/**
   * Computes the greatest subtype of two related templatized types.
   *
   * @return The greatest subtype.
   */
  JSType getGreatestSubtypeHelper(JSType rawThat) {
    Preconditions.checkNotNull(rawThat);

    if (!wrapsSameRawType(rawThat)) {
      if (!rawThat.isTemplatizedType()) {
        if (this.isSubtype(rawThat)) {
          return this;
        } else if (rawThat.isSubtype(this)) {
          return filterNoResolvedType(rawThat);
        }
      }
      if (this.isObject() && rawThat.isObject()) {
        return this.getNativeType(JSTypeNative.NO_OBJECT_TYPE);
      }
      return this.getNativeType(JSTypeNative.NO_TYPE);
    }

    TemplatizedType that = rawThat.toMaybeTemplatizedType();
    Preconditions.checkNotNull(that);

    if (getTemplateTypeMap()
        .checkEquivalenceHelper(
            that.getTemplateTypeMap(), EquivalenceMethod.INVARIANT, SubtypingMode.NORMAL)) {
      return this;
    }

    // For types that have the same raw type but different type parameters,
    // we simply create a type has a "unknown" type parameter.  This is
    // equivalent to the raw type.
    return getReferencedObjTypeInternal();
  }
  /** Adds an alternate to the union type under construction. Returns this for easy chaining. */
  public UnionTypeBuilder addAlternate(JSType alternate, boolean isStructural) {
    // build() returns the bottom type by default, so we can
    // just bail out early here.
    if (alternate.isNoType()) {
      return this;
    }

    isAllType = isAllType || alternate.isAllType();
    containsVoidType = containsVoidType || alternate.isVoidType();

    boolean isAlternateUnknown = alternate instanceof UnknownType;
    isNativeUnknownType = isNativeUnknownType || isAlternateUnknown;
    if (isAlternateUnknown) {
      areAllUnknownsChecked = areAllUnknownsChecked && alternate.isCheckedUnknownType();
    }
    if (!isAllType && !isNativeUnknownType) {
      if (alternate.isUnionType()) {
        UnionType union = alternate.toMaybeUnionType();
        for (JSType unionAlt : union.getAlternatesWithoutStructuralTyping()) {
          addAlternate(unionAlt);
        }
      } else {
        if (alternates.size() > maxUnionSize) {
          return this;
        }

        // Function types are special, because they have their
        // own bizarre sub-lattice. See the comments on
        // FunctionType#supAndInf helper and above at functionTypePosition.
        if (alternate.isFunctionType() && functionTypePosition != -1) {
          // See the comments on functionTypePosition above.
          FunctionType other = alternates.get(functionTypePosition).toMaybeFunctionType();
          FunctionType supremum = alternate.toMaybeFunctionType().supAndInfHelper(other, true);
          alternates.set(functionTypePosition, supremum);
          result = null;
          return this;
        }

        // Look through the alternates we've got so far,
        // and check if any of them are duplicates of
        // one another.
        int currentIndex = 0;
        Iterator<JSType> it = alternates.iterator();
        while (it.hasNext()) {
          boolean removeCurrent = false;
          JSType current = it.next();

          // Unknown and NoResolved types may just be names that haven't
          // been resolved yet. So keep these in the union, and just use
          // equality checking for simple de-duping.
          if (alternate.isUnknownType()
              || current.isUnknownType()
              || alternate.isNoResolvedType()
              || current.isNoResolvedType()
              || alternate.hasAnyTemplateTypes()
              || current.hasAnyTemplateTypes()) {
            if (alternate.isEquivalentTo(current, isStructural)) {
              // Alternate is unnecessary.
              return this;
            }
          } else {

            // Because "Foo" and "Foo.<?>" are roughly equivalent
            // templatized types, special care is needed when building the
            // union. For example:
            //   Object is consider a subtype of Object.<string>
            // but we want to leave "Object" not "Object.<string>" when
            // building the subtype.
            //

            if (alternate.isTemplatizedType() || current.isTemplatizedType()) {
              // Cases:
              // 1) alternate:Array.<string> and current:Object ==> Object
              // 2) alternate:Array.<string> and current:Array ==> Array
              // 3) alternate:Object.<string> and
              //    current:Array ==> Array|Object.<string>
              // 4) alternate:Object and current:Array.<string> ==> Object
              // 5) alternate:Array and current:Array.<string> ==> Array
              // 6) alternate:Array and
              //    current:Object.<string> ==> Array|Object.<string>
              // 7) alternate:Array.<string> and
              //    current:Array.<number> ==> Array.<?>
              // 8) alternate:Array.<string> and
              //    current:Array.<string> ==> Array.<string>
              // 9) alternate:Array.<string> and
              //    current:Object.<string> ==> Object.<string>|Array.<string>

              if (!current.isTemplatizedType()) {
                if (isSubtype(alternate, current, isStructural)) {
                  // case 1, 2
                  return this;
                }
                // case 3: leave current, add alternate
              } else if (!alternate.isTemplatizedType()) {
                if (isSubtype(current, alternate, isStructural)) {
                  // case 4, 5
                  removeCurrent = true;
                }
                // case 6: leave current, add alternate
              } else {
                Preconditions.checkState(
                    current.isTemplatizedType() && alternate.isTemplatizedType());
                TemplatizedType templatizedAlternate = alternate.toMaybeTemplatizedType();
                TemplatizedType templatizedCurrent = current.toMaybeTemplatizedType();

                if (templatizedCurrent.wrapsSameRawType(templatizedAlternate)) {
                  if (alternate
                      .getTemplateTypeMap()
                      .checkEquivalenceHelper(
                          current.getTemplateTypeMap(),
                          EquivalenceMethod.IDENTITY,
                          SubtypingMode.NORMAL)) {
                    // case 8
                    return this;
                  } else {
                    // TODO(johnlenz): should we leave both types?
                    // case 7: add a merged alternate
                    // We currently merge to the templatized types to "unknown"
                    // which is equivalent to the raw type.
                    JSType merged = templatizedCurrent.getReferencedObjTypeInternal();
                    return addAlternate(merged);
                  }
                }
                // case 9: leave current, add alternate
              }
              // Otherwise leave both templatized types.
            } else if (isSubtype(alternate, current, isStructural)) {
              // Alternate is unnecessary.
              return this;
            } else if (isSubtype(current, alternate, isStructural)) {
              // Alternate makes current obsolete
              removeCurrent = true;
            }
          }

          if (removeCurrent) {
            it.remove();

            if (currentIndex == functionTypePosition) {
              functionTypePosition = -1;
            } else if (currentIndex < functionTypePosition) {
              functionTypePosition--;
              currentIndex--;
            }
          }
          currentIndex++;
        }

        if (alternate.isFunctionType()) {
          // See the comments on functionTypePosition above.
          Preconditions.checkState(functionTypePosition == -1);
          functionTypePosition = alternates.size();
        }

        alternates.add(alternate);
        result = null; // invalidate the memoized result
      }
    } else {
      result = null;
    }
    return this;
  }