep << loc.firstLine() << minor_sep << loc.firstColumn()
         << minor_sep << loc.lastLine() << minor_sep << loc.lastColumn() << minor_sep;
      switch (e->eid()) {
        case Expression::E_INTLIT:
          os << "il" << minor_sep << *e;
          break;
        case Expression::E_FLOATLIT:
          os << "fl" << minor_sep << *e;
          break;
        case Expression::E_SETLIT:
          os << "sl" << minor_sep << *e;
          break;
        case Expression::E_BOOLLIT:
          os << "bl" << minor_sep << *e;
          break;
        case Expression::E_STRINGLIT:
          os << "stl" << minor_sep << *e;
          break;
        case Expression::E_ID:
          if (isCompIter) {
            // if (e->cast<Id>()->decl()->e()->type().isPar())
            os << *e << "=" << *e->cast<Id>()->decl()->e();
            // else
            //  os << *e << "=?";
          } else {
            os << "id" << minor_sep << *e;
          }
          break;
        case Expression::E_ANON:
          os << "anon";
          break;
        case Expression::E_ARRAYLIT:
          os << "al";
          break;
        case Expression::E_ARRAYACCESS:
          os << "aa";
          break;
        case Expression::E_COMP: {
          const Comprehension* cmp = e->cast<Comprehension>();
          if (cmp->set()) {
            os << "sc";
          } else {
            os << "ac";
          }
        } break;
        case Expression::E_ITE:
          os << "ite";
          break;
        case Expression::E_BINOP:
          os << "bin" << minor_sep << e->cast<BinOp>()->opToString();
          break;
        case Expression::E_UNOP:
          os << "un" << minor_sep << e->cast<UnOp>()->opToString();
          break;
        case Expression::E_CALL:
          if (fopts.onlyToplevelPaths) {
            return false;
          }
          os << "ca" << minor_sep << e->cast<Call>()->id();
          break;
        case Expression::E_VARDECL:
          os << "vd";
          break;
        case Expression::E_LET:
          os << "l";
          break;
        case Expression::E_TI:
          os << "ti";
          break;
        case Expression::E_TIID:
          os << "ty";
          break;
        default:
          assert(false);
          os << "unknown expression (internal error)";
          break;
      }
      os << major_sep;
    } else {
      os << e->cast<StringLit>()->v() << major_sep;
    }
  }
  return true;
}

std::ostream& EnvI::dumpStack(std::ostream& os, bool errStack) {
  int lastError = 0;

  std::vector<Expression*> errStackCopy;
  if (errStack) {
    errStackCopy.resize(errorStack.size());
    for (unsigned int i = 0; i < errorStack.size(); i++) {
      Expression* e = errorStack[i].first();
      if (errorStack[i].second) {
        e = e->tag();
      }
      errStackCopy[i] = e;
    }
  }

  std::vector<Expression*>& stack = errStack ? errStackCopy : callStack;

  for (; lastError < stack.size(); lastError++) {
    Expression* e = stack[lastError]->untag();
    bool isCompIter = stack[lastError]->isTagged();
    if (e->loc().isIntroduced()) {
      continue;
    }
    if (!isCompIter && e->isa<Id>()) {
      break;
    }
  }

  if (lastError == 0 && !stack.empty() && stack[0]->untag()->isa<Id>()) {
    Expression* e = stack[0]->untag();
    ASTString newloc_f = e->loc().filename();
    if (!e->loc().isIntroduced()) {
      unsigned int newloc_l = e->loc().firstLine();
      os << "  " << newloc_f << ":" << newloc_l << ":" << std::endl;
      os << "  in variable declaration " << *e << std::endl;
    }
  } else {
    ASTString curloc_f;
    long long int curloc_l = -1;

    for (int i = lastError - 1; i >= 0; i--) {
      Expression* e = stack[i]->untag();
      bool isCompIter = stack[i]->isTagged();
      ASTString newloc_f = e->loc().filename();
      if (e->loc().isIntroduced()) {
        continue;
      }
      auto newloc_l = static_cast<long long int>(e->loc().firstLine());
      if (newloc_f != curloc_f || newloc_l != curloc_l) {
        os << "  " << newloc_f << ":" << newloc_l << ":" << std::endl;
        curloc_f = newloc_f;
        curloc_l = newloc_l;
      }
      if (isCompIter) {
        os << "    with ";
      } else {
        os << "  in ";
      }
      switch (e->eid()) {
        case Expression::E_INTLIT:
          os << "integer literal" << std::endl;
          break;
        case Expression::E_FLOATLIT:
          os << "float literal" << std::endl;
          break;
        case Expression::E_SETLIT:
          os << "set literal" << std::endl;
          break;
        case Expression::E_BOOLLIT:
          os << "bool literal" << std::endl;
          break;
        case Expression::E_STRINGLIT:
          os << "string literal" << std::endl;
          break;
        case Expression::E_ID:
          if (isCompIter) {
            if ((e->cast<Id>()->decl()->e() != nullptr) &&
                e->cast<Id>()->decl()->e()->type().isPar()) {
              os << *e << " = " << *e->cast<Id>()->decl()->e() << std::endl;
            } else {
              os << *e << " = <expression>" << std::endl;
            }
          } else {
            os << "identifier" << *e << std::endl;
          }
          break;
        case Expression::E_ANON:
          os << "anonymous variable" << std::endl;
          break;
        case Expression::E_ARRAYLIT:
          os << "array literal" << std::endl;
          break;
        case Expression::E_ARRAYACCESS:
          os << "array access" << std::endl;
          break;
        case Expression::E_COMP: {
          const Comprehension* cmp = e->cast<Comprehension>();
          if (cmp->set()) {
            os << "set ";
          } else {
            os << "array ";
          }
          os << "comprehension expression" << std::endl;
        } break;
        case Expression::E_ITE:
          os << "if-then-else expression" << std::endl;
          break;
        case Expression::E_BINOP:
          os << "binary " << e->cast<BinOp>()->opToString() << " operator expression" << std::endl;
          break;
        case Expression::E_UNOP:
          os << "unary " << e->cast<UnOp>()->opToString() << " operator expression" << std::endl;
          break;
        case Expression::E_CALL:
          os << "call '" << e->cast<Call>()->id() << "'" << std::endl;
          break;
        case Expression::E_VARDECL: {
          GCLock lock;
          os << "variable declaration for '" << e->cast<VarDecl>()->id()->str() << "'" << std::endl;
        } break;
        case Expression::E_LET:
          os << "let expression" << std::endl;
          break;
        case Expression::E_TI:
          os << "type-inst expression" << std::endl;
          break;
        case Expression::E_TIID:
          os << "type identifier" << std::endl;
          break;
        default:
          assert(false);
          os << "unknown expression (internal error)" << std::endl;
          break;
      }
    }
  }
  return os;
}

void populate_output(Env& env) {
  EnvI& envi = env.envi();
  Model* _flat = envi.flat();
  Model* _output = envi.output;
  std::vector<Expression*> outputVars;
  for (VarDeclIterator it = _flat->vardecls().begin(); it != _flat->vardecls().end(); ++it) {
    VarDecl* vd = it->e();
    Annotation& ann = vd->ann();
    ArrayLit* dims = nullptr;
    bool has_output_ann = false;
    if (!ann.isEmpty()) {
      for (ExpressionSetIter ait = ann.begin(); ait != ann.end(); ++ait) {
        if (Call* c = (*ait)->dynamicCast<Call>()) {
          if (c->id() == constants().ann.output_array) {
            dims = c->arg(0)->cast<ArrayLit>();
            has_output_ann = true;
            break;
          }
        } else if ((*ait)->isa<Id>() &&
                   (*ait)->cast<Id>()->str() == constants().ann.output_var->str()) {
          has_output_ann = true;
        }
      }
      if (has_output_ann) {
        std::ostringstream s;
        s << vd->id()->str() << " = ";

        auto* vd_output = copy(env.envi(), vd)->cast<VarDecl>();
        Type vd_t = vd_output->type();
        vd_t.ti(Type::TI_PAR);
        vd_output->type(vd_t);
        vd_output->ti()->type(vd_t);

        if (dims != nullptr) {
          std::vector<TypeInst*> ranges(dims->size());
          s << "array" << dims->size() << "d(";
          for (unsigned int i = 0; i < dims->size(); i++) {
            IntSetVal* idxset = eval_intset(envi, (*dims)[i]);
            ranges[i] = new TypeInst(Location().introduce(), Type(),
                                     new SetLit(Location().introduce(), idxset));
            s << *idxset << ",";
          }
          Type t = vd_t;
          vd_t.dim(static_cast<int>(dims->size()));
          vd_output->type(t);
          vd_output->ti(new TypeInst(Location().introduce(), vd_t, ranges));
        }
        _output->addItem(new VarDeclI(Location().introduce(), vd_output));

        auto* sl = new StringLit(Location().introduce(), s.str());
        outputVars.push_back(sl);

        std::vector<Expression*> showArgs(1);
        showArgs[0] = vd_output->id();
        Call* show = new Call(Location().introduce(), constants().ids.show, showArgs);
        show->type(Type::parstring());
        FunctionI* fi = _flat->matchFn(envi, show, false);
        assert(fi);
        show->decl(fi);
        outputVars.push_back(show);
        std::string ends = dims != nullptr ? ")" : "";
        ends += ";\n";
        auto* eol = new StringLit(Location().introduce(), ends);
        outputVars.push_back(eol);
      }
    }
  }
  auto* newOutputItem =
      new OutputI(Location().introduce(), new ArrayLit(Location().introduce(), outputVars));
  _output->addItem(newOutputItem);
  envi.flat()->mergeStdLib(envi, _output);
}

std::ostream& EnvI::evalOutput(std::ostream& os, std::ostream& log) {
  GCLock lock;
  warnings.clear();
  ArrayLit* al = eval_array_lit(*this, output->outputItem()->e());
  bool fLastEOL = true;
  for (unsigned int i = 0; i < al->size(); i++) {
    std::string s = eval_string(*this, (*al)[i]);
    if (!s.empty()) {
      os << s;
      fLastEOL = ('\n' == s.back());
    }
  }
  if (!fLastEOL) {
    os << '\n';
  }
  for (auto w : warnings) {
    log << "  WARNING: " << w << "\n";
  }
  return os;
}

const std::vector<std::string>& Env::warnings() { return envi().warnings; }

void Env::clearWarnings() { envi().warnings.clear(); }

unsigned int Env::maxCallStack() const { return envi().maxCallStack; }

void check_index_sets(EnvI& env, VarDecl* vd, Expression* e) {
  ASTExprVec<TypeInst> tis = vd->ti()->ranges();
  std::vector<TypeInst*> newtis(tis.size());
  bool needNewTypeInst = false;
  GCLock lock;
  switch (e->eid()) {
    case Expression::E_ID: {
      Id* id = e->cast<Id>();
      ASTExprVec<TypeInst> e_tis = id->decl()->ti()->ranges();
      assert(tis.size() == e_tis.size());
      for (unsigned int i = 0; i < tis.size(); i++) {
        if (tis[i]->domain() == nullptr) {
          newtis[i] = e_tis[i];
          needNewTypeInst = true;
        } else {
          IntSetVal* isv0 = eval_intset(env, tis[i]->domain());
          IntSetVal* isv1 = eval_intset(env, e_tis[i]->domain());
          if (!isv0->equal(isv1)) {
            std::ostringstream oss;
            oss << "Index set mismatch. Declared index " << (tis.size() == 1 ? "set" : "sets");
            oss << " of `" << *vd->id() << "' " << (tis.size() == 1 ? "is [" : "are [");
            for (unsigned int j = 0; j < tis.size(); j++) {
              if (tis[j]->domain() != nullptr) {
                oss << *eval_intset(env, tis[j]->domain());
              } else {
                oss << "int";
              }
              if (j < tis.size() - 1) {
                oss << ", ";
              }
            }
            oss << "], but is assigned to array `" << *id << "' with index "
                << (tis.size() == 1 ? "set [" : "sets [");
            for (unsigned int j = 0; j < e_tis.size(); j++) {
              oss << *eval_intset(env, e_tis[j]->domain());
              if (j < e_tis.size() - 1) {
                oss << ", ";
              }
            }
            oss << "]. You may need to coerce the index sets using the array" << tis.size()
                << "d function.";
            throw EvalError(env, vd->loc(), oss.str());
          }
          newtis[i] = tis[i];
        }
      }
    } break;
    case Expression::E_ARRAYLIT: {
      auto* al = e->cast<ArrayLit>();
      for (unsigned int i = 0; i < tis.size(); i++) {
        if (tis[i]->domain() == nullptr) {
          newtis[i] = new TypeInst(
              Location().introduce(), Type(),
              new SetLit(Location().introduce(), IntSetVal::a(al->min(i), al->max(i))));
          needNewTypeInst = true;
        } else if (i == 0 || al->size() != 0) {
          IntSetVal* isv = eval_intset(env, tis[i]->domain());
          assert(isv->size() <= 1);
          if ((isv->size() == 0 && al->min(i) <= al->max(i)) ||
              (isv->size() != 0 && (isv->min(0) != al->min(i) || isv->max(0) != al->max(i)))) {
            std::ostringstream oss;
            oss << "Index set mismatch. Declared index " << (tis.size() == 1 ? "set" : "sets");
            oss << " of `" << *vd->id() << "' " << (tis.size() == 1 ? "is [" : "are [");
            for (unsigned int j = 0; j < tis.size(); j++) {
              if (tis[j]->domain() != nullptr) {
                oss << *eval_intset(env, tis[j]->domain());
              } else {
                oss << "int";
              }
              if (j < tis.size() - 1) {
                oss << ",";
              }
            }
            oss << "], but is assigned to array with index "
                << (tis.size() == 1 ? "set [" : "sets [");
            for (unsigned int j = 0; j < al->dims(); j++) {
              oss << al->min(j) << ".." << al->max(j);
              if (j < al->dims() - 1) {
                oss << ", ";
              }
            }
            oss << "]. You may need to coerce the index sets using the array" << tis.size()
                << "d function.";
            throw EvalError(env, vd->loc(), oss.str());
          }
          newtis[i] = tis[i];
        }
      }
    } break;
    default:
      throw InternalError("not supported yet");
  }
  if (needNewTypeInst) {
    auto* tic = copy(env, vd->ti())->cast<TypeInst>();
    tic->setRanges(newtis);
    vd->ti(tic);
  }
}

