on-restart-benchmarks/lib/typecheck.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/flatten_internal.hh>
#include <minizinc/hash.hh>
#include <minizinc/prettyprinter.hh>
#include <minizinc/typecheck.hh>

#include <sstream>
#include <string>
#include <unordered_map>

namespace MiniZinc {

Scopes::Scopes(void) {
  s.push_back(Scope());
  s.back().toplevel = true;
}

void Scopes::add(EnvI& env, VarDecl* vd) {
  if (!s.back().toplevel && vd->ti()->isEnum() && vd->e()) {
    throw TypeError(env, vd->loc(), "enums are only allowed at top level");
  }
  if (vd->id()->idn() == -1 && vd->id()->v() == "") return;
  DeclMap::iterator vdi = s.back().m.find(vd->id());
  if (vdi == s.back().m.end()) {
    s.back().m.insert(vd->id(), vd);
  } else {
    GCLock lock;
    throw TypeError(env, vd->loc(), "identifier `" + vd->id()->str().str() + "' already defined");
  }
}

void Scopes::push(bool toplevel) {
  s.push_back(Scope());
  s.back().toplevel = toplevel;
}

void Scopes::pop(void) { s.pop_back(); }

VarDecl* Scopes::find(Id* ident) {
  int cur = static_cast<int>(s.size()) - 1;
  for (;;) {
    DeclMap::iterator vdi = s[cur].m.find(ident);
    if (vdi == s[cur].m.end()) {
      if (s[cur].toplevel) {
        if (cur > 0)
          cur = 0;
        else
          return NULL;
      } else {
        cur--;
      }
    } else {
      return vdi->second;
    }
  }
}

struct VarDeclCmp {
  std::unordered_map<VarDecl*, int>& _pos;
  VarDeclCmp(std::unordered_map<VarDecl*, int>& pos) : _pos(pos) {}
  bool operator()(Expression* e0, Expression* e1) {
    if (VarDecl* vd0 = Expression::dyn_cast<VarDecl>(e0)) {
      if (VarDecl* vd1 = Expression::dyn_cast<VarDecl>(e1)) {
        return _pos[vd0] < _pos[vd1];
      } else {
        return true;
      }
    } else {
      return false;
    }
  }
};
struct ItemCmp {
  std::unordered_map<VarDecl*, int>& _pos;
  ItemCmp(std::unordered_map<VarDecl*, int>& pos) : _pos(pos) {}
  bool operator()(Item* i0, Item* i1) {
    if (VarDeclI* vd0 = i0->cast<VarDeclI>()) {
      if (VarDeclI* vd1 = i1->cast<VarDeclI>()) {
        return _pos[vd0->e()] < _pos[vd1->e()];
      } else {
        return true;
      }
    } else {
      return false;
    }
  }
};

std::string createEnumToStringName(Id* ident, std::string prefix) {
  std::string name = ident->str().str();
  if (name[0] == '\'') {
    name = "'" + prefix + name.substr(1);
  } else {
    name = prefix + name;
  }
  return name;
}

AssignI* createEnumMapper(EnvI& env, Model* m, unsigned int enumId, VarDecl* vd,
                          VarDecl* vd_enumToString, Model* enumItems) {
  Id* ident = vd->id();
  SetLit* sl = vd->e()->dyn_cast<SetLit>();
  ArrayLit* enum_init_al = NULL;
  AssignI* ret = NULL;

  GCLock lock;
  if (ArrayLit* al = vd->e()->dyn_cast<ArrayLit>()) {
    enum_init_al = al;
  } else if (Call* c = vd->e()->dyn_cast<Call>()) {
    if (c->id() != "anon_enum") {
      throw TypeError(env, c->loc(), "invalid initialisation for enum `" + ident->v().str() + "'");
    }
    if (c->n_args() == 1 && c->arg(0)->isa<ArrayLit>()) {
      enum_init_al = c->arg(0)->cast<ArrayLit>();
    }
  }
  if (enum_init_al) {
    std::vector<Expression*> enumIds(enum_init_al->size());
    for (unsigned int i = 0; i < enum_init_al->size(); i++) {
      if (Id* eid = (*enum_init_al)[i]->dyn_cast<Id>()) {
        enumIds[i] = eid;
      } else {
        throw TypeError(env, vd->e()->loc(),
                        "invalid initialisation for enum `" + ident->v().str() + "'");
      }
    }
    sl = new SetLit(vd->e()->loc(), enumIds);
  }
  if (sl) {
    for (unsigned int i = 0; i < sl->v().size(); i++) {
      if (!sl->v()[i]->isa<Id>()) {
        throw TypeError(env, sl->v()[i]->loc(),
                        "invalid initialisation for enum `" + ident->v().str() + "'");
      }
      TypeInst* ti_id = new TypeInst(sl->v()[i]->loc(), Type::parenum(enumId));

      std::vector<Expression*> toEnumArgs(2);
      toEnumArgs[0] = vd->id();
      toEnumArgs[1] = IntLit::a(i + 1);
      Call* toEnum = new Call(sl->v()[i]->loc(), ASTString("to_enum"), toEnumArgs);
      toEnum->decl(env.model->matchFn(env, toEnum, false));
      VarDecl* vd_id = new VarDecl(ti_id->loc(), ti_id, sl->v()[i]->cast<Id>()->str(), toEnum);
      enumItems->addItem(new VarDeclI(vd_id->loc(), vd_id));
    }
    SetLit* nsl = new SetLit(vd->loc(), IntSetVal::a(1, sl->v().size()));
    Type tt = nsl->type();
    tt.enumId(vd->type().enumId());
    nsl->type(tt);
    vd->e(nsl);
  } else if (!vd->e()->isa<Call>()) {
    throw TypeError(env, vd->e()->loc(),
                    "invalid initialisation for enum `" + ident->v().str() + "'");
  }

  if (sl) {
    std::string name = createEnumToStringName(ident, "_enum_to_string_");
    std::vector<Expression*> al_args(sl->v().size());
    for (unsigned int i = 0; i < sl->v().size(); i++) {
      std::string str = sl->v()[i]->cast<Id>()->str().str();
      if (str.size() >= 2 && str[0] == '\'' && str[str.size() - 1] == '\'') {
        al_args[i] =
            new StringLit(Location().introduce(), ASTString(str.substr(1, str.size() - 2)));
      } else {
        al_args[i] = new StringLit(Location().introduce(), ASTString(str));
      }
      env.reverseEnum[str] = i + 1;
    }
    ArrayLit* al = new ArrayLit(Location().introduce(), al_args);

    if (vd_enumToString) {
      ret = new AssignI(Location().introduce(), name, al);
      ret->decl(vd_enumToString);
    } else {
      std::vector<TypeInst*> ranges(1);
      ranges[0] = new TypeInst(Location().introduce(), Type::parint());
      TypeInst* ti = new TypeInst(Location().introduce(), Type::parstring(1));
      ti->setRanges(ranges);
      vd_enumToString = new VarDecl(Location().introduce(), ti, name, al);
      enumItems->addItem(new VarDeclI(Location().introduce(), vd_enumToString));
    }

    Type tx = Type::parint();
    tx.ot(Type::OT_OPTIONAL);
    TypeInst* ti_aa = new TypeInst(Location().introduce(), tx);
    VarDecl* vd_aa = new VarDecl(Location().introduce(), ti_aa, "x");
    vd_aa->toplevel(false);
    TypeInst* ti_ab = new TypeInst(Location().introduce(), Type::parbool());
    VarDecl* vd_ab = new VarDecl(Location().introduce(), ti_ab, "b");
    vd_ab->toplevel(false);
    TypeInst* ti_aj = new TypeInst(Location().introduce(), Type::parbool());
    VarDecl* vd_aj = new VarDecl(Location().introduce(), ti_aj, "json");
    vd_aj->toplevel(false);
    TypeInst* ti_fi = new TypeInst(Location().introduce(), Type::parstring());
    std::vector<VarDecl*> fi_params(3);
    fi_params[0] = vd_aa;
    fi_params[1] = vd_ab;
    fi_params[2] = vd_aj;

    std::vector<Expression*> deopt_args(1);
    deopt_args[0] = vd_aa->id();
    Call* deopt = new Call(Location().introduce(), "deopt", deopt_args);
    Call* occurs = new Call(Location().introduce(), "occurs", deopt_args);
    std::vector<Expression*> aa_args(1);
    aa_args[0] = deopt;
    ArrayAccess* aa = new ArrayAccess(Location().introduce(), vd_enumToString->id(), aa_args);

    StringLit* sl_absent = new StringLit(Location().introduce(), "<>");

    ITE* if_absent =
        new ITE(Location().introduce(),
                {vd_aj->id(), new StringLit(Location().introduce(), ASTString("null"))}, sl_absent);

    StringLit* json_e_quote = new StringLit(Location().introduce(), ASTString("{\"e\":\""));
    StringLit* json_e_quote_end = new StringLit(Location().introduce(), ASTString("\"}"));
    BinOp* quote_aa = new BinOp(Location().introduce(), json_e_quote, BOT_PLUSPLUS, aa);
    BinOp* quote_aa2 = new BinOp(Location().introduce(), quote_aa, BOT_PLUSPLUS, json_e_quote_end);

    Call* quote_dzn = new Call(Location().introduce(), ASTString("showDznId"), {aa});

    std::vector<Expression*> ite_ifelse(2);
    ite_ifelse[0] = occurs;
    ite_ifelse[1] =
        new ITE(Location().introduce(), {vd_ab->id(), quote_dzn, vd_aj->id(), quote_aa2}, aa);

    ITE* ite = new ITE(Location().introduce(), ite_ifelse, if_absent);

    FunctionI* fi = new FunctionI(
        Location().introduce(), createEnumToStringName(ident, "_toString_"), ti_fi, fi_params, ite);
    enumItems->addItem(fi);
  } else {
    if (vd_enumToString) {
      /// TODO: find a better solution (don't introduce the vd_enumToString until we
      ///       know it's a non-anonymous enum)
      vd_enumToString->e(new ArrayLit(Location().introduce(), std::vector<Expression*>()));
    }
    {
      Type tx = Type::parint();
      tx.ot(Type::OT_OPTIONAL);
      TypeInst* ti_aa = new TypeInst(Location().introduce(), tx);
      VarDecl* vd_aa = new VarDecl(Location().introduce(), ti_aa, "x");
      vd_aa->toplevel(false);

      TypeInst* ti_ab = new TypeInst(Location().introduce(), Type::parbool());
      VarDecl* vd_ab = new VarDecl(Location().introduce(), ti_ab, "b");
      vd_ab->toplevel(false);

      TypeInst* ti_aj = new TypeInst(Location().introduce(), Type::parbool());
      VarDecl* vd_aj = new VarDecl(Location().introduce(), ti_aj, "json");
      vd_aj->toplevel(false);

      std::vector<Expression*> deopt_args(1);
      deopt_args[0] = vd_aa->id();
      Call* deopt = new Call(Location().introduce(), "deopt", deopt_args);
      Call* if_absent = new Call(Location().introduce(), "absent", deopt_args);
      StringLit* sl_absent_dzn = new StringLit(Location().introduce(), "<>");
      ITE* sl_absent = new ITE(
          Location().introduce(),
          {vd_aj->id(), new StringLit(Location().introduce(), ASTString("null"))}, sl_absent_dzn);

      StringLit* sl_dzn =
          new StringLit(Location().introduce(), ASTString("to_enum(" + ident->str().str() + ","));
      std::vector<Expression*> showIntArgs(1);
      showIntArgs[0] = deopt;
      Call* showInt = new Call(Location().introduce(), constants().ids.show, showIntArgs);
      BinOp* construct_string_dzn =
          new BinOp(Location().introduce(), sl_dzn, BOT_PLUSPLUS, showInt);
      StringLit* closing_bracket = new StringLit(Location().introduce(), ASTString(")"));
      BinOp* construct_string_dzn_2 =
          new BinOp(Location().introduce(), construct_string_dzn, BOT_PLUSPLUS, closing_bracket);

      StringLit* sl = new StringLit(Location().introduce(), ASTString(ident->str().str() + "_"));
      BinOp* construct_string = new BinOp(Location().introduce(), sl, BOT_PLUSPLUS, showInt);

