xref: /external/v8/test/cctest/test-types.cc

// Copyright 2013 the V8 project authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.

#include <vector>

#include "src/hydrogen-types.h"
#include "src/isolate-inl.h"
#include "src/types.h"
#include "test/cctest/cctest.h"

using namespace v8::internal;

// Testing auxiliaries (breaking the Type abstraction).
typedef uint32_t bitset;

struct ZoneRep {
  typedef void* Struct;

  static bool IsStruct(Type* t, int tag) {
    return !IsBitset(t) && reinterpret_cast<intptr_t>(AsStruct(t)[0]) == tag;
  }
  static bool IsBitset(Type* t) { return reinterpret_cast<uintptr_t>(t) & 1; }
  static bool IsUnion(Type* t) { return IsStruct(t, 6); }

  static Struct* AsStruct(Type* t) {
    return reinterpret_cast<Struct*>(t);
  }
  static bitset AsBitset(Type* t) {
    return static_cast<bitset>(reinterpret_cast<uintptr_t>(t) ^ 1u);
  }
  static Struct* AsUnion(Type* t) {
    return AsStruct(t);
  }
  static int Length(Struct* structured) {
    return static_cast<int>(reinterpret_cast<intptr_t>(structured[1]));
  }

  static Zone* ToRegion(Zone* zone, Isolate* isolate) { return zone; }

  struct BitsetType : Type::BitsetType {
    using Type::BitsetType::New;
    using Type::BitsetType::Glb;
    using Type::BitsetType::Lub;
    using Type::BitsetType::IsInhabited;
  };
};


struct HeapRep {
  typedef FixedArray Struct;

  static bool IsStruct(Handle<HeapType> t, int tag) {
    return t->IsFixedArray() && Smi::cast(AsStruct(t)->get(0))->value() == tag;
  }
  static bool IsBitset(Handle<HeapType> t) { return t->IsSmi(); }
  static bool IsUnion(Handle<HeapType> t) { return IsStruct(t, 6); }

  static Struct* AsStruct(Handle<HeapType> t) { return FixedArray::cast(*t); }
  static bitset AsBitset(Handle<HeapType> t) {
    return static_cast<bitset>(reinterpret_cast<uintptr_t>(*t));
  }
  static Struct* AsUnion(Handle<HeapType> t) { return AsStruct(t); }
  static int Length(Struct* structured) { return structured->length() - 1; }

  static Isolate* ToRegion(Zone* zone, Isolate* isolate) { return isolate; }

  struct BitsetType : HeapType::BitsetType {
    using HeapType::BitsetType::New;
    using HeapType::BitsetType::Glb;
    using HeapType::BitsetType::Lub;
    using HeapType::BitsetType::IsInhabited;
    static bitset Glb(Handle<HeapType> type) { return Glb(*type); }
    static bitset Lub(Handle<HeapType> type) { return Lub(*type); }
  };
};


template<class Type, class TypeHandle, class Region>
class Types {
 public:
  Types(Region* region, Isolate* isolate)
      : region_(region), rng_(isolate->random_number_generator()) {
    #define DECLARE_TYPE(name, value) \
      name = Type::name(region); \
      types.push_back(name);
    PROPER_BITSET_TYPE_LIST(DECLARE_TYPE)
    #undef DECLARE_TYPE

    object_map = isolate->factory()->NewMap(
        JS_OBJECT_TYPE, JSObject::kHeaderSize);
    array_map = isolate->factory()->NewMap(
        JS_ARRAY_TYPE, JSArray::kSize);
    number_map = isolate->factory()->NewMap(
        HEAP_NUMBER_TYPE, HeapNumber::kSize);
    uninitialized_map = isolate->factory()->uninitialized_map();
    ObjectClass = Type::Class(object_map, region);
    ArrayClass = Type::Class(array_map, region);
    NumberClass = Type::Class(number_map, region);
    UninitializedClass = Type::Class(uninitialized_map, region);

    maps.push_back(object_map);
    maps.push_back(array_map);
    maps.push_back(uninitialized_map);
    for (MapVector::iterator it = maps.begin(); it != maps.end(); ++it) {
      types.push_back(Type::Class(*it, region));
    }

    smi = handle(Smi::FromInt(666), isolate);
    signed32 = isolate->factory()->NewHeapNumber(0x40000000);
    object1 = isolate->factory()->NewJSObjectFromMap(object_map);
    object2 = isolate->factory()->NewJSObjectFromMap(object_map);
    array = isolate->factory()->NewJSArray(20);
    uninitialized = isolate->factory()->uninitialized_value();
    SmiConstant = Type::Constant(smi, region);
    Signed32Constant = Type::Constant(signed32, region);
    ObjectConstant1 = Type::Constant(object1, region);
    ObjectConstant2 = Type::Constant(object2, region);
    ArrayConstant = Type::Constant(array, region);
    UninitializedConstant = Type::Constant(uninitialized, region);

    values.push_back(smi);
    values.push_back(signed32);
    values.push_back(object1);
    values.push_back(object2);
    values.push_back(array);
    values.push_back(uninitialized);
    for (ValueVector::iterator it = values.begin(); it != values.end(); ++it) {
      types.push_back(Type::Constant(*it, region));
    }

    integers.push_back(isolate->factory()->NewNumber(-V8_INFINITY));
    integers.push_back(isolate->factory()->NewNumber(+V8_INFINITY));
    integers.push_back(isolate->factory()->NewNumber(-rng_->NextInt(10)));
    integers.push_back(isolate->factory()->NewNumber(+rng_->NextInt(10)));
    for (int i = 0; i < 10; ++i) {
      double x = rng_->NextInt();
      integers.push_back(isolate->factory()->NewNumber(x));
      x *= rng_->NextInt();
      if (!IsMinusZero(x)) integers.push_back(isolate->factory()->NewNumber(x));
    }

    NumberArray = Type::Array(Number, region);
    StringArray = Type::Array(String, region);
    AnyArray = Type::Array(Any, region);

    SignedFunction1 = Type::Function(SignedSmall, SignedSmall, region);
    NumberFunction1 = Type::Function(Number, Number, region);
    NumberFunction2 = Type::Function(Number, Number, Number, region);
    MethodFunction = Type::Function(String, Object, 0, region);

    for (int i = 0; i < 30; ++i) {
      types.push_back(Fuzz());
    }
  }

  Handle<i::Map> object_map;
  Handle<i::Map> array_map;
  Handle<i::Map> number_map;
  Handle<i::Map> uninitialized_map;

  Handle<i::Smi> smi;
  Handle<i::HeapNumber> signed32;
  Handle<i::JSObject> object1;
  Handle<i::JSObject> object2;
  Handle<i::JSArray> array;
  Handle<i::Oddball> uninitialized;

  #define DECLARE_TYPE(name, value) TypeHandle name;
  BITSET_TYPE_LIST(DECLARE_TYPE)
  #undef DECLARE_TYPE

  TypeHandle ObjectClass;
  TypeHandle ArrayClass;
  TypeHandle NumberClass;
  TypeHandle UninitializedClass;

  TypeHandle SmiConstant;
  TypeHandle Signed32Constant;
  TypeHandle ObjectConstant1;
  TypeHandle ObjectConstant2;
  TypeHandle ArrayConstant;
  TypeHandle UninitializedConstant;

  TypeHandle NumberArray;
  TypeHandle StringArray;
  TypeHandle AnyArray;

  TypeHandle SignedFunction1;
  TypeHandle NumberFunction1;
  TypeHandle NumberFunction2;
  TypeHandle MethodFunction;

  typedef std::vector<TypeHandle> TypeVector;
  typedef std::vector<Handle<i::Map> > MapVector;
  typedef std::vector<Handle<i::Object> > ValueVector;

  TypeVector types;
  MapVector maps;
  ValueVector values;
  ValueVector integers;  // "Integer" values used for range limits.

  TypeHandle Of(Handle<i::Object> value) {
    return Type::Of(value, region_);
  }

  TypeHandle NowOf(Handle<i::Object> value) {
    return Type::NowOf(value, region_);
  }

  TypeHandle Class(Handle<i::Map> map) {
    return Type::Class(map, region_);
  }

  TypeHandle Constant(Handle<i::Object> value) {
    return Type::Constant(value, region_);
  }

  TypeHandle Range(Handle<i::Object> min, Handle<i::Object> max) {
    return Type::Range(min, max, region_);
  }

  TypeHandle Context(TypeHandle outer) {
    return Type::Context(outer, region_);
  }

  TypeHandle Array1(TypeHandle element) {
    return Type::Array(element, region_);
  }

  TypeHandle Function0(TypeHandle result, TypeHandle receiver) {
    return Type::Function(result, receiver, 0, region_);
  }

  TypeHandle Function1(TypeHandle result, TypeHandle receiver, TypeHandle arg) {
    TypeHandle type = Type::Function(result, receiver, 1, region_);
    type->AsFunction()->InitParameter(0, arg);
    return type;
  }

  TypeHandle Function2(TypeHandle result, TypeHandle arg1, TypeHandle arg2) {
    return Type::Function(result, arg1, arg2, region_);
  }

  TypeHandle Union(TypeHandle t1, TypeHandle t2) {
    return Type::Union(t1, t2, region_);
  }
  TypeHandle Intersect(TypeHandle t1, TypeHandle t2) {
    return Type::Intersect(t1, t2, region_);
  }

  template<class Type2, class TypeHandle2>
  TypeHandle Convert(TypeHandle2 t) {
    return Type::template Convert<Type2>(t, region_);
  }

  TypeHandle Random() {
    return types[rng_->NextInt(static_cast<int>(types.size()))];
  }

