return new ImmutableList<E>() {

      @Override
      public int size() {
        return axes.size();
      }

      @Override
      public E get(int axis) {
        checkElementIndex(axis, size());
        int axisIndex = getAxisIndexForProductIndex(index, axis);
        return axes.get(axis).get(axisIndex);
      }

      @Override
      boolean isPartialView() {
        return true;

    return new ImmutableList<E>() {

      @Override
      public int size() {
        return axes.size();
      }

      @Override
      public E get(int axis) {
        checkElementIndex(axis, size());
        int axisIndex = getAxisIndexForProductIndex(index, axis);
        return axes.get(axis).get(axisIndex);
      }

      @Override
      boolean isPartialView() {
        return true;

      } else {
        // Generalize differing axis lengths to "variable"/"unknown".
        for (int axis_index = 0; axis_index < combined_shape.dims();
             ++axis_index) {
          int64_t axis_length = combined_shape.dim_size(axis_index);
          if (axis_length != component_shape.dim_size(axis_index)) {
            axis_length = -1;
          }
          TF_RETURN_IF_ERROR(

// Return a 1-D INT32 tensor containing a single value 1.
TFE_TensorHandle* TestAxisTensorHandle(TFE_Context* ctx);

// Return an op taking minimum of `input` long `axis` dimension.
TFE_Op* MinOp(TFE_Context* ctx, TFE_TensorHandle* input,
              TFE_TensorHandle* axis);

// If there is a device of type `device_type`, returns true
// and sets 'device_name' accordingly.
// `device_type` must be either "GPU" or "TPU".

  // Returns number of elements across all dimensions.
  virtual Status NumElements(int64_t* num_elements) const = 0;
  // Returns size of specified dimension
  //
  // -1 indicates an unknown axis length; this is unreachable for most standard
  // ImmediateExecutionTensorHandles, but comes up for example when computing
  // the shape of a parallel tensor with component shapes differing across
  // devices.

TFE_Op* MinOp(TFE_Context* ctx, TFE_TensorHandle* input,
              TFE_TensorHandle* axis) {
  TF_Status* status = TF_NewStatus();

  TFE_Op* op = TFE_NewOp(ctx, "Min", status);
  CHECK_EQ(TF_OK, TF_GetCode(status)) << TF_Message(status);
  TFE_OpAddInput(op, input, status);
  CHECK_EQ(TF_OK, TF_GetCode(status)) << TF_Message(status);
  TFE_OpAddInput(op, axis, status);
  CHECK_EQ(TF_OK, TF_GetCode(status)) << TF_Message(status);

      int adjust = size() - 1;
      for (int i = 0; i < axes.size(); i++) {
        adjust *= 31;
        adjust = ~~adjust;
        // in GWT, we have to deal with integer overflow carefully
      }
      int hash = 1;
      for (Set<E> axis : axes) {
        hash = 31 * hash + (size() / axis.size() * axis.hashCode());

        hash = ~~hash;
      }
      hash += adjust;

`tf.reduce_join`: `reduction_indices` becomes `axis` * `tf.reduce_logsumexp`:
`reduction_indices` becomes `axis` * `tf.reduce_max`: `reduction_indices`
becomes `axis` * `tf.reduce_mean`: `reduction_indices` becomes `axis` *
`tf.reduce_min`: `reduction_indices` becomes `axis` * `tf.reduce_prod`:
`reduction_indices` becomes `axis` * `tf.reduce_sum`: `reduction_indices`

  TFE_TensorHandle* axis = TestAxisTensorHandle(ctx);
  TFE_Op* minOp = MinOp(ctx, input, axis);
  TFE_TensorHandle* retvals[1] = {nullptr};
  int num_retvals = 1;
  TFE_Execute(minOp, &retvals[0], &num_retvals, status);
  EXPECT_EQ(TF_OK, TF_GetCode(status)) << TF_Message(status);
  TFE_DeleteOp(minOp);
  TFE_DeleteTensorHandle(input);
  TFE_DeleteTensorHandle(axis);
  ASSERT_EQ(1, num_retvals);

        // Non-parallel tensors from _EagerConst/tf.constant are implicitly
        // broadcast, i.e. set as the input to each parallel operation. This
        // allows code like "tf.constant(1.)" or "tf.reduce_sum(..., axis=1)"
        // (where the value starts on the host), without allowing other implicit
        // copies/broadcasts. Other implicit copies may be supported eventually,