      StringLit* json_e_quote = new StringLit(Location().introduce(), ASTString("{\"e\":\""));
      StringLit* json_e_quote_end = new StringLit(Location().introduce(), ASTString("\"}"));
      BinOp* construct_string_json =
          new BinOp(Location().introduce(), json_e_quote, BOT_PLUSPLUS, construct_string);
      BinOp* construct_string_json_2 =
          new BinOp(Location().introduce(), construct_string_json, BOT_PLUSPLUS, json_e_quote_end);

      std::vector<Expression*> if_then(6);
      if_then[0] = if_absent;
      if_then[1] = sl_absent;
      if_then[2] = vd_ab->id();
      if_then[3] = construct_string_dzn_2;
      if_then[4] = vd_aj->id();
      if_then[5] = construct_string_json_2;
      ITE* ite = new ITE(Location().introduce(), if_then, construct_string);

      TypeInst* ti_fi = new TypeInst(Location().introduce(), Type::parstring());
      std::vector<VarDecl*> fi_params(3);
      fi_params[0] = vd_aa;
      fi_params[1] = vd_ab;
      fi_params[2] = vd_aj;
      FunctionI* fi =
          new FunctionI(Location().introduce(), createEnumToStringName(ident, "_toString_"), ti_fi,
                        fi_params, ite);
      enumItems->addItem(fi);
    }
  }

  {
    /*

     function _toString_ENUM(array[$U] of opt Foo: x, bool: b, bool: json) =
       let {
         array[int] of opt ENUM: xx = array1d(x)
       } in "[" ++ join(", ", [ _toString_ENUM(xx[i],b,json) | i in index_set(xx) ]) ++ "]";

     */

    TIId* tiid = new TIId(Location().introduce(), "U");
    TypeInst* ti_range = new TypeInst(Location().introduce(), Type::parint(), tiid);
    std::vector<TypeInst*> ranges(1);
    ranges[0] = ti_range;

    Type tx = Type::parint(-1);
    tx.ot(Type::OT_OPTIONAL);
    TypeInst* x_ti = new TypeInst(Location().introduce(), tx, ranges, ident);
    VarDecl* vd_x = new VarDecl(Location().introduce(), x_ti, "x");
    vd_x->toplevel(false);

    TypeInst* b_ti = new TypeInst(Location().introduce(), Type::parbool());
    VarDecl* vd_b = new VarDecl(Location().introduce(), b_ti, "b");
    vd_b->toplevel(false);

    TypeInst* j_ti = new TypeInst(Location().introduce(), Type::parbool());
    VarDecl* vd_j = new VarDecl(Location().introduce(), j_ti, "json");
    vd_j->toplevel(false);

    TypeInst* xx_range = new TypeInst(Location().introduce(), Type::parint(), NULL);
    std::vector<TypeInst*> xx_ranges(1);
    xx_ranges[0] = xx_range;
    TypeInst* xx_ti = new TypeInst(Location().introduce(), tx, xx_ranges, ident);

    std::vector<Expression*> array1dArgs(1);
    array1dArgs[0] = vd_x->id();
    Call* array1dCall = new Call(Location().introduce(), "array1d", array1dArgs);

    VarDecl* vd_xx = new VarDecl(Location().introduce(), xx_ti, "xx", array1dCall);
    vd_xx->toplevel(false);

    TypeInst* idx_i_ti = new TypeInst(Location().introduce(), Type::parint());
    VarDecl* idx_i = new VarDecl(Location().introduce(), idx_i_ti, "i");
    idx_i->toplevel(false);

    std::vector<Expression*> aa_xxi_idx(1);
    aa_xxi_idx[0] = idx_i->id();
    ArrayAccess* aa_xxi = new ArrayAccess(Location().introduce(), vd_xx->id(), aa_xxi_idx);

    std::vector<Expression*> _toString_ENUMArgs(3);
    _toString_ENUMArgs[0] = aa_xxi;
    _toString_ENUMArgs[1] = vd_b->id();
    _toString_ENUMArgs[2] = vd_j->id();
    Call* _toString_ENUM = new Call(
        Location().introduce(), createEnumToStringName(ident, "_toString_"), _toString_ENUMArgs);

    std::vector<Expression*> index_set_xx_args(1);
    index_set_xx_args[0] = vd_xx->id();
    Call* index_set_xx = new Call(Location().introduce(), "index_set", index_set_xx_args);
    std::vector<VarDecl*> gen_exps(1);
    gen_exps[0] = idx_i;
    Generator gen(gen_exps, index_set_xx, NULL);

    Generators generators;
    generators._g.push_back(gen);
    Comprehension* comp =
        new Comprehension(Location().introduce(), _toString_ENUM, generators, false);

    std::vector<Expression*> join_args(2);
    join_args[0] = new StringLit(Location().introduce(), ", ");
    join_args[1] = comp;
    Call* join = new Call(Location().introduce(), "join", join_args);

    StringLit* sl_open = new StringLit(Location().introduce(), "[");
    BinOp* bopp0 = new BinOp(Location().introduce(), sl_open, BOT_PLUSPLUS, join);
    StringLit* sl_close = new StringLit(Location().introduce(), "]");
    BinOp* bopp1 = new BinOp(Location().introduce(), bopp0, BOT_PLUSPLUS, sl_close);

    std::vector<Expression*> let_args(1);
    let_args[0] = vd_xx;
    Let* let = new Let(Location().introduce(), let_args, bopp1);

    TypeInst* ti_fi = new TypeInst(Location().introduce(), Type::parstring());
    std::vector<VarDecl*> fi_params(3);
    fi_params[0] = vd_x;
    fi_params[1] = vd_b;
    fi_params[2] = vd_j;
    FunctionI* fi = new FunctionI(
        Location().introduce(), createEnumToStringName(ident, "_toString_"), ti_fi, fi_params, let);
    enumItems->addItem(fi);
  }

  {
    /*

     function _toString_ENUM(opt set of ENUM: x, bool: b, bool: json) =
       if absent(x) then "<>" else "{" ++ join(", ", [ _toString_ENUM(i,b,json) | i in x ]) ++ "}"
     endif;

     */

    Type argType = Type::parsetenum(ident->type().enumId());
    argType.ot(Type::OT_OPTIONAL);
    TypeInst* x_ti = new TypeInst(Location().introduce(), argType, ident);
    VarDecl* vd_x = new VarDecl(Location().introduce(), x_ti, "x");
    vd_x->toplevel(false);

    TypeInst* b_ti = new TypeInst(Location().introduce(), Type::parbool());
    VarDecl* vd_b = new VarDecl(Location().introduce(), b_ti, "b");
    vd_b->toplevel(false);

    TypeInst* j_ti = new TypeInst(Location().introduce(), Type::parbool());
    VarDecl* vd_j = new VarDecl(Location().introduce(), j_ti, "json");
    vd_j->toplevel(false);

    TypeInst* idx_i_ti = new TypeInst(Location().introduce(), Type::parint());
    VarDecl* idx_i = new VarDecl(Location().introduce(), idx_i_ti, "i");
    idx_i->toplevel(false);

    std::vector<Expression*> _toString_ENUMArgs(3);
    _toString_ENUMArgs[0] = idx_i->id();
    _toString_ENUMArgs[1] = vd_b->id();
    _toString_ENUMArgs[2] = vd_j->id();
    Call* _toString_ENUM = new Call(
        Location().introduce(), createEnumToStringName(ident, "_toString_"), _toString_ENUMArgs);

    std::vector<Expression*> deopt_args(1);
    deopt_args[0] = vd_x->id();
    Call* deopt = new Call(Location().introduce(), "deopt", deopt_args);
    Call* if_absent = new Call(Location().introduce(), "absent", deopt_args);
    StringLit* sl_absent_dzn = new StringLit(Location().introduce(), "<>");
    ITE* sl_absent = new ITE(Location().introduce(),
                             {vd_j->id(), new StringLit(Location().introduce(), ASTString("null"))},
                             sl_absent_dzn);

    std::vector<VarDecl*> gen_exps(1);
    gen_exps[0] = idx_i;
    Generator gen(gen_exps, deopt, NULL);

    Generators generators;
    generators._g.push_back(gen);
    Comprehension* comp =
        new Comprehension(Location().introduce(), _toString_ENUM, generators, false);

    std::vector<Expression*> join_args(2);
    join_args[0] = new StringLit(Location().introduce(), ", ");
    join_args[1] = comp;
    Call* join = new Call(Location().introduce(), "join", join_args);

    ITE* json_set =
        new ITE(Location().introduce(),
                {vd_j->id(), new StringLit(Location().introduce(), ASTString("\"set\":["))},
                new StringLit(Location().introduce(), ASTString("")));
    ITE* json_set_close = new ITE(
        Location().introduce(), {vd_j->id(), new StringLit(Location().introduce(), ASTString("]"))},
        new StringLit(Location().introduce(), ASTString("")));

    StringLit* sl_open = new StringLit(Location().introduce(), "{");
    BinOp* bopp0 = new BinOp(Location().introduce(), sl_open, BOT_PLUSPLUS, json_set);
    BinOp* bopp1 = new BinOp(Location().introduce(), bopp0, BOT_PLUSPLUS, join);
    BinOp* bopp2 = new BinOp(Location().introduce(), bopp1, BOT_PLUSPLUS, json_set_close);
    StringLit* sl_close = new StringLit(Location().introduce(), "}");
    BinOp* bopp3 = new BinOp(Location().introduce(), bopp2, BOT_PLUSPLUS, sl_close);

    std::vector<Expression*> if_then(2);
    if_then[0] = if_absent;
    if_then[1] = sl_absent;
    ITE* ite = new ITE(Location().introduce(), if_then, bopp3);

    TypeInst* ti_fi = new TypeInst(Location().introduce(), Type::parstring());
    std::vector<VarDecl*> fi_params(3);
    fi_params[0] = vd_x;
    fi_params[1] = vd_b;
    fi_params[2] = vd_j;
    FunctionI* fi = new FunctionI(
        Location().introduce(), createEnumToStringName(ident, "_toString_"), ti_fi, fi_params, ite);
    enumItems->addItem(fi);
  }

  {
    /*

     function _toString_ENUM(array[$U] of opt set of ENUM: x, bool: b, bool: json) =
     let {
     array[int] of opt set of ENUM: xx = array1d(x)
     } in "[" ++ join(", ", [ _toString_ENUM(xx[i],b,json) | i in index_set(xx) ]) ++ "]";

     */

    TIId* tiid = new TIId(Location().introduce(), "U");
    TypeInst* ti_range = new TypeInst(Location().introduce(), Type::parint(), tiid);
    std::vector<TypeInst*> ranges(1);
    ranges[0] = ti_range;

    Type tx = Type::parsetint(-1);
    tx.ot(Type::OT_OPTIONAL);
    TypeInst* x_ti = new TypeInst(Location().introduce(), tx, ranges, ident);
    VarDecl* vd_x = new VarDecl(Location().introduce(), x_ti, "x");
    vd_x->toplevel(false);

    TypeInst* b_ti = new TypeInst(Location().introduce(), Type::parbool());
    VarDecl* vd_b = new VarDecl(Location().introduce(), b_ti, "b");
    vd_b->toplevel(false);

    TypeInst* j_ti = new TypeInst(Location().introduce(), Type::parbool());
    VarDecl* vd_j = new VarDecl(Location().introduce(), j_ti, "json");
    vd_j->toplevel(false);

    TypeInst* xx_range = new TypeInst(Location().introduce(), Type::parint(), NULL);
    std::vector<TypeInst*> xx_ranges(1);
    xx_ranges[0] = xx_range;
    TypeInst* xx_ti = new TypeInst(Location().introduce(), tx, xx_ranges, ident);

    std::vector<Expression*> array1dArgs(1);
    array1dArgs[0] = vd_x->id();
    Call* array1dCall = new Call(Location().introduce(), "array1d", array1dArgs);

    VarDecl* vd_xx = new VarDecl(Location().introduce(), xx_ti, "xx", array1dCall);
    vd_xx->toplevel(false);

    TypeInst* idx_i_ti = new TypeInst(Location().introduce(), Type::parint());
    VarDecl* idx_i = new VarDecl(Location().introduce(), idx_i_ti, "i");
    idx_i->toplevel(false);

    std::vector<Expression*> aa_xxi_idx(1);
    aa_xxi_idx[0] = idx_i->id();
    ArrayAccess* aa_xxi = new ArrayAccess(Location().introduce(), vd_xx->id(), aa_xxi_idx);

    std::vector<Expression*> _toString_ENUMArgs(3);
    _toString_ENUMArgs[0] = aa_xxi;
    _toString_ENUMArgs[1] = vd_b->id();
    _toString_ENUMArgs[2] = vd_j->id();
    Call* _toString_ENUM = new Call(
        Location().introduce(), createEnumToStringName(ident, "_toString_"), _toString_ENUMArgs);

    std::vector<Expression*> index_set_xx_args(1);
    index_set_xx_args[0] = vd_xx->id();
    Call* index_set_xx = new Call(Location().introduce(), "index_set", index_set_xx_args);
    std::vector<VarDecl*> gen_exps(1);
    gen_exps[0] = idx_i;
    Generator gen(gen_exps, index_set_xx, NULL);