  TypeHandle Fuzz(int depth = 4) {
    switch (rng_->NextInt(depth == 0 ? 3 : 20)) {
      case 0: {  // bitset
        int n = 0
        #define COUNT_BITSET_TYPES(type, value) + 1
        PROPER_BITSET_TYPE_LIST(COUNT_BITSET_TYPES)
        #undef COUNT_BITSET_TYPES
        ;
        int i = rng_->NextInt(n);
        #define PICK_BITSET_TYPE(type, value) \
          if (i-- == 0) return Type::type(region_);
        PROPER_BITSET_TYPE_LIST(PICK_BITSET_TYPE)
        #undef PICK_BITSET_TYPE
        UNREACHABLE();
      }
      case 1: {  // class
        int i = rng_->NextInt(static_cast<int>(maps.size()));
        return Type::Class(maps[i], region_);
      }
      case 2: {  // constant
        int i = rng_->NextInt(static_cast<int>(values.size()));
        return Type::Constant(values[i], region_);
      }
      case 3: {  // range
        int i = rng_->NextInt(static_cast<int>(integers.size()));
        int j = rng_->NextInt(static_cast<int>(integers.size()));
        i::Handle<i::Object> min = integers[i];
        i::Handle<i::Object> max = integers[j];
        if (min->Number() > max->Number()) std::swap(min, max);
        return Type::Range(min, max, region_);
      }
      case 4: {  // context
        int depth = rng_->NextInt(3);
        TypeHandle type = Type::Internal(region_);
        for (int i = 0; i < depth; ++i) type = Type::Context(type, region_);
        return type;
      }
      case 5: {  // array
        TypeHandle element = Fuzz(depth / 2);
        return Type::Array(element, region_);
      }
      case 6:
      case 7: {  // function
        TypeHandle result = Fuzz(depth / 2);
        TypeHandle receiver = Fuzz(depth / 2);
        int arity = rng_->NextInt(3);
        TypeHandle type = Type::Function(result, receiver, arity, region_);
        for (int i = 0; i < type->AsFunction()->Arity(); ++i) {
          TypeHandle parameter = Fuzz(depth / 2);
          type->AsFunction()->InitParameter(i, parameter);
        }
        return type;
      }
      default: {  // union
        int n = rng_->NextInt(10);
        TypeHandle type = None;
        for (int i = 0; i < n; ++i) {
          TypeHandle operand = Fuzz(depth - 1);
          type = Type::Union(type, operand, region_);
        }
        return type;
      }
    }
    UNREACHABLE();
  }

  Region* region() { return region_; }

 private:
  Region* region_;
  v8::base::RandomNumberGenerator* rng_;
};


template<class Type, class TypeHandle, class Region, class Rep>
struct Tests : Rep {
  typedef Types<Type, TypeHandle, Region> TypesInstance;
  typedef typename TypesInstance::TypeVector::iterator TypeIterator;
  typedef typename TypesInstance::MapVector::iterator MapIterator;
  typedef typename TypesInstance::ValueVector::iterator ValueIterator;

  Isolate* isolate;
  HandleScope scope;
  Zone zone;
  TypesInstance T;

  Tests() :
      isolate(CcTest::i_isolate()),
      scope(isolate),
      zone(isolate),
      T(Rep::ToRegion(&zone, isolate), isolate) {
  }

  bool Equal(TypeHandle type1, TypeHandle type2) {
    return
        type1->Equals(type2) &&
        this->IsBitset(type1) == this->IsBitset(type2) &&
        this->IsUnion(type1) == this->IsUnion(type2) &&
        type1->NumClasses() == type2->NumClasses() &&
        type1->NumConstants() == type2->NumConstants() &&
        (!this->IsBitset(type1) ||
          this->AsBitset(type1) == this->AsBitset(type2)) &&
        (!this->IsUnion(type1) ||
          this->Length(this->AsUnion(type1)) ==
              this->Length(this->AsUnion(type2)));
  }

  void CheckEqual(TypeHandle type1, TypeHandle type2) {
    CHECK(Equal(type1, type2));
  }

  void CheckSub(TypeHandle type1, TypeHandle type2) {
    CHECK(type1->Is(type2));
    CHECK(!type2->Is(type1));
    if (this->IsBitset(type1) && this->IsBitset(type2)) {
      CHECK(this->AsBitset(type1) != this->AsBitset(type2));
    }
  }

  void CheckUnordered(TypeHandle type1, TypeHandle type2) {
    CHECK(!type1->Is(type2));
    CHECK(!type2->Is(type1));
    if (this->IsBitset(type1) && this->IsBitset(type2)) {
      CHECK(this->AsBitset(type1) != this->AsBitset(type2));
    }
  }

  void CheckOverlap(TypeHandle type1, TypeHandle type2) {
    CHECK(type1->Maybe(type2));
    CHECK(type2->Maybe(type1));
  }

  void CheckDisjoint(TypeHandle type1, TypeHandle type2) {
    CHECK(!type1->Is(type2));
    CHECK(!type2->Is(type1));
    CHECK(!type1->Maybe(type2));
    CHECK(!type2->Maybe(type1));
  }

  void IsSomeType() {
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle t = *it;
      CHECK(1 ==
          this->IsBitset(t) + t->IsClass() + t->IsConstant() + t->IsRange() +
          this->IsUnion(t) + t->IsArray() + t->IsFunction() + t->IsContext());
    }
  }

  void Bitset() {
    // None and Any are bitsets.
    CHECK(this->IsBitset(T.None));
    CHECK(this->IsBitset(T.Any));

    CHECK(bitset(0) == this->AsBitset(T.None));
    CHECK(bitset(0xfffffffeu) == this->AsBitset(T.Any));

    // Union(T1, T2) is bitset for bitsets T1,T2
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        TypeHandle union12 = T.Union(type1, type2);
        CHECK(!(this->IsBitset(type1) && this->IsBitset(type2)) ||
              this->IsBitset(union12));
      }
    }

    // Intersect(T1, T2) is bitset for bitsets T1,T2
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        TypeHandle intersect12 = T.Intersect(type1, type2);
        CHECK(!(this->IsBitset(type1) && this->IsBitset(type2)) ||
              this->IsBitset(intersect12));
      }
    }

    // Union(T1, T2) is bitset if T2 is bitset and T1->Is(T2)
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        TypeHandle union12 = T.Union(type1, type2);
        CHECK(!(this->IsBitset(type2) && type1->Is(type2)) ||
              this->IsBitset(union12));
      }
    }

    // Union(T1, T2) is bitwise disjunction for bitsets T1,T2
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        TypeHandle union12 = T.Union(type1, type2);
        if (this->IsBitset(type1) && this->IsBitset(type2)) {
          CHECK(
              (this->AsBitset(type1) | this->AsBitset(type2)) ==
              this->AsBitset(union12));
        }
      }
    }

    // Intersect(T1, T2) is bitwise conjunction for bitsets T1,T2 (modulo None)
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        TypeHandle intersect12 = T.Intersect(type1, type2);
        if (this->IsBitset(type1) && this->IsBitset(type2)) {
          bitset bits = this->AsBitset(type1) & this->AsBitset(type2);
          CHECK(
              (Rep::BitsetType::IsInhabited(bits) ? bits : 0) ==
              this->AsBitset(intersect12));
        }
      }
    }
  }

  void Class() {
    // Constructor
    for (MapIterator mt = T.maps.begin(); mt != T.maps.end(); ++mt) {
      Handle<i::Map> map = *mt;
      TypeHandle type = T.Class(map);
      CHECK(type->IsClass());
    }

    // Map attribute
    for (MapIterator mt = T.maps.begin(); mt != T.maps.end(); ++mt) {
      Handle<i::Map> map = *mt;
      TypeHandle type = T.Class(map);
      CHECK(*map == *type->AsClass()->Map());
    }

    // Functionality & Injectivity: Class(M1) = Class(M2) iff M1 = M2
    for (MapIterator mt1 = T.maps.begin(); mt1 != T.maps.end(); ++mt1) {
      for (MapIterator mt2 = T.maps.begin(); mt2 != T.maps.end(); ++mt2) {
        Handle<i::Map> map1 = *mt1;
        Handle<i::Map> map2 = *mt2;
        TypeHandle type1 = T.Class(map1);
        TypeHandle type2 = T.Class(map2);
        CHECK(Equal(type1, type2) == (*map1 == *map2));
      }
    }
  }

  void Constant() {
    // Constructor
    for (ValueIterator vt = T.values.begin(); vt != T.values.end(); ++vt) {
      Handle<i::Object> value = *vt;
      TypeHandle type = T.Constant(value);
      CHECK(type->IsConstant());
    }

    // Value attribute
    for (ValueIterator vt = T.values.begin(); vt != T.values.end(); ++vt) {
      Handle<i::Object> value = *vt;
      TypeHandle type = T.Constant(value);
      CHECK(*value == *type->AsConstant()->Value());
    }

    // Functionality & Injectivity: Constant(V1) = Constant(V2) iff V1 = V2
    for (ValueIterator vt1 = T.values.begin(); vt1 != T.values.end(); ++vt1) {
      for (ValueIterator vt2 = T.values.begin(); vt2 != T.values.end(); ++vt2) {
        Handle<i::Object> value1 = *vt1;
        Handle<i::Object> value2 = *vt2;
        TypeHandle type1 = T.Constant(value1);
        TypeHandle type2 = T.Constant(value2);
        CHECK(Equal(type1, type2) == (*value1 == *value2));
      }
    }