/// Turn \a c into domain constraints if possible.
/// Return whether \a c is still required in the model.
bool check_domain_constraints(EnvI& env, Call* c) {
  if (env.fopts.recordDomainChanges) {
    return true;
  }
  if (c->id() == constants().ids.int_.le) {
    Expression* e0 = c->arg(0);
    Expression* e1 = c->arg(1);
    if (e0->type().isPar() && e1->isa<Id>()) {
      // greater than
      Id* id = e1->cast<Id>();
      IntVal lb = eval_int(env, e0);
      if (id->decl()->ti()->domain() != nullptr) {
        IntSetVal* domain = eval_intset(env, id->decl()->ti()->domain());
        if (domain->min() >= lb) {
          return false;
        }
        if (domain->max() < lb) {
          env.fail();
          return false;
        }
        IntSetRanges dr(domain);
        Ranges::Const<IntVal> cr(lb, IntVal::infinity());
        Ranges::Inter<IntVal, IntSetRanges, Ranges::Const<IntVal>> i(dr, cr);
        IntSetVal* newibv = IntSetVal::ai(i);
        id->decl()->ti()->domain(new SetLit(Location().introduce(), newibv));
        id->decl()->ti()->setComputedDomain(false);
      } else {
        id->decl()->ti()->domain(
            new SetLit(Location().introduce(), IntSetVal::a(lb, IntVal::infinity())));
      }
      return false;
    }
    if (e1->type().isPar() && e0->isa<Id>()) {
      // less than
      Id* id = e0->cast<Id>();
      IntVal ub = eval_int(env, e1);
      if (id->decl()->ti()->domain() != nullptr) {
        IntSetVal* domain = eval_intset(env, id->decl()->ti()->domain());
        if (domain->max() <= ub) {
          return false;
        }
        if (domain->min() > ub) {
          env.fail();
          return false;
        }
        IntSetRanges dr(domain);
        Ranges::Const<IntVal> cr(-IntVal::infinity(), ub);
        Ranges::Inter<IntVal, IntSetRanges, Ranges::Const<IntVal>> i(dr, cr);
        IntSetVal* newibv = IntSetVal::ai(i);
        id->decl()->ti()->domain(new SetLit(Location().introduce(), newibv));
        id->decl()->ti()->setComputedDomain(false);
      } else {
        id->decl()->ti()->domain(
            new SetLit(Location().introduce(), IntSetVal::a(-IntVal::infinity(), ub)));
      }
    }
  } else if (c->id() == constants().ids.int_.lin_le) {
    auto* al_c = follow_id(c->arg(0))->cast<ArrayLit>();
    if (al_c->size() == 1) {
      auto* al_x = follow_id(c->arg(1))->cast<ArrayLit>();
      IntVal coeff = eval_int(env, (*al_c)[0]);
      IntVal y = eval_int(env, c->arg(2));
      IntVal lb = -IntVal::infinity();
      IntVal ub = IntVal::infinity();
      IntVal r = y % coeff;
      if (coeff >= 0) {
        ub = y / coeff;
        if (r < 0) {
          --ub;
        }
      } else {
        lb = y / coeff;
        if (r < 0) {
          ++lb;
        }
      }
      if (Id* id = (*al_x)[0]->dynamicCast<Id>()) {
        if (id->decl()->ti()->domain() != nullptr) {
          IntSetVal* domain = eval_intset(env, id->decl()->ti()->domain());
          if (domain->max() <= ub && domain->min() >= lb) {
            return false;
          }
          if (domain->min() > ub || domain->max() < lb) {
            env.fail();
            return false;
          }
          IntSetRanges dr(domain);
          Ranges::Const<IntVal> cr(lb, ub);
          Ranges::Inter<IntVal, IntSetRanges, Ranges::Const<IntVal>> i(dr, cr);
          IntSetVal* newibv = IntSetVal::ai(i);
          id->decl()->ti()->domain(new SetLit(Location().introduce(), newibv));
          id->decl()->ti()->setComputedDomain(false);
        } else {
          id->decl()->ti()->domain(new SetLit(Location().introduce(), IntSetVal::a(lb, ub)));
        }
        return false;
      }
    }
  }
  return true;
}

KeepAlive bind(EnvI& env, Ctx ctx, VarDecl* vd, Expression* e) {
  assert(e == nullptr || !e->isa<VarDecl>());
  if (vd == constants().varIgnore) {
    return e;
  }
  if (Id* ident = e->dynamicCast<Id>()) {
    if (ident->decl() != nullptr) {
      auto* e_vd = follow_id_to_decl(ident)->cast<VarDecl>();
      e = e_vd->id();
      if (!env.inReverseMapVar && ctx.b != C_ROOT && e->type() == Type::varbool()) {
        add_ctx_ann(e_vd, ctx.b);
        if (e_vd != ident->decl()) {
          add_ctx_ann(ident->decl(), ctx.b);
        }
      }
    }
  }
  if (ctx.neg) {
    assert(e->type().bt() == Type::BT_BOOL);
    if (vd == constants().varTrue) {
      if (!isfalse(env, e)) {
        if (Id* id = e->dynamicCast<Id>()) {
          while (id != nullptr) {
            assert(id->decl() != nullptr);
            if ((id->decl()->ti()->domain() != nullptr) &&
                istrue(env, id->decl()->ti()->domain())) {
              GCLock lock;
              env.flatAddItem(new ConstraintI(Location().introduce(), constants().literalFalse));
            } else {
              GCLock lock;
              std::vector<Expression*> args(2);
              args[0] = id;
              args[1] = constants().literalFalse;
              Call* c = new Call(Location().introduce(), constants().ids.bool_eq, args);
              c->decl(env.model->matchFn(env, c, false));
              c->type(c->decl()->rtype(env, args, false));
              if (c->decl()->e() != nullptr) {
                flat_exp(env, Ctx(), c, constants().varTrue, constants().varTrue);
              }
              set_computed_domain(env, id->decl(), constants().literalFalse,
                                  id->decl()->ti()->computedDomain());
            }
            id = id->decl()->e() != nullptr ? id->decl()->e()->dynamicCast<Id>() : nullptr;
          }
          return constants().literalTrue;
        }
        GC::lock();
        Call* bn = new Call(e->loc(), constants().ids.bool_not, {e});
        bn->type(e->type());
        bn->decl(env.model->matchFn(env, bn, false));
        KeepAlive ka(bn);
        GC::unlock();
        EE ee = flat_exp(env, Ctx(), bn, vd, constants().varTrue);
        return ee.r;
      }
      return constants().literalTrue;
    }
    GC::lock();
    Call* bn = new Call(e->loc(), constants().ids.bool_not, {e});
    bn->type(e->type());
    bn->decl(env.model->matchFn(env, bn, false));
    KeepAlive ka(bn);
    GC::unlock();
    EE ee = flat_exp(env, Ctx(), bn, vd, constants().varTrue);
    return ee.r;
  }
  if (vd == constants().varTrue) {
    if (!istrue(env, e)) {
      if (Id* id = e->dynamicCast<Id>()) {
        assert(id->decl() != nullptr);
        while (id != nullptr) {
          if ((id->decl()->ti()->domain() != nullptr) && isfalse(env, id->decl()->ti()->domain())) {
            GCLock lock;
            env.flatAddItem(new ConstraintI(Location().introduce(), constants().literalFalse));
          } else if (id->decl()->ti()->domain() == nullptr) {
            GCLock lock;
            std::vector<Expression*> args(2);
            args[0] = id;
            args[1] = constants().literalTrue;
            Call* c = new Call(Location().introduce(), constants().ids.bool_eq, args);
            c->decl(env.model->matchFn(env, c, false));
            c->type(c->decl()->rtype(env, args, false));
            if (c->decl()->e() != nullptr) {
              flat_exp(env, Ctx(), c, constants().varTrue, constants().varTrue);
            }
            set_computed_domain(env, id->decl(), constants().literalTrue,
                                id->decl()->ti()->computedDomain());
          }
          id = id->decl()->e() != nullptr ? id->decl()->e()->dynamicCast<Id>() : nullptr;
        }
      } else {
        GCLock lock;
        // extract domain information from added constraint if possible
        if (!e->isa<Call>() || check_domain_constraints(env, e->cast<Call>())) {
          env.flatAddItem(new ConstraintI(Location().introduce(), e));
        }
      }
    }
    return constants().literalTrue;
  }
  if (vd == constants().varFalse) {
    if (!isfalse(env, e)) {
      throw InternalError("not supported yet");
    }
    return constants().literalTrue;
  }
  if (vd == nullptr) {
    if (e == nullptr) {
      return nullptr;
    }
    switch (e->eid()) {
      case Expression::E_INTLIT:
      case Expression::E_FLOATLIT:
      case Expression::E_BOOLLIT:
      case Expression::E_STRINGLIT:
      case Expression::E_ANON:
      case Expression::E_ID:
      case Expression::E_TIID:
      case Expression::E_SETLIT:
      case Expression::E_VARDECL:
      case Expression::E_BINOP:  // TODO: should not happen once operators are evaluated
      case Expression::E_UNOP:   // TODO: should not happen once operators are evaluated
        return e;
      case Expression::E_ARRAYACCESS:
      case Expression::E_COMP:
      case Expression::E_ITE:
      case Expression::E_LET:
      case Expression::E_TI:
        throw InternalError("unevaluated expression");
      case Expression::E_ARRAYLIT: {
        GCLock lock;
        auto* al = e->cast<ArrayLit>();
        /// TODO: review if limit of 10 is a sensible choice
        if (al->type().bt() == Type::BT_ANN || al->size() <= 10) {
          return e;
        }

        auto it = env.cseMapFind(al);
        if (it != env.cseMapEnd()) {
          return it->second.r()->cast<VarDecl>()->id();
        }

        std::vector<TypeInst*> ranges(al->dims());
        for (unsigned int i = 0; i < ranges.size(); i++) {
          ranges[i] = new TypeInst(
              e->loc(), Type(),
              new SetLit(Location().introduce(), IntSetVal::a(al->min(i), al->max(i))));
        }
        ASTExprVec<TypeInst> ranges_v(ranges);
        assert(!al->type().isbot());
        Expression* domain = nullptr;
        if (al->size() > 0 && (*al)[0]->type().isint()) {
          IntVal min = IntVal::infinity();
          IntVal max = -IntVal::infinity();
          for (unsigned int i = 0; i < al->size(); i++) {
            IntBounds ib = compute_int_bounds(env, (*al)[i]);
            if (!ib.valid) {
              min = -IntVal::infinity();
              max = IntVal::infinity();
              break;
            }
            min = std::min(min, ib.l);
            max = std::max(max, ib.u);
          }
          if (min != -IntVal::infinity() && max != IntVal::infinity()) {
            domain = new SetLit(Location().introduce(), IntSetVal::a(min, max));
          }
        }
        auto* ti = new TypeInst(e->loc(), al->type(), ranges_v, domain);
        if (domain != nullptr) {
          ti->setComputedDomain(true);
        }

        VarDecl* nvd = new_vardecl(env, ctx, ti, nullptr, nullptr, al);
        EE ee(nvd, nullptr);
        env.cseMapInsert(al, ee);
        env.cseMapInsert(nvd->e(), ee);
        return nvd->id();
      }
      case Expression::E_CALL: {
        if (e->type().isAnn()) {
          return e;
        }
        GCLock lock;
        /// TODO: handle array types
        auto* ti = new TypeInst(Location().introduce(), e->type());
        VarDecl* nvd = new_vardecl(env, ctx, ti, nullptr, nullptr, e);
        if (nvd->e()->type().bt() == Type::BT_INT && nvd->e()->type().dim() == 0) {
          IntSetVal* ibv = nullptr;
          if (nvd->e()->type().isSet()) {
            ibv = compute_intset_bounds(env, nvd->e());
          } else {
            IntBounds ib = compute_int_bounds(env, nvd->e());
            if (ib.valid) {
              ibv = IntSetVal::a(ib.l, ib.u);
            }
          }
          if (ibv != nullptr) {
            Id* id = nvd->id();
            while (id != nullptr) {
              bool is_computed = id->decl()->ti()->computedDomain();
              if (id->decl()->ti()->domain() != nullptr) {
                IntSetVal* domain = eval_intset(env, id->decl()->ti()->domain());
                IntSetRanges dr(domain);
                IntSetRanges ibr(ibv);
                Ranges::Inter<IntVal, IntSetRanges, IntSetRanges> i(dr, ibr);
                IntSetVal* newibv = IntSetVal::ai(i);
                if (ibv->card() == newibv->card()) {
                  is_computed = true;
                } else {
                  ibv = newibv;
                }
              } else {
                is_computed = true;
              }
              if (id->type().st() == Type::ST_PLAIN && ibv->size() == 0) {
                env.fail();
              } else {
                set_computed_domain(env, id->decl(), new SetLit(Location().introduce(), ibv),
                                    is_computed);
              }
              id = id->decl()->e() != nullptr ? id->decl()->e()->dynamicCast<Id>() : nullptr;
            }
          }
        } else if (nvd->e()->type().isbool()) {
          add_ctx_ann(nvd, ctx.b);
        } else if (nvd->e()->type().bt() == Type::BT_FLOAT && nvd->e()->type().dim() == 0) {
          FloatBounds fb = compute_float_bounds(env, nvd->e());
          FloatSetVal* ibv = LinearTraits<FloatLit>::intersectDomain(nullptr, fb.l, fb.u);
          if (fb.valid) {
            Id* id = nvd->id();
            while (id != nullptr) {
              bool is_computed = id->decl()->ti()->computedDomain();
              if (id->decl()->ti()->domain() != nullptr) {
                FloatSetVal* domain = eval_floatset(env, id->decl()->ti()->domain());
                FloatSetVal* ndomain = LinearTraits<FloatLit>::intersectDomain(domain, fb.l, fb.u);
                if ((ibv != nullptr) && ndomain == domain) {
                  is_computed = true;
                } else {
                  ibv = ndomain;
                }
              } else {
                is_computed = true;
              }
              if (LinearTraits<FloatLit>::domainEmpty(ibv)) {
                env.fail();
              } else {
                set_computed_domain(env, id->decl(), new SetLit(Location().introduce(), ibv),
                                    is_computed);
              }
              id = id->decl()->e() != nullptr ? id->decl()->e()->dynamicCast<Id>() : nullptr;
            }
          }
        }

        return nvd->id();
      }
      default:
        assert(false);
        return nullptr;
    }
  } else {
    if (vd->e() == nullptr) {
      Expression* ret = e;
      if (e == nullptr || (e->type().isPar() && e->type().isbool())) {
        GCLock lock;
        bool isTrue = (e == nullptr || eval_bool(env, e));

        // Check if redefinition of bool_eq exists, if yes call it
        std::vector<Expression*> args(2);
        args[0] = vd->id();
        args[1] = constants().boollit(isTrue);
        Call* c = new Call(Location().introduce(), constants().ids.bool_eq, args);
        c->decl(env.model->matchFn(env, c, false));
        c->type(c->decl()->rtype(env, args, false));
        bool didRewrite = false;
        if (c->decl()->e() != nullptr) {
          flat_exp(env, Ctx(), c, constants().varTrue, constants().varTrue);
          didRewrite = true;
        }