    Generators generators;
    generators._g.push_back(gen);
    Comprehension* comp =
        new Comprehension(Location().introduce(), _toString_ENUM, generators, false);

    std::vector<Expression*> join_args(2);
    join_args[0] = new StringLit(Location().introduce(), ", ");
    join_args[1] = comp;
    Call* join = new Call(Location().introduce(), "join", join_args);

    StringLit* sl_open = new StringLit(Location().introduce(), "[");
    BinOp* bopp0 = new BinOp(Location().introduce(), sl_open, BOT_PLUSPLUS, join);
    StringLit* sl_close = new StringLit(Location().introduce(), "]");
    BinOp* bopp1 = new BinOp(Location().introduce(), bopp0, BOT_PLUSPLUS, sl_close);

    std::vector<Expression*> let_args(1);
    let_args[0] = vd_xx;
    Let* let = new Let(Location().introduce(), let_args, bopp1);

    TypeInst* ti_fi = new TypeInst(Location().introduce(), Type::parstring());
    std::vector<VarDecl*> fi_params(3);
    fi_params[0] = vd_x;
    fi_params[1] = vd_b;
    fi_params[2] = vd_j;
    FunctionI* fi = new FunctionI(
        Location().introduce(), createEnumToStringName(ident, "_toString_"), ti_fi, fi_params, let);
    enumItems->addItem(fi);
  }
  return ret;
}

void TopoSorter::add(EnvI& env, VarDeclI* vdi, bool handleEnums, Model* enumItems) {
  VarDecl* vd = vdi->e();
  if (handleEnums && vd->ti()->isEnum()) {
    unsigned int enumId = env.registerEnum(vdi);
    Type vdt = vd->type();
    vdt.enumId(enumId);
    vd->ti()->type(vdt);
    vd->type(vdt);

    if (vd->e()) {
      (void)createEnumMapper(env, model, enumId, vd, NULL, enumItems);
    } else {
      GCLock lock;
      std::string name = createEnumToStringName(vd->id(), "_enum_to_string_");
      std::vector<TypeInst*> ranges(1);
      ranges[0] = new TypeInst(Location().introduce(), Type::parint());
      TypeInst* ti = new TypeInst(Location().introduce(), Type::parstring(1));
      ti->setRanges(ranges);
      VarDecl* vd_enumToString = new VarDecl(Location().introduce(), ti, name, NULL);
      enumItems->addItem(new VarDeclI(Location().introduce(), vd_enumToString));
    }
  }
  scopes.add(env, vd);
}

VarDecl* TopoSorter::get(EnvI& env, const ASTString& id_v, const Location& loc) {
  GCLock lock;
  Id* id = new Id(Location(), id_v, NULL);
  VarDecl* decl = scopes.find(id);
  if (decl == NULL) {
    throw TypeError(env, loc, "undefined identifier `" + id->str().str() + "'");
  }
  return decl;
}

VarDecl* TopoSorter::checkId(EnvI& env, Id* ident, const Location& loc) {
  VarDecl* decl = scopes.find(ident);
  if (decl == NULL) {
    GCLock lock;
    throw TypeError(env, loc, "undefined identifier `" + ident->str().str() + "'");
  }
  PosMap::iterator pi = pos.find(decl);
  if (pi == pos.end()) {
    // new id
    scopes.push(true);
    run(env, decl);
    scopes.pop();
  } else {
    // previously seen, check if circular
    if (pi->second == -1) {
      GCLock lock;
      throw TypeError(env, loc, "circular definition of `" + ident->str().str() + "'");
    }
  }
  return decl;
}

VarDecl* TopoSorter::checkId(EnvI& env, const ASTString& id_v, const Location& loc) {
  GCLock lock;
  Id* id = new Id(loc, id_v, NULL);
  return checkId(env, id, loc);
}

void TopoSorter::run(EnvI& env, Expression* e) {
  if (e == NULL) return;
  switch (e->eid()) {
    case Expression::E_INTLIT:
    case Expression::E_FLOATLIT:
    case Expression::E_BOOLLIT:
    case Expression::E_STRINGLIT:
    case Expression::E_ANON:
      break;
    case Expression::E_SETLIT: {
      SetLit* sl = e->cast<SetLit>();
      if (sl->isv() == NULL && sl->fsv() == NULL)
        for (unsigned int i = 0; i < sl->v().size(); i++) run(env, sl->v()[i]);
    } break;
    case Expression::E_ID: {
      if (e != constants().absent) {
        VarDecl* vd = checkId(env, e->cast<Id>(), e->loc());
        e->cast<Id>()->decl(vd);
      }
    } break;
    case Expression::E_ARRAYLIT: {
      ArrayLit* al = e->cast<ArrayLit>();
      for (unsigned int i = 0; i < al->size(); i++) run(env, (*al)[i]);
    } break;
    case Expression::E_ARRAYACCESS: {
      ArrayAccess* ae = e->cast<ArrayAccess>();
      run(env, ae->v());
      for (unsigned int i = 0; i < ae->idx().size(); i++) run(env, ae->idx()[i]);
    } break;
    case Expression::E_COMP: {
      Comprehension* ce = e->cast<Comprehension>();
      scopes.push(false);
      for (int i = 0; i < ce->n_generators(); i++) {
        run(env, ce->in(i));
        for (int j = 0; j < ce->n_decls(i); j++) {
          run(env, ce->decl(i, j));
          scopes.add(env, ce->decl(i, j));
        }
        if (ce->where(i)) run(env, ce->where(i));
      }
      run(env, ce->e());
      scopes.pop();
    } break;
    case Expression::E_ITE: {
      ITE* ite = e->cast<ITE>();
      for (int i = 0; i < ite->size(); i++) {
        run(env, ite->e_if(i));
        run(env, ite->e_then(i));
      }
      run(env, ite->e_else());
    } break;
    case Expression::E_BINOP: {
      BinOp* be = e->cast<BinOp>();
      std::vector<Expression*> todo;
      todo.push_back(be->lhs());
      todo.push_back(be->rhs());
      while (!todo.empty()) {
        Expression* e = todo.back();
        todo.pop_back();
        if (BinOp* e_bo = e->dyn_cast<BinOp>()) {
          todo.push_back(e_bo->lhs());
          todo.push_back(e_bo->rhs());
          for (ExpressionSetIter it = e_bo->ann().begin(); it != e_bo->ann().end(); ++it)
            run(env, *it);
        } else {
          run(env, e);
        }
      }
    } break;
    case Expression::E_UNOP: {
      UnOp* ue = e->cast<UnOp>();
      run(env, ue->e());
    } break;
    case Expression::E_CALL: {
      Call* ce = e->cast<Call>();
      for (unsigned int i = 0; i < ce->n_args(); i++) run(env, ce->arg(i));
    } break;
    case Expression::E_VARDECL: {
      VarDecl* ve = e->cast<VarDecl>();
      PosMap::iterator pi = pos.find(ve);
      if (pi == pos.end()) {
        pos.insert(std::pair<VarDecl*, int>(ve, -1));
        run(env, ve->ti());
        run(env, ve->e());
        ve->payload(static_cast<int>(decls.size()));
        decls.push_back(ve);
        pi = pos.find(ve);
        pi->second = static_cast<int>(decls.size()) - 1;
      } else {
        assert(pi->second != -1);
      }
    } break;
    case Expression::E_TI: {
      TypeInst* ti = e->cast<TypeInst>();
      for (unsigned int i = 0; i < ti->ranges().size(); i++) run(env, ti->ranges()[i]);
      run(env, ti->domain());
    } break;
    case Expression::E_TIID:
      break;
    case Expression::E_LET: {
      Let* let = e->cast<Let>();
      scopes.push(false);
      for (unsigned int i = 0; i < let->let().size(); i++) {
        run(env, let->let()[i]);
        if (VarDecl* vd = let->let()[i]->dyn_cast<VarDecl>()) {
          scopes.add(env, vd);
        }
      }
      run(env, let->in());
      VarDeclCmp poscmp(pos);
      std::stable_sort(let->let().begin(), let->let().end(), poscmp);
      for (unsigned int i = 0; i < let->let().size(); i++) {
        if (VarDecl* vd = let->let()[i]->dyn_cast<VarDecl>()) {
          let->let_orig()[i] = vd->e();
        } else {
          let->let_orig()[i] = NULL;
        }
      }
      scopes.pop();
    } break;
  }
  if (env.ignoreUnknownIds) {
    std::vector<Expression*> toDelete;
    for (ExpressionSetIter it = e->ann().begin(); it != e->ann().end(); ++it) {
      try {
        run(env, *it);
      } catch (TypeError&) {
        toDelete.push_back(*it);
      }
      for (Expression* de : toDelete) e->ann().remove(de);
    }
  } else {
    for (ExpressionSetIter it = e->ann().begin(); it != e->ann().end(); ++it) {
      run(env, *it);
    }
  }
}

KeepAlive addCoercion(EnvI& env, Model* m, Expression* e, const Type& funarg_t) {
  if (e->isa<ArrayAccess>() && e->type().dim() > 0) {
    ArrayAccess* aa = e->cast<ArrayAccess>();
    // Turn ArrayAccess into a slicing operation
    std::vector<Expression*> slice;
    slice.reserve(aa->idx().size());
    std::vector<Expression*> ndims;
    GCLock lock;
    for (unsigned int i = 0; i < aa->idx().size(); i++) {
      if (aa->idx()[i]->type().is_set()) {
        bool needIdxSet = true;
        bool needInter = true;
        if (SetLit* sl = aa->idx()[i]->dyn_cast<SetLit>()) {
          if (sl->isv() && sl->isv()->size() == 1) {
            if (sl->isv()->min().isFinite() && sl->isv()->max().isFinite()) {
              ndims.push_back(sl);
              needIdxSet = false;
            } else if (sl->isv()->min() == -IntVal::infinity() &&
                       sl->isv()->max() == IntVal::infinity()) {
              needInter = false;
            }
          }
        }
        if (needIdxSet) {
          std::ostringstream oss;
          oss << "index_set";
          if (aa->idx().size() > 1) {
            oss << "_" << (i + 1) << "of" << aa->idx().size();
          }
          std::vector<Expression*> origIdxsetArgs(1);
          origIdxsetArgs[0] = aa->v();
          Call* origIdxset = new Call(aa->v()->loc(), ASTString(oss.str()), origIdxsetArgs);
          FunctionI* fi = m->matchFn(env, origIdxset, false);
          if (!fi) throw TypeError(env, e->loc(), "missing builtin " + oss.str());
          origIdxset->type(fi->rtype(env, origIdxsetArgs, false));
          origIdxset->decl(fi);
          if (needInter) {
            BinOp* inter = new BinOp(aa->idx()[i]->loc(), aa->idx()[i], BOT_INTERSECT, origIdxset);
            inter->type(Type::parsetint());
            ndims.push_back(inter);
          } else {
            ndims.push_back(origIdxset);
          }
        }
        slice.push_back(aa->idx()[i]);
      } else {
        BinOp* bo = new BinOp(aa->idx()[i]->loc(), aa->idx()[i], BOT_DOTDOT, aa->idx()[i]);
        bo->type(Type::parsetint());
        slice.push_back(bo);
      }
    }
    ArrayLit* a_slice = new ArrayLit(e->loc().introduce(), slice);
    a_slice->type(Type::parsetint(1));
    ArrayLit* a_ndims = new ArrayLit(e->loc().introduce(), ndims);
    a_ndims->type(Type::parsetint(1));
    std::vector<Expression*> args = {aa->v(), a_slice, a_ndims};
    Call* c = new Call(e->loc(), ASTString("slice_Xd"), args);
    FunctionI* fi = m->matchFn(env, c, false);
    if (!fi) throw TypeError(env, e->loc(), "missing builtin slice_Xd");
    c->type(fi->rtype(env, args, false));
    c->decl(fi);
    e = c;
  }
  if (e->type().dim() == funarg_t.dim() &&
      (funarg_t.bt() == Type::BT_BOT || funarg_t.bt() == Type::BT_TOP ||
       e->type().bt() == funarg_t.bt() || e->type().bt() == Type::BT_BOT))
    return e;
  std::vector<Expression*> args(1);
  args[0] = e;
  GCLock lock;
  Call* c = NULL;
  if (e->type().dim() == 0 && funarg_t.dim() != 0) {
    if (e->type().isvar()) {
      throw TypeError(env, e->loc(), "cannot coerce var set into array");
    }
    if (e->type().isopt()) {
      throw TypeError(env, e->loc(), "cannot coerce opt set into array");
    }
    std::vector<Expression*> set2a_args(1);
    set2a_args[0] = e;
    Call* set2a = new Call(e->loc(), ASTString("set2array"), set2a_args);
    FunctionI* fi = m->matchFn(env, set2a, false);
    if (fi) {
      set2a->type(fi->rtype(env, args, false));
      set2a->decl(fi);
      e = set2a;
    }
  }
  if (funarg_t.bt() == Type::BT_TOP || e->type().bt() == funarg_t.bt() ||
      e->type().bt() == Type::BT_BOT) {
    KeepAlive ka(e);
    return ka;
  }
  if (e->type().bt() == Type::BT_BOOL) {
    if (funarg_t.bt() == Type::BT_INT) {
      c = new Call(e->loc(), constants().ids.bool2int, args);
    } else if (funarg_t.bt() == Type::BT_FLOAT) {
      c = new Call(e->loc(), constants().ids.bool2float, args);
    }
  } else if (e->type().bt() == Type::BT_INT) {
    if (funarg_t.bt() == Type::BT_FLOAT) {
      c = new Call(e->loc(), constants().ids.int2float, args);
    }
  }
  if (c) {
    FunctionI* fi = m->matchFn(env, c, false);
    assert(fi);
    c->type(fi->rtype(env, args, false));
    c->decl(fi);
    KeepAlive ka(c);
    return ka;
  }
  throw TypeError(env, e->loc(),
                  "cannot determine coercion from type " + e->type().toString(env) + " to type " +
                      funarg_t.toString(env));
}
KeepAlive addCoercion(EnvI& env, Model* m, Expression* e, Expression* funarg) {
  return addCoercion(env, m, e, funarg->type());
}