    // Typing of numbers
    Factory* fac = isolate->factory();
    CHECK(T.Constant(fac->NewNumber(0))->Is(T.UnsignedSmall));
    CHECK(T.Constant(fac->NewNumber(1))->Is(T.UnsignedSmall));
    CHECK(T.Constant(fac->NewNumber(0x3fffffff))->Is(T.UnsignedSmall));
    CHECK(T.Constant(fac->NewNumber(-1))->Is(T.OtherSignedSmall));
    CHECK(T.Constant(fac->NewNumber(-0x3fffffff))->Is(T.OtherSignedSmall));
    CHECK(T.Constant(fac->NewNumber(-0x40000000))->Is(T.OtherSignedSmall));
    if (SmiValuesAre31Bits()) {
      CHECK(T.Constant(fac->NewNumber(0x40000000))->Is(T.OtherUnsigned31));
      CHECK(T.Constant(fac->NewNumber(0x7fffffff))->Is(T.OtherUnsigned31));
      CHECK(T.Constant(fac->NewNumber(-0x40000001))->Is(T.OtherSigned32));
      CHECK(T.Constant(fac->NewNumber(-0x7fffffff))->Is(T.OtherSigned32));
      CHECK(T.Constant(fac->NewNumber(-0x7fffffff-1))->Is(T.OtherSigned32));
    } else {
      CHECK(SmiValuesAre32Bits());
      CHECK(T.Constant(fac->NewNumber(0x40000000))->Is(T.UnsignedSmall));
      CHECK(T.Constant(fac->NewNumber(0x7fffffff))->Is(T.UnsignedSmall));
      CHECK(!T.Constant(fac->NewNumber(0x40000000))->Is(T.OtherUnsigned31));
      CHECK(!T.Constant(fac->NewNumber(0x7fffffff))->Is(T.OtherUnsigned31));
      CHECK(T.Constant(fac->NewNumber(-0x40000001))->Is(T.OtherSignedSmall));
      CHECK(T.Constant(fac->NewNumber(-0x7fffffff))->Is(T.OtherSignedSmall));
      CHECK(T.Constant(fac->NewNumber(-0x7fffffff-1))->Is(T.OtherSignedSmall));
      CHECK(!T.Constant(fac->NewNumber(-0x40000001))->Is(T.OtherSigned32));
      CHECK(!T.Constant(fac->NewNumber(-0x7fffffff))->Is(T.OtherSigned32));
      CHECK(!T.Constant(fac->NewNumber(-0x7fffffff-1))->Is(T.OtherSigned32));
    }
    CHECK(T.Constant(fac->NewNumber(0x80000000u))->Is(T.OtherUnsigned32));
    CHECK(T.Constant(fac->NewNumber(0xffffffffu))->Is(T.OtherUnsigned32));
    CHECK(T.Constant(fac->NewNumber(0xffffffffu+1.0))->Is(T.OtherNumber));
    CHECK(T.Constant(fac->NewNumber(-0x7fffffff-2.0))->Is(T.OtherNumber));
    CHECK(T.Constant(fac->NewNumber(0.1))->Is(T.OtherNumber));
    CHECK(T.Constant(fac->NewNumber(-10.1))->Is(T.OtherNumber));
    CHECK(T.Constant(fac->NewNumber(10e60))->Is(T.OtherNumber));
    CHECK(T.Constant(fac->NewNumber(-1.0*0.0))->Is(T.MinusZero));
    CHECK(T.Constant(fac->NewNumber(v8::base::OS::nan_value()))->Is(T.NaN));
    CHECK(T.Constant(fac->NewNumber(V8_INFINITY))->Is(T.OtherNumber));
    CHECK(T.Constant(fac->NewNumber(-V8_INFINITY))->Is(T.OtherNumber));
  }

  void Range() {
    // Constructor
    for (ValueIterator i = T.integers.begin(); i != T.integers.end(); ++i) {
      for (ValueIterator j = T.integers.begin(); j != T.integers.end(); ++j) {
        i::Handle<i::Object> min = *i;
        i::Handle<i::Object> max = *j;
        if (min->Number() > max->Number()) std::swap(min, max);
        TypeHandle type = T.Range(min, max);
        CHECK(type->IsRange());
      }
    }

    // Range attributes
    for (ValueIterator i = T.integers.begin(); i != T.integers.end(); ++i) {
      for (ValueIterator j = T.integers.begin(); j != T.integers.end(); ++j) {
        i::Handle<i::Object> min = *i;
        i::Handle<i::Object> max = *j;
        if (min->Number() > max->Number()) std::swap(min, max);
        TypeHandle type = T.Range(min, max);
        CHECK(*min == *type->AsRange()->Min());
        CHECK(*max == *type->AsRange()->Max());
      }
    }

    // Functionality & Injectivity:
    // Range(min1, max1) = Range(min2, max2) <=> min1 = min2 /\ max1 = max2
    for (ValueIterator i1 = T.integers.begin();
        i1 != T.integers.end(); ++i1) {
      for (ValueIterator j1 = T.integers.begin();
          j1 != T.integers.end(); ++j1) {
        for (ValueIterator i2 = T.integers.begin();
            i2 != T.integers.end(); ++i2) {
          for (ValueIterator j2 = T.integers.begin();
              j2 != T.integers.end(); ++j2) {
            i::Handle<i::Object> min1 = *i1;
            i::Handle<i::Object> max1 = *j1;
            i::Handle<i::Object> min2 = *i2;
            i::Handle<i::Object> max2 = *j2;
            if (min1->Number() > max1->Number()) std::swap(min1, max1);
            if (min2->Number() > max2->Number()) std::swap(min2, max2);
            TypeHandle type1 = T.Range(min1, max1);
            TypeHandle type2 = T.Range(min2, max2);
            CHECK(Equal(type1, type2) == (*min1 == *min2 && *max1 == *max2));
          }
        }
      }
    }
  }

  void Array() {
    // Constructor
    for (int i = 0; i < 20; ++i) {
      TypeHandle type = T.Random();
      TypeHandle array = T.Array1(type);
      CHECK(array->IsArray());
    }

    // Attributes
    for (int i = 0; i < 20; ++i) {
      TypeHandle type = T.Random();
      TypeHandle array = T.Array1(type);
      CheckEqual(type, array->AsArray()->Element());
    }

    // Functionality & Injectivity: Array(T1) = Array(T2) iff T1 = T2
    for (int i = 0; i < 20; ++i) {
      for (int j = 0; j < 20; ++j) {
        TypeHandle type1 = T.Random();
        TypeHandle type2 = T.Random();
        TypeHandle array1 = T.Array1(type1);
        TypeHandle array2 = T.Array1(type2);
        CHECK(Equal(array1, array2) == Equal(type1, type2));
      }
    }
  }

  void Function() {
    // Constructors
    for (int i = 0; i < 20; ++i) {
      for (int j = 0; j < 20; ++j) {
        for (int k = 0; k < 20; ++k) {
          TypeHandle type1 = T.Random();
          TypeHandle type2 = T.Random();
          TypeHandle type3 = T.Random();
          TypeHandle function0 = T.Function0(type1, type2);
          TypeHandle function1 = T.Function1(type1, type2, type3);
          TypeHandle function2 = T.Function2(type1, type2, type3);
          CHECK(function0->IsFunction());
          CHECK(function1->IsFunction());
          CHECK(function2->IsFunction());
        }
      }
    }

    // Attributes
    for (int i = 0; i < 20; ++i) {
      for (int j = 0; j < 20; ++j) {
        for (int k = 0; k < 20; ++k) {
          TypeHandle type1 = T.Random();
          TypeHandle type2 = T.Random();
          TypeHandle type3 = T.Random();
          TypeHandle function0 = T.Function0(type1, type2);
          TypeHandle function1 = T.Function1(type1, type2, type3);
          TypeHandle function2 = T.Function2(type1, type2, type3);
          CHECK_EQ(0, function0->AsFunction()->Arity());
          CHECK_EQ(1, function1->AsFunction()->Arity());
          CHECK_EQ(2, function2->AsFunction()->Arity());
          CheckEqual(type1, function0->AsFunction()->Result());
          CheckEqual(type1, function1->AsFunction()->Result());
          CheckEqual(type1, function2->AsFunction()->Result());
          CheckEqual(type2, function0->AsFunction()->Receiver());
          CheckEqual(type2, function1->AsFunction()->Receiver());
          CheckEqual(T.Any, function2->AsFunction()->Receiver());
          CheckEqual(type3, function1->AsFunction()->Parameter(0));
          CheckEqual(type2, function2->AsFunction()->Parameter(0));
          CheckEqual(type3, function2->AsFunction()->Parameter(1));
        }
      }
    }

    // Functionality & Injectivity: Function(Ts1) = Function(Ts2) iff Ts1 = Ts2
    for (int i = 0; i < 20; ++i) {
      for (int j = 0; j < 20; ++j) {
        for (int k = 0; k < 20; ++k) {
          TypeHandle type1 = T.Random();
          TypeHandle type2 = T.Random();
          TypeHandle type3 = T.Random();
          TypeHandle function01 = T.Function0(type1, type2);
          TypeHandle function02 = T.Function0(type1, type3);
          TypeHandle function03 = T.Function0(type3, type2);
          TypeHandle function11 = T.Function1(type1, type2, type2);
          TypeHandle function12 = T.Function1(type1, type2, type3);
          TypeHandle function21 = T.Function2(type1, type2, type2);
          TypeHandle function22 = T.Function2(type1, type2, type3);
          TypeHandle function23 = T.Function2(type1, type3, type2);
          CHECK(Equal(function01, function02) == Equal(type2, type3));
          CHECK(Equal(function01, function03) == Equal(type1, type3));
          CHECK(Equal(function11, function12) == Equal(type2, type3));
          CHECK(Equal(function21, function22) == Equal(type2, type3));
          CHECK(Equal(function21, function23) == Equal(type2, type3));
        }
      }
    }
  }

  void Of() {
    // Constant(V)->Is(Of(V))
    for (ValueIterator vt = T.values.begin(); vt != T.values.end(); ++vt) {
      Handle<i::Object> value = *vt;
      TypeHandle const_type = T.Constant(value);
      TypeHandle of_type = T.Of(value);
      CHECK(const_type->Is(of_type));
    }