        vd->e(constants().boollit(isTrue));
        if (vd->ti()->domain() != nullptr) {
          if (vd->ti()->domain() != vd->e()) {
            env.fail();
            return vd->id();
          }
        } else {
          set_computed_domain(env, vd, vd->e(), true);
        }
        if (didRewrite) {
          return vd->id();
        }
      } else {
        if (e->type().dim() > 0) {
          // Check that index sets match
          env.errorStack.clear();
          check_index_sets(env, vd, e);
          auto* al =
              Expression::dynamicCast<ArrayLit>(e->isa<Id>() ? e->cast<Id>()->decl()->e() : e);
          if ((al != nullptr) && (vd->ti()->domain() != nullptr) &&
              !vd->ti()->domain()->isa<TIId>()) {
            if (e->type().bt() == Type::BT_INT) {
              IntSetVal* isv = eval_intset(env, vd->ti()->domain());
              for (unsigned int i = 0; i < al->size(); i++) {
                if (Id* id = (*al)[i]->dynamicCast<Id>()) {
                  if (id == constants().absent) {
                    continue;
                  }
                  VarDecl* vdi = id->decl();
                  if (vdi->ti()->domain() == nullptr) {
                    set_computed_domain(env, vdi, vd->ti()->domain(), vdi->ti()->computedDomain());
                  } else {
                    IntSetVal* vdi_dom = eval_intset(env, vdi->ti()->domain());
                    IntSetRanges isvr(isv);
                    IntSetRanges vdi_domr(vdi_dom);
                    Ranges::Inter<IntVal, IntSetRanges, IntSetRanges> inter(isvr, vdi_domr);
                    IntSetVal* newdom = IntSetVal::ai(inter);
                    if (newdom->size() == 0) {
                      env.fail();
                    } else {
                      IntSetRanges vdi_domr2(vdi_dom);
                      IntSetRanges newdomr(newdom);
                      if (!Ranges::equal(vdi_domr2, newdomr)) {
                        set_computed_domain(env, vdi, new SetLit(Location().introduce(), newdom),
                                            false);
                      }
                    }
                  }
                } else {
                  // at this point, can only be a constant
                  assert((*al)[i]->type().isPar());
                  if (e->type().st() == Type::ST_PLAIN) {
                    IntVal iv = eval_int(env, (*al)[i]);
                    if (!isv->contains(iv)) {
                      std::ostringstream oss;
                      oss << "value " << iv << " outside declared array domain " << *isv;
                      env.fail(oss.str());
                    }
                  } else {
                    IntSetVal* aisv = eval_intset(env, (*al)[i]);
                    IntSetRanges aisv_r(aisv);
                    IntSetRanges isv_r(isv);
                    if (!Ranges::subset(aisv_r, isv_r)) {
                      std::ostringstream oss;
                      oss << "value " << *aisv << " outside declared array domain " << *isv;
                      env.fail(oss.str());
                    }
                  }
                }
              }
              vd->ti()->setComputedDomain(true);
            } else if (e->type().bt() == Type::BT_FLOAT) {
              FloatSetVal* fsv = eval_floatset(env, vd->ti()->domain());
              for (unsigned int i = 0; i < al->size(); i++) {
                if (Id* id = (*al)[i]->dynamicCast<Id>()) {
                  VarDecl* vdi = id->decl();
                  if (vdi->ti()->domain() == nullptr) {
                    set_computed_domain(env, vdi, vd->ti()->domain(), vdi->ti()->computedDomain());
                  } else {
                    FloatSetVal* vdi_dom = eval_floatset(env, vdi->ti()->domain());
                    FloatSetRanges fsvr(fsv);
                    FloatSetRanges vdi_domr(vdi_dom);
                    Ranges::Inter<FloatVal, FloatSetRanges, FloatSetRanges> inter(fsvr, vdi_domr);
                    FloatSetVal* newdom = FloatSetVal::ai(inter);
                    if (newdom->size() == 0) {
                      env.fail();
                    } else {
                      FloatSetRanges vdi_domr2(vdi_dom);
                      FloatSetRanges newdomr(newdom);
                      if (!Ranges::equal(vdi_domr2, newdomr)) {
                        set_computed_domain(env, vdi, new SetLit(Location().introduce(), newdom),
                                            false);
                      }
                    }
                  }
                } else {
                  // at this point, can only be a constant
                  assert((*al)[i]->type().isPar());
                  FloatVal fv = eval_float(env, (*al)[i]);
                  if (!fsv->contains(fv)) {
                    std::ostringstream oss;
                    oss << "value " << fv << " outside declared array domain " << *fsv;
                    env.fail(oss.str());
                  }
                }
              }
              vd->ti()->setComputedDomain(true);
            }
          }
        } else if (Id* e_id = e->dynamicCast<Id>()) {
          if (e_id == vd->id()) {
            ret = vd->id();
          } else {
            ASTString cid;
            if (e->type().isint()) {
              if (e->type().isOpt()) {
                cid = ASTString("int_opt_eq");
              } else {
                cid = constants().ids.int_.eq;
              }
            } else if (e->type().isbool()) {
              if (e->type().isOpt()) {
                cid = ASTString("bool_opt_eq");
              } else {
                cid = constants().ids.bool_eq;
              }
            } else if (e->type().isSet()) {
              cid = constants().ids.set_eq;
            } else if (e->type().isfloat()) {
              cid = constants().ids.float_.eq;
            }
            if (cid != "" && env.hasReverseMapper(vd->id())) {
              GCLock lock;
              std::vector<Expression*> args(2);
              args[0] = vd->id();
              args[1] = e_id;
              Call* c = new Call(Location().introduce(), cid, args);
              c->decl(env.model->matchFn(env, c, false));
              c->type(c->decl()->rtype(env, args, false));
              if (c->type().isbool() && ctx.b != C_ROOT) {
                add_ctx_ann(vd, ctx.b);
                add_ctx_ann(e_id->decl(), ctx.b);
              }
              if (c->decl()->e() != nullptr) {
                flat_exp(env, Ctx(), c, constants().varTrue, constants().varTrue);
                ret = vd->id();
                vd->e(e);
                env.voAddExp(vd);
              }
            }
          }
        }

        if (ret != vd->id()) {
          vd->e(ret);
          add_path_annotation(env, ret);
          env.voAddExp(vd);
          ret = vd->id();
        }
        Id* vde_id = Expression::dynamicCast<Id>(vd->e());
        if (vde_id == constants().absent) {
          // no need to do anything
        } else if ((vde_id != nullptr) && vde_id->decl()->ti()->domain() == nullptr) {
          if (vd->ti()->domain() != nullptr) {
            GCLock lock;
            Expression* vd_dom = eval_par(env, vd->ti()->domain());
            set_computed_domain(env, vde_id->decl(), vd_dom,
                                vde_id->decl()->ti()->computedDomain());
          }
        } else if ((vd->e() != nullptr) && vd->e()->type().bt() == Type::BT_INT &&
                   vd->e()->type().dim() == 0) {
          GCLock lock;
          IntSetVal* ibv = nullptr;
          if (vd->e()->type().isSet()) {
            ibv = compute_intset_bounds(env, vd->e());
          } else {
            IntBounds ib = compute_int_bounds(env, vd->e());
            if (ib.valid) {
              Call* call = vd->e()->dynamicCast<Call>();
              if ((call != nullptr) && call->id() == constants().ids.lin_exp) {
                ArrayLit* al = eval_array_lit(env, call->arg(1));
                if (al->size() == 1) {
                  IntBounds check_zeroone = compute_int_bounds(env, (*al)[0]);
                  if (check_zeroone.l == 0 && check_zeroone.u == 1) {
                    ArrayLit* coeffs = eval_array_lit(env, call->arg(0));
                    std::vector<IntVal> newdom(2);
                    newdom[0] = 0;
                    newdom[1] = eval_int(env, (*coeffs)[0]) + eval_int(env, call->arg(2));
                    ibv = IntSetVal::a(newdom);
                  }
                }
              }
              if (ibv == nullptr) {
                ibv = IntSetVal::a(ib.l, ib.u);
              }
            }
          }
          if (ibv != nullptr) {
            if (vd->ti()->domain() != nullptr) {
              IntSetVal* domain = eval_intset(env, vd->ti()->domain());
              IntSetRanges dr(domain);
              IntSetRanges ibr(ibv);
              Ranges::Inter<IntVal, IntSetRanges, IntSetRanges> i(dr, ibr);
              IntSetVal* newibv = IntSetVal::ai(i);
              if (newibv->card() == 0) {
                env.fail();
              } else if (ibv->card() == newibv->card()) {
                vd->ti()->setComputedDomain(true);
              } else {
                ibv = newibv;
              }
            } else {
              vd->ti()->setComputedDomain(true);
            }
            SetLit* ibv_l = nullptr;
            if (Id* rhs_ident = vd->e()->dynamicCast<Id>()) {
              if (rhs_ident->decl()->ti()->domain() != nullptr) {
                IntSetVal* rhs_domain = eval_intset(env, rhs_ident->decl()->ti()->domain());
                IntSetRanges dr(rhs_domain);
                IntSetRanges ibr(ibv);
                Ranges::Inter<IntVal, IntSetRanges, IntSetRanges> i(dr, ibr);
                IntSetVal* rhs_newibv = IntSetVal::ai(i);
                if (rhs_domain->card() != rhs_newibv->card()) {
                  ibv_l = new SetLit(Location().introduce(), rhs_newibv);
                  set_computed_domain(env, rhs_ident->decl(), ibv_l, false);
                  if (rhs_ident->decl()->type().isOpt()) {
                    std::vector<Expression*> args(2);
                    args[0] = rhs_ident;
                    args[1] = ibv_l;
                    Call* c = new Call(Location().introduce(), "var_dom", args);
                    c->type(Type::varbool());
                    c->decl(env.model->matchFn(env, c, false));
                    (void)flat_exp(env, Ctx(), c, constants().varTrue, constants().varTrue);
                  }
                } else if (ibv->card() != rhs_newibv->card()) {
                  ibv_l = new SetLit(Location().introduce(), rhs_newibv);
                }
              }
            }
            if (ibv_l == nullptr) {
              ibv_l = new SetLit(Location().introduce(), ibv);
            }
            set_computed_domain(env, vd, ibv_l, vd->ti()->computedDomain());

            if (vd->type().isOpt()) {
              std::vector<Expression*> args(2);
              args[0] = vd->id();
              args[1] = ibv_l;
              Call* c = new Call(Location().introduce(), "var_dom", args);
              c->type(Type::varbool());
              c->decl(env.model->matchFn(env, c, false));
              (void)flat_exp(env, Ctx(), c, constants().varTrue, constants().varTrue);
            }
          }
        } else if ((vd->e() != nullptr) && vd->e()->type().bt() == Type::BT_FLOAT &&
                   vd->e()->type().dim() == 0) {
          GCLock lock;
          FloatSetVal* fbv = nullptr;
          FloatBounds fb = compute_float_bounds(env, vd->e());
          if (fb.valid) {
            fbv = FloatSetVal::a(fb.l, fb.u);
          }
          if (fbv != nullptr) {
            if (vd->ti()->domain() != nullptr) {
              FloatSetVal* domain = eval_floatset(env, vd->ti()->domain());
              FloatSetRanges dr(domain);
              FloatSetRanges fbr(fbv);
              Ranges::Inter<FloatVal, FloatSetRanges, FloatSetRanges> i(dr, fbr);
              FloatSetVal* newfbv = FloatSetVal::ai(i);
              if (newfbv->size() == 0) {
                env.fail();
              }
              FloatSetRanges dr_eq(domain);
              FloatSetRanges newfbv_eq(newfbv);
              if (Ranges::equal(dr_eq, newfbv_eq)) {
                vd->ti()->setComputedDomain(true);
              } else {
                fbv = newfbv;
              }
            } else {
              vd->ti()->setComputedDomain(true);
            }
            SetLit* fbv_l = nullptr;
            if (Id* rhs_ident = vd->e()->dynamicCast<Id>()) {
              if (rhs_ident->decl()->ti()->domain() != nullptr) {
                FloatSetVal* rhs_domain = eval_floatset(env, rhs_ident->decl()->ti()->domain());
                FloatSetRanges dr(rhs_domain);
                FloatSetRanges ibr(fbv);
                Ranges::Inter<FloatVal, FloatSetRanges, FloatSetRanges> i(dr, ibr);
                FloatSetVal* rhs_newfbv = FloatSetVal::ai(i);
                if (rhs_domain->card() != rhs_newfbv->card()) {
                  fbv_l = new SetLit(Location().introduce(), rhs_newfbv);
                  set_computed_domain(env, rhs_ident->decl(), fbv_l, false);
                  if (rhs_ident->decl()->type().isOpt()) {
                    std::vector<Expression*> args(2);
                    args[0] = rhs_ident;
                    args[1] = fbv_l;
                    Call* c = new Call(Location().introduce(), "var_dom", args);
                    c->type(Type::varbool());
                    c->decl(env.model->matchFn(env, c, false));
                    (void)flat_exp(env, Ctx(), c, constants().varTrue, constants().varTrue);
                  }
                } else if (fbv->card() != rhs_newfbv->card()) {
                  fbv_l = new SetLit(Location().introduce(), rhs_newfbv);
                }
              }
            }
            fbv_l = new SetLit(Location().introduce(), fbv);
            set_computed_domain(env, vd, fbv_l, vd->ti()->computedDomain());

            if (vd->type().isOpt()) {
              std::vector<Expression*> args(2);
              args[0] = vd->id();
              args[1] = fbv_l;
              Call* c = new Call(Location().introduce(), "var_dom", args);
              c->type(Type::varbool());
              c->decl(env.model->matchFn(env, c, false));
              (void)flat_exp(env, Ctx(), c, constants().varTrue, constants().varTrue);
            }
          }
        }
      }
      return ret;
    }
    if (vd == e) {
      return vd->id();
    }
    if (vd->e() != e) {
      e = follow_id_to_decl(e);
      if (vd == e) {
        return vd->id();
      }
      switch (e->eid()) {
        case Expression::E_BOOLLIT: {
          Id* id = vd->id();
          while (id != nullptr) {
            if ((id->decl()->ti()->domain() != nullptr) &&
                eval_bool(env, id->decl()->ti()->domain()) == e->cast<BoolLit>()->v()) {
              return constants().literalTrue;
            }
            if ((id->decl()->ti()->domain() != nullptr) &&
                eval_bool(env, id->decl()->ti()->domain()) != e->cast<BoolLit>()->v()) {
              GCLock lock;
              env.flatAddItem(new ConstraintI(Location().introduce(), constants().literalFalse));
            } else {
              GCLock lock;
              std::vector<Expression*> args(2);
              args[0] = id;
              args[1] = e;
              Call* c = new Call(Location().introduce(), constants().ids.bool_eq, args);
              c->decl(env.model->matchFn(env, c, false));
              c->type(c->decl()->rtype(env, args, false));
              if (c->decl()->e() != nullptr) {
                flat_exp(env, Ctx(), c, constants().varTrue, constants().varTrue);
              }
              set_computed_domain(env, id->decl(), e, id->decl()->ti()->computedDomain());
            }
            id = id->decl()->e() != nullptr ? id->decl()->e()->dynamicCast<Id>() : nullptr;
          }
          return constants().literalTrue;
        }
        case Expression::E_VARDECL: {
          auto* e_vd = e->cast<VarDecl>();
          if (vd->e() == e_vd->id() || e_vd->e() == vd->id()) {
            return vd->id();
          }
          if (e->type().dim() != 0) {
            throw InternalError("not supported yet");
          }
          GCLock lock;
          ASTString cid;
          if (e->type().isint()) {
            cid = constants().ids.int_.eq;
          } else if (e->type().isbool()) {
            cid = constants().ids.bool_eq;
          } else if (e->type().isSet()) {
            cid = constants().ids.set_eq;
          } else if (e->type().isfloat()) {
            cid = constants().ids.float_.eq;
          } else {
            throw InternalError("not yet implemented");
          }
          std::vector<Expression*> args(2);
          args[0] = vd->id();
          args[1] = e_vd->id();
          Call* c = new Call(vd->loc().introduce(), cid, args);
          c->decl(env.model->matchFn(env, c, false));
          c->type(c->decl()->rtype(env, args, false));
          flat_exp(env, Ctx(), c, constants().varTrue, constants().varTrue);
          return vd->id();
        }
        case Expression::E_CALL: {
          Call* c = e->cast<Call>();
          GCLock lock;
          Call* nc;
          std::vector<Expression*> args;
          if (c->id() == constants().ids.lin_exp) {
            auto* le_c = follow_id(c->arg(0))->cast<ArrayLit>();
            std::vector<Expression*> ncoeff(le_c->size());
            for (auto i = static_cast<unsigned int>(ncoeff.size()); (i--) != 0U;) {
              ncoeff[i] = (*le_c)[i];
            }
            ncoeff.push_back(IntLit::a(-1));
            args.push_back(new ArrayLit(Location().introduce(), ncoeff));
            args[0]->type(le_c->type());
            auto* le_x = follow_id(c->arg(1))->cast<ArrayLit>();
            std::vector<Expression*> nx(le_x->size());
            for (auto i = static_cast<unsigned int>(nx.size()); (i--) != 0U;) {
              nx[i] = (*le_x)[i];
            }
            nx.push_back(vd->id());
            args.push_back(new ArrayLit(Location().introduce(), nx));
            args[1]->type(le_x->type());
            args.push_back(c->arg(2));
            nc = new Call(c->loc().introduce(), constants().ids.lin_exp, args);
            nc->decl(env.model->matchFn(env, nc, false));
            if (nc->decl() == nullptr) {
              std::ostringstream ss;
              ss << "undeclared function or predicate " << nc->id();
              throw InternalError(ss.str());
            }
            nc->type(nc->decl()->rtype(env, args, false));
            auto* bop = new BinOp(nc->loc(), nc, BOT_EQ, IntLit::a(0));
            bop->type(Type::varbool());
            flat_exp(env, Ctx(), bop, constants().varTrue, constants().varTrue);
            return vd->id();
          }
          args.resize(c->argCount());
          for (auto i = static_cast<unsigned int>(args.size()); (i--) != 0U;) {
            args[i] = c->arg(i);
          }
          args.push_back(vd->id());
          ASTString nid = c->id();

          if (c->id() == constants().ids.exists) {
            nid = constants().ids.array_bool_or;
          } else if (c->id() == constants().ids.forall) {
            nid = constants().ids.array_bool_and;
          } else if (vd->type().isbool()) {
            if (env.fopts.enableHalfReification && vd->ann().contains(constants().ctx.pos)) {
              nid = env.halfReifyId(c->id());
              if (env.model->matchFn(env, nid, args, false) == nullptr) {
                nid = env.reifyId(c->id());
              }
            } else {
              nid = env.reifyId(c->id());
            }
          }
          nc = new Call(c->loc().introduce(), nid, args);
          FunctionI* nc_decl = env.model->matchFn(env, nc, false);
          if (nc_decl == nullptr) {
            std::ostringstream ss;
            ss << "undeclared function or predicate " << nc->id();
            throw InternalError(ss.str());
          }
          nc->decl(nc_decl);
          nc->type(nc->decl()->rtype(env, args, false));
          make_defined_var(vd, nc);
          flat_exp(env, Ctx(), nc, constants().varTrue, constants().varTrue);
          return vd->id();
        } break;
        default:
          throw InternalError("not supported yet");
      }
    } else {
      return e;
    }
  }
}