template <bool ignoreVarDecl>
class Typer {
public:
  EnvI& _env;
  Model* _model;
  std::vector<TypeError>& _typeErrors;
  bool _ignoreUndefined;
  Typer(EnvI& env, Model* model, std::vector<TypeError>& typeErrors, bool ignoreUndefined)
      : _env(env), _model(model), _typeErrors(typeErrors), _ignoreUndefined(ignoreUndefined) {}
  /// Check annotations when expression is finished
  void exit(Expression* e) {
    for (ExpressionSetIter it = e->ann().begin(); it != e->ann().end(); ++it)
      if (!(*it)->type().isann())
        throw TypeError(_env, (*it)->loc(),
                        "expected annotation, got `" + (*it)->type().toString(_env) + "'");
  }
  bool enter(Expression*) { return true; }
  /// Visit integer literal
  void vIntLit(const IntLit&) {}
  /// Visit floating point literal
  void vFloatLit(const FloatLit&) {}
  /// Visit Boolean literal
  void vBoolLit(const BoolLit&) {}
  /// Visit set literal
  void vSetLit(SetLit& sl) {
    Type ty;
    ty.st(Type::ST_SET);
    if (sl.isv()) {
      ty.bt(Type::BT_INT);
      ty.enumId(sl.type().enumId());
      sl.type(ty);
      return;
    }
    unsigned int enumId = sl.v().size() > 0 ? sl.v()[0]->type().enumId() : 0;
    for (unsigned int i = 0; i < sl.v().size(); i++) {
      if (sl.v()[i]->type().dim() > 0)
        throw TypeError(_env, sl.v()[i]->loc(), "set literals cannot contain arrays");
      if (sl.v()[i]->type().isvar()) ty.ti(Type::TI_VAR);
      if (sl.v()[i]->type().isopt())
        throw TypeError(_env, sl.v()[i]->loc(), "set literals cannot contain option type values");
      if (sl.v()[i]->type().cv()) ty.cv(true);
      if (enumId != sl.v()[i]->type().enumId()) enumId = 0;
      if (!Type::bt_subtype(sl.v()[i]->type(), ty, true)) {
        if (ty.bt() == Type::BT_UNKNOWN || Type::bt_subtype(ty, sl.v()[i]->type(), true)) {
          ty.bt(sl.v()[i]->type().bt());
        } else {
          throw TypeError(_env, sl.loc(), "non-uniform set literal");
        }
      }
    }
    ty.enumId(enumId);
    if (ty.bt() == Type::BT_UNKNOWN) {
      ty.bt(Type::BT_BOT);
    } else {
      if (ty.isvar() && ty.bt() != Type::BT_INT) {
        if (ty.bt() == Type::BT_BOOL)
          ty.bt(Type::BT_INT);
        else
          throw TypeError(_env, sl.loc(), "cannot coerce set literal element to var int");
      }
      for (unsigned int i = 0; i < sl.v().size(); i++) {
        sl.v()[i] = addCoercion(_env, _model, sl.v()[i], ty)();
      }
    }
    sl.type(ty);
  }
  /// Visit string literal
  void vStringLit(const StringLit&) {}
  /// Visit identifier
  void vId(Id& id) {
    if (&id != constants().absent) {
      assert(!id.decl()->type().isunknown());
      id.type(id.decl()->type());
    }
  }
  /// Visit anonymous variable
  void vAnonVar(const AnonVar&) {}
  /// Visit array literal
  void vArrayLit(ArrayLit& al) {
    Type ty;
    ty.dim(al.dims());
    std::vector<AnonVar*> anons;
    bool haveAbsents = false;
    bool haveInferredType = false;
    for (unsigned int i = 0; i < al.size(); i++) {
      Expression* vi = al[i];
      if (vi->type().dim() > 0)
        throw TypeError(_env, vi->loc(), "arrays cannot be elements of arrays");
      if (vi == constants().absent) haveAbsents = true;
      AnonVar* av = vi->dyn_cast<AnonVar>();
      if (av) {
        ty.ti(Type::TI_VAR);
        anons.push_back(av);
      } else if (vi->type().isvar()) {
        ty.ti(Type::TI_VAR);
      }
      if (vi->type().cv()) ty.cv(true);
      if (vi->type().isopt()) {
        ty.ot(Type::OT_OPTIONAL);
      }

      if (ty.bt() == Type::BT_UNKNOWN) {
        if (av == NULL) {
          if (haveInferredType) {
            if (ty.st() != vi->type().st() && vi->type().ot() != Type::OT_OPTIONAL) {
              throw TypeError(_env, al.loc(), "non-uniform array literal");
            }
          } else {
            haveInferredType = true;
            ty.st(vi->type().st());
          }
          if (vi->type().bt() != Type::BT_BOT) {
            ty.bt(vi->type().bt());
            ty.enumId(vi->type().enumId());
          }
        }
      } else {
        if (av == NULL) {
          if (vi->type().bt() == Type::BT_BOT) {
            if (vi->type().st() != ty.st() && vi->type().ot() != Type::OT_OPTIONAL) {
              throw TypeError(_env, al.loc(), "non-uniform array literal");
            }
            if (vi->type().enumId() != 0 && ty.enumId() != vi->type().enumId()) {
              ty.enumId(0);
            }
          } else {
            unsigned int tyEnumId = ty.enumId();
            ty.enumId(vi->type().enumId());
            if (Type::bt_subtype(ty, vi->type(), true)) {
              ty.bt(vi->type().bt());
            }
            if (tyEnumId != vi->type().enumId()) ty.enumId(0);
            if (!Type::bt_subtype(vi->type(), ty, true) || ty.st() != vi->type().st()) {
              throw TypeError(_env, al.loc(), "non-uniform array literal");
            }
          }
        }
      }
    }
    if (ty.bt() == Type::BT_UNKNOWN) {
      ty.bt(Type::BT_BOT);
      if (!anons.empty())
        throw TypeError(_env, al.loc(),
                        "array literal must contain at least one non-anonymous variable");
      if (haveAbsents)
        throw TypeError(_env, al.loc(), "array literal must contain at least one non-absent value");
    } else {
      Type at = ty;
      at.dim(0);
      if (at.ti() == Type::TI_VAR && at.st() == Type::ST_SET && at.bt() != Type::BT_INT) {
        if (at.bt() == Type::BT_BOOL) {
          ty.bt(Type::BT_INT);
          at.bt(Type::BT_INT);
        } else {
          throw TypeError(_env, al.loc(), "cannot coerce array element to var set of int");
        }
      }
      for (unsigned int i = 0; i < anons.size(); i++) {
        anons[i]->type(at);
      }
      for (unsigned int i = 0; i < al.size(); i++) {
        al.set(i, addCoercion(_env, _model, al[i], at)());
      }
    }
    if (ty.enumId() != 0) {
      std::vector<unsigned int> enumIds(ty.dim() + 1);
      for (int i = 0; i < ty.dim(); i++) enumIds[i] = 0;
      enumIds[ty.dim()] = ty.enumId();
      ty.enumId(_env.registerArrayEnum(enumIds));
    }
    al.type(ty);
  }
  /// Visit array access
  void vArrayAccess(ArrayAccess& aa) {
    if (aa.v()->type().dim() == 0) {
      if (aa.v()->type().st() == Type::ST_SET) {
        Type tv = aa.v()->type();
        tv.st(Type::ST_PLAIN);
        tv.dim(1);
        aa.v(addCoercion(_env, _model, aa.v(), tv)());
      } else {
        std::ostringstream oss;
        oss << "array access attempted on expression of type `" << aa.v()->type().toString(_env)
            << "'";
        throw TypeError(_env, aa.v()->loc(), oss.str());
      }
    } else if (aa.v()->isa<ArrayAccess>()) {
      aa.v(addCoercion(_env, _model, aa.v(), aa.v()->type())());
    }
    if (aa.v()->type().dim() != aa.idx().size()) {
      std::ostringstream oss;
      oss << aa.v()->type().dim() << "-dimensional array accessed with " << aa.idx().size()
          << (aa.idx().size() == 1 ? " expression" : " expressions");
      throw TypeError(_env, aa.v()->loc(), oss.str());
    }
    Type tt = aa.v()->type();
    if (tt.enumId() != 0) {
      const std::vector<unsigned int>& arrayEnumIds = _env.getArrayEnum(tt.enumId());

      for (unsigned int i = 0; i < arrayEnumIds.size() - 1; i++) {
        Expression* aai = aa.idx()[i];
        // Check if index is slice operator, and convert to correct enum type
        if (SetLit* aai_sl = aai->dyn_cast<SetLit>()) {
          if (IntSetVal* aai_isv = aai_sl->isv()) {
            if (aai_isv->min() == -IntVal::infinity() && aai_isv->max() == IntVal::infinity()) {
              Type aai_sl_t = aai_sl->type();
              aai_sl_t.enumId(arrayEnumIds[i]);
              aai_sl->type(aai_sl_t);
            }
          }
        } else if (BinOp* aai_bo = aai->dyn_cast<BinOp>()) {
          if (aai_bo->op() == BOT_DOTDOT) {
            Type aai_bo_t = aai_bo->type();
            if (IntLit* il = aai_bo->lhs()->dyn_cast<IntLit>()) {
              if (il->v() == -IntVal::infinity()) {
                // Expression is ..X, so result gets enum type of X
                aai_bo_t.enumId(aai_bo->rhs()->type().enumId());
              }
            } else if (IntLit* il = aai_bo->rhs()->dyn_cast<IntLit>()) {
              if (il->v() == IntVal::infinity()) {
                // Expression is X.., so result gets enum type of X
                aai_bo_t.enumId(aai_bo->lhs()->type().enumId());
              }
            }
            aai_bo->type(aai_bo_t);
          }
        }

        if (arrayEnumIds[i] != 0) {
          if (aa.idx()[i]->type().enumId() != arrayEnumIds[i]) {
            std::ostringstream oss;
            oss << "array index ";
            if (aa.idx().size() > 1) {
              oss << (i + 1) << " ";
            }
            oss << "must be `" << _env.getEnum(arrayEnumIds[i])->e()->id()->str().str()
                << "', but is `" << aa.idx()[i]->type().toString(_env) << "'";
            throw TypeError(_env, aa.loc(), oss.str());
          }
        }
      }
      tt.enumId(arrayEnumIds[arrayEnumIds.size() - 1]);
    }
    int n_dimensions = 0;
    bool isVarAccess = false;
    bool isSlice = false;
    for (unsigned int i = 0; i < aa.idx().size(); i++) {
      Expression* aai = aa.idx()[i];
      if (aai->isa<AnonVar>()) {
        aai->type(Type::varint());
      }
      if ((aai->type().bt() != Type::BT_INT && aai->type().bt() != Type::BT_BOOL) ||
          aai->type().dim() != 0) {
        throw TypeError(_env, aa.loc(),
                        "array index must be `int' or `set of int', but is `" +
                            aai->type().toString(_env) + "'");
      }
      if (aai->type().is_set()) {
        if (isVarAccess || aai->type().isvar()) {
          throw TypeError(_env, aa.loc(),
                          "array slicing with variable range or index not supported");
        }
        isSlice = true;
        aa.idx()[i] = addCoercion(_env, _model, aai, Type::varsetint())();
        n_dimensions++;
      } else {
        aa.idx()[i] = addCoercion(_env, _model, aai, Type::varint())();
      }