    // If Of(V)->Is(T), then Constant(V)->Is(T)
    for (ValueIterator vt = T.values.begin(); vt != T.values.end(); ++vt) {
      for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
        Handle<i::Object> value = *vt;
        TypeHandle type = *it;
        TypeHandle const_type = T.Constant(value);
        TypeHandle of_type = T.Of(value);
        CHECK(!of_type->Is(type) || const_type->Is(type));
      }
    }

    // If Constant(V)->Is(T), then Of(V)->Is(T) or T->Maybe(Constant(V))
    for (ValueIterator vt = T.values.begin(); vt != T.values.end(); ++vt) {
      for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
        Handle<i::Object> value = *vt;
        TypeHandle type = *it;
        TypeHandle const_type = T.Constant(value);
        TypeHandle of_type = T.Of(value);
        CHECK(!const_type->Is(type) ||
              of_type->Is(type) || type->Maybe(const_type));
      }
    }
  }

  void NowOf() {
    // Constant(V)->NowIs(NowOf(V))
    for (ValueIterator vt = T.values.begin(); vt != T.values.end(); ++vt) {
      Handle<i::Object> value = *vt;
      TypeHandle const_type = T.Constant(value);
      TypeHandle nowof_type = T.NowOf(value);
      CHECK(const_type->NowIs(nowof_type));
    }

    // NowOf(V)->Is(Of(V))
    for (ValueIterator vt = T.values.begin(); vt != T.values.end(); ++vt) {
      Handle<i::Object> value = *vt;
      TypeHandle nowof_type = T.NowOf(value);
      TypeHandle of_type = T.Of(value);
      CHECK(nowof_type->Is(of_type));
    }

    // If NowOf(V)->NowIs(T), then Constant(V)->NowIs(T)
    for (ValueIterator vt = T.values.begin(); vt != T.values.end(); ++vt) {
      for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
        Handle<i::Object> value = *vt;
        TypeHandle type = *it;
        TypeHandle const_type = T.Constant(value);
        TypeHandle nowof_type = T.NowOf(value);
        CHECK(!nowof_type->NowIs(type) || const_type->NowIs(type));
      }
    }

    // If Constant(V)->NowIs(T),
    // then NowOf(V)->NowIs(T) or T->Maybe(Constant(V))
    for (ValueIterator vt = T.values.begin(); vt != T.values.end(); ++vt) {
      for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
        Handle<i::Object> value = *vt;
        TypeHandle type = *it;
        TypeHandle const_type = T.Constant(value);
        TypeHandle nowof_type = T.NowOf(value);
        CHECK(!const_type->NowIs(type) ||
              nowof_type->NowIs(type) || type->Maybe(const_type));
      }
    }

    // If Constant(V)->Is(T),
    // then NowOf(V)->Is(T) or T->Maybe(Constant(V))
    for (ValueIterator vt = T.values.begin(); vt != T.values.end(); ++vt) {
      for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
        Handle<i::Object> value = *vt;
        TypeHandle type = *it;
        TypeHandle const_type = T.Constant(value);
        TypeHandle nowof_type = T.NowOf(value);
        CHECK(!const_type->Is(type) ||
              nowof_type->Is(type) || type->Maybe(const_type));
      }
    }
  }

  void BitsetGlb() {
    // Lower: (T->BitsetGlb())->Is(T)
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      TypeHandle glb =
          Rep::BitsetType::New(Rep::BitsetType::Glb(type), T.region());
      CHECK(glb->Is(type));
    }

    // Greatest: If T1->IsBitset() and T1->Is(T2), then T1->Is(T2->BitsetGlb())
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        TypeHandle glb2 =
            Rep::BitsetType::New(Rep::BitsetType::Glb(type2), T.region());
        CHECK(!this->IsBitset(type1) || !type1->Is(type2) || type1->Is(glb2));
      }
    }

    // Monotonicity: T1->Is(T2) implies (T1->BitsetGlb())->Is(T2->BitsetGlb())
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        TypeHandle glb1 =
            Rep::BitsetType::New(Rep::BitsetType::Glb(type1), T.region());
        TypeHandle glb2 =
            Rep::BitsetType::New(Rep::BitsetType::Glb(type2), T.region());
        CHECK(!type1->Is(type2) || glb1->Is(glb2));
      }
    }
  }

  void BitsetLub() {
    // Upper: T->Is(T->BitsetLub())
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      TypeHandle lub =
          Rep::BitsetType::New(Rep::BitsetType::Lub(type), T.region());
      CHECK(type->Is(lub));
    }

    // Least: If T2->IsBitset() and T1->Is(T2), then (T1->BitsetLub())->Is(T2)
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        TypeHandle lub1 =
            Rep::BitsetType::New(Rep::BitsetType::Lub(type1), T.region());
        CHECK(!this->IsBitset(type2) || !type1->Is(type2) || lub1->Is(type2));
      }
    }

    // Monotonicity: T1->Is(T2) implies (T1->BitsetLub())->Is(T2->BitsetLub())
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        TypeHandle lub1 =
            Rep::BitsetType::New(Rep::BitsetType::Lub(type1), T.region());
        TypeHandle lub2 =
            Rep::BitsetType::New(Rep::BitsetType::Lub(type2), T.region());
        CHECK(!type1->Is(type2) || lub1->Is(lub2));
      }
    }
  }

  void Is() {
    // Least Element (Bottom): None->Is(T)
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      CHECK(T.None->Is(type));
    }

    // Greatest Element (Top): T->Is(Any)
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      CHECK(type->Is(T.Any));
    }

    // Bottom Uniqueness: T->Is(None) implies T = None
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      if (type->Is(T.None)) CheckEqual(type, T.None);
    }

    // Top Uniqueness: Any->Is(T) implies T = Any
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      if (T.Any->Is(type)) CheckEqual(type, T.Any);
    }

    // Reflexivity: T->Is(T)
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      CHECK(type->Is(type));
    }

    // Transitivity: T1->Is(T2) and T2->Is(T3) implies T1->Is(T3)
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
          TypeHandle type1 = *it1;
          TypeHandle type2 = *it2;
          TypeHandle type3 = *it3;
          CHECK(!(type1->Is(type2) && type2->Is(type3)) || type1->Is(type3));
        }
      }
    }

    // Antisymmetry: T1->Is(T2) and T2->Is(T1) iff T1 = T2
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        CHECK((type1->Is(type2) && type2->Is(type1)) == Equal(type1, type2));
      }
    }

    // Class(M1)->Is(Class(M2)) iff M1 = M2
    for (MapIterator mt1 = T.maps.begin(); mt1 != T.maps.end(); ++mt1) {
      for (MapIterator mt2 = T.maps.begin(); mt2 != T.maps.end(); ++mt2) {
        Handle<i::Map> map1 = *mt1;
        Handle<i::Map> map2 = *mt2;
        TypeHandle class_type1 = T.Class(map1);
        TypeHandle class_type2 = T.Class(map2);
        CHECK(class_type1->Is(class_type2) == (*map1 == *map2));
      }
    }

    // Constant(V1)->Is(Constant(V2)) iff V1 = V2
    for (ValueIterator vt1 = T.values.begin(); vt1 != T.values.end(); ++vt1) {
      for (ValueIterator vt2 = T.values.begin(); vt2 != T.values.end(); ++vt2) {
        Handle<i::Object> value1 = *vt1;
        Handle<i::Object> value2 = *vt2;
        TypeHandle const_type1 = T.Constant(value1);
        TypeHandle const_type2 = T.Constant(value2);
        CHECK(const_type1->Is(const_type2) == (*value1 == *value2));
      }
    }

    // Range(min1, max1)->Is(Range(min2, max2)) iff
    // min1 >= min2 /\ max1 <= max2
    for (ValueIterator i1 = T.integers.begin();
        i1 != T.integers.end(); ++i1) {
      for (ValueIterator j1 = T.integers.begin();
          j1 != T.integers.end(); ++j1) {
        for (ValueIterator i2 = T.integers.begin();
             i2 != T.integers.end(); ++i2) {
          for (ValueIterator j2 = T.integers.begin();
               j2 != T.integers.end(); ++j2) {
            i::Handle<i::Object> min1 = *i1;
            i::Handle<i::Object> max1 = *j1;
            i::Handle<i::Object> min2 = *i2;
            i::Handle<i::Object> max2 = *j2;
            if (min1->Number() > max1->Number()) std::swap(min1, max1);
            if (min2->Number() > max2->Number()) std::swap(min2, max2);
            TypeHandle type1 = T.Range(min1, max1);
            TypeHandle type2 = T.Range(min2, max2);
            CHECK(type1->Is(type2) ==
                (min2->Number() <= min1->Number() &&
                 max1->Number() <= max2->Number()));
          }
        }
      }
    }

    // Context(T1)->Is(Context(T2)) iff T1 = T2
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle outer1 = *it1;
        TypeHandle outer2 = *it2;
        TypeHandle type1 = T.Context(outer1);
        TypeHandle type2 = T.Context(outer2);
        CHECK(type1->Is(type2) == outer1->Equals(outer2));
      }
    }

    // Array(T1)->Is(Array(T2)) iff T1 = T2
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle element1 = *it1;
        TypeHandle element2 = *it2;
        TypeHandle type1 = T.Array1(element1);
        TypeHandle type2 = T.Array1(element2);
        CHECK(type1->Is(type2) == element1->Equals(element2));
      }
    }

    // Function0(S1, T1)->Is(Function0(S2, T2)) iff S1 = S2 and T1 = T2
    for (TypeIterator i = T.types.begin(); i != T.types.end(); ++i) {
      for (TypeIterator j = T.types.begin(); j != T.types.end(); ++j) {
        TypeHandle result1 = *i;
        TypeHandle receiver1 = *j;
        TypeHandle type1 = T.Function0(result1, receiver1);
        TypeHandle result2 = T.Random();
        TypeHandle receiver2 = T.Random();
        TypeHandle type2 = T.Function0(result2, receiver2);
        CHECK(type1->Is(type2) ==
            (result1->Equals(result2) && receiver1->Equals(receiver2)));
      }
    }

