const ParallelDevice& device_;
  std::vector<TensorHandlePtr> tensors_;
  // Parallel tensors are immutable but compute their shape lazily unless it is
  // provided on construction. The optional has a value if the lazy computation
  // has been completed or the shape was provided on construction.
  mutable absl::optional<std::vector<int64_t>> shape_;
  const TF_DataType dtype_;
};

template <typename DataType>

  /// Notification for stopping the cache pruning thread.
  absl::Notification stop_pruning_thread_;

  /// Guards access to the block map, LRU list, and cached byte count.
  mutable absl::Mutex mu_;

  /// The block map (map from Key to Block).
  BlockMap block_map_ ABSL_GUARDED_BY(mu_);

  /// The LRU list of block keys. The front of the list identifies the most
  /// recently accessed block.