      if (aai->type().isopt()) {
        tt.ot(Type::OT_OPTIONAL);
      }
      if (aai->type().isvar()) {
        isVarAccess = true;
        if (isSlice) {
          throw TypeError(_env, aa.loc(),
                          "array slicing with variable range or index not supported");
        }
        tt.ti(Type::TI_VAR);
        if (tt.bt() == Type::BT_ANN || tt.bt() == Type::BT_STRING) {
          throw TypeError(_env, aai->loc(),
                          std::string("array access using a variable not supported for array of ") +
                              (tt.bt() == Type::BT_ANN ? "ann" : "string"));
        }
      }
      tt.dim(n_dimensions);
      if (aai->type().cv()) tt.cv(true);
    }
    aa.type(tt);
  }
  /// Visit array comprehension
  void vComprehension(Comprehension& c) {
    Type tt = c.e()->type();
    typedef std::unordered_map<VarDecl*, std::pair<int, int> > genMap_t;
    typedef std::unordered_map<VarDecl*, std::vector<Expression*> > whereMap_t;
    genMap_t generatorMap;
    whereMap_t whereMap;
    int declCount = 0;
    bool didMoveWheres = false;
    for (int i = 0; i < c.n_generators(); i++) {
      for (int j = 0; j < c.n_decls(i); j++) {
        generatorMap[c.decl(i, j)] = std::pair<int, int>(i, declCount++);
        whereMap[c.decl(i, j)] = std::vector<Expression*>();
      }
      Expression* g_in = c.in(i);
      if (g_in) {
        const Type& ty_in = g_in->type();
        if (ty_in == Type::varsetint()) {
          tt.ot(Type::OT_OPTIONAL);
          tt.ti(Type::TI_VAR);
          tt.cv(true);
        }
        if (ty_in.cv()) tt.cv(true);
        if (c.where(i)) {
          if (c.where(i)->type() == Type::varbool()) {
            tt.ot(Type::OT_OPTIONAL);
            tt.ti(Type::TI_VAR);
            tt.cv(true);
          } else if (c.where(i)->type() != Type::parbool()) {
            throw TypeError(
                _env, c.where(i)->loc(),
                "where clause must be bool, but is `" + c.where(i)->type().toString(_env) + "'");
          }
          if (c.where(i)->type().cv()) tt.cv(true);

          // Try to move parts of the where clause to earlier generators
          std::vector<Expression*> wherePartsStack;
          std::vector<Expression*> whereParts;
          wherePartsStack.push_back(c.where(i));
          while (!wherePartsStack.empty()) {
            Expression* e = wherePartsStack.back();
            wherePartsStack.pop_back();
            if (BinOp* bo = e->dyn_cast<BinOp>()) {
              if (bo->op() == BOT_AND) {
                wherePartsStack.push_back(bo->rhs());
                wherePartsStack.push_back(bo->lhs());
              } else {
                whereParts.push_back(e);
              }
            } else {
              whereParts.push_back(e);
            }
          }

          for (unsigned int wpi = 0; wpi < whereParts.size(); wpi++) {
            Expression* wp = whereParts[wpi];
            class FindLatestGen : public EVisitor {
            public:
              int decl_idx;
              VarDecl* decl;
              const genMap_t& generatorMap;
              Comprehension* comp;
              FindLatestGen(const genMap_t& generatorMap0, Comprehension* comp0)
                  : decl_idx(-1),
                    decl(comp0->decl(0, 0)),
                    generatorMap(generatorMap0),
                    comp(comp0) {}
              void vId(const Id& ident) {
                genMap_t::const_iterator it = generatorMap.find(ident.decl());
                if (it != generatorMap.end() && it->second.second > decl_idx) {
                  decl_idx = it->second.second;
                  decl = ident.decl();
                  int gen = it->second.first;
                  while (comp->in(gen) == NULL && gen < comp->n_generators() - 1) {
                    decl_idx++;
                    gen++;
                    decl = comp->decl(gen, 0);
                  }
                }
              }
            } flg(generatorMap, &c);
            topDown(flg, wp);
            whereMap[flg.decl].push_back(wp);

            if (flg.decl_idx < declCount - 1) didMoveWheres = true;
          }
        }
      } else {
        assert(c.where(i) != NULL);
        whereMap[c.decl(i, 0)].push_back(c.where(i));
      }
    }

    if (didMoveWheres) {
      Generators generators;
      for (int i = 0; i < c.n_generators(); i++) {
        std::vector<VarDecl*> decls;
        for (int j = 0; j < c.n_decls(i); j++) {
          decls.push_back(c.decl(i, j));
          if (whereMap[c.decl(i, j)].size() != 0) {
            // need a generator for all the decls up to this point
            Expression* whereExpr = whereMap[c.decl(i, j)][0];
            for (unsigned int k = 1; k < whereMap[c.decl(i, j)].size(); k++) {
              GCLock lock;
              BinOp* bo =
                  new BinOp(Location().introduce(), whereExpr, BOT_AND, whereMap[c.decl(i, j)][k]);
              Type bo_t = whereMap[c.decl(i, j)][k]->type().ispar() && whereExpr->type().ispar()
                              ? Type::parbool()
                              : Type::varbool();
              bo->type(bo_t);
              whereExpr = bo;
            }
            generators._g.push_back(Generator(decls, c.in(i), whereExpr));
            decls.clear();
          } else if (j == c.n_decls(i) - 1) {
            generators._g.push_back(Generator(decls, c.in(i), NULL));
            decls.clear();
          }
        }
      }
      GCLock lock;
      c.init(c.e(), generators);
    }

    if (c.set()) {
      if (c.e()->type().dim() != 0 || c.e()->type().st() == Type::ST_SET)
        throw TypeError(_env, c.e()->loc(),
                        "set comprehension expression must be scalar, but is `" +
                            c.e()->type().toString(_env) + "'");
      tt.st(Type::ST_SET);
      if (tt.isvar()) {
        c.e(addCoercion(_env, _model, c.e(), Type::varint())());
        tt.bt(Type::BT_INT);
      }
    } else {
      if (c.e()->type().dim() != 0)
        throw TypeError(_env, c.e()->loc(), "array comprehension expression cannot be an array");
      tt.dim(1);
      if (tt.enumId() != 0) {
        std::vector<unsigned int> enumIds(2);
        enumIds[0] = 0;
        enumIds[1] = tt.enumId();
        tt.enumId(_env.registerArrayEnum(enumIds));
      }
    }
    c.type(tt);
  }
  /// Visit array comprehension generator
  void vComprehensionGenerator(Comprehension& c, int gen_i) {
    Expression* g_in = c.in(gen_i);
    if (g_in == NULL) {
      // This is an "assignment generator" (i = expr)
      assert(c.where(gen_i) != NULL);
      assert(c.n_decls(gen_i) == 1);
      const Type& ty_where = c.where(gen_i)->type();
      c.decl(gen_i, 0)->type(ty_where);
      c.decl(gen_i, 0)->ti()->type(ty_where);
    } else {
      const Type& ty_in = g_in->type();
      if (ty_in != Type::varsetint() && ty_in != Type::parsetint() && ty_in.dim() != 1) {
        throw TypeError(_env, g_in->loc(),
                        "generator expression must be (par or var) set of int or one-dimensional "
                        "array, but is `" +
                            ty_in.toString(_env) + "'");
      }
      Type ty_id;
      bool needIntLit = false;
      if (ty_in.dim() == 0) {
        ty_id = Type::parint();
        ty_id.enumId(ty_in.enumId());
        needIntLit = true;
      } else {
        ty_id = ty_in;
        if (ty_in.enumId() != 0) {
          const std::vector<unsigned int>& enumIds = _env.getArrayEnum(ty_in.enumId());
          ty_id.enumId(enumIds.back());
        }
        ty_id.dim(0);
      }
      for (int j = 0; j < c.n_decls(gen_i); j++) {
        if (needIntLit) {
          GCLock lock;
          c.decl(gen_i, j)->e(IntLit::aEnum(0, ty_id.enumId()));
        }
        c.decl(gen_i, j)->type(ty_id);
        c.decl(gen_i, j)->ti()->type(ty_id);
      }
    }
  }
  /// Visit if-then-else
  void vITE(ITE& ite) {
    bool mustBeBool = false;
    if (ite.e_else() == NULL) {
      // this is an "if <cond> then <expr> endif" so the <expr> must be bool
      ite.e_else(constants().boollit(true));
      mustBeBool = true;
    }
    Type tret = ite.e_else()->type();
    std::vector<AnonVar*> anons;
    bool allpar = !(tret.isvar());
    if (tret.isunknown()) {
      if (AnonVar* av = ite.e_else()->dyn_cast<AnonVar>()) {
        allpar = false;
        anons.push_back(av);
      } else {
        throw TypeError(_env, ite.e_else()->loc(),
                        "cannot infer type of expression in `else' branch of conditional");
      }
    }
    bool allpresent = !(tret.isopt());
    bool varcond = false;
    for (int i = 0; i < ite.size(); i++) {
      Expression* eif = ite.e_if(i);
      Expression* ethen = ite.e_then(i);
      varcond = varcond || (eif->type() == Type::varbool());
      if (eif->type() != Type::parbool() && eif->type() != Type::varbool())
        throw TypeError(
            _env, eif->loc(),
            "expected bool conditional expression, got `" + eif->type().toString(_env) + "'");
      if (eif->type().cv()) tret.cv(true);
      if (ethen->type().isunknown()) {
        if (AnonVar* av = ethen->dyn_cast<AnonVar>()) {
          allpar = false;
          anons.push_back(av);
        } else {
          throw TypeError(_env, ethen->loc(),
                          "cannot infer type of expression in `then' branch of conditional");
        }
      } else {
        if (tret.isbot() || tret.isunknown()) tret.bt(ethen->type().bt());
        if (mustBeBool &&
            (ethen->type().bt() != Type::BT_BOOL || ethen->type().dim() > 0 ||
             ethen->type().st() != Type::ST_PLAIN || ethen->type().ot() != Type::OT_PRESENT)) {
          throw TypeError(_env, ite.loc(),
                          std::string("conditional without `else' branch must have bool type, ") +
                              "but `then' branch has type `" + ethen->type().toString(_env) + "'");
        }
        if ((!ethen->type().isbot() && !Type::bt_subtype(ethen->type(), tret, true) &&
             !Type::bt_subtype(tret, ethen->type(), true)) ||
            ethen->type().st() != tret.st() || ethen->type().dim() != tret.dim()) {
          throw TypeError(_env, ethen->loc(),
                          "type mismatch in branches of conditional. `then' branch has type `" +
                              ethen->type().toString(_env) + "', but `else' branch has type `" +
                              tret.toString(_env) + "'");
        }
        if (Type::bt_subtype(tret, ethen->type(), true)) {
          tret.bt(ethen->type().bt());
        }
        if (ethen->type().isvar()) allpar = false;
        if (ethen->type().isopt()) allpresent = false;
        if (ethen->type().cv()) tret.cv(true);
      }
    }
    Type tret_var(tret);
    tret_var.ti(Type::TI_VAR);
    for (unsigned int i = 0; i < anons.size(); i++) {
      anons[i]->type(tret_var);
    }
    for (int i = 0; i < ite.size(); i++) {
      ite.e_then(i, addCoercion(_env, _model, ite.e_then(i), tret)());
    }
    ite.e_else(addCoercion(_env, _model, ite.e_else(), tret)());
    /// TODO: perhaps extend flattener to array types, but for now throw an error
    if (varcond && tret.dim() > 0)
      throw TypeError(_env, ite.loc(), "conditional with var condition cannot have array type");
    if (varcond || !allpar) tret.ti(Type::TI_VAR);
    if (!allpresent) tret.ot(Type::OT_OPTIONAL);
    ite.type(tret);
  }
  /// Visit binary operator
  void vBinOp(BinOp& bop) {
    std::vector<Expression*> args(2);
    args[0] = bop.lhs();
    args[1] = bop.rhs();
    if (FunctionI* fi = _model->matchFn(_env, bop.opToString(), args, true)) {
      bop.lhs(addCoercion(_env, _model, bop.lhs(), fi->argtype(_env, args, 0))());
      bop.rhs(addCoercion(_env, _model, bop.rhs(), fi->argtype(_env, args, 1))());
      args[0] = bop.lhs();
      args[1] = bop.rhs();
      Type ty = fi->rtype(_env, args, true);
      ty.cv(bop.lhs()->type().cv() || bop.rhs()->type().cv());
      bop.type(ty);