    // (In-)Compatibilities.
    for (TypeIterator i = T.types.begin(); i != T.types.end(); ++i) {
      for (TypeIterator j = T.types.begin(); j != T.types.end(); ++j) {
        TypeHandle type1 = *i;
        TypeHandle type2 = *j;
        CHECK(!type1->Is(type2) || this->IsBitset(type2) ||
              this->IsUnion(type2) || this->IsUnion(type1) ||
              (type1->IsClass() && type2->IsClass()) ||
              (type1->IsConstant() && type2->IsConstant()) ||
              (type1->IsConstant() && type2->IsRange()) ||
              (type1->IsRange() && type2->IsRange()) ||
              (type1->IsContext() && type2->IsContext()) ||
              (type1->IsArray() && type2->IsArray()) ||
              (type1->IsFunction() && type2->IsFunction()) ||
              type1->Equals(T.None));
      }
    }

    // Basic types
    CheckUnordered(T.Boolean, T.Null);
    CheckUnordered(T.Undefined, T.Null);
    CheckUnordered(T.Boolean, T.Undefined);

    CheckSub(T.SignedSmall, T.Number);
    CheckSub(T.Signed32, T.Number);
    CheckSub(T.SignedSmall, T.Signed32);
    CheckUnordered(T.SignedSmall, T.MinusZero);
    CheckUnordered(T.Signed32, T.Unsigned32);

    CheckSub(T.UniqueName, T.Name);
    CheckSub(T.String, T.Name);
    CheckSub(T.InternalizedString, T.String);
    CheckSub(T.InternalizedString, T.UniqueName);
    CheckSub(T.InternalizedString, T.Name);
    CheckSub(T.Symbol, T.UniqueName);
    CheckSub(T.Symbol, T.Name);
    CheckUnordered(T.String, T.UniqueName);
    CheckUnordered(T.String, T.Symbol);
    CheckUnordered(T.InternalizedString, T.Symbol);

    CheckSub(T.Object, T.Receiver);
    CheckSub(T.Array, T.Object);
    CheckSub(T.Function, T.Object);
    CheckSub(T.Proxy, T.Receiver);
    CheckUnordered(T.Object, T.Proxy);
    CheckUnordered(T.Array, T.Function);

    // Structural types
    CheckSub(T.ObjectClass, T.Object);
    CheckSub(T.ArrayClass, T.Object);
    CheckSub(T.ArrayClass, T.Array);
    CheckSub(T.UninitializedClass, T.Internal);
    CheckUnordered(T.ObjectClass, T.ArrayClass);
    CheckUnordered(T.UninitializedClass, T.Null);
    CheckUnordered(T.UninitializedClass, T.Undefined);

    CheckSub(T.SmiConstant, T.SignedSmall);
    CheckSub(T.SmiConstant, T.Signed32);
    CheckSub(T.SmiConstant, T.Number);
    CheckSub(T.ObjectConstant1, T.Object);
    CheckSub(T.ObjectConstant2, T.Object);
    CheckSub(T.ArrayConstant, T.Object);
    CheckSub(T.ArrayConstant, T.Array);
    CheckSub(T.UninitializedConstant, T.Internal);
    CheckUnordered(T.ObjectConstant1, T.ObjectConstant2);
    CheckUnordered(T.ObjectConstant1, T.ArrayConstant);
    CheckUnordered(T.UninitializedConstant, T.Null);
    CheckUnordered(T.UninitializedConstant, T.Undefined);

    CheckUnordered(T.ObjectConstant1, T.ObjectClass);
    CheckUnordered(T.ObjectConstant2, T.ObjectClass);
    CheckUnordered(T.ObjectConstant1, T.ArrayClass);
    CheckUnordered(T.ObjectConstant2, T.ArrayClass);
    CheckUnordered(T.ArrayConstant, T.ObjectClass);

    CheckSub(T.NumberArray, T.Array);
    CheckSub(T.NumberArray, T.Object);
    CheckUnordered(T.StringArray, T.AnyArray);

    CheckSub(T.MethodFunction, T.Function);
    CheckSub(T.NumberFunction1, T.Object);
    CheckUnordered(T.SignedFunction1, T.NumberFunction1);
    CheckUnordered(T.NumberFunction1, T.NumberFunction2);
  }

  void NowIs() {
    // Least Element (Bottom): None->NowIs(T)
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      CHECK(T.None->NowIs(type));
    }

    // Greatest Element (Top): T->NowIs(Any)
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      CHECK(type->NowIs(T.Any));
    }

    // Bottom Uniqueness: T->NowIs(None) implies T = None
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      if (type->NowIs(T.None)) CheckEqual(type, T.None);
    }

    // Top Uniqueness: Any->NowIs(T) implies T = Any
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      if (T.Any->NowIs(type)) CheckEqual(type, T.Any);
    }

    // Reflexivity: T->NowIs(T)
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      CHECK(type->NowIs(type));
    }

    // Transitivity: T1->NowIs(T2) and T2->NowIs(T3) implies T1->NowIs(T3)
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
          TypeHandle type1 = *it1;
          TypeHandle type2 = *it2;
          TypeHandle type3 = *it3;
          CHECK(!(type1->NowIs(type2) && type2->NowIs(type3)) ||
                type1->NowIs(type3));
        }
      }
    }

    // Antisymmetry: T1->NowIs(T2) and T2->NowIs(T1) iff T1 = T2
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        CHECK((type1->NowIs(type2) && type2->NowIs(type1)) ==
              Equal(type1, type2));
      }
    }

    // T1->Is(T2) implies T1->NowIs(T2)
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        CHECK(!type1->Is(type2) || type1->NowIs(type2));
      }
    }

    // Constant(V1)->NowIs(Constant(V2)) iff V1 = V2
    for (ValueIterator vt1 = T.values.begin(); vt1 != T.values.end(); ++vt1) {
      for (ValueIterator vt2 = T.values.begin(); vt2 != T.values.end(); ++vt2) {
        Handle<i::Object> value1 = *vt1;
        Handle<i::Object> value2 = *vt2;
        TypeHandle const_type1 = T.Constant(value1);
        TypeHandle const_type2 = T.Constant(value2);
        CHECK(const_type1->NowIs(const_type2) == (*value1 == *value2));
      }
    }

    // Class(M1)->NowIs(Class(M2)) iff M1 = M2
    for (MapIterator mt1 = T.maps.begin(); mt1 != T.maps.end(); ++mt1) {
      for (MapIterator mt2 = T.maps.begin(); mt2 != T.maps.end(); ++mt2) {
        Handle<i::Map> map1 = *mt1;
        Handle<i::Map> map2 = *mt2;
        TypeHandle class_type1 = T.Class(map1);
        TypeHandle class_type2 = T.Class(map2);
        CHECK(class_type1->NowIs(class_type2) == (*map1 == *map2));
      }
    }

    // Constant(V)->NowIs(Class(M)) iff V has map M
    for (MapIterator mt = T.maps.begin(); mt != T.maps.end(); ++mt) {
      for (ValueIterator vt = T.values.begin(); vt != T.values.end(); ++vt) {
        Handle<i::Map> map = *mt;
        Handle<i::Object> value = *vt;
        TypeHandle const_type = T.Constant(value);
        TypeHandle class_type = T.Class(map);
        CHECK((value->IsHeapObject() &&
               i::HeapObject::cast(*value)->map() == *map)
              == const_type->NowIs(class_type));
      }
    }

    // Class(M)->NowIs(Constant(V)) never
    for (MapIterator mt = T.maps.begin(); mt != T.maps.end(); ++mt) {
      for (ValueIterator vt = T.values.begin(); vt != T.values.end(); ++vt) {
        Handle<i::Map> map = *mt;
        Handle<i::Object> value = *vt;
        TypeHandle const_type = T.Constant(value);
        TypeHandle class_type = T.Class(map);
        CHECK(!class_type->NowIs(const_type));
      }
    }
  }

  void Contains() {
    // T->Contains(V) iff Constant(V)->Is(T)
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      for (ValueIterator vt = T.values.begin(); vt != T.values.end(); ++vt) {
        TypeHandle type = *it;
        Handle<i::Object> value = *vt;
        TypeHandle const_type = T.Constant(value);
        CHECK(type->Contains(value) == const_type->Is(type));
      }
    }
  }

  void NowContains() {
    // T->NowContains(V) iff Constant(V)->NowIs(T)
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      for (ValueIterator vt = T.values.begin(); vt != T.values.end(); ++vt) {
        TypeHandle type = *it;
        Handle<i::Object> value = *vt;
        TypeHandle const_type = T.Constant(value);
        CHECK(type->NowContains(value) == const_type->NowIs(type));
      }
    }

    // T->Contains(V) implies T->NowContains(V)
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      for (ValueIterator vt = T.values.begin(); vt != T.values.end(); ++vt) {
        TypeHandle type = *it;
        Handle<i::Object> value = *vt;
        CHECK(!type->Contains(value) || type->NowContains(value));
      }
    }

    // NowOf(V)->Is(T) implies T->NowContains(V)
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      for (ValueIterator vt = T.values.begin(); vt != T.values.end(); ++vt) {
        TypeHandle type = *it;
        Handle<i::Object> value = *vt;
        TypeHandle nowof_type = T.Of(value);
        CHECK(!nowof_type->NowIs(type) || type->NowContains(value));
      }
    }
  }

  void Maybe() {
    // T->Maybe(Any) iff T inhabited
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      CHECK(type->Maybe(T.Any) == type->IsInhabited());
    }

    // T->Maybe(None) never
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      CHECK(!type->Maybe(T.None));
    }