KeepAlive conj(EnvI& env, VarDecl* b, const Ctx& ctx, const std::vector<EE>& e) {
  if (!ctx.neg) {
    std::vector<Expression*> nontrue;
    for (const auto& i : e) {
      if (istrue(env, i.b())) {
        continue;
      }
      if (isfalse(env, i.b())) {
        return bind(env, Ctx(), b, constants().literalFalse);
      }
      nontrue.push_back(i.b());
    }
    if (nontrue.empty()) {
      return bind(env, Ctx(), b, constants().literalTrue);
    }
    if (nontrue.size() == 1) {
      return bind(env, ctx, b, nontrue[0]);
    }
    if (b == constants().varTrue) {
      for (auto& i : nontrue) {
        bind(env, ctx, b, i);
      }
      return constants().literalTrue;
    }
    GC::lock();
    std::vector<Expression*> args;
    auto* al = new ArrayLit(Location().introduce(), nontrue);
    al->type(Type::varbool(1));
    args.push_back(al);
    Call* ret = new Call(nontrue[0]->loc().introduce(), constants().ids.forall, args);
    ret->decl(env.model->matchFn(env, ret, false));
    ret->type(ret->decl()->rtype(env, args, false));
    KeepAlive ka(ret);
    GC::unlock();
    return flat_exp(env, ctx, ret, b, constants().varTrue).r;
  }
  Ctx nctx = ctx;
  nctx.neg = false;
  nctx.b = -nctx.b;
  // negated
  std::vector<Expression*> nonfalse;
  for (const auto& i : e) {
    if (istrue(env, i.b())) {
      continue;
    }
    if (isfalse(env, i.b())) {
      return bind(env, Ctx(), b, constants().literalTrue);
    }
    nonfalse.push_back(i.b());
  }
  if (nonfalse.empty()) {
    return bind(env, Ctx(), b, constants().literalFalse);
  }
  if (nonfalse.size() == 1) {
    GC::lock();
    UnOp* uo = new UnOp(nonfalse[0]->loc(), UOT_NOT, nonfalse[0]);
    uo->type(Type::varbool());
    KeepAlive ka(uo);
    GC::unlock();
    return flat_exp(env, nctx, uo, b, constants().varTrue).r;
  }
  if (b == constants().varFalse) {
    for (auto& i : nonfalse) {
      bind(env, nctx, b, i);
    }
    return constants().literalFalse;
  }
  GC::lock();
  std::vector<Expression*> args;
  for (auto& i : nonfalse) {
    UnOp* uo = new UnOp(i->loc(), UOT_NOT, i);
    uo->type(Type::varbool());
    i = uo;
  }
  auto* al = new ArrayLit(Location().introduce(), nonfalse);
  al->type(Type::varbool(1));
  args.push_back(al);
  Call* ret = new Call(Location().introduce(), constants().ids.exists, args);
  ret->decl(env.model->matchFn(env, ret, false));
  ret->type(ret->decl()->rtype(env, args, false));
  assert(ret->decl());
  KeepAlive ka(ret);
  GC::unlock();
  return flat_exp(env, nctx, ret, b, constants().varTrue).r;
}

TypeInst* eval_typeinst(EnvI& env, const Ctx& ctx, VarDecl* vd) {
  bool hasTiVars = (vd->ti()->domain() != nullptr) && vd->ti()->domain()->isa<TIId>();
  for (unsigned int i = 0; i < vd->ti()->ranges().size(); i++) {
    hasTiVars = hasTiVars || ((vd->ti()->ranges()[i]->domain() != nullptr) &&
                              vd->ti()->ranges()[i]->domain()->isa<TIId>());
  }
  if (hasTiVars) {
    assert(vd->e());
    if (vd->e()->type().dim() == 0) {
      return new TypeInst(Location().introduce(), vd->e()->type());
    }
    ArrayLit* al = eval_array_lit(env, vd->e());
    std::vector<TypeInst*> dims(al->dims());
    for (unsigned int i = 0; i < dims.size(); i++) {
      dims[i] =
          new TypeInst(Location().introduce(), Type(),
                       new SetLit(Location().introduce(), IntSetVal::a(al->min(i), al->max(i))));
    }
    return new TypeInst(Location().introduce(), vd->e()->type(), dims,
                        flat_cv_exp(env, ctx, vd->ti()->domain())());
  }
  std::vector<TypeInst*> dims(vd->ti()->ranges().size());
  for (unsigned int i = 0; i < vd->ti()->ranges().size(); i++) {
    if (vd->ti()->ranges()[i]->domain() != nullptr) {
      KeepAlive range = flat_cv_exp(env, ctx, vd->ti()->ranges()[i]->domain());
      IntSetVal* isv = eval_intset(env, range());
      if (isv->size() > 1) {
        throw EvalError(env, vd->ti()->ranges()[i]->domain()->loc(),
                        "array index set must be contiguous range");
      }
      auto* sl = new SetLit(vd->ti()->ranges()[i]->loc(), isv);
      sl->type(Type::parsetint());
      dims[i] = new TypeInst(vd->ti()->ranges()[i]->loc(), Type(), sl);
    } else {
      dims[i] = new TypeInst(vd->ti()->ranges()[i]->loc(), Type(), nullptr);
    }
  }
  Type t = ((vd->e() != nullptr) && !vd->e()->type().isbot()) ? vd->e()->type() : vd->ti()->type();
  return new TypeInst(vd->ti()->loc(), t, dims, flat_cv_exp(env, ctx, vd->ti()->domain())());
}

KeepAlive flat_cv_exp(EnvI& env, Ctx ctx, Expression* e) {
  if (e == nullptr) {
    return nullptr;
  }
  GCLock lock;
  if (e->type().isPar() && !e->type().cv()) {
    return eval_par(env, e);
  }
  if (e->type().isvar()) {
    EE ee = flat_exp(env, ctx, e, nullptr, nullptr);
    if (isfalse(env, ee.b())) {
      throw ResultUndefinedError(env, e->loc(), "");
    }
    return ee.r();
  }
  switch (e->eid()) {
    case Expression::E_INTLIT:
    case Expression::E_FLOATLIT:
    case Expression::E_BOOLLIT:
    case Expression::E_STRINGLIT:
    case Expression::E_TIID:
    case Expression::E_VARDECL:
    case Expression::E_TI:
    case Expression::E_ANON:
      assert(false);
      return nullptr;
    case Expression::E_ID: {
      Id* id = e->cast<Id>();
      return flat_cv_exp(env, ctx, id->decl()->e());
    }
    case Expression::E_SETLIT: {
      auto* sl = e->cast<SetLit>();
      if ((sl->isv() != nullptr) || (sl->fsv() != nullptr)) {
        return sl;
      }
      std::vector<Expression*> es(sl->v().size());
      GCLock lock;
      for (unsigned int i = 0; i < sl->v().size(); i++) {
        es[i] = flat_cv_exp(env, ctx, sl->v()[i])();
      }
      auto* sl_ret = new SetLit(Location().introduce(), es);
      Type t = sl->type();
      t.cv(false);
      sl_ret->type(t);
      return eval_par(env, sl_ret);
    }
    case Expression::E_ARRAYLIT: {
      auto* al = e->cast<ArrayLit>();
      std::vector<Expression*> es(al->size());
      GCLock lock;
      for (unsigned int i = 0; i < al->size(); i++) {
        es[i] = flat_cv_exp(env, ctx, (*al)[i])();
      }
      std::vector<std::pair<int, int>> dims(al->dims());
      for (int i = 0; i < al->dims(); i++) {
        dims[i] = std::make_pair(al->min(i), al->max(i));
      }
      Expression* al_ret = eval_par(env, new ArrayLit(Location().introduce(), es, dims));
      Type t = al->type();
      t.cv(false);
      al_ret->type(t);
      return al_ret;
    }
    case Expression::E_ARRAYACCESS: {
      auto* aa = e->cast<ArrayAccess>();
      GCLock lock;
      Expression* av = flat_cv_exp(env, ctx, aa->v())();
      std::vector<Expression*> idx(aa->idx().size());
      for (unsigned int i = 0; i < aa->idx().size(); i++) {
        idx[i] = flat_cv_exp(env, ctx, aa->idx()[i])();
      }
      auto* aa_ret = new ArrayAccess(Location().introduce(), av, idx);
      Type t = aa->type();
      t.cv(false);
      aa_ret->type(t);
      return eval_par(env, aa_ret);
    }
    case Expression::E_COMP: {
      auto* c = e->cast<Comprehension>();
      GCLock lock;
      class EvalFlatCvExp : public EvalBase {
      public:
        Ctx ctx;
        EvalFlatCvExp(Ctx& ctx0) : ctx(ctx0) {}
        typedef Expression* ArrayVal;
        Expression* e(EnvI& env, Expression* e) const { return flat_cv_exp(env, ctx, e)(); }
        static Expression* exp(Expression* e) { return e; }
      } eval(ctx);
      std::vector<Expression*> a = eval_comp<EvalFlatCvExp>(env, eval, c);

      Type t = Type::bot();
      bool allPar = true;
      for (auto& i : a) {
        if (t == Type::bot()) {
          t = i->type();
        }
        if (!i->type().isPar()) {
          allPar = false;
        }
      }
      if (!allPar) {
        t.ti(Type::TI_VAR);
      }
      if (c->set()) {
        t.st(Type::ST_SET);
      } else {
        t.dim(c->type().dim());
      }
      t.cv(false);
      if (c->set()) {
        if (c->type().isPar() && allPar) {
          auto* sl = new SetLit(c->loc().introduce(), a);
          sl->type(t);
          Expression* slr = eval_par(env, sl);
          slr->type(t);
          return slr;
        }
        throw InternalError("var set comprehensions not supported yet");
      }
      auto* alr = new ArrayLit(Location().introduce(), a);
      alr->type(t);
      alr->flat(true);
      return alr;
    }
    case Expression::E_ITE: {
      ITE* ite = e->cast<ITE>();
      for (int i = 0; i < ite->size(); i++) {
        KeepAlive ka = flat_cv_exp(env, ctx, ite->ifExpr(i));
        if (eval_bool(env, ka())) {
          return flat_cv_exp(env, ctx, ite->thenExpr(i));
        }
      }
      return flat_cv_exp(env, ctx, ite->elseExpr());
    }
    case Expression::E_BINOP: {
      auto* bo = e->cast<BinOp>();
      if (bo->op() == BOT_AND) {
        GCLock lock;
        Expression* lhs = flat_cv_exp(env, ctx, bo->lhs())();
        if (!eval_bool(env, lhs)) {
          return constants().literalFalse;
        }
        return eval_par(env, flat_cv_exp(env, ctx, bo->rhs())());
      }
      if (bo->op() == BOT_OR) {
        GCLock lock;
        Expression* lhs = flat_cv_exp(env, ctx, bo->lhs())();
        if (eval_bool(env, lhs)) {
          return constants().literalTrue;
        }
        return eval_par(env, flat_cv_exp(env, ctx, bo->rhs())());
      }
      GCLock lock;
      auto* nbo = new BinOp(bo->loc().introduce(), flat_cv_exp(env, ctx, bo->lhs())(), bo->op(),
                            flat_cv_exp(env, ctx, bo->rhs())());
      nbo->type(bo->type());
      nbo->decl(bo->decl());
      return eval_par(env, nbo);
    }
    case Expression::E_UNOP: {
      UnOp* uo = e->cast<UnOp>();
      GCLock lock;
      UnOp* nuo = new UnOp(uo->loc(), uo->op(), flat_cv_exp(env, ctx, uo->e())());
      nuo->type(uo->type());
      return eval_par(env, nuo);
    }
    case Expression::E_CALL: {
      Call* c = e->cast<Call>();
      if (c->id() == "mzn_in_root_context") {
        return constants().boollit(ctx.b == C_ROOT);
      }
      if (ctx.b == C_ROOT && (c->decl()->e() != nullptr) && c->decl()->e()->isa<BoolLit>()) {
        bool allBool = true;
        for (unsigned int i = 0; i < c->argCount(); i++) {
          if (c->arg(i)->type().bt() != Type::BT_BOOL) {
            allBool = false;
            break;
          }
        }
        if (allBool) {
          return c->decl()->e();
        }
      }
      std::vector<Expression*> args(c->argCount());
      GCLock lock;
      for (unsigned int i = 0; i < c->argCount(); i++) {
        Ctx c_mix;
        c_mix.b = C_MIX;
        c_mix.i = C_MIX;
        args[i] = flat_cv_exp(env, c_mix, c->arg(i))();
      }
      Call* nc = new Call(c->loc(), c->id(), args);
      nc->decl(c->decl());
      Type nct(c->type());
      if ((nc->decl()->e() != nullptr) && nc->decl()->e()->type().cv()) {
        nct.cv(false);
        nct.ti(Type::TI_VAR);
        nc->type(nct);
        EE ee = flat_exp(env, ctx, nc, nullptr, nullptr);
        if (isfalse(env, ee.b())) {
          std::ostringstream ss;
          ss << "evaluation of `" << nc->id() << "was undefined";
          throw ResultUndefinedError(env, e->loc(), ss.str());
        }
        return ee.r();
      }
      nc->type(nct);
      return eval_par(env, nc);
    }
    case Expression::E_LET: {
      Let* l = e->cast<Let>();
      EE ee = flat_exp(env, ctx, l, nullptr, nullptr);
      if (isfalse(env, ee.b())) {
        throw ResultUndefinedError(env, e->loc(), "evaluation of let expression was undefined");
      }
      return ee.r();
    }
  }
  throw InternalError("internal error");
}

class ItemTimer {
public:
  using TimingMap =
      std::map<std::pair<ASTString, unsigned int>, std::chrono::high_resolution_clock::duration>;
  ItemTimer(const Location& loc, TimingMap* tm)
      : _loc(loc), _tm(tm), _start(std::chrono::high_resolution_clock::now()) {}