      if (fi->e())
        bop.decl(fi);
      else
        bop.decl(NULL);
    } else {
      throw TypeError(_env, bop.loc(),
                      std::string("type error in operator application for `") +
                          bop.opToString().str() +
                          "'. No matching operator found with left-hand side type `" +
                          bop.lhs()->type().toString(_env) + "' and right-hand side type `" +
                          bop.rhs()->type().toString(_env) + "'");
    }
  }
  /// Visit unary operator
  void vUnOp(UnOp& uop) {
    std::vector<Expression*> args(1);
    args[0] = uop.e();
    if (FunctionI* fi = _model->matchFn(_env, uop.opToString(), args, true)) {
      uop.e(addCoercion(_env, _model, uop.e(), fi->argtype(_env, args, 0))());
      args[0] = uop.e();
      Type ty = fi->rtype(_env, args, true);
      ty.cv(uop.e()->type().cv());
      uop.type(ty);
      if (fi->e()) uop.decl(fi);
    } else {
      throw TypeError(_env, uop.loc(),
                      std::string("type error in operator application for `") +
                          uop.opToString().str() + "'. No matching operator found with type `" +
                          uop.e()->type().toString(_env) + "'");
    }
  }
  static std::string createEnumToStringName(Id* ident, std::string prefix) {
    std::string name = ident->str().str();
    if (name[0] == '\'') {
      name = "'" + prefix + name.substr(1);
    } else {
      name = prefix + name;
    }
    return name;
  }

  /// Visit call
  void vCall(Call& call) {
    std::vector<Expression*> args(call.n_args());
    for (unsigned int i = static_cast<unsigned int>(args.size()); i--;) args[i] = call.arg(i);
    if (FunctionI* fi = _model->matchFn(_env, call.id(), args, true)) {
      bool cv = false;
      for (unsigned int i = 0; i < args.size(); i++) {
        if (Comprehension* c = call.arg(i)->dyn_cast<Comprehension>()) {
          Type t_before = c->e()->type();
          Type t = fi->argtype(_env, args, i);
          t.dim(0);
          c->e(addCoercion(_env, _model, c->e(), t)());
          Type t_after = c->e()->type();
          if (t_before != t_after) {
            Type ct = c->type();
            ct.bt(t_after.bt());
            c->type(ct);
          }
        } else {
          args[i] = addCoercion(_env, _model, call.arg(i), fi->argtype(_env, args, i))();
          call.arg(i, args[i]);
        }
        cv = cv || args[i]->type().cv();
      }
      // Replace par enums with their string versions
      if (call.id() == "format" || call.id() == "show" || call.id() == "showDzn" ||
          call.id() == "showJSON") {
        if (call.arg(call.n_args() - 1)->type().ispar()) {
          int enumId = call.arg(call.n_args() - 1)->type().enumId();
          if (enumId != 0 && call.arg(call.n_args() - 1)->type().dim() != 0) {
            const std::vector<unsigned int>& enumIds = _env.getArrayEnum(enumId);
            enumId = enumIds[enumIds.size() - 1];
          }
          if (enumId > 0) {
            VarDecl* enumDecl = _env.getEnum(enumId)->e();
            if (enumDecl->e()) {
              Id* ti_id = _env.getEnum(enumId)->e()->id();
              GCLock lock;
              std::vector<Expression*> args(3);
              args[0] = call.arg(call.n_args() - 1);
              if (args[0]->type().dim() > 1) {
                std::vector<Expression*> a1dargs(1);
                a1dargs[0] = args[0];
                Call* array1d = new Call(Location().introduce(), ASTString("array1d"), a1dargs);
                Type array1dt = args[0]->type();
                array1dt.dim(1);
                array1d->type(array1dt);
                args[0] = array1d;
              }
              args[1] = constants().boollit(call.id() == "showDzn");
              args[2] = constants().boollit(call.id() == "showJSON");
              ASTString enumName(createEnumToStringName(ti_id, "_toString_"));
              call.id(enumName);
              call.args(args);
              if (call.id() == "showDzn") {
                call.id(constants().ids.show);
              }
              fi = _model->matchFn(_env, &call, false);
              if (fi == NULL) {
                std::ostringstream oss;
                oss << "no function or predicate with this signature found: `";
                oss << call.id() << "(";
                for (unsigned int i = 0; i < call.n_args(); i++) {
                  oss << call.arg(i)->type().toString(_env);
                  if (i < call.n_args() - 1) oss << ",";
                }
                oss << ")'";
                throw TypeError(_env, call.loc(), oss.str());
              }
            }
          }
        }
      }

      // Set type and decl
      Type ty = fi->rtype(_env, args, true);
      ty.cv(cv);
      call.type(ty);
      call.decl(fi);
    } else {
      std::ostringstream oss;
      oss << "no function or predicate with this signature found: `";
      oss << call.id() << "(";
      for (unsigned int i = 0; i < call.n_args(); i++) {
        oss << call.arg(i)->type().toString(_env);
        if (i < call.n_args() - 1) oss << ",";
      }
      oss << ")'";
      throw TypeError(_env, call.loc(), oss.str());
    }
  }
  /// Visit let
  void vLet(Let& let) {
    bool cv = false;
    bool isVar = false;
    for (unsigned int i = 0; i < let.let().size(); i++) {
      Expression* li = let.let()[i];
      cv = cv || li->type().cv();
      if (VarDecl* vdi = li->dyn_cast<VarDecl>()) {
        if (vdi->e() == NULL && vdi->type().is_set() && vdi->type().isvar() &&
            vdi->ti()->domain() == NULL) {
          _typeErrors.push_back(
              TypeError(_env, vdi->loc(),
                        "set element type for `" + vdi->id()->str().str() + "' is not finite"));
        }
        if (vdi->type().ispar() && vdi->e() == NULL)
          throw TypeError(_env, vdi->loc(),
                          "let variable `" + vdi->id()->v().str() + "' must be initialised");
        if (vdi->ti()->hasTiVariable()) {
          _typeErrors.push_back(
              TypeError(_env, vdi->loc(),
                        "type-inst variables not allowed in type-inst for let variable `" +
                            vdi->id()->str().str() + "'"));
        }
        let.let_orig()[i] = vdi->e();
      }
      isVar |= li->type().isvar();
    }
    Type ty = let.in()->type();
    ty.cv(cv);
    if (isVar && ty.bt() == Type::BT_BOOL && ty.dim() == 0) ty.ti(Type::TI_VAR);
    let.type(ty);
  }
  /// Visit variable declaration
  void vVarDecl(VarDecl& vd) {
    if (ignoreVarDecl) {
      if (vd.e()) {
        Type vdt = vd.ti()->type();
        Type vet = vd.e()->type();
        if (vdt.enumId() != 0 && vdt.dim() > 0 &&
            (vd.e()->isa<ArrayLit>() || vd.e()->isa<Comprehension>() ||
             (vd.e()->isa<BinOp>() && vd.e()->cast<BinOp>()->op() == BOT_PLUSPLUS))) {
          // Special case: index sets of array literals and comprehensions automatically
          // coerce to any enum index set
          const std::vector<unsigned int>& enumIds = _env.getArrayEnum(vdt.enumId());
          if (enumIds[enumIds.size() - 1] == 0) {
            vdt.enumId(0);
          } else {
            std::vector<unsigned int> nEnumIds(enumIds.size());
            for (unsigned int i = 0; i < nEnumIds.size() - 1; i++) nEnumIds[i] = 0;
            nEnumIds[nEnumIds.size() - 1] = enumIds[enumIds.size() - 1];
            vdt.enumId(_env.registerArrayEnum(nEnumIds));
          }
        } else if (vd.ti()->isEnum() && vd.e()->isa<Call>()) {
          if (vd.e()->cast<Call>()->id() == "anon_enum") {
            vet.enumId(vdt.enumId());
          }
        }

        if (vd.type().isunknown()) {
          vd.ti()->type(vet);
          vd.type(vet);
        } else if (!_env.isSubtype(vet, vdt, true)) {
          if (vet == Type::bot(1) && vd.e()->isa<ArrayLit>() &&
              vd.e()->cast<ArrayLit>()->size() == 0 && vdt.dim() != 0) {
            // this is okay: assigning an empty array (one-dimensional) to an array variable
          } else {
            _typeErrors.push_back(TypeError(_env, vd.e()->loc(),
                                            "initialisation value for `" + vd.id()->str().str() +
                                                "' has invalid type-inst: expected `" +
                                                vd.ti()->type().toString(_env) + "', actual `" +
                                                vd.e()->type().toString(_env) + "'"));
          }
        } else {
          vd.e(addCoercion(_env, _model, vd.e(), vd.ti()->type())());
        }
      } else {
        assert(!vd.type().isunknown());
      }
    } else {
      vd.type(vd.ti()->type());
      vd.id()->type(vd.type());
    }
  }
  /// Visit type inst
  void vTypeInst(TypeInst& ti) {
    Type tt = ti.type();
    bool foundEnum = ti.ranges().size() > 0 && ti.domain() && ti.domain()->type().enumId() != 0;
    if (ti.ranges().size() > 0) {
      bool foundTIId = false;
      for (unsigned int i = 0; i < ti.ranges().size(); i++) {
        TypeInst* ri = ti.ranges()[i];
        assert(ri != NULL);
        if (ri->type().cv()) tt.cv(true);
        if (ri->type().enumId() != 0) {
          foundEnum = true;
        }
        if (ri->type() == Type::top()) {
          //            if (foundTIId) {
          //              throw TypeError(_env,ri->loc(),
          //                "only one type-inst variable allowed in array index");
          //            } else {
          foundTIId = true;
          //            }
        } else if (ri->type() != Type::parint()) {
          assert(ri->isa<TypeInst>());
          TypeInst* riti = ri->cast<TypeInst>();
          if (riti->domain()) {
            throw TypeError(_env, ri->loc(),
                            "array index set expression has invalid type, expected `set of int', "
                            "actual `set of " +
                                ri->type().toString(_env) + "'");
          } else {
            throw TypeError(_env, ri->loc(),
                            "cannot use `" + ri->type().toString(_env) +
                                "' as array index set (did you mean `int'?)");
          }
        }
      }
      tt.dim(foundTIId ? -1 : ti.ranges().size());
    }
    if (ti.domain() && ti.domain()->type().cv()) tt.cv(true);
    if (ti.domain()) {
      if (TIId* tiid = ti.domain()->dyn_cast<TIId>()) {
        if (tiid->isEnum()) {
          tt.bt(Type::BT_INT);
        }
      } else {
        if (ti.domain()->type().ti() != Type::TI_PAR || ti.domain()->type().st() != Type::ST_SET)
          throw TypeError(
              _env, ti.domain()->loc(),
              "type-inst must be par set but is `" + ti.domain()->type().toString(_env) + "'");
        if (ti.domain()->type().dim() != 0)
          throw TypeError(_env, ti.domain()->loc(), "type-inst cannot be an array");
      }
    }
    if (tt.isunknown() && ti.domain()) {
      assert(ti.domain());
      switch (ti.domain()->type().bt()) {
        case Type::BT_INT:
        case Type::BT_FLOAT:
          break;
        case Type::BT_BOT: {
          Type tidt = ti.domain()->type();
          tidt.bt(Type::BT_INT);
          ti.domain()->type(tidt);
        } break;
        default:
          throw TypeError(_env, ti.domain()->loc(), "type-inst must be int or float");
      }
      tt.bt(ti.domain()->type().bt());
      tt.enumId(ti.domain()->type().enumId());
    } else {
      //        assert(ti.domain()==NULL || ti.domain()->isa<TIId>());
    }
    if (foundEnum) {
      std::vector<unsigned int> enumIds(ti.ranges().size() + 1);
      for (unsigned int i = 0; i < ti.ranges().size(); i++) {
        enumIds[i] = ti.ranges()[i]->type().enumId();
      }
      enumIds[ti.ranges().size()] = ti.domain() ? ti.domain()->type().enumId() : 0;
      int arrayEnumId = _env.registerArrayEnum(enumIds);
      tt.enumId(arrayEnumId);
    }

    if (tt.st() == Type::ST_SET && tt.ti() == Type::TI_VAR && tt.bt() != Type::BT_INT &&
        tt.bt() != Type::BT_TOP)
      throw TypeError(_env, ti.loc(), "var set element types other than `int' not allowed");
    ti.type(tt);
  }
  void vTIId(TIId& id) {}
};

void typecheck(Env& env, Model* origModel, std::vector<TypeError>& typeErrors,
               bool ignoreUndefinedParameters, bool allowMultiAssignment, bool isFlatZinc) {
  Model* m;
  if (!isFlatZinc && origModel == env.model()) {
    // Combine all items into single model
    Model* combinedModel = new Model;
    class Combiner : public ItemVisitor {
    public:
      Model* m;
      Combiner(Model* m0) : m(m0) {}
      bool enter(Item* i) {
        if (!i->isa<IncludeI>()) m->addItem(i);
        return true;
      }
    } _combiner(combinedModel);
    iterItems(_combiner, origModel);
    env.envi().orig_model = origModel;
    env.envi().model = combinedModel;
    m = combinedModel;
  } else {
    m = origModel;
  }