    // Reflexivity upto Inhabitation: T->Maybe(T) iff T inhabited
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      CHECK(type->Maybe(type) == type->IsInhabited());
    }

    // Symmetry: T1->Maybe(T2) iff T2->Maybe(T1)
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        CHECK(type1->Maybe(type2) == type2->Maybe(type1));
      }
    }

    // T1->Maybe(T2) implies T1, T2 inhabited
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        CHECK(!type1->Maybe(type2) ||
              (type1->IsInhabited() && type2->IsInhabited()));
      }
    }

    // T1->Maybe(T2) implies Intersect(T1, T2) inhabited
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        TypeHandle intersect12 = T.Intersect(type1, type2);
        CHECK(!type1->Maybe(type2) || intersect12->IsInhabited());
      }
    }

    // T1->Is(T2) and T1 inhabited implies T1->Maybe(T2)
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        CHECK(!(type1->Is(type2) && type1->IsInhabited()) ||
              type1->Maybe(type2));
      }
    }

    // Constant(V1)->Maybe(Constant(V2)) iff V1 = V2
    for (ValueIterator vt1 = T.values.begin(); vt1 != T.values.end(); ++vt1) {
      for (ValueIterator vt2 = T.values.begin(); vt2 != T.values.end(); ++vt2) {
        Handle<i::Object> value1 = *vt1;
        Handle<i::Object> value2 = *vt2;
        TypeHandle const_type1 = T.Constant(value1);
        TypeHandle const_type2 = T.Constant(value2);
        CHECK(const_type1->Maybe(const_type2) == (*value1 == *value2));
      }
    }

    // Class(M1)->Maybe(Class(M2)) iff M1 = M2
    for (MapIterator mt1 = T.maps.begin(); mt1 != T.maps.end(); ++mt1) {
      for (MapIterator mt2 = T.maps.begin(); mt2 != T.maps.end(); ++mt2) {
        Handle<i::Map> map1 = *mt1;
        Handle<i::Map> map2 = *mt2;
        TypeHandle class_type1 = T.Class(map1);
        TypeHandle class_type2 = T.Class(map2);
        CHECK(class_type1->Maybe(class_type2) == (*map1 == *map2));
      }
    }

    // Constant(V)->Maybe(Class(M)) never
    // This does NOT hold!
    /*
    for (MapIterator mt = T.maps.begin(); mt != T.maps.end(); ++mt) {
      for (ValueIterator vt = T.values.begin(); vt != T.values.end(); ++vt) {
        Handle<i::Map> map = *mt;
        Handle<i::Object> value = *vt;
        TypeHandle const_type = T.Constant(value);
        TypeHandle class_type = T.Class(map);
        CHECK(!const_type->Maybe(class_type));
      }
    }
    */

    // Class(M)->Maybe(Constant(V)) never
    // This does NOT hold!
    /*
    for (MapIterator mt = T.maps.begin(); mt != T.maps.end(); ++mt) {
      for (ValueIterator vt = T.values.begin(); vt != T.values.end(); ++vt) {
        Handle<i::Map> map = *mt;
        Handle<i::Object> value = *vt;
        TypeHandle const_type = T.Constant(value);
        TypeHandle class_type = T.Class(map);
        CHECK(!class_type->Maybe(const_type));
      }
    }
    */

    // Basic types
    CheckDisjoint(T.Boolean, T.Null);
    CheckDisjoint(T.Undefined, T.Null);
    CheckDisjoint(T.Boolean, T.Undefined);
    CheckOverlap(T.SignedSmall, T.Number);
    CheckOverlap(T.NaN, T.Number);
    CheckDisjoint(T.Signed32, T.NaN);
    CheckOverlap(T.UniqueName, T.Name);
    CheckOverlap(T.String, T.Name);
    CheckOverlap(T.InternalizedString, T.String);
    CheckOverlap(T.InternalizedString, T.UniqueName);
    CheckOverlap(T.InternalizedString, T.Name);
    CheckOverlap(T.Symbol, T.UniqueName);
    CheckOverlap(T.Symbol, T.Name);
    CheckOverlap(T.String, T.UniqueName);
    CheckDisjoint(T.String, T.Symbol);
    CheckDisjoint(T.InternalizedString, T.Symbol);
    CheckOverlap(T.Object, T.Receiver);
    CheckOverlap(T.Array, T.Object);
    CheckOverlap(T.Function, T.Object);
    CheckOverlap(T.Proxy, T.Receiver);
    CheckDisjoint(T.Object, T.Proxy);
    CheckDisjoint(T.Array, T.Function);

    // Structural types
    CheckOverlap(T.ObjectClass, T.Object);
    CheckOverlap(T.ArrayClass, T.Object);
    CheckOverlap(T.ObjectClass, T.ObjectClass);
    CheckOverlap(T.ArrayClass, T.ArrayClass);
    CheckDisjoint(T.ObjectClass, T.ArrayClass);
    CheckOverlap(T.SmiConstant, T.SignedSmall);
    CheckOverlap(T.SmiConstant, T.Signed32);
    CheckOverlap(T.SmiConstant, T.Number);
    CheckOverlap(T.ObjectConstant1, T.Object);
    CheckOverlap(T.ObjectConstant2, T.Object);
    CheckOverlap(T.ArrayConstant, T.Object);
    CheckOverlap(T.ArrayConstant, T.Array);
    CheckOverlap(T.ObjectConstant1, T.ObjectConstant1);
    CheckDisjoint(T.ObjectConstant1, T.ObjectConstant2);
    CheckDisjoint(T.ObjectConstant1, T.ArrayConstant);
    CheckDisjoint(T.ObjectConstant1, T.ArrayClass);
    CheckDisjoint(T.ObjectConstant2, T.ArrayClass);
    CheckDisjoint(T.ArrayConstant, T.ObjectClass);
    CheckOverlap(T.NumberArray, T.Array);
    CheckDisjoint(T.NumberArray, T.AnyArray);
    CheckDisjoint(T.NumberArray, T.StringArray);
    CheckOverlap(T.MethodFunction, T.Function);
    CheckDisjoint(T.SignedFunction1, T.NumberFunction1);
    CheckDisjoint(T.SignedFunction1, T.NumberFunction2);
    CheckDisjoint(T.NumberFunction1, T.NumberFunction2);
    CheckDisjoint(T.SignedFunction1, T.MethodFunction);
    CheckOverlap(T.ObjectConstant1, T.ObjectClass);  // !!!
    CheckOverlap(T.ObjectConstant2, T.ObjectClass);  // !!!
    CheckOverlap(T.NumberClass, T.Intersect(T.Number, T.Untagged));  // !!!
  }

  void Union1() {
    // Identity: Union(T, None) = T
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      TypeHandle union_type = T.Union(type, T.None);
      CheckEqual(union_type, type);
    }

    // Domination: Union(T, Any) = Any
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      TypeHandle union_type = T.Union(type, T.Any);
      CheckEqual(union_type, T.Any);
    }

    // Idempotence: Union(T, T) = T
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      TypeHandle union_type = T.Union(type, type);
      CheckEqual(union_type, type);
    }

    // Commutativity: Union(T1, T2) = Union(T2, T1)
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        TypeHandle union12 = T.Union(type1, type2);
        TypeHandle union21 = T.Union(type2, type1);
        CheckEqual(union12, union21);
      }
    }

    // Associativity: Union(T1, Union(T2, T3)) = Union(Union(T1, T2), T3)
    // This does NOT hold!
    /*
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
          TypeHandle type1 = *it1;
          TypeHandle type2 = *it2;
          TypeHandle type3 = *it3;
          TypeHandle union12 = T.Union(type1, type2);
          TypeHandle union23 = T.Union(type2, type3);
          TypeHandle union1_23 = T.Union(type1, union23);
          TypeHandle union12_3 = T.Union(union12, type3);
          CheckEqual(union1_23, union12_3);
        }
      }
    }
    */

    // Meet: T1->Is(Union(T1, T2)) and T2->Is(Union(T1, T2))
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        TypeHandle union12 = T.Union(type1, type2);
        CHECK(type1->Is(union12));
        CHECK(type2->Is(union12));
      }
    }

    // Upper Boundedness: T1->Is(T2) implies Union(T1, T2) = T2
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        TypeHandle union12 = T.Union(type1, type2);
        if (type1->Is(type2)) CheckEqual(union12, type2);
      }
    }

    // Monotonicity: T1->Is(T2) implies Union(T1, T3)->Is(Union(T2, T3))
    // This does NOT hold.
    /*
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
          TypeHandle type1 = *it1;
          TypeHandle type2 = *it2;
          TypeHandle type3 = *it3;
          TypeHandle union13 = T.Union(type1, type3);
          TypeHandle union23 = T.Union(type2, type3);
          CHECK(!type1->Is(type2) || union13->Is(union23));
        }
      }
    }
    */
  }

  void Union2() {
    // Monotonicity: T1->Is(T3) and T2->Is(T3) implies Union(T1, T2)->Is(T3)
    // This does NOT hold.  TODO(neis): Could fix this by splitting
    // OtherNumber into a negative and a positive part.
    /*
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
          TypeHandle type1 = *it1;
          TypeHandle type2 = *it2;
          TypeHandle type3 = *it3;
          TypeHandle union12 = T.Union(type1, type2);
          CHECK(!(type1->Is(type3) && type2->Is(type3)) || union12->Is(type3));
        }
      }
    }
    */
  }

  void Union3() {
    // Monotonicity: T1->Is(T2) or T1->Is(T3) implies T1->Is(Union(T2, T3))
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
          TypeHandle type1 = *it1;
          TypeHandle type2 = *it2;
          TypeHandle type3 = *it3;
          TypeHandle union23 = T.Union(type2, type3);
          CHECK(!(type1->Is(type2) || type1->Is(type3)) || type1->Is(union23));
        }
      }
    }
  }

  void Union4() {
    // Class-class
    CheckSub(T.Union(T.ObjectClass, T.ArrayClass), T.Object);
    CheckUnordered(T.Union(T.ObjectClass, T.ArrayClass), T.Array);
    CheckOverlap(T.Union(T.ObjectClass, T.ArrayClass), T.Array);
    CheckDisjoint(T.Union(T.ObjectClass, T.ArrayClass), T.Number);

    // Constant-constant
    CheckSub(T.Union(T.ObjectConstant1, T.ObjectConstant2), T.Object);
    CheckUnordered(T.Union(T.ObjectConstant1, T.ArrayConstant), T.Array);
    CheckUnordered(
        T.Union(T.ObjectConstant1, T.ObjectConstant2), T.ObjectClass);
    CheckOverlap(
        T.Union(T.ObjectConstant1, T.ArrayConstant), T.Array);
    CheckDisjoint(
        T.Union(T.ObjectConstant1, T.ArrayConstant), T.Number);
    CheckOverlap(
        T.Union(T.ObjectConstant1, T.ArrayConstant), T.ObjectClass);  // !!!