  ~ItemTimer() {
    try {
      if (_tm != nullptr) {
        std::chrono::high_resolution_clock::time_point end =
            std::chrono::high_resolution_clock::now();
        unsigned int line = _loc.firstLine();
        auto it = _tm->find(std::make_pair(_loc.filename(), line));
        if (it != _tm->end()) {
          it->second += end - _start;
        } else {
          _tm->insert(std::make_pair(std::make_pair(_loc.filename(), line), end - _start));
        }
      }
    } catch (std::exception& e) {
      assert(false);  // Invariant: Operations on the TimingMap will not throw an exception
    }
  }

private:
  const Location& _loc;
  TimingMap* _tm;
  std::chrono::high_resolution_clock::time_point _start;
};

void flatten(Env& e, FlatteningOptions opt) {
  ItemTimer::TimingMap timingMap_o;
  ItemTimer::TimingMap* timingMap = opt.detailedTiming ? &timingMap_o : nullptr;
  try {
    EnvI& env = e.envi();
    env.fopts = opt;

    bool onlyRangeDomains = false;
    if (opt.onlyRangeDomains) {
      onlyRangeDomains = true;  // compulsory
    } else {
      GCLock lock;
      Call* check_only_range =
          new Call(Location(), "mzn_check_only_range_domains", std::vector<Expression*>());
      check_only_range->type(Type::parbool());
      check_only_range->decl(env.model->matchFn(e.envi(), check_only_range, false));
      onlyRangeDomains = eval_bool(e.envi(), check_only_range);
    }

    bool hadSolveItem = false;
    // Flatten main model
    class FV : public ItemVisitor {
    public:
      EnvI& env;
      bool& hadSolveItem;
      ItemTimer::TimingMap* timingMap;
      FV(EnvI& env0, bool& hadSolveItem0, ItemTimer::TimingMap* timingMap0)
          : env(env0), hadSolveItem(hadSolveItem0), timingMap(timingMap0) {}
      bool enter(Item* i) const { return !(i->isa<ConstraintI>() && env.failed()); }
      void vVarDeclI(VarDeclI* v) {
        ItemTimer item_timer(v->loc(), timingMap);
        v->e()->ann().remove(constants().ann.output_var);
        v->e()->ann().removeCall(constants().ann.output_array);
        if (v->e()->ann().contains(constants().ann.output_only)) {
          return;
        }
        if (v->e()->type().isPar() && !v->e()->type().isOpt() && !v->e()->type().cv() &&
            v->e()->type().dim() > 0 && v->e()->ti()->domain() == nullptr &&
            (v->e()->type().bt() == Type::BT_INT || v->e()->type().bt() == Type::BT_FLOAT)) {
          // Compute bounds for array literals
          CallStackItem csi(env, v->e());
          GCLock lock;
          ArrayLit* al = eval_array_lit(env, v->e()->e());
          v->e()->e(al);
          check_index_sets(env, v->e(), v->e()->e());
          if (al->size() > 0) {
            if (v->e()->type().bt() == Type::BT_INT && v->e()->type().st() == Type::ST_PLAIN) {
              IntVal lb = IntVal::infinity();
              IntVal ub = -IntVal::infinity();
              for (unsigned int i = 0; i < al->size(); i++) {
                IntVal vi = eval_int(env, (*al)[i]);
                lb = std::min(lb, vi);
                ub = std::max(ub, vi);
              }
              GCLock lock;
              set_computed_domain(env, v->e(),
                                  new SetLit(Location().introduce(), IntSetVal::a(lb, ub)), true);
            } else if (v->e()->type().bt() == Type::BT_FLOAT &&
                       v->e()->type().st() == Type::ST_PLAIN) {
              FloatVal lb = FloatVal::infinity();
              FloatVal ub = -FloatVal::infinity();
              for (unsigned int i = 0; i < al->size(); i++) {
                FloatVal vi = eval_float(env, (*al)[i]);
                lb = std::min(lb, vi);
                ub = std::max(ub, vi);
              }
              GCLock lock;
              set_computed_domain(env, v->e(),
                                  new SetLit(Location().introduce(), FloatSetVal::a(lb, ub)), true);
            }
          }
        } else if (v->e()->type().isvar() || v->e()->type().isAnn()) {
          (void)flatten_id(env, Ctx(), v->e()->id(), nullptr, constants().varTrue, true);
        } else {
          if (v->e()->e() == nullptr) {
            if (!v->e()->type().isAnn()) {
              throw EvalError(env, v->e()->loc(), "Undefined parameter", v->e()->id()->v());
            }
          } else {
            CallStackItem csi(env, v->e());
            GCLock lock;
            Location v_loc = v->e()->e()->loc();
            if (!v->e()->e()->type().cv()) {
              v->e()->e(eval_par(env, v->e()->e()));
            } else {
              EE ee = flat_exp(env, Ctx(), v->e()->e(), nullptr, constants().varTrue);
              v->e()->e(ee.r());
            }
            check_par_declaration(env, v->e());
          }
        }
      }
      void vConstraintI(ConstraintI* ci) {
        ItemTimer item_timer(ci->loc(), timingMap);
        (void)flat_exp(env, Ctx(), ci->e(), constants().varTrue, constants().varTrue);
      }
      void vSolveI(SolveI* si) {
        if (hadSolveItem) {
          throw FlatteningError(env, si->loc(), "Only one solve item allowed");
        }
        ItemTimer item_timer(si->loc(), timingMap);
        hadSolveItem = true;
        GCLock lock;
        SolveI* nsi = nullptr;
        switch (si->st()) {
          case SolveI::ST_SAT:
            nsi = SolveI::sat(Location());
            break;
          case SolveI::ST_MIN: {
            Ctx ctx;
            ctx.i = C_NEG;
            nsi = SolveI::min(Location().introduce(),
                              flat_exp(env, ctx, si->e(), nullptr, constants().varTrue).r());
          } break;
          case SolveI::ST_MAX: {
            Ctx ctx;
            ctx.i = C_POS;
            nsi = SolveI::max(Location().introduce(),
                              flat_exp(env, Ctx(), si->e(), nullptr, constants().varTrue).r());
          } break;
        }
        for (ExpressionSetIter it = si->ann().begin(); it != si->ann().end(); ++it) {
          auto* c = (*it)->dynamicCast<Call>();
          if (c != nullptr && c->id() == "on_restart") {
            assert(c->argCount() == 1);
            auto* pred = c->arg(0)->cast<StringLit>();
            Call* nc = new Call(c->loc().introduce(), pred->v(), std::vector<Expression*>());
            nc->type(Type::varbool());
            FunctionI* decl = env.model->matchFn(env, nc, false);
            if (decl == nullptr) {
              std::ostringstream ss;
              ss << "Unknown predicate `" << pred->v()
                 << "' found while evaluating on_restart annotation";
              throw FlatteningError(env, pred->loc(), ss.str());
            }
            nc->decl(decl);
            env.flatAddItem(new ConstraintI(c->loc().introduce(), nc));
          } else {
            nsi->ann().add(flat_exp(env, Ctx(), *it, nullptr, constants().varTrue).r());
          }
        }
        env.flatAddItem(nsi);
      }
    } _fv(env, hadSolveItem, timingMap);
    iter_items<FV>(_fv, e.model());

    if (!hadSolveItem) {
      GCLock lock;
      e.envi().flatAddItem(SolveI::sat(Location().introduce()));
    }

    // Create output model
    if (opt.keepOutputInFzn) {
      copy_output(env);
    } else {
      create_output(env, opt.outputMode, opt.outputObjective, opt.outputOutputItem, opt.hasChecker);
    }

    // Flatten remaining redefinitions
    Model& m = *e.flat();
    int startItem = 0;
    int endItem = static_cast<int>(m.size()) - 1;

    FunctionI* int_lin_eq;
    {
      std::vector<Type> int_lin_eq_t(3);
      int_lin_eq_t[0] = Type::parint(1);
      int_lin_eq_t[1] = Type::varint(1);
      int_lin_eq_t[2] = Type::parint(0);
      GCLock lock;
      FunctionI* fi = env.model->matchFn(env, constants().ids.int_.lin_eq, int_lin_eq_t, false);
      int_lin_eq = ((fi != nullptr) && (fi->e() != nullptr)) ? fi : nullptr;
    }
    FunctionI* float_lin_eq;
    {
      std::vector<Type> float_lin_eq_t(3);
      float_lin_eq_t[0] = Type::parfloat(1);
      float_lin_eq_t[1] = Type::varfloat(1);
      float_lin_eq_t[2] = Type::parfloat(0);
      GCLock lock;
      FunctionI* fi = env.model->matchFn(env, constants().ids.float_.lin_eq, float_lin_eq_t, false);
      float_lin_eq = ((fi != nullptr) && (fi->e() != nullptr)) ? fi : nullptr;
    }
    FunctionI* array_bool_and;
    FunctionI* array_bool_or;
    FunctionI* array_bool_clause;
    FunctionI* array_bool_clause_reif;
    FunctionI* bool_xor;
    {
      std::vector<Type> array_bool_andor_t(2);
      array_bool_andor_t[0] = Type::varbool(1);
      array_bool_andor_t[1] = Type::varbool(0);
      GCLock lock;
      FunctionI* fi =
          env.model->matchFn(env, ASTString("array_bool_and"), array_bool_andor_t, false);
      array_bool_and = ((fi != nullptr) && (fi->e() != nullptr)) ? fi : nullptr;
      fi = env.model->matchFn(env, ASTString("array_bool_or"), array_bool_andor_t, false);
      array_bool_or = ((fi != nullptr) && (fi->e() != nullptr)) ? fi : nullptr;

      array_bool_andor_t[1] = Type::varbool(1);
      fi = env.model->matchFn(env, ASTString("bool_clause"), array_bool_andor_t, false);
      array_bool_clause = ((fi != nullptr) && (fi->e() != nullptr)) ? fi : nullptr;

      array_bool_andor_t.push_back(Type::varbool());
      fi = env.model->matchFn(env, ASTString("bool_clause_reif"), array_bool_andor_t, false);
      array_bool_clause_reif = ((fi != nullptr) && (fi->e() != nullptr)) ? fi : nullptr;

      std::vector<Type> bool_xor_t(3);
      bool_xor_t[0] = Type::varbool();
      bool_xor_t[1] = Type::varbool();
      bool_xor_t[2] = Type::varbool();
      fi = env.model->matchFn(env, constants().ids.bool_xor, bool_xor_t, false);
      bool_xor = ((fi != nullptr) && (fi->e() != nullptr)) ? fi : nullptr;
    }

    std::vector<int> convertToRangeDomain;
    env.collectVarDecls(true);

    while (startItem <= endItem || !env.modifiedVarDecls.empty() || !convertToRangeDomain.empty()) {
      if (env.failed()) {
        return;
      }
      std::vector<int> agenda;
      for (int i = startItem; i <= endItem; i++) {
        agenda.push_back(i);
      }
      for (int modifiedVarDecl : env.modifiedVarDecls) {
        agenda.push_back(modifiedVarDecl);
      }
      env.modifiedVarDecls.clear();

      bool doConvertToRangeDomain = false;
      if (agenda.empty()) {
        for (auto i : convertToRangeDomain) {
          agenda.push_back(i);
        }
        convertToRangeDomain.clear();
        doConvertToRangeDomain = true;
      }

      for (int i : agenda) {
        if (auto* vdi = m[i]->dynamicCast<VarDeclI>()) {
          if (vdi->removed()) {
            continue;
          }
          /// Look at constraints
          if (!is_output(vdi->e())) {
            if (0 < env.varOccurrences.occurrences(vdi->e())) {
              const auto it = env.varOccurrences.itemMap.find(vdi->e()->id());
              if (env.varOccurrences.itemMap.end() != it) {
                bool hasRedundantOccurrenciesOnly = true;
                for (const auto& c : it->second) {
                  if (auto* constrI = c->dynamicCast<ConstraintI>()) {
                    if (auto* call = constrI->e()->dynamicCast<Call>()) {
                      if (call->id() == "mzn_reverse_map_var") {
                        continue;  // all good
                      }
                    }
                  }
                  hasRedundantOccurrenciesOnly = false;
                  break;
                }
                if (hasRedundantOccurrenciesOnly) {
                  env.flatRemoveItem(vdi);
                  env.varOccurrences.removeAllOccurrences(vdi->e());
                  for (const auto& c : it->second) {
                    c->remove();
                  }
                  continue;
                }
              }
            } else {  // 0 occurrencies
              if ((vdi->e()->e() != nullptr) && (vdi->e()->ti()->domain() != nullptr)) {
                if (vdi->e()->type().isvar() && vdi->e()->type().isbool() &&
                    !vdi->e()->type().isOpt() &&
                    Expression::equal(vdi->e()->ti()->domain(), constants().literalTrue)) {
                  GCLock lock;
                  auto* ci = new ConstraintI(vdi->loc(), vdi->e()->e());
                  if (vdi->e()->introduced()) {
                    env.flatAddItem(ci);
                    env.flatRemoveItem(vdi);
                    continue;
                  }
                  vdi->e()->e(nullptr);
                  env.flatAddItem(ci);
                } else if (vdi->e()->type().isPar() || vdi->e()->ti()->computedDomain()) {
                  env.flatRemoveItem(vdi);
                  continue;
                }
              } else {
                env.flatRemoveItem(vdi);
                continue;
              }
            }
          }
          if (vdi->e()->type().dim() > 0 && vdi->e()->type().isvar()) {
            vdi->e()->ti()->domain(nullptr);
          }
          if (vdi->e()->type().isint() && vdi->e()->type().isvar() &&
              vdi->e()->ti()->domain() != nullptr) {
            GCLock lock;
            IntSetVal* dom = eval_intset(env, vdi->e()->ti()->domain());

            if (0 == dom->size()) {
              std::ostringstream oss;
              oss << "Variable has empty domain: " << (*vdi->e());
              env.fail(oss.str());
            }

            bool needRangeDomain = onlyRangeDomains && !vdi->e()->type().isOpt();
            if (!needRangeDomain && !vdi->e()->type().isOpt()) {
              if (dom->min(0).isMinusInfinity() || dom->max(dom->size() - 1).isPlusInfinity()) {
                needRangeDomain = true;
              }
            }
            if (needRangeDomain) {
              if (doConvertToRangeDomain) {
                if (dom->min(0).isMinusInfinity() || dom->max(dom->size() - 1).isPlusInfinity()) {
                  auto* nti = copy(env, vdi->e()->ti())->cast<TypeInst>();
                  nti->domain(nullptr);
                  vdi->e()->ti(nti);
                  if (dom->min(0).isFinite()) {
                    std::vector<Expression*> args(2);
                    args[0] = IntLit::a(dom->min(0));
                    args[1] = vdi->e()->id();
                    Call* call = new Call(Location().introduce(), constants().ids.int_.le, args);
                    call->type(Type::varbool());
                    call->decl(env.model->matchFn(env, call, false));
                    env.flatAddItem(new ConstraintI(Location().introduce(), call));
                  } else if (dom->max(dom->size() - 1).isFinite()) {
                    std::vector<Expression*> args(2);
                    args[0] = vdi->e()->id();
                    args[1] = IntLit::a(dom->max(dom->size() - 1));
                    Call* call = new Call(Location().introduce(), constants().ids.int_.le, args);
                    call->type(Type::varbool());
                    call->decl(env.model->matchFn(env, call, false));
                    env.flatAddItem(new ConstraintI(Location().introduce(), call));
                  }
                } else if (dom->size() > 1) {
                  auto* newDom = new SetLit(Location().introduce(),
                                            IntSetVal::a(dom->min(0), dom->max(dom->size() - 1)));
                  auto* nti = copy(env, vdi->e()->ti())->cast<TypeInst>();
                  nti->domain(newDom);
                  vdi->e()->ti(nti);
                }
                if (dom->size() > 1) {
                  std::vector<Expression*> args(2);
                  args[0] = vdi->e()->id();
                  args[1] = new SetLit(vdi->e()->loc(), dom);
                  Call* call = new Call(vdi->e()->loc(), constants().ids.mzn_set_in_internal, args);
                  call->type(Type::varbool());
                  call->decl(env.model->matchFn(env, call, false));
                  // Give distinct call stack
                  Annotation& ann = vdi->e()->ann();
                  Expression* tmp = call;
                  if (Expression* mznpath_ann = ann.getCall(constants().ann.mzn_path)) {
                    tmp = mznpath_ann->cast<Call>()->arg(0);
                  }
                  CallStackItem csi(env, tmp);
                  env.flatAddItem(new ConstraintI(Location().introduce(), call));
                }
              } else {
                convertToRangeDomain.push_back(i);
              }
            }
          }
          if (vdi->e()->type().isfloat() && vdi->e()->type().isvar() &&
              vdi->e()->ti()->domain() != nullptr) {
            GCLock lock;
            FloatSetVal* vdi_dom = eval_floatset(env, vdi->e()->ti()->domain());
            if (0 == vdi_dom->size()) {
              std::ostringstream oss;
              oss << "Variable has empty domain: " << (*vdi->e());
              env.fail(oss.str());
            }
            FloatVal vmin = vdi_dom->min();
            FloatVal vmax = vdi_dom->max();
            if (vmin == -FloatVal::infinity() && vmax == FloatVal::infinity()) {
              vdi->e()->ti()->domain(nullptr);
            } else if (vmin == -FloatVal::infinity()) {
              vdi->e()->ti()->domain(nullptr);
              std::vector<Expression*> args(2);
              args[0] = vdi->e()->id();
              args[1] = FloatLit::a(vmax);
              Call* call = new Call(Location().introduce(), constants().ids.float_.le, args);
              call->type(Type::varbool());
              call->decl(env.model->matchFn(env, call, false));
              env.flatAddItem(new ConstraintI(Location().introduce(), call));
            } else if (vmax == FloatVal::infinity()) {
              vdi->e()->ti()->domain(nullptr);
              std::vector<Expression*> args(2);
              args[0] = FloatLit::a(vmin);
              args[1] = vdi->e()->id();
              Call* call = new Call(Location().introduce(), constants().ids.float_.le, args);
              call->type(Type::varbool());
              call->decl(env.model->matchFn(env, call, false));
              env.flatAddItem(new ConstraintI(Location().introduce(), call));
            } else if (vdi_dom->size() > 1) {
              auto* dom_ranges = new BinOp(vdi->e()->ti()->domain()->loc().introduce(),
                                           FloatLit::a(vmin), BOT_DOTDOT, FloatLit::a(vmax));
              vdi->e()->ti()->domain(dom_ranges);

              std::vector<Expression*> ranges;
              for (FloatSetRanges vdi_r(vdi_dom); vdi_r(); ++vdi_r) {
                ranges.push_back(FloatLit::a(vdi_r.min()));
                ranges.push_back(FloatLit::a(vdi_r.max()));
              }
              auto* al = new ArrayLit(Location().introduce(), ranges);
              al->type(Type::parfloat(1));
              std::vector<Expression*> args(2);
              args[0] = vdi->e()->id();
              args[1] = al;
              Call* call = new Call(Location().introduce(), constants().ids.float_.dom, args);
              call->type(Type::varbool());
              call->decl(env.model->matchFn(env, call, false));
              env.flatAddItem(new ConstraintI(Location().introduce(), call));
            }
          }
        }
      }