  // Topological sorting
  TopoSorter ts(m);

  std::vector<FunctionI*> functionItems;
  std::vector<AssignI*> assignItems;
  Model* enumItems = new Model;

  class TSVFuns : public ItemVisitor {
  public:
    EnvI& env;
    Model* model;
    std::vector<FunctionI*>& fis;
    TSVFuns(EnvI& env0, Model* model0, std::vector<FunctionI*>& fis0)
        : env(env0), model(model0), fis(fis0) {}
    void vFunctionI(FunctionI* i) {
      model->registerFn(env, i);
      fis.push_back(i);
    }
  } _tsvf(env.envi(), m, functionItems);
  iterItems(_tsvf, m);

  class TSV0 : public ItemVisitor {
  public:
    EnvI& env;
    TopoSorter& ts;
    Model* model;
    bool hadSolveItem;
    std::vector<AssignI*>& ais;
    VarDeclI* objective;
    Model* enumis;
    TSV0(EnvI& env0, TopoSorter& ts0, Model* model0, std::vector<AssignI*>& ais0, Model* enumis0)
        : env(env0),
          ts(ts0),
          model(model0),
          hadSolveItem(false),
          ais(ais0),
          objective(NULL),
          enumis(enumis0) {}
    void vAssignI(AssignI* i) { ais.push_back(i); }
    void vVarDeclI(VarDeclI* i) {
      ts.add(env, i, true, enumis);
      // initialise new identifier counter to be larger than existing identifier
      if (i->e()->id()->idn() >= 0) {
        env.minId(i->e()->id()->idn());
      } else if (i->e()->id()->v().beginsWith("X_INTRODUCED_") && i->e()->id()->v().endsWith("_")) {
        std::string numId = i->e()->id()->v().str().substr(std::string("X_INTRODUCED_").size());
        if (numId.size() > 0) {
          numId = numId.substr(0, numId.size() - 1);
          if (numId.size() > 0) {
            int vId = -1;
            try {
              vId = std::stoi(numId);
            } catch (std::exception&) {
            }
            if (vId >= 0) env.minId(vId);
          }
        }
      }
    }
    void vSolveI(SolveI* si) {
      if (hadSolveItem) throw TypeError(env, si->loc(), "Only one solve item allowed");
      hadSolveItem = true;
      if (si->e()) {
        GCLock lock;
        TypeInst* ti = new TypeInst(Location().introduce(), Type());
        VarDecl* obj = new VarDecl(Location().introduce(), ti, "_objective", si->e());
        si->e(obj->id());
        objective = new VarDeclI(Location().introduce(), obj);
      }
    }
  } _tsv0(env.envi(), ts, m, assignItems, enumItems);
  iterItems(_tsv0, m);
  if (_tsv0.objective) {
    m->addItem(_tsv0.objective);
    ts.add(env.envi(), _tsv0.objective, true, enumItems);
  }

  for (unsigned int i = 0; i < enumItems->size(); i++) {
    if (AssignI* ai = (*enumItems)[i]->dyn_cast<AssignI>()) {
      assignItems.push_back(ai);
    } else if (VarDeclI* vdi = (*enumItems)[i]->dyn_cast<VarDeclI>()) {
      m->addItem(vdi);
      ts.add(env.envi(), vdi, false, enumItems);
    } else {
      FunctionI* fi = (*enumItems)[i]->dyn_cast<FunctionI>();
      m->addItem(fi);
      m->registerFn(env.envi(), fi);
      functionItems.push_back(fi);
    }
  }

  Model* enumItems2 = new Model;

  for (unsigned int i = 0; i < assignItems.size(); i++) {
    AssignI* ai = assignItems[i];
    VarDecl* vd = NULL;
    if (env.envi().ignoreUnknownIds) {
      try {
        vd = ts.get(env.envi(), ai->id(), ai->loc());
      } catch (TypeError&) {
      }
    } else {
      vd = ts.get(env.envi(), ai->id(), ai->loc());
    }
    if (vd) {
      if (vd->e()) {
        if (allowMultiAssignment) {
          GCLock lock;
          m->addItem(new ConstraintI(
              ai->loc(),
              new BinOp(ai->loc(), new Id(Location().introduce(), ai->id(), vd), BOT_EQ, ai->e())));
        } else {
          throw TypeError(env.envi(), ai->loc(), "multiple assignment to the same variable");
        }
      } else {
        vd->e(ai->e());
        vd->ann().add(constants().ann.rhs_from_assignment);
        if (vd->ti()->isEnum()) {
          GCLock lock;
          ASTString name(createEnumToStringName(vd->id(), "_enum_to_string_"));
          VarDecl* vd_enum = ts.get(env.envi(), name, vd->loc());
          if (vd_enum->e())
            throw TypeError(env.envi(), ai->loc(), "multiple definition of the same enum");
          AssignI* ai_enum =
              createEnumMapper(env.envi(), m, vd->ti()->type().enumId(), vd, vd_enum, enumItems2);
          if (ai_enum) {
            vd_enum->e(ai_enum->e());
            ai_enum->remove();
          }
        }
      }
    }
    ai->remove();
  }

  for (unsigned int i = 0; i < enumItems2->size(); i++) {
    if (VarDeclI* vdi = (*enumItems2)[i]->dyn_cast<VarDeclI>()) {
      m->addItem(vdi);
      ts.add(env.envi(), vdi, false, enumItems);
    } else {
      FunctionI* fi = (*enumItems2)[i]->cast<FunctionI>();
      m->addItem(fi);
      m->registerFn(env.envi(), fi);
      functionItems.push_back(fi);
    }
  }

  delete enumItems;
  delete enumItems2;

  class TSV1 : public ItemVisitor {
  public:
    EnvI& env;
    TopoSorter& ts;
    TSV1(EnvI& env0, TopoSorter& ts0) : env(env0), ts(ts0) {}
    void vVarDeclI(VarDeclI* i) { ts.run(env, i->e()); }
    void vAssignI(AssignI* i) {}
    void vConstraintI(ConstraintI* i) { ts.run(env, i->e()); }
    void vSolveI(SolveI* i) {
      for (ExpressionSetIter it = i->ann().begin(); it != i->ann().end(); ++it) ts.run(env, *it);
      ts.run(env, i->e());
    }
    void vOutputI(OutputI* i) { ts.run(env, i->e()); }
    void vFunctionI(FunctionI* fi) {
      ts.run(env, fi->ti());
      for (unsigned int i = 0; i < fi->params().size(); i++) ts.run(env, fi->params()[i]);
      for (ExpressionSetIter it = fi->ann().begin(); it != fi->ann().end(); ++it) ts.run(env, *it);
      ts.scopes.push(false);
      for (unsigned int i = 0; i < fi->params().size(); i++) ts.scopes.add(env, fi->params()[i]);
      ts.run(env, fi->e());
      ts.scopes.pop();
    }
  } _tsv1(env.envi(), ts);
  iterItems(_tsv1, m);

  m->sortFn();

  {
    struct SortByPayload {
      bool operator()(Item* i0, Item* i1) {
        if (i0->isa<IncludeI>()) return !i1->isa<IncludeI>();
        if (VarDeclI* vdi0 = i0->dyn_cast<VarDeclI>()) {
          if (VarDeclI* vdi1 = i1->dyn_cast<VarDeclI>()) {
            return vdi0->e()->payload() < vdi1->e()->payload();
          } else {
            return !i1->isa<IncludeI>();
          }
        }
        return false;
      }
    } _sbp;

    std::stable_sort(m->begin(), m->end(), _sbp);
  }

  {
    Typer<false> ty(env.envi(), m, typeErrors, ignoreUndefinedParameters);
    BottomUpIterator<Typer<false> > bu_ty(ty);
    for (unsigned int i = 0; i < ts.decls.size(); i++) {
      ts.decls[i]->payload(0);
      bu_ty.run(ts.decls[i]->ti());
      ty.vVarDecl(*ts.decls[i]);
    }
    for (unsigned int i = 0; i < functionItems.size(); i++) {
      bu_ty.run(functionItems[i]->ti());
      for (unsigned int j = 0; j < functionItems[i]->params().size(); j++)
        bu_ty.run(functionItems[i]->params()[j]);
    }
  }

  m->fixFnMap();

  {
    Typer<true> ty(env.envi(), m, typeErrors, ignoreUndefinedParameters);
    BottomUpIterator<Typer<true> > bu_ty(ty);

    class TSV2 : public ItemVisitor {
    public:
      EnvI& env;
      Model* m;
      BottomUpIterator<Typer<true> >& bu_ty;
      std::vector<TypeError>& _typeErrors;
      TSV2(EnvI& env0, Model* m0, BottomUpIterator<Typer<true> >& b,
           std::vector<TypeError>& typeErrors)
          : env(env0), m(m0), bu_ty(b), _typeErrors(typeErrors) {}
      void vVarDeclI(VarDeclI* i) {
        bu_ty.run(i->e());
        if (i->e()->ti()->hasTiVariable()) {
          _typeErrors.push_back(TypeError(env, i->e()->loc(),
                                          "type-inst variables not allowed in type-inst for `" +
                                              i->e()->id()->str().str() + "'"));
        }
        VarDecl* vdi = i->e();
        if (vdi->e() == NULL && vdi->type().is_set() && vdi->type().isvar() &&
            vdi->ti()->domain() == NULL) {
          _typeErrors.push_back(
              TypeError(env, vdi->loc(),
                        "set element type for `" + vdi->id()->str().str() + "' is not finite"));
        }
        if (i->e()->ann().contains(constants().ann.output_only) && vdi->e()->type().isvar()) {
          _typeErrors.push_back(
              TypeError(env, vdi->loc(), "variables annotated with ::output_only must be par"));
        }
      }
      void vAssignI(AssignI* i) {
        bu_ty.run(i->e());
        if (!env.isSubtype(i->e()->type(), i->decl()->ti()->type(), true)) {
          _typeErrors.push_back(TypeError(env, i->loc(),
                                          "assignment value for `" + i->decl()->id()->str().str() +
                                              "' has invalid type-inst: expected `" +
                                              i->decl()->ti()->type().toString(env) +
                                              "', actual `" + i->e()->type().toString(env) + "'"));
          // Assign to "true" constant to avoid generating further errors that the parameter
          // is undefined
          i->decl()->e(constants().lit_true);
        }
      }
      void vConstraintI(ConstraintI* i) {
        bu_ty.run(i->e());
        if (!env.isSubtype(i->e()->type(), Type::varbool(), true))
          throw TypeError(env, i->loc(),
                          "invalid type of constraint, expected `" + Type::varbool().toString(env) +
                              "', actual `" + i->e()->type().toString(env) + "'");
      }
      void vSolveI(SolveI* i) {
        for (ExpressionSetIter it = i->ann().begin(); it != i->ann().end(); ++it) {
          bu_ty.run(*it);
          if (!(*it)->type().isann())
            throw TypeError(env, (*it)->loc(),
                            "expected annotation, got `" + (*it)->type().toString(env) + "'");
        }
        bu_ty.run(i->e());
        if (i->e()) {
          Type et = i->e()->type();

          bool needOptCoercion = et.isopt() && et.isint();
          if (needOptCoercion) {
            et.ot(Type::OT_PRESENT);
          }