    // Bitset-array
    CHECK(this->IsBitset(T.Union(T.AnyArray, T.Array)));
    CHECK(this->IsUnion(T.Union(T.NumberArray, T.Number)));

    CheckEqual(T.Union(T.AnyArray, T.Array), T.Array);
    CheckUnordered(T.Union(T.AnyArray, T.String), T.Array);
    CheckOverlap(T.Union(T.NumberArray, T.String), T.Object);
    CheckDisjoint(T.Union(T.NumberArray, T.String), T.Number);

    // Bitset-function
    CHECK(this->IsBitset(T.Union(T.MethodFunction, T.Function)));
    CHECK(this->IsUnion(T.Union(T.NumberFunction1, T.Number)));

    CheckEqual(T.Union(T.MethodFunction, T.Function), T.Function);
    CheckUnordered(T.Union(T.NumberFunction1, T.String), T.Function);
    CheckOverlap(T.Union(T.NumberFunction2, T.String), T.Object);
    CheckDisjoint(T.Union(T.NumberFunction1, T.String), T.Number);

    // Bitset-class
    CheckSub(
        T.Union(T.ObjectClass, T.SignedSmall), T.Union(T.Object, T.Number));
    CheckSub(T.Union(T.ObjectClass, T.Array), T.Object);
    CheckUnordered(T.Union(T.ObjectClass, T.String), T.Array);
    CheckOverlap(T.Union(T.ObjectClass, T.String), T.Object);
    CheckDisjoint(T.Union(T.ObjectClass, T.String), T.Number);

    // Bitset-constant
    CheckSub(
        T.Union(T.ObjectConstant1, T.Signed32), T.Union(T.Object, T.Number));
    CheckSub(T.Union(T.ObjectConstant1, T.Array), T.Object);
    CheckUnordered(T.Union(T.ObjectConstant1, T.String), T.Array);
    CheckOverlap(T.Union(T.ObjectConstant1, T.String), T.Object);
    CheckDisjoint(T.Union(T.ObjectConstant1, T.String), T.Number);

    // Class-constant
    CheckSub(T.Union(T.ObjectConstant1, T.ArrayClass), T.Object);
    CheckUnordered(T.ObjectClass, T.Union(T.ObjectConstant1, T.ArrayClass));
    CheckSub(
        T.Union(T.ObjectConstant1, T.ArrayClass), T.Union(T.Array, T.Object));
    CheckUnordered(T.Union(T.ObjectConstant1, T.ArrayClass), T.ArrayConstant);
    CheckDisjoint(
        T.Union(T.ObjectConstant1, T.ArrayClass), T.ObjectConstant2);
    CheckOverlap(
        T.Union(T.ObjectConstant1, T.ArrayClass), T.ObjectClass);  // !!!

    // Bitset-union
    CheckSub(
        T.NaN,
        T.Union(T.Union(T.ArrayClass, T.ObjectConstant1), T.Number));
    CheckSub(
        T.Union(T.Union(T.ArrayClass, T.ObjectConstant1), T.Signed32),
        T.Union(T.ObjectConstant1, T.Union(T.Number, T.ArrayClass)));

    // Class-union
    CheckSub(
        T.Union(T.ObjectClass, T.Union(T.ObjectConstant1, T.ObjectClass)),
        T.Object);
    CheckEqual(
        T.Union(T.Union(T.ArrayClass, T.ObjectConstant2), T.ArrayClass),
        T.Union(T.ArrayClass, T.ObjectConstant2));

    // Constant-union
    CheckEqual(
        T.Union(
            T.ObjectConstant1, T.Union(T.ObjectConstant1, T.ObjectConstant2)),
        T.Union(T.ObjectConstant2, T.ObjectConstant1));
    CheckEqual(
        T.Union(
            T.Union(T.ArrayConstant, T.ObjectConstant2), T.ObjectConstant1),
        T.Union(
            T.ObjectConstant2, T.Union(T.ArrayConstant, T.ObjectConstant1)));

    // Array-union
    CheckEqual(
        T.Union(T.AnyArray, T.Union(T.NumberArray, T.AnyArray)),
        T.Union(T.AnyArray, T.NumberArray));
    CheckSub(T.Union(T.AnyArray, T.NumberArray), T.Array);

    // Function-union
    CheckEqual(
        T.Union(T.NumberFunction1, T.NumberFunction2),
        T.Union(T.NumberFunction2, T.NumberFunction1));
    CheckSub(T.Union(T.SignedFunction1, T.MethodFunction), T.Function);

    // Union-union
    CheckEqual(
        T.Union(
            T.Union(T.ObjectConstant2, T.ObjectConstant1),
            T.Union(T.ObjectConstant1, T.ObjectConstant2)),
        T.Union(T.ObjectConstant2, T.ObjectConstant1));
    CheckEqual(
        T.Union(
            T.Union(T.Number, T.ArrayClass),
            T.Union(T.SignedSmall, T.Array)),
        T.Union(T.Number, T.Array));
  }

  void Intersect() {
    // Identity: Intersect(T, Any) = T
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      TypeHandle intersect_type = T.Intersect(type, T.Any);
      CheckEqual(intersect_type, type);
    }

    // Domination: Intersect(T, None) = None
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      TypeHandle intersect_type = T.Intersect(type, T.None);
      CheckEqual(intersect_type, T.None);
    }

    // Idempotence: Intersect(T, T) = T
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type = *it;
      TypeHandle intersect_type = T.Intersect(type, type);
      CheckEqual(intersect_type, type);
    }

    // Commutativity: Intersect(T1, T2) = Intersect(T2, T1)
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        TypeHandle intersect12 = T.Intersect(type1, type2);
        TypeHandle intersect21 = T.Intersect(type2, type1);
        CheckEqual(intersect12, intersect21);
      }
    }

    // Associativity:
    // Intersect(T1, Intersect(T2, T3)) = Intersect(Intersect(T1, T2), T3)
    // This does NOT hold.
    /*
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
          TypeHandle type1 = *it1;
          TypeHandle type2 = *it2;
          TypeHandle type3 = *it3;
          TypeHandle intersect12 = T.Intersect(type1, type2);
          TypeHandle intersect23 = T.Intersect(type2, type3);
          TypeHandle intersect1_23 = T.Intersect(type1, intersect23);
          TypeHandle intersect12_3 = T.Intersect(intersect12, type3);
          CheckEqual(intersect1_23, intersect12_3);
        }
      }
    }
    */

    // Join: Intersect(T1, T2)->Is(T1) and Intersect(T1, T2)->Is(T2)
    // This does NOT hold.  Not even the disjunction.
    /*
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        TypeHandle intersect12 = T.Intersect(type1, type2);
        CHECK(intersect12->Is(type1));
        CHECK(intersect12->Is(type2));
      }
    }
    */

    // Lower Boundedness: T1->Is(T2) implies Intersect(T1, T2) = T1
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        TypeHandle intersect12 = T.Intersect(type1, type2);
        if (type1->Is(type2)) CheckEqual(intersect12, type1);
      }
    }

    // Monotonicity: T1->Is(T2) implies Intersect(T1, T3)->Is(Intersect(T2, T3))
    // This does NOT hold.
    /*
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
          TypeHandle type1 = *it1;
          TypeHandle type2 = *it2;
          TypeHandle type3 = *it3;
          TypeHandle intersect13 = T.Intersect(type1, type3);
          TypeHandle intersect23 = T.Intersect(type2, type3);
          CHECK(!type1->Is(type2) || intersect13->Is(intersect23));
        }
      }
    }
    */

    // Monotonicity: T1->Is(T3) or T2->Is(T3) implies Intersect(T1, T2)->Is(T3)
    // This does NOT hold.
    /*
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
          TypeHandle type1 = *it1;
          TypeHandle type2 = *it2;
          TypeHandle type3 = *it3;
          TypeHandle intersect12 = T.Intersect(type1, type2);
          CHECK(!(type1->Is(type3) || type2->Is(type3)) ||
                intersect12->Is(type3));
        }
      }
    }
    */

    // Monotonicity: T1->Is(T2) and T1->Is(T3) implies T1->Is(Intersect(T2, T3))
    // This does NOT hold.
    /*
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
          TypeHandle type1 = *it1;
          TypeHandle type2 = *it2;
          TypeHandle type3 = *it3;
          TypeHandle intersect23 = T.Intersect(type2, type3);
          CHECK(!(type1->Is(type2) && type1->Is(type3)) ||
                type1->Is(intersect23));
        }
      }
    }
    */

    // Bitset-class
    CheckEqual(T.Intersect(T.ObjectClass, T.Object), T.ObjectClass);
    CheckEqual(T.Intersect(T.ObjectClass, T.Array), T.None);
    CheckEqual(T.Intersect(T.ObjectClass, T.Number), T.None);