      // rewrite some constraints if there are redefinitions
      for (int i : agenda) {
        if (m[i]->removed()) {
          continue;
        }
        if (auto* vdi = m[i]->dynamicCast<VarDeclI>()) {
          VarDecl* vd = vdi->e();
          if (vd->e() != nullptr) {
            bool isTrueVar = vd->type().isbool() &&
                             Expression::equal(vd->ti()->domain(), constants().literalTrue);
            if (Call* c = vd->e()->dynamicCast<Call>()) {
              GCLock lock;
              Call* nc = nullptr;
              if (c->id() == constants().ids.lin_exp) {
                if (c->type().isfloat() && (float_lin_eq != nullptr)) {
                  std::vector<Expression*> args(c->argCount());
                  auto* le_c = follow_id(c->arg(0))->cast<ArrayLit>();
                  std::vector<Expression*> nc_c(le_c->size());
                  for (auto ii = static_cast<unsigned int>(nc_c.size()); (ii--) != 0U;) {
                    nc_c[ii] = (*le_c)[ii];
                  }
                  nc_c.push_back(FloatLit::a(-1));
                  args[0] = new ArrayLit(Location().introduce(), nc_c);
                  args[0]->type(Type::parfloat(1));
                  auto* le_x = follow_id(c->arg(1))->cast<ArrayLit>();
                  std::vector<Expression*> nx(le_x->size());
                  for (auto ii = static_cast<unsigned int>(nx.size()); (ii--) != 0U;) {
                    nx[ii] = (*le_x)[ii];
                  }
                  nx.push_back(vd->id());
                  args[1] = new ArrayLit(Location().introduce(), nx);
                  args[1]->type(Type::varfloat(1));
                  FloatVal d = c->arg(2)->cast<FloatLit>()->v();
                  args[2] = FloatLit::a(-d);
                  args[2]->type(Type::parfloat(0));
                  nc = new Call(c->loc().introduce(), ASTString("float_lin_eq"), args);
                  nc->type(Type::varbool());
                  nc->decl(float_lin_eq);
                } else if (int_lin_eq != nullptr) {
                  assert(c->type().isint());
                  std::vector<Expression*> args(c->argCount());
                  auto* le_c = follow_id(c->arg(0))->cast<ArrayLit>();
                  std::vector<Expression*> nc_c(le_c->size());
                  for (auto ii = static_cast<unsigned int>(nc_c.size()); (ii--) != 0U;) {
                    nc_c[ii] = (*le_c)[ii];
                  }
                  nc_c.push_back(IntLit::a(-1));
                  args[0] = new ArrayLit(Location().introduce(), nc_c);
                  args[0]->type(Type::parint(1));
                  auto* le_x = follow_id(c->arg(1))->cast<ArrayLit>();
                  std::vector<Expression*> nx(le_x->size());
                  for (auto ii = static_cast<unsigned int>(nx.size()); (ii--) != 0U;) {
                    nx[ii] = (*le_x)[ii];
                  }
                  nx.push_back(vd->id());
                  args[1] = new ArrayLit(Location().introduce(), nx);
                  args[1]->type(Type::varint(1));
                  IntVal d = c->arg(2)->cast<IntLit>()->v();
                  args[2] = IntLit::a(-d);
                  args[2]->type(Type::parint(0));
                  nc = new Call(c->loc().introduce(), ASTString("int_lin_eq"), args);
                  nc->type(Type::varbool());
                  nc->decl(int_lin_eq);
                }
              } else if (c->id() == constants().ids.exists) {
                if (array_bool_or != nullptr) {
                  std::vector<Expression*> args(2);
                  args[0] = c->arg(0);
                  args[1] = vd->id();
                  nc = new Call(c->loc().introduce(), array_bool_or->id(), args);
                  nc->type(Type::varbool());
                  nc->decl(array_bool_or);
                }
              } else if (!isTrueVar && c->id() == constants().ids.forall) {
                if (array_bool_and != nullptr) {
                  std::vector<Expression*> args(2);
                  args[0] = c->arg(0);
                  args[1] = vd->id();
                  nc = new Call(c->loc().introduce(), array_bool_and->id(), args);
                  nc->type(Type::varbool());
                  nc->decl(array_bool_and);
                }
              } else if (isTrueVar && c->id() == constants().ids.clause &&
                         (array_bool_clause != nullptr)) {
                std::vector<Expression*> args(2);
                args[0] = c->arg(0);
                args[1] = c->arg(1);
                nc = new Call(c->loc().introduce(), array_bool_clause->id(), args);
                nc->type(Type::varbool());
                nc->decl(array_bool_clause);
              } else if (c->id() == constants().ids.clause && (array_bool_clause_reif != nullptr)) {
                std::vector<Expression*> args(3);
                args[0] = c->arg(0);
                args[1] = c->arg(1);
                args[2] = vd->id();
                nc = new Call(c->loc().introduce(), array_bool_clause_reif->id(), args);
                nc->type(Type::varbool());
                nc->decl(array_bool_clause_reif);

              } else if (c->id() == constants().ids.bool_not && c->argCount() == 1 &&
                         c->decl()->e() == nullptr) {
                bool isFalseVar = Expression::equal(vd->ti()->domain(), constants().literalFalse);
                if (c->arg(0) == constants().boollit(true)) {
                  if (isTrueVar) {
                    env.fail();
                  } else {
                    env.flatRemoveExpr(c, vdi);
                    env.cseMapRemove(c);
                    vd->e(constants().literalFalse);
                    vd->ti()->domain(constants().literalFalse);
                  }
                } else if (c->arg(0) == constants().boollit(false)) {
                  if (isFalseVar) {
                    env.fail();
                  } else {
                    env.flatRemoveExpr(c, vdi);
                    env.cseMapRemove(c);
                    vd->e(constants().literalTrue);
                    vd->ti()->domain(constants().literalTrue);
                  }
                } else if (c->arg(0)->isa<Id>() && (isTrueVar || isFalseVar)) {
                  VarDecl* arg_vd = c->arg(0)->cast<Id>()->decl();
                  if (arg_vd->ti()->domain() == nullptr) {
                    arg_vd->e(constants().boollit(!isTrueVar));
                    arg_vd->ti()->domain(constants().boollit(!isTrueVar));
                  } else if (arg_vd->ti()->domain() == constants().boollit(isTrueVar)) {
                    env.fail();
                  } else {
                    arg_vd->e(arg_vd->ti()->domain());
                  }
                  env.flatRemoveExpr(c, vdi);
                  vd->e(nullptr);
                  // Need to remove right hand side from CSE map, otherwise
                  // flattening of nc could assume c has already been flattened
                  // to vd
                  env.cseMapRemove(c);
                } else {
                  // don't know how to handle, use bool_not/2
                  nc = new Call(c->loc().introduce(), c->id(), {c->arg(0), vd->id()});
                  nc->type(Type::varbool());
                  nc->decl(env.model->matchFn(env, nc, false));
                }
              } else {
                if (isTrueVar) {
                  FunctionI* decl = env.model->matchFn(env, c, false);
                  env.cseMapRemove(c);
                  if ((decl->e() != nullptr) || c->id() == constants().ids.forall) {
                    if (decl->e() != nullptr) {
                      add_path_annotation(env, decl->e());
                    }
                    c->decl(decl);
                    nc = c;
                  }
                } else {
                  std::vector<Expression*> args(c->argCount());
                  for (auto i = static_cast<unsigned int>(args.size()); (i--) != 0U;) {
                    args[i] = c->arg(i);
                  }
                  args.push_back(vd->id());
                  ASTString cid = c->id();
                  if (cid == constants().ids.clause && (array_bool_clause_reif != nullptr)) {
                    nc = new Call(c->loc().introduce(), array_bool_clause_reif->id(), args);
                    nc->type(Type::varbool());
                    nc->decl(array_bool_clause_reif);
                  } else {
                    FunctionI* decl = nullptr;
                    if (c->type().isbool() && vd->type().isbool()) {
                      if (env.fopts.enableHalfReification &&
                          vd->ann().contains(constants().ctx.pos)) {
                        cid = env.halfReifyId(c->id());
                        decl = env.model->matchFn(env, cid, args, false);
                        if (decl == nullptr) {
                          cid = env.reifyId(c->id());
                          decl = env.model->matchFn(env, cid, args, false);
                        }
                      } else {
                        cid = env.reifyId(c->id());
                        decl = env.model->matchFn(env, cid, args, false);
                      }
                      if (decl == nullptr) {
                        std::ostringstream ss;
                        ss << "'" << c->id()
                           << "' is used in a reified context but no reified version is "
                              "available";
                        throw FlatteningError(env, c->loc(), ss.str());
                      }
                    } else {
                      decl = env.model->matchFn(env, cid, args, false);
                    }
                    if ((decl != nullptr) && (decl->e() != nullptr)) {
                      add_path_annotation(env, decl->e());
                      nc = new Call(c->loc().introduce(), cid, args);
                      nc->type(Type::varbool());
                      nc->decl(decl);
                    }
                  }
                }
              }
              if (nc != nullptr) {
                // Note: Removal of VarDecl's referenced by c must be delayed
                // until nc is flattened
                std::vector<VarDecl*> toRemove;
                CollectDecls cd(env.varOccurrences, toRemove, vdi);
                top_down(cd, c);
                vd->e(nullptr);
                // Need to remove right hand side from CSE map, otherwise
                // flattening of nc could assume c has already been flattened
                // to vd
                env.cseMapRemove(c);
                /// TODO: check if removing variables here makes sense:
                //                  if (!is_output(vd) && env.varOccurrences.occurrences(vd)==0) {
                //                    removedItems.push_back(vdi);
                //                  }
                if (nc != c) {
                  make_defined_var(vd, nc);
                  for (ExpressionSetIter it = c->ann().begin(); it != c->ann().end(); ++it) {
                    EE ee_ann = flat_exp(env, Ctx(), *it, nullptr, constants().varTrue);
                    nc->addAnnotation(ee_ann.r());
                  }
                }
                StringLit* vsl = get_longest_mzn_path_annotation(env, vdi->e());
                StringLit* csl = get_longest_mzn_path_annotation(env, c);
                CallStackItem* vsi = nullptr;
                CallStackItem* csi = nullptr;
                if (vsl != nullptr) {
                  vsi = new CallStackItem(env, vsl);
                }
                if (csl != nullptr) {
                  csi = new CallStackItem(env, csl);
                }
                Location orig_loc = nc->loc();
                if (csl != nullptr) {
                  ASTString loc = csl->v();
                  size_t sep = loc.find('|');
                  std::string filename = loc.substr(0, sep);
                  std::string start_line_s = loc.substr(sep + 1, loc.find('|', sep + 1) - sep - 1);
                  int start_line = std::stoi(start_line_s);
                  Location new_loc(ASTString(filename), start_line, 0, start_line, 0);
                  orig_loc = new_loc;
                }
                ItemTimer item_timer(orig_loc, timingMap);
                (void)flat_exp(env, Ctx(), nc, constants().varTrue, constants().varTrue);

                delete csi;

                delete vsi;

                // Remove VarDecls becoming unused through the removal of c
                // because they are not used by nc
                while (!toRemove.empty()) {
                  VarDecl* cur = toRemove.back();
                  toRemove.pop_back();
                  if (env.varOccurrences.occurrences(cur) == 0 && CollectDecls::varIsFree(cur)) {
                    auto cur_idx = env.varOccurrences.idx.find(cur->id());
                    if (cur_idx != env.varOccurrences.idx.end()) {
                      auto* vdi = m[cur_idx->second]->cast<VarDeclI>();
                      if (!is_output(cur) && !m[cur_idx->second]->removed()) {
                        CollectDecls cd(env.varOccurrences, toRemove, vdi);
                        top_down(cd, vdi->e()->e());
                        vdi->remove();
                      }
                    }
                  }
                }
              }
            }
          }
        } else if (auto* ci = m[i]->dynamicCast<ConstraintI>()) {
          if (Call* c = ci->e()->dynamicCast<Call>()) {
            GCLock lock;
            Call* nc = nullptr;
            if (c->id() == constants().ids.exists) {
              if (array_bool_or != nullptr) {
                std::vector<Expression*> args(2);
                args[0] = c->arg(0);
                args[1] = constants().literalTrue;
                nc = new Call(c->loc().introduce(), array_bool_or->id(), args);
                nc->type(Type::varbool());
                nc->decl(array_bool_or);
              }
            } else if (c->id() == constants().ids.forall) {
              if (array_bool_and != nullptr) {
                std::vector<Expression*> args(2);
                args[0] = c->arg(0);
                args[1] = constants().literalTrue;
                nc = new Call(c->loc().introduce(), array_bool_and->id(), args);
                nc->type(Type::varbool());
                nc->decl(array_bool_and);
              }
            } else if (c->id() == constants().ids.clause) {
              if (array_bool_clause != nullptr) {
                std::vector<Expression*> args(2);
                args[0] = c->arg(0);
                args[1] = c->arg(1);
                nc = new Call(c->loc().introduce(), array_bool_clause->id(), args);
                nc->type(Type::varbool());
                nc->decl(array_bool_clause);
              }
            } else if (c->id() == constants().ids.bool_xor) {
              if (bool_xor != nullptr) {
                std::vector<Expression*> args(3);
                args[0] = c->arg(0);
                args[1] = c->arg(1);
                args[2] = c->argCount() == 2 ? constants().literalTrue : c->arg(2);
                nc = new Call(c->loc().introduce(), bool_xor->id(), args);
                nc->type(Type::varbool());
                nc->decl(bool_xor);
              }
            } else if (c->id() == constants().ids.bool_not && c->argCount() == 1 &&
                       c->decl()->e() == nullptr) {
              if (c->arg(0) == constants().boollit(true)) {
                env.fail();
              } else if (c->arg(0) == constants().boollit(false)) {
                // nothing to do, not false = true
              } else if (c->arg(0)->isa<Id>()) {
                VarDecl* vd = c->arg(0)->cast<Id>()->decl();
                if (vd->ti()->domain() == nullptr) {
                  vd->ti()->domain(constants().boollit(false));
                } else if (vd->ti()->domain() == constants().boollit(true)) {
                  env.fail();
                }
              } else {
                // don't know how to handle, use bool_not/2
                nc =
                    new Call(c->loc().introduce(), c->id(), {c->arg(0), constants().boollit(true)});
                nc->type(Type::varbool());
                nc->decl(env.model->matchFn(env, nc, false));
              }
              if (nc == nullptr) {
                env.flatRemoveItem(ci);
              }
            } else {
              FunctionI* decl = env.model->matchFn(env, c, false);
              if ((decl != nullptr) && (decl->e() != nullptr)) {
                nc = c;
                nc->decl(decl);
              }
            }
            if (nc != nullptr) {
              if (nc != c) {
                for (ExpressionSetIter it = c->ann().begin(); it != c->ann().end(); ++it) {
                  EE ee_ann = flat_exp(env, Ctx(), *it, nullptr, constants().varTrue);
                  nc->addAnnotation(ee_ann.r());
                }
              }
              StringLit* sl = get_longest_mzn_path_annotation(env, c);
              CallStackItem* csi = nullptr;
              if (sl != nullptr) {
                csi = new CallStackItem(env, sl);
              }
              ItemTimer item_timer(nc->loc(), timingMap);
              (void)flat_exp(env, Ctx(), nc, constants().varTrue, constants().varTrue);
              env.flatRemoveItem(ci);