          if (!(env.isSubtype(et, Type::varint(), true) ||
                env.isSubtype(et, Type::varfloat(), true)))
            throw TypeError(env, i->e()->loc(),
                            "objective has invalid type, expected int or float, actual `" +
                                et.toString(env) + "'");

          if (needOptCoercion) {
            GCLock lock;
            std::vector<Expression*> args(2);
            args[0] = i->e();
            args[1] = constants().boollit(i->st() == SolveI::ST_MAX);
            Call* c = new Call(Location().introduce(), ASTString("objective_deopt_"), args);
            c->decl(env.model->matchFn(env, c, false));
            assert(c->decl());
            c->type(et);
            i->e(c);
          }
        }
      }
      void vOutputI(OutputI* i) {
        bu_ty.run(i->e());
        if (i->e()->type() != Type::parstring(1) && i->e()->type() != Type::bot(1))
          throw TypeError(env, i->e()->loc(),
                          "invalid type in output item, expected `" +
                              Type::parstring(1).toString(env) + "', actual `" +
                              i->e()->type().toString(env) + "'");
      }
      void vFunctionI(FunctionI* i) {
        for (ExpressionSetIter it = i->ann().begin(); it != i->ann().end(); ++it) {
          bu_ty.run(*it);
          if (!(*it)->type().isann())
            throw TypeError(env, (*it)->loc(),
                            "expected annotation, got `" + (*it)->type().toString(env) + "'");
        }
        bu_ty.run(i->ti());
        bu_ty.run(i->e());
        if (i->e() && !env.isSubtype(i->e()->type(), i->ti()->type(), true))
          throw TypeError(env, i->e()->loc(),
                          "return type of function does not match body, declared type is `" +
                              i->ti()->type().toString(env) + "', body type is `" +
                              i->e()->type().toString(env) + "'");
        if (i->e() && i->e()->type().ispar() && i->ti()->type().isvar()) {
          // this is a par function declared as var, so change declared return type
          Type i_t = i->ti()->type();
          i_t.ti(Type::TI_PAR);
          i->ti()->type(i_t);
        }
        if (i->e()) i->e(addCoercion(env, m, i->e(), i->ti()->type())());
      }
    } _tsv2(env.envi(), m, bu_ty, typeErrors);
    iterItems(_tsv2, m);
  }

  class TSV3 : public ItemVisitor {
  public:
    EnvI& env;
    Model* m;
    OutputI* outputItem;
    TSV3(EnvI& env0, Model* m0) : env(env0), m(m0), outputItem(NULL) {}
    void vAssignI(AssignI* i) { i->decl()->e(addCoercion(env, m, i->e(), i->decl()->type())()); }
    void vOutputI(OutputI* oi) {
      if (outputItem == NULL) {
        outputItem = oi;
      } else {
        GCLock lock;
        BinOp* bo = new BinOp(Location().introduce(), outputItem->e(), BOT_PLUSPLUS, oi->e());
        bo->type(Type::parstring(1));
        outputItem->e(bo);
        oi->remove();
        m->setOutputItem(outputItem);
      }
    }
  } _tsv3(env.envi(), m);
  if (typeErrors.empty()) {
    iterItems(_tsv3, m);
  }

  try {
    m->checkFnOverloading(env.envi());
  } catch (TypeError& e) {
    typeErrors.push_back(e);
  }

  for (unsigned int i = 0; i < ts.decls.size(); i++) {
    if (ts.decls[i]->toplevel() && ts.decls[i]->type().ispar() && !ts.decls[i]->type().isann() &&
        ts.decls[i]->e() == NULL) {
      if (ts.decls[i]->type().isopt() && ts.decls[i]->type().dim() == 0) {
        ts.decls[i]->e(constants().absent);
      } else if (!ignoreUndefinedParameters) {
        typeErrors.push_back(
            TypeError(env.envi(), ts.decls[i]->loc(),
                      "  symbol error: variable `" + ts.decls[i]->id()->str().str() +
                          "' must be defined (did you forget to specify a data file?)"));
      }
    }
    if (ts.decls[i]->ti()->isEnum()) {
      ts.decls[i]->ti()->setIsEnum(false);
      Type vdt = ts.decls[i]->ti()->type();
      vdt.enumId(0);
      ts.decls[i]->ti()->type(vdt);
    }
  }

  for (auto vd_k : env.envi().checkVars) {
    try {
      VarDecl* vd =
          ts.get(env.envi(), vd_k()->cast<VarDecl>()->id()->str(), vd_k()->cast<VarDecl>()->loc());
      vd->ann().add(constants().ann.mzn_check_var);
      if (vd->type().enumId() != 0) {
        GCLock lock;
        int enumId = vd->type().enumId();
        if (vd->type().dim() > 0) {
          const std::vector<unsigned int>& arrayEnumIds =
              env.envi().getArrayEnum(vd->type().enumId());
          enumId = arrayEnumIds[arrayEnumIds.size() - 1];
        }
        if (enumId > 0) {
          std::vector<Expression*> args({env.envi().getEnum(enumId)->e()->id()});
          Call* checkEnum =
              new Call(Location().introduce(), constants().ann.mzn_check_enum_var, args);
          checkEnum->type(Type::ann());
          checkEnum->decl(env.envi().model->matchFn(env.envi(), checkEnum, false));
          vd->ann().add(checkEnum);
        }
      }
      Type vdktype = vd_k()->type();
      vdktype.ti(Type::TI_VAR);
      if (!vd_k()->type().isSubtypeOf(vd->type(), false)) {
        GCLock lock;

        typeErrors.push_back(TypeError(env.envi(), vd->loc(),
                                       "Solution checker requires `" + vd->id()->str().str() +
                                           "' to be of type `" + vdktype.toString(env.envi()) +
                                           "'"));
      }
    } catch (TypeError& e) {
      typeErrors.push_back(
          TypeError(env.envi(), e.loc(), e.msg() + " (required by solution checker model)"));
    }
  }
}

void typecheck(Env& env, Model* m, AssignI* ai) {
  std::vector<TypeError> typeErrors;
  Typer<true> ty(env.envi(), m, typeErrors, false);
  BottomUpIterator<Typer<true> > bu_ty(ty);
  bu_ty.run(ai->e());
  if (!typeErrors.empty()) {
    throw typeErrors[0];
  }
  if (!env.envi().isSubtype(ai->e()->type(), ai->decl()->ti()->type(), true)) {
    throw TypeError(env.envi(), ai->e()->loc(),
                    "assignment value for `" + ai->decl()->id()->str().str() +
                        "' has invalid type-inst: expected `" +
                        ai->decl()->ti()->type().toString(env.envi()) + "', actual `" +
                        ai->e()->type().toString(env.envi()) + "'");
  }
}

void output_var_desc_json(Env& env, VarDecl* vd, std::ostream& os, bool extra = false) {
  os << "    \"" << *vd->id() << "\" : {";
  os << "\"type\" : ";
  switch (vd->type().bt()) {
    case Type::BT_INT:
      os << "\"int\"";
      break;
    case Type::BT_BOOL:
      os << "\"bool\"";
      break;
    case Type::BT_FLOAT:
      os << "\"float\"";
      break;
    case Type::BT_STRING:
      os << "\"string\"";
      break;
    case Type::BT_ANN:
      os << "\"ann\"";
      break;
    default:
      os << "\"?\"";
      break;
  }
  if (vd->type().ot() == Type::OT_OPTIONAL) {
    os << ", \"optional\" : true";
  }
  if (vd->type().st() == Type::ST_SET) {
    os << ", \"set\" : true";
  }
  if (vd->type().dim() > 0) {
    os << ", \"dim\" : " << vd->type().dim();

    if (extra) {
      os << ", \"dims\" : [";
      bool had_dim = false;
      ASTExprVec<TypeInst> ranges = vd->ti()->ranges();
      for (int i = 0; i < static_cast<int>(ranges.size()); i++) {
        if (ranges[i]->type().enumId() > 0) {
          os << (had_dim ? "," : "") << "\""
             << *env.envi().getEnum(ranges[i]->type().enumId())->e()->id() << "\"";
        } else {
          os << (had_dim ? "," : "") << "\"int\"";
        }
        had_dim = true;
      }
      os << "]";

      if (vd->type().enumId() > 0) {
        const std::vector<unsigned int>& enumIds = env.envi().getArrayEnum(vd->type().enumId());
        if (enumIds.back() > 0) {
          os << ", \"enum_type\" : \"" << *env.envi().getEnum(enumIds.back())->e()->id() << "\"";
        }
      }
    }

  } else {
    if (extra) {
      if (vd->type().enumId() > 0) {
        os << ", \"enum_type\" : \"" << *env.envi().getEnum(vd->type().enumId())->e()->id() << "\"";
      }
    }
  }
  os << "}";
}

void output_model_variable_types(Env& env, Model* m, std::ostream& os) {
  class VInfVisitor : public ItemVisitor {
  public:
    Env& env;
    bool had_var;
    bool had_enum;
    std::ostringstream oss_vars;
    std::ostringstream oss_enums;
    VInfVisitor(Env& env0) : env(env0), had_var(false), had_enum(false) {}
    bool enter(Item* i) {
      if (IncludeI* ii = i->dyn_cast<IncludeI>()) {
        std::string prefix =
            ii->m()->filepath().str().substr(0, ii->m()->filepath().size() - ii->f().size());
        return (prefix.empty() || prefix == "./");
      }
      return true;
    }
    void vVarDeclI(VarDeclI* vdi) {
      if (!vdi->e()->type().isann() && !vdi->e()->ti()->isEnum()) {
        if (had_var) oss_vars << ",\n";
        output_var_desc_json(env, vdi->e(), oss_vars, true);
        had_var = true;
      } else if (vdi->e()->type().st() == Type::ST_SET && vdi->e()->type().enumId() != 0 &&
                 !vdi->e()->type().isann()) {
        if (had_enum) oss_enums << ", ";
        oss_enums << "\"" << *env.envi().getEnum(vdi->e()->type().enumId())->e()->id() << "\"";
        had_enum = true;
      }
    }
  } _vinf(env);
  iterItems(_vinf, m);
  os << "{\"var_types\": {";
  os << "\n  \"vars\": {\n" << _vinf.oss_vars.str() << "\n  },";
  os << "\n  \"enums\": [" << _vinf.oss_enums.str() << "]\n";
  os << "}}\n";
}

void output_model_interface(Env& env, Model* m, std::ostream& os) {
  class IfcVisitor : public ItemVisitor {
  public:
    Env& env;
    bool had_input;
    bool had_output;
    bool had_add_to_output = false;
    std::ostringstream oss_input;
    std::ostringstream oss_output;
    std::string method;
    IfcVisitor(Env& env0) : env(env0), had_input(false), had_output(false), method("sat") {}
    bool enter(Item* i) {
      if (IncludeI* ii = i->dyn_cast<IncludeI>()) {
        std::string prefix =
            ii->m()->filepath().str().substr(0, ii->m()->filepath().size() - ii->f().size());
        return (prefix.empty() || prefix == "./");
      }
      return true;
    }
    void vVarDeclI(VarDeclI* vdi) {
      VarDecl* vd = vdi->e();
      if (vd->type().ispar() && !vd->type().isann() &&
          (vd->e() == NULL || vd->e() == constants().absent)) {
        if (had_input) oss_input << ",\n";
        output_var_desc_json(env, vd, oss_input);
        had_input = true;
      } else {
        bool process_var = false;
        if (vd->ann().contains(constants().ann.add_to_output)) {
          if (!had_add_to_output) {
            oss_output.str("");
            had_output = false;
          }
          had_add_to_output = true;
          process_var = true;
        } else if (!had_add_to_output) {
          process_var =
              vd->type().isvar() &&
              (vd->e() == NULL || vd->ann().contains(constants().ann.rhs_from_assignment));
        }
        if (process_var) {
          if (had_output) {
            oss_output << ",\n";
          }
          output_var_desc_json(env, vd, oss_output);
          had_output = true;
        }
      }
    }
    void vSolveI(SolveI* si) {
      switch (si->st()) {
        case SolveI::ST_MIN:
          method = "min";
          break;
        case SolveI::ST_MAX:
          method = "max";
          break;
        case SolveI::ST_SAT:
          method = "sat";
          break;
      }
    }
  } _ifc(env);
  iterItems(_ifc, m);
  os << "{\n  \"input\" : {\n"
     << _ifc.oss_input.str() << "\n  },\n  \"output\" : {\n"
     << _ifc.oss_output.str() << "\n  }";
  os << ",\n  \"method\": \"";
  os << _ifc.method;
  os << "\"";
  os << "\n}\n";
}

}  // namespace MiniZinc