    // Bitset-array
    CheckEqual(T.Intersect(T.NumberArray, T.Object), T.NumberArray);
    CheckEqual(T.Intersect(T.AnyArray, T.Function), T.None);

    // Bitset-function
    CheckEqual(T.Intersect(T.MethodFunction, T.Object), T.MethodFunction);
    CheckEqual(T.Intersect(T.NumberFunction1, T.Array), T.None);

    // Bitset-union
    CheckEqual(
        T.Intersect(T.Object, T.Union(T.ObjectConstant1, T.ObjectClass)),
        T.Union(T.ObjectConstant1, T.ObjectClass));
    CHECK(
        !T.Intersect(T.Union(T.ArrayClass, T.ObjectConstant1), T.Number)
            ->IsInhabited());

    // Class-constant
    CHECK(T.Intersect(T.ObjectConstant1, T.ObjectClass)->IsInhabited());  // !!!
    CHECK(!T.Intersect(T.ArrayClass, T.ObjectConstant2)->IsInhabited());

    // Array-union
    CheckEqual(
        T.Intersect(T.NumberArray, T.Union(T.NumberArray, T.ArrayClass)),
        T.NumberArray);
    CheckEqual(
        T.Intersect(T.AnyArray, T.Union(T.Object, T.SmiConstant)),
        T.AnyArray);
    CHECK(
        !T.Intersect(T.Union(T.AnyArray, T.ArrayConstant), T.NumberArray)
            ->IsInhabited());

    // Function-union
    CheckEqual(
        T.Intersect(T.MethodFunction, T.Union(T.String, T.MethodFunction)),
        T.MethodFunction);
    CheckEqual(
        T.Intersect(T.NumberFunction1, T.Union(T.Object, T.SmiConstant)),
        T.NumberFunction1);
    CHECK(
        !T.Intersect(T.Union(T.MethodFunction, T.Name), T.NumberFunction2)
            ->IsInhabited());

    // Class-union
    CheckEqual(
        T.Intersect(T.ArrayClass, T.Union(T.ObjectConstant2, T.ArrayClass)),
        T.ArrayClass);
    CheckEqual(
        T.Intersect(T.ArrayClass, T.Union(T.Object, T.SmiConstant)),
        T.ArrayClass);
    CHECK(
        T.Intersect(T.Union(T.ObjectClass, T.ArrayConstant), T.ArrayClass)
            ->IsInhabited());  // !!!

    // Constant-union
    CheckEqual(
        T.Intersect(
            T.ObjectConstant1, T.Union(T.ObjectConstant1, T.ObjectConstant2)),
        T.ObjectConstant1);
    CheckEqual(
        T.Intersect(T.SmiConstant, T.Union(T.Number, T.ObjectConstant2)),
        T.SmiConstant);
    CHECK(
        T.Intersect(
            T.Union(T.ArrayConstant, T.ObjectClass), T.ObjectConstant1)
                ->IsInhabited());  // !!!

    // Union-union
    CheckEqual(
        T.Intersect(
            T.Union(T.Number, T.ArrayClass),
            T.Union(T.SignedSmall, T.Array)),
        T.Union(T.SignedSmall, T.ArrayClass));
    CheckEqual(
        T.Intersect(
            T.Union(T.Number, T.ObjectClass),
            T.Union(T.Signed32, T.Array)),
        T.Signed32);
    CheckEqual(
        T.Intersect(
            T.Union(T.ObjectConstant2, T.ObjectConstant1),
            T.Union(T.ObjectConstant1, T.ObjectConstant2)),
        T.Union(T.ObjectConstant2, T.ObjectConstant1));
    CheckEqual(
        T.Intersect(
            T.Union(
                T.ArrayClass,
                T.Union(T.ObjectConstant2, T.ObjectConstant1)),
            T.Union(
                T.ObjectConstant1,
                T.Union(T.ArrayConstant, T.ObjectConstant2))),
        T.Union(
            T.ArrayConstant,
            T.Union(T.ObjectConstant2, T.ObjectConstant1)));  // !!!
  }

  void Distributivity() {
    // Union(T1, Intersect(T2, T3)) = Intersect(Union(T1, T2), Union(T1, T3))
    // This does NOT hold.
    /*
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
          TypeHandle type1 = *it1;
          TypeHandle type2 = *it2;
          TypeHandle type3 = *it3;
          TypeHandle union12 = T.Union(type1, type2);
          TypeHandle union13 = T.Union(type1, type3);
          TypeHandle intersect23 = T.Intersect(type2, type3);
          TypeHandle union1_23 = T.Union(type1, intersect23);
          TypeHandle intersect12_13 = T.Intersect(union12, union13);
          CHECK(Equal(union1_23, intersect12_13));
        }
      }
    }
    */

    // Intersect(T1, Union(T2, T3)) = Union(Intersect(T1, T2), Intersect(T1,T3))
    // This does NOT hold.
    /*
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
          TypeHandle type1 = *it1;
          TypeHandle type2 = *it2;
          TypeHandle type3 = *it3;
          TypeHandle intersect12 = T.Intersect(type1, type2);
          TypeHandle intersect13 = T.Intersect(type1, type3);
          TypeHandle union23 = T.Union(type2, type3);
          TypeHandle intersect1_23 = T.Intersect(type1, union23);
          TypeHandle union12_13 = T.Union(intersect12, intersect13);
          CHECK(Equal(intersect1_23, union12_13));
        }
      }
    }
    */
  }

  template<class Type2, class TypeHandle2, class Region2, class Rep2>
  void Convert() {
    Types<Type2, TypeHandle2, Region2> T2(
        Rep2::ToRegion(&zone, isolate), isolate);
    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
      TypeHandle type1 = *it;
      TypeHandle2 type2 = T2.template Convert<Type>(type1);
      TypeHandle type3 = T.template Convert<Type2>(type2);
      CheckEqual(type1, type3);
    }
  }

  void HTypeFromType() {
    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
        TypeHandle type1 = *it1;
        TypeHandle type2 = *it2;
        HType htype1 = HType::FromType<Type>(type1);
        HType htype2 = HType::FromType<Type>(type2);
        CHECK(!type1->Is(type2) || htype1.IsSubtypeOf(htype2));
      }
    }
  }
};

typedef Tests<Type, Type*, Zone, ZoneRep> ZoneTests;
typedef Tests<HeapType, Handle<HeapType>, Isolate, HeapRep> HeapTests;


TEST(IsSomeType) {
  CcTest::InitializeVM();
  ZoneTests().IsSomeType();
  HeapTests().IsSomeType();
}


TEST(BitsetType) {
  CcTest::InitializeVM();
  ZoneTests().Bitset();
  HeapTests().Bitset();
}


TEST(ClassType) {
  CcTest::InitializeVM();
  ZoneTests().Class();
  HeapTests().Class();
}


TEST(ConstantType) {
  CcTest::InitializeVM();
  ZoneTests().Constant();
  HeapTests().Constant();
}


TEST(RangeType) {
  CcTest::InitializeVM();
  ZoneTests().Range();
  HeapTests().Range();
}


TEST(ArrayType) {
  CcTest::InitializeVM();
  ZoneTests().Array();
  HeapTests().Array();
}


TEST(FunctionType) {
  CcTest::InitializeVM();
  ZoneTests().Function();
  HeapTests().Function();
}


TEST(Of) {
  CcTest::InitializeVM();
  ZoneTests().Of();
  HeapTests().Of();
}


TEST(NowOf) {
  CcTest::InitializeVM();
  ZoneTests().NowOf();
  HeapTests().NowOf();
}


TEST(BitsetGlb) {
  CcTest::InitializeVM();
  ZoneTests().BitsetGlb();
  HeapTests().BitsetGlb();
}


TEST(BitsetLub) {
  CcTest::InitializeVM();
  ZoneTests().BitsetLub();
  HeapTests().BitsetLub();
}


TEST(Is) {
  CcTest::InitializeVM();
  ZoneTests().Is();
  HeapTests().Is();
}


TEST(NowIs) {
  CcTest::InitializeVM();
  ZoneTests().NowIs();
  HeapTests().NowIs();
}


TEST(Contains) {
  CcTest::InitializeVM();
  ZoneTests().Contains();
  HeapTests().Contains();
}


TEST(NowContains) {
  CcTest::InitializeVM();
  ZoneTests().NowContains();
  HeapTests().NowContains();
}


TEST(Maybe) {
  CcTest::InitializeVM();
  ZoneTests().Maybe();
  HeapTests().Maybe();
}


TEST(Union1) {
  CcTest::InitializeVM();
  ZoneTests().Union1();
  HeapTests().Union1();
}


/*
TEST(Union2) {
  CcTest::InitializeVM();
  ZoneTests().Union2();
  HeapTests().Union2();
}
*/


TEST(Union3) {
  CcTest::InitializeVM();
  ZoneTests().Union3();
  HeapTests().Union3();
}


TEST(Union4) {
  CcTest::InitializeVM();
  ZoneTests().Union4();
  HeapTests().Union4();
}


TEST(Intersect) {
  CcTest::InitializeVM();
  ZoneTests().Intersect();
  HeapTests().Intersect();
}


/*
TEST(Distributivity) {
  CcTest::InitializeVM();
  ZoneTests().Distributivity();
  HeapTests().Distributivity();
}
*/


TEST(Convert) {
  CcTest::InitializeVM();
  ZoneTests().Convert<HeapType, Handle<HeapType>, Isolate, HeapRep>();
  HeapTests().Convert<Type, Type*, Zone, ZoneRep>();
}


TEST(HTypeFromType) {
  CcTest::InitializeVM();
  ZoneTests().HTypeFromType();
  HeapTests().HTypeFromType();
}