              delete csi;
            }
          }
        }
      }

      startItem = endItem + 1;
      endItem = static_cast<int>(m.size()) - 1;
    }

    // Add redefinitions for output variables that may have been redefined since create_output
    for (unsigned int i = 0; i < env.output->size(); i++) {
      if (auto* vdi = (*env.output)[i]->dynamicCast<VarDeclI>()) {
        IdMap<KeepAlive>::iterator it;
        if (vdi->e()->e() == nullptr &&
            (it = env.reverseMappers.find(vdi->e()->id())) != env.reverseMappers.end()) {
          GCLock lock;
          Call* rhs = copy(env, env.cmap, it->second())->cast<Call>();
          check_output_par_fn(env, rhs);
          output_vardecls(env, vdi, rhs);

          remove_is_output(vdi->e()->flat());
          vdi->e()->e(rhs);
        }
      }
    }

    if (!opt.keepOutputInFzn) {
      finalise_output(env);
    }

    for (auto& i : m) {
      if (auto* ci = i->dynamicCast<ConstraintI>()) {
        if (Call* c = ci->e()->dynamicCast<Call>()) {
          if (c->decl() == constants().varRedef) {
            env.flatRemoveItem(ci);
          }
        }
      }
    }

    cleanup_output(env);
  } catch (ModelInconsistent&) {
  }

  if (opt.detailedTiming) {
    e.envi().outstream << "% Compilation profile (file,line,milliseconds)\n";
    if (opt.collectMznPaths) {
      e.envi().outstream << "% (time is allocated to toplevel item)\n";
    } else {
      e.envi().outstream << "% (locations are approximate, use --keep-paths to allocate times to "
                            "toplevel items)\n";
    }
    for (auto& entry : *timingMap) {
      std::chrono::milliseconds time_taken =
          std::chrono::duration_cast<std::chrono::milliseconds>(entry.second);
      if (time_taken > std::chrono::milliseconds(0)) {
        e.envi().outstream << "%%%mzn-stat: profiling=[\"" << entry.first.first << "\","
                           << entry.first.second << "," << time_taken.count() << "]\n";
      }
    }
    e.envi().outstream << "%%%mzn-stat-end\n";
  }
}

void clear_internal_annotations(Expression* e, bool keepDefinesVar) {
  e->ann().remove(constants().ann.promise_total);
  e->ann().remove(constants().ann.maybe_partial);
  e->ann().remove(constants().ann.add_to_output);
  e->ann().remove(constants().ann.rhs_from_assignment);
  e->ann().remove(constants().ann.mzn_was_undefined);
  // Remove defines_var(x) annotation where x is par
  std::vector<Expression*> removeAnns;
  for (ExpressionSetIter anns = e->ann().begin(); anns != e->ann().end(); ++anns) {
    if (Call* c = (*anns)->dynamicCast<Call>()) {
      if (c->id() == constants().ann.defines_var &&
          (!keepDefinesVar || c->arg(0)->type().isPar())) {
        removeAnns.push_back(c);
      }
    }
  }
  for (auto& removeAnn : removeAnns) {
    e->ann().remove(removeAnn);
  }
}

std::vector<Expression*> cleanup_vardecl(EnvI& env, VarDeclI* vdi, VarDecl* vd,
                                         bool keepDefinesVar) {
  std::vector<Expression*> added_constraints;

  // In FlatZinc par variables have RHSs, not domains
  if (vd->type().isPar()) {
    vd->ann().clear();
    vd->introduced(false);
    vd->ti()->domain(nullptr);
  }

  // In FlatZinc the RHS of a VarDecl must be a literal, Id or empty
  // Example:
  //   var 1..5: x = function(y)
  // becomes:
  //   var 1..5: x;
  //   relation(x, y);
  if (vd->type().isvar() && vd->type().isbool()) {
    bool is_fixed = (vd->ti()->domain() != nullptr);
    if (Expression::equal(vd->ti()->domain(), constants().literalTrue)) {
      // Ex: var true: b = e()

      // Store RHS
      Expression* ve = vd->e();
      vd->e(constants().literalTrue);
      vd->ti()->domain(nullptr);
      // Ex: var bool: b = true

      // If vd had a RHS
      if (ve != nullptr) {
        if (Call* vcc = ve->dynamicCast<Call>()) {
          // Convert functions to relations:
          //   exists([x]) => array_bool_or([x],true)
          //   forall([x]) => array_bool_and([x],true)
          //   clause([x]) => bool_clause([x])
          ASTString cid;
          std::vector<Expression*> args;
          if (vcc->id() == constants().ids.exists) {
            cid = constants().ids.array_bool_or;
            args.push_back(vcc->arg(0));
            args.push_back(constants().literalTrue);
          } else if (vcc->id() == constants().ids.forall) {
            cid = constants().ids.array_bool_and;
            args.push_back(vcc->arg(0));
            args.push_back(constants().literalTrue);
          } else if (vcc->id() == constants().ids.clause) {
            cid = constants().ids.bool_clause;
            args.push_back(vcc->arg(0));
            args.push_back(vcc->arg(1));
          }

          if (args.empty()) {
            // Post original RHS as stand alone constraint
            ve = vcc;
          } else {
            // Create new call, retain annotations from original RHS
            Call* nc = new Call(vcc->loc().introduce(), cid, args);
            nc->type(vcc->type());
            nc->ann().merge(vcc->ann());
            ve = nc;
          }
        } else if (Id* id = ve->dynamicCast<Id>()) {
          if (id->decl()->ti()->domain() != constants().literalTrue) {
            // Inconsistent assignment: post bool_eq(y, true)
            std::vector<Expression*> args(2);
            args[0] = id;
            args[1] = constants().literalTrue;
            GCLock lock;
            ve = new Call(Location().introduce(), constants().ids.bool_eq, args);
          } else {
            // Don't post this
            ve = constants().literalTrue;
          }
        }
        // Post new constraint
        if (ve != constants().literalTrue) {
          clear_internal_annotations(ve, keepDefinesVar);
          added_constraints.push_back(ve);
        }
      }
    } else {
      // Ex: var false: b = e()
      if (vd->e() != nullptr) {
        if (vd->e()->eid() == Expression::E_CALL) {
          // Convert functions to relations:
          //  var false: b = exists([x]) => array_bool_or([x], b)
          //  var false: b = forall([x]) => array_bool_and([x], b)
          //  var false: b = clause([x]) => bool_clause_reif([x], b)
          const Call* c = vd->e()->cast<Call>();
          GCLock lock;
          vd->e(nullptr);
          ASTString cid;
          std::vector<Expression*> args(c->argCount());
          for (unsigned int i = args.size(); (i--) != 0U;) {
            args[i] = c->arg(i);
          }
          if (is_fixed) {
            args.push_back(constants().literalFalse);
          } else {
            args.push_back(vd->id());
          }
          if (c->id() == constants().ids.exists) {
            cid = constants().ids.array_bool_or;
          } else if (c->id() == constants().ids.forall) {
            cid = constants().ids.array_bool_and;
          } else if (c->id() == constants().ids.clause) {
            cid = constants().ids.bool_clause_reif;
          } else {
            if (env.fopts.enableHalfReification && vd->ann().contains(constants().ctx.pos)) {
              cid = env.halfReifyId(c->id());
              if (env.model->matchFn(env, cid, args, false) == nullptr) {
                cid = env.reifyId(c->id());
              }
            } else {
              cid = env.reifyId(c->id());
            }
          }
          Call* nc = new Call(c->loc().introduce(), cid, args);
          nc->type(c->type());
          FunctionI* decl = env.model->matchFn(env, nc, false);
          if (decl == nullptr) {
            std::ostringstream ss;
            ss << "'" << c->id()
               << "' is used in a reified context but no reified version is available";
            throw FlatteningError(env, c->loc(), ss.str());
          }
          nc->decl(decl);
          if (!is_fixed) {
            make_defined_var(vd, nc);
          }
          nc->ann().merge(c->ann());
          clear_internal_annotations(nc, keepDefinesVar);
          added_constraints.push_back(nc);
        } else {
          assert(vd->e()->eid() == Expression::E_ID || vd->e()->eid() == Expression::E_BOOLLIT);
        }
      }
      if (Expression::equal(vd->ti()->domain(), constants().literalFalse)) {
        vd->ti()->domain(nullptr);
        vd->e(constants().literalFalse);
      }
    }
    if (vdi != nullptr && is_fixed && env.varOccurrences.occurrences(vd) == 0) {
      if (is_output(vd)) {
        VarDecl* vd_output =
            (*env.output)[env.outputFlatVarOccurrences.find(vd)]->cast<VarDeclI>()->e();
        if (vd_output->e() == nullptr) {
          vd_output->e(vd->e());
        }
      }
      env.flatRemoveItem(vdi);
    }
  } else if (vd->type().isvar() && vd->type().dim() == 0) {
    // Int or Float var
    if (vd->e() != nullptr) {
      if (const Call* cc = vd->e()->dynamicCast<Call>()) {
        // Remove RHS from vd
        vd->e(nullptr);

        std::vector<Expression*> args(cc->argCount());
        ASTString cid;
        if (cc->id() == constants().ids.lin_exp) {
          // a = lin_exp([1],[b],5) => int_lin_eq([1,-1],[b,a],-5):: defines_var(a)
          auto* le_c = follow_id(cc->arg(0))->cast<ArrayLit>();
          std::vector<Expression*> nc(le_c->size());
          for (auto i = static_cast<unsigned int>(nc.size()); (i--) != 0U;) {
            nc[i] = (*le_c)[i];
          }
          if (le_c->type().bt() == Type::BT_INT) {
            cid = constants().ids.int_.lin_eq;
            nc.push_back(IntLit::a(-1));
            args[0] = new ArrayLit(Location().introduce(), nc);
            args[0]->type(Type::parint(1));
            auto* le_x = follow_id(cc->arg(1))->cast<ArrayLit>();
            std::vector<Expression*> nx(le_x->size());
            for (auto i = static_cast<unsigned int>(nx.size()); (i--) != 0U;) {
              nx[i] = (*le_x)[i];
            }
            nx.push_back(vd->id());
            args[1] = new ArrayLit(Location().introduce(), nx);
            args[1]->type(le_x->type());
            IntVal d = cc->arg(2)->cast<IntLit>()->v();
            args[2] = IntLit::a(-d);
          } else {
            // float
            cid = constants().ids.float_.lin_eq;
            nc.push_back(FloatLit::a(-1.0));
            args[0] = new ArrayLit(Location().introduce(), nc);
            args[0]->type(Type::parfloat(1));
            auto* le_x = follow_id(cc->arg(1))->cast<ArrayLit>();
            std::vector<Expression*> nx(le_x->size());
            for (auto i = static_cast<unsigned int>(nx.size()); (i--) != 0U;) {
              nx[i] = (*le_x)[i];
            }
            nx.push_back(vd->id());
            args[1] = new ArrayLit(Location().introduce(), nx);
            args[1]->type(le_x->type());
            FloatVal d = cc->arg(2)->cast<FloatLit>()->v();
            args[2] = FloatLit::a(-d);
          }
        } else {
          if (cc->id() == "card") {
            // card is 'set_card' in old FlatZinc
            cid = constants().ids.set_card;
          } else {
            cid = cc->id();
          }
          for (auto i = static_cast<unsigned int>(args.size()); (i--) != 0U;) {
            args[i] = cc->arg(i);
          }
          args.push_back(vd->id());
        }
        Call* nc = new Call(cc->loc().introduce(), cid, args);
        nc->type(cc->type());
        make_defined_var(vd, nc);
        nc->ann().merge(cc->ann());

        clear_internal_annotations(nc, keepDefinesVar);
        added_constraints.push_back(nc);
      } else {
        // RHS must be literal or Id
        assert(vd->e()->eid() == Expression::E_ID || vd->e()->eid() == Expression::E_INTLIT ||
               vd->e()->eid() == Expression::E_FLOATLIT ||
               vd->e()->eid() == Expression::E_BOOLLIT || vd->e()->eid() == Expression::E_SETLIT);
      }
    }
  } else if (vd->type().dim() > 0) {
    // vd is an array

    // If RHS is an Id, follow id to RHS
    // a = [1,2,3]; b = a;
    // vd = b => vd = [1,2,3]
    if (!vd->e()->isa<ArrayLit>()) {
      vd->e(follow_id(vd->e()));
    }

    // If empty array or 1 indexed, continue
    if (vd->ti()->ranges().size() == 1 && vd->ti()->ranges()[0]->domain() != nullptr &&
        vd->ti()->ranges()[0]->domain()->isa<SetLit>()) {
      IntSetVal* isv = vd->ti()->ranges()[0]->domain()->cast<SetLit>()->isv();
      if ((isv != nullptr) && (isv->size() == 0 || isv->min(0) == 1)) {
        return added_constraints;
      }
    }

    // Array should be 1 indexed since ArrayLit is 1 indexed
    assert(vd->e() != nullptr);
    ArrayLit* al = nullptr;
    Expression* e = vd->e();
    while (al == nullptr) {
      switch (e->eid()) {
        case Expression::E_ARRAYLIT:
          al = e->cast<ArrayLit>();
          break;
        case Expression::E_ID:
          e = e->cast<Id>()->decl()->e();
          break;
        default:
          assert(false);
      }
    }
    al->make1d();
    IntSetVal* isv = IntSetVal::a(1, al->length());
    if (vd->ti()->ranges().size() == 1) {
      vd->ti()->ranges()[0]->domain(new SetLit(Location().introduce(), isv));
    } else {
      std::vector<TypeInst*> r(1);
      r[0] = new TypeInst(vd->ti()->ranges()[0]->loc(), vd->ti()->ranges()[0]->type(),
                          new SetLit(Location().introduce(), isv));
      ASTExprVec<TypeInst> ranges(r);
      auto* ti = new TypeInst(vd->ti()->loc(), vd->ti()->type(), ranges, vd->ti()->domain());
      vd->ti(ti);
    }
  }

  // Remove boolean context annotations used only on compilation
  vd->ann().remove(constants().ctx.mix);
  vd->ann().remove(constants().ctx.pos);
  vd->ann().remove(constants().ctx.neg);
  vd->ann().remove(constants().ctx.root);
  vd->ann().remove(constants().ann.promise_total);
  vd->ann().remove(constants().ann.add_to_output);
  vd->ann().remove(constants().ann.mzn_check_var);
  vd->ann().remove(constants().ann.rhs_from_assignment);
  vd->ann().remove(constants().ann.mzn_was_undefined);
  vd->ann().removeCall(constants().ann.mzn_check_enum_var);

  return added_constraints;
}

Expression* cleanup_constraint(EnvI& env, std::unordered_set<Item*>& globals, Expression* ce,
                               bool keepDefinesVar) {
  clear_internal_annotations(ce, keepDefinesVar);

  if (Call* vc = ce->dynamicCast<Call>()) {
    for (unsigned int i = 0; i < vc->argCount(); i++) {
      // Change array indicies to be 1 indexed
      if (auto* al = vc->arg(i)->dynamicCast<ArrayLit>()) {
        if (al->dims() > 1 || al->min(0) != 1) {
          al->make1d();
        }
      }
    }
    // Convert functions to relations:
    //   exists([x]) => array_bool_or([x],true)
    //   forall([x]) => array_bool_and([x],true)
    //   clause([x]) => bool_clause([x])
    //   bool_xor([x],[y]) => bool_xor([x],[y],true)
    if (vc->id() == constants().ids.exists) {
      GCLock lock;
      vc->id(constants().ids.array_bool_or);
      std::vector<Expression*> args(2);
      args[0] = vc->arg(0);
      args[1] = constants().literalTrue;
      ASTExprVec<Expression> argsv(args);
      vc->args(argsv);
      vc->decl(env.model->matchFn(env, vc, false));
    } else if (vc->id() == constants().ids.forall) {
      GCLock lock;
      vc->id(constants().ids.array_bool_and);
      std::vector<Expression*> args(2);
      args[0] = vc->arg(0);
      args[1] = constants().literalTrue;
      ASTExprVec<Expression> argsv(args);
      vc->args(argsv);
      vc->decl(env.model->matchFn(env, vc, false));
    } else if (vc->id() == constants().ids.clause) {
      GCLock lock;
      vc->id(constants().ids.bool_clause);
      vc->decl(env.model->matchFn(env, vc, false));
    } else if (vc->id() == constants().ids.bool_xor && vc->argCount() == 2) {
      GCLock lock;
      std::vector<Expression*> args(3);
      args[0] = vc->arg(0);
      args[1] = vc->arg(1);
      args[2] = constants().literalTrue;
      ASTExprVec<Expression> argsv(args);
      vc->args(argsv);
      vc->decl(env.model->matchFn(env, vc, false));
    }

    // If vc->decl() is a solver builtin and has not been added to the
    // FlatZinc, add it
    if ((vc->decl() != nullptr) && vc->decl() != constants().varRedef &&
        !vc->decl()->fromStdLib() && globals.find(vc->decl()) == globals.end()) {
      std::vector<VarDecl*> params(vc->decl()->params().size());
      for (unsigned int i = 0; i < params.size(); i++) {
        params[i] = vc->decl()->params()[i];
      }
      GCLock lock;
      auto* vc_decl_copy = new FunctionI(vc->decl()->loc(), vc->decl()->id(), vc->decl()->ti(),
                                         params, vc->decl()->e());
      env.flatAddItem(vc_decl_copy);
      globals.insert(vc->decl());
    }
    return ce;
  }
  if (Id* id = ce->dynamicCast<Id>()) {
    // Ex: constraint b; => constraint bool_eq(b, true);
    std::vector<Expression*> args(2);
    args[0] = id;
    args[1] = constants().literalTrue;
    GCLock lock;
    return new Call(Location().introduce(), constants().ids.bool_eq, args);
  }
  if (auto* bl = ce->dynamicCast<BoolLit>()) {
    // Ex: true => delete; false => bool_eq(false, true);
    if (!bl->v()) {
      GCLock lock;
      std::vector<Expression*> args(2);
      args[0] = constants().literalFalse;
      args[1] = constants().literalTrue;
      Call* neq = new Call(Location().introduce(), constants().ids.bool_eq, args);
      return neq;
    }
    return nullptr;
  }
  return ce;
}

void oldflatzinc(Env& e) {
  Model* m = e.flat();

  // Check wheter we need to keep defines_var annotations
  bool keepDefinesVar = true;
  {
    GCLock lock;
    Call* c = new Call(Location().introduce(), "mzn_check_annotate_defines_var", {});
    c->type(Type::parbool());
    FunctionI* fi = e.model()->matchFn(e.envi(), c, true);
    if (fi != nullptr) {
      c->decl(fi);
      keepDefinesVar = eval_bool(e.envi(), c);
    }
  }

  // Mark annotations and optional variables for removal, and clear flags
  for (auto& vdi : m->vardecls()) {
    if (vdi.e()->type().ot() == Type::OT_OPTIONAL || vdi.e()->type().bt() == Type::BT_ANN) {
      vdi.remove();
    }
  }

  EnvI& env = e.envi();

  unsigned int msize = m->size();

  // Predicate declarations of solver builtins
  std::unordered_set<Item*> globals;

  // Variables mapped to the index of the constraint that defines them
  enum DFS_STATUS { DFS_UNKNOWN, DFS_SEEN, DFS_DONE };
  std::unordered_map<VarDecl*, std::pair<int, DFS_STATUS>> definition_map;

  // Record indices of VarDeclIs with Id RHS for sorting & unification
  std::vector<int> declsWithIds;
  for (int i = 0; i < msize; i++) {
    if ((*m)[i]->removed()) {
      continue;
    }
    if (auto* vdi = (*m)[i]->dynamicCast<VarDeclI>()) {
      GCLock lock;
      VarDecl* vd = vdi->e();
      std::vector<Expression*> added_constraints =
          cleanup_vardecl(e.envi(), vdi, vd, keepDefinesVar);
      // Record whether this VarDecl is equal to an Id (aliasing)
      if ((vd->e() != nullptr) && vd->e()->isa<Id>()) {
        declsWithIds.push_back(i);
        vdi->e()->payload(-static_cast<int>(i) - 1);
      } else {
        vdi->e()->payload(i);
      }
      for (auto* nc : added_constraints) {
        Expression* new_ce = cleanup_constraint(e.envi(), globals, nc, keepDefinesVar);
        if (new_ce != nullptr) {
          e.envi().flatAddItem(new ConstraintI(Location().introduce(), new_ce));
        }
      }
    } else if (auto* ci = (*m)[i]->dynamicCast<ConstraintI>()) {
      Expression* new_ce = cleanup_constraint(e.envi(), globals, ci->e(), keepDefinesVar);
      if (new_ce != nullptr) {
        ci->e(new_ce);
        if (keepDefinesVar) {
          if (Call* defines_var = new_ce->ann().getCall(constants().ann.defines_var)) {
            if (Id* ident = defines_var->arg(0)->dynamicCast<Id>()) {
              if (definition_map.find(ident->decl()) != definition_map.end()) {
                // This is the second definition, remove it
                new_ce->ann().removeCall(constants().ann.defines_var);
              } else {
                definition_map.insert({ident->decl(), {i, DFS_UNKNOWN}});
              }
            }
          }
        }
      } else {
        ci->remove();
      }
    } else if (auto* fi = (*m)[i]->dynamicCast<FunctionI>()) {
      if (Let* let = Expression::dynamicCast<Let>(fi->e())) {
        GCLock lock;
        std::vector<Expression*> new_let;
        for (unsigned int i = 0; i < let->let().size(); i++) {
          Expression* let_e = let->let()[i];
          if (auto* vd = let_e->dynamicCast<VarDecl>()) {
            std::vector<Expression*> added_constraints =
                cleanup_vardecl(e.envi(), nullptr, vd, keepDefinesVar);
            new_let.push_back(vd);
            for (auto* nc : added_constraints) {
              new_let.push_back(nc);
            }
          } else {
            Expression* new_ce = cleanup_constraint(e.envi(), globals, let_e, keepDefinesVar);
            if (new_ce != nullptr) {
              new_let.push_back(new_ce);
            }
          }
        }
        fi->e(new Let(let->loc(), new_let, let->in()));
      }
    } else if (auto* si = (*m)[i]->dynamicCast<SolveI>()) {
      if ((si->e() != nullptr) && si->e()->type().isPar()) {
        // Introduce VarDecl if objective expression is par
        GCLock lock;
        auto* ti = new TypeInst(Location().introduce(), si->e()->type(), nullptr);
        auto* constantobj = new VarDecl(Location().introduce(), ti, e.envi().genId(), si->e());
        si->e(constantobj->id());
        e.envi().flatAddItem(new VarDeclI(Location().introduce(), constantobj));
      }
    }
  }

  if (keepDefinesVar) {
    // Detect and break cycles in defines_var annotations
    std::vector<VarDecl*> definesStack;
    auto checkId = [&definesStack, &definition_map, &m](VarDecl* cur, Id* ident) {
      if (cur == ident->decl()) {
        // Never push the variable we're currently looking at
        return;
      }
      auto it = definition_map.find(ident->decl());
      if (it != definition_map.end()) {
        if (it->second.second == 0) {
          // not yet visited, push
          definesStack.push_back(it->first);
        } else if (it->second.second == 1) {
          // Found a cycle through variable ident
          // Break cycle by removing annotations
          ident->decl()->ann().remove(constants().ann.is_defined_var);
          Call* c = (*m)[it->second.first]->cast<ConstraintI>()->e()->cast<Call>();
          c->ann().removeCall(constants().ann.defines_var);
        }
      }
    };
    for (auto& it : definition_map) {
      if (it.second.second == 0) {
        // not yet visited
        definesStack.push_back(it.first);
        while (!definesStack.empty()) {
          VarDecl* cur = definesStack.back();
          if (definition_map[cur].second != DFS_UNKNOWN) {
            // already visited (or already finished), now finished
            definition_map[cur].second = DFS_DONE;
            definesStack.pop_back();
          } else {
            // now visited and on stack
            definition_map[cur].second = DFS_SEEN;
            if (Call* c = (*m)[definition_map[cur].first]
                              ->cast<ConstraintI>()
                              ->e()
                              ->dynamicCast<Call>()) {
              // Variable is defined by a call, push all arguments
              for (unsigned int i = 0; i < c->argCount(); i++) {
                if (c->arg(i)->type().isPar()) {
                  continue;
                }
                if (Id* ident = c->arg(i)->dynamicCast<Id>()) {
                  if (ident->type().dim() > 0) {
                    if (auto* al = Expression::dynamicCast<ArrayLit>(ident->decl()->e())) {
                      for (auto* e : al->getVec()) {
                        if (auto* ident = e->dynamicCast<Id>()) {
                          checkId(cur, ident);
                        }
                      }
                    }
                  } else if (ident->type().isvar()) {
                    checkId(cur, ident);
                  }
                } else if (auto* al = c->arg(i)->dynamicCast<ArrayLit>()) {
                  for (auto* e : al->getVec()) {
                    if (auto* ident = e->dynamicCast<Id>()) {
                      checkId(cur, ident);
                    }
                  }
                }
              }
            }
          }
        }
      }
    }
  }

  // Sort VarDecls in FlatZinc so that VarDecls are declared before use
  std::vector<VarDeclI*> sortedVarDecls(declsWithIds.size());
  int vdCount = 0;
  for (int declsWithId : declsWithIds) {
    VarDecl* cur = (*m)[declsWithId]->cast<VarDeclI>()->e();
    std::vector<int> stack;
    while ((cur != nullptr) && cur->payload() < 0) {
      stack.push_back(cur->payload());
      if (Id* id = cur->e()->dynamicCast<Id>()) {
        cur = id->decl();
      } else {
        cur = nullptr;
      }
    }
    for (auto i = static_cast<unsigned int>(stack.size()); (i--) != 0U;) {
      auto* vdi = (*m)[-stack[i] - 1]->cast<VarDeclI>();
      vdi->e()->payload(-vdi->e()->payload() - 1);
      sortedVarDecls[vdCount++] = vdi;
    }
  }
  for (unsigned int i = 0; i < declsWithIds.size(); i++) {
    (*m)[declsWithIds[i]] = sortedVarDecls[i];
  }

  // Remove marked items
  m->compact();
  e.envi().output->compact();

  for (auto& it : env.varOccurrences.itemMap) {
    std::vector<Item*> toRemove;
    for (auto* iit : it.second) {
      if (iit->removed()) {
        toRemove.push_back(iit);
      }
    }
    for (auto& i : toRemove) {
      it.second.erase(i);
    }
  }

  class Cmp {
  public:
    bool operator()(Item* i, Item* j) {
      if (i->iid() == Item::II_FUN || j->iid() == Item::II_FUN) {
        if (i->iid() == j->iid()) {
          return false;
        }
        return i->iid() == Item::II_FUN;
      }
      if (i->iid() == Item::II_SOL) {
        assert(j->iid() != i->iid());
        return false;
      }
      if (j->iid() == Item::II_SOL) {
        assert(j->iid() != i->iid());
        return true;
      }
      if (i->iid() == Item::II_VD) {
        if (j->iid() != i->iid()) {
          return true;
        }
        if (i->cast<VarDeclI>()->e()->type().isPar() && j->cast<VarDeclI>()->e()->type().isvar()) {
          return true;
        }
        if (j->cast<VarDeclI>()->e()->type().isPar() && i->cast<VarDeclI>()->e()->type().isvar()) {
          return false;
        }
        if (i->cast<VarDeclI>()->e()->type().dim() == 0 &&
            j->cast<VarDeclI>()->e()->type().dim() != 0) {
          return true;
        }
        if (i->cast<VarDeclI>()->e()->type().dim() != 0 &&
            j->cast<VarDeclI>()->e()->type().dim() == 0) {
          return false;
        }
        if (i->cast<VarDeclI>()->e()->e() == nullptr && j->cast<VarDeclI>()->e()->e() != nullptr) {
          return true;
        }
        if ((i->cast<VarDeclI>()->e()->e() != nullptr) &&
            (j->cast<VarDeclI>()->e()->e() != nullptr) &&
            !i->cast<VarDeclI>()->e()->e()->isa<Id>() && j->cast<VarDeclI>()->e()->e()->isa<Id>()) {
          return true;
        }
      }
      return false;
    }
  } _cmp;
  // Perform final sorting
  std::stable_sort(m->begin(), m->end(), _cmp);
}

FlatModelStatistics statistics(Env& m) {
  Model* flat = m.flat();
  FlatModelStatistics stats;
  stats.n_reif_ct = m.envi().counters.reifConstraints;
  stats.n_imp_ct = m.envi().counters.impConstraints;
  stats.n_imp_del = m.envi().counters.impDel;
  stats.n_lin_del = m.envi().counters.linDel;
  for (auto& i : *flat) {
    if (!i->removed()) {
      if (auto* vdi = i->dynamicCast<VarDeclI>()) {
        Type t = vdi->e()->type();
        if (t.isvar() && t.dim() == 0) {
          if (t.isSet()) {
            stats.n_set_vars++;
          } else if (t.isint()) {
            stats.n_int_vars++;
          } else if (t.isbool()) {
            stats.n_bool_vars++;
          } else if (t.isfloat()) {
            stats.n_float_vars++;
          }
        }
      } else if (auto* ci = i->dynamicCast<ConstraintI>()) {
        if (Call* call = ci->e()->dynamicCast<Call>()) {
          if (call->id().endsWith("_reif")) {
            stats.n_reif_ct++;
          } else if (call->id().endsWith("_imp")) {
            stats.n_imp_ct++;
          }
          if (call->argCount() > 0) {
            Type all_t;
            for (unsigned int i = 0; i < call->argCount(); i++) {
              Type t = call->arg(i)->type();
              if (t.isvar()) {
                if (t.st() == Type::ST_SET ||
                    (t.bt() == Type::BT_FLOAT && all_t.st() != Type::ST_SET) ||
                    (t.bt() == Type::BT_INT && all_t.bt() != Type::BT_FLOAT &&
                     all_t.st() != Type::ST_SET) ||
                    (t.bt() == Type::BT_BOOL && all_t.bt() != Type::BT_INT &&
                     all_t.bt() != Type::BT_FLOAT && all_t.st() != Type::ST_SET)) {
                  all_t = t;
                }
              }
            }
            if (all_t.isvar()) {
              if (all_t.st() == Type::ST_SET) {
                stats.n_set_ct++;
              } else if (all_t.bt() == Type::BT_INT) {
                stats.n_int_ct++;
              } else if (all_t.bt() == Type::BT_BOOL) {
                stats.n_bool_ct++;
              } else if (all_t.bt() == Type::BT_FLOAT) {
                stats.n_float_ct++;
              }
            }
          }
        }
      }
    }
  }
  return stats;
}

}  // namespace MiniZinc