code: # Nodes represent a definition of a value in our graph of operators.
  from typing import TYPE_CHECKING, Union, Callable, Any, Tuple, List, Optional, Dict
  from .immutable_collections import immutable_dict, immutable_list
  import torch
  
  if TYPE_CHECKING:
      from .graph import Graph
  
  BaseArgumentTypes = Union[str, int, float, bool, torch.dtype, torch.Tensor]
  base_types = BaseArgumentTypes.__args__  # type: ignore
  
  Target = Union[Callable[..., Any], str]
  
  Argument = Optional[Union[
      Tuple[Any, ...],  # actually Argument, but mypy can't represent recursive types
      List[Any],  # actually Argument
      Dict[str, Any],  # actually Argument
      slice,  # Slice[Argument, Argument, Argument], but slice is not a templated type in typing
      'Node',
      BaseArgumentTypes
  ]]
  
  class Node:
      """
      ``Node`` is the data structure that represents individual operations within
      a ``Graph``. For the most part, Nodes represent callsites to various entities,
      such as operators, methods, and Modules (some exceptions include nodes that
      specify function inputs and outputs). Each ``Node`` has a function specified
      by its ``op`` property. The ``Node`` semantics for each value of ``op`` are as follows:
  
      - ``placeholder`` represents a function input. The ``name`` attribute specifies the name this value will take on.
        ``target`` is similarly the name of the argument. ``args`` holds either: 1) nothing, or 2) a single argument
        denoting the default parameter of the function input. ``kwargs`` is don't-care. Placeholders correspond to
        the function parameters (e.g. ``x``) in the graph printout.
      - ``get_attr`` retrieves a parameter from the module hierarchy. ``name`` is similarly the name the result of the
        fetch is assigned to. ``target`` is the fully-qualified name of the parameter's position in the module hierarchy.
        ``args`` and ``kwargs`` are don't-care
      - ``call_function`` applies a free function to some values. ``name`` is similarly the name of the value to assign
        to. ``target`` is the function to be applied. ``args`` and ``kwargs`` represent the arguments to the function,
        following the Python calling convention
      - ``call_module`` applies a module in the module hierarchy's ``forward()`` method to given arguments. ``name`` is
        as previous. ``target`` is the fully-qualified name of the module in the module hierarchy to call.
        ``args`` and ``kwargs`` represent the arguments to invoke the module on, *including the self argument*.
      - ``call_method`` calls a method on a value. ``name`` is as similar. ``target`` is the string name of the method
        to apply to the ``self`` argument. ``args`` and ``kwargs`` represent the arguments to invoke the module on,
        *including the self argument*
      - ``output`` contains the output of the traced function in its ``args[0]`` attribute. This corresponds to the "return" statement
        in the Graph printout.
      """
      def __init__(self, graph: 'Graph', name: str, op: str, target: 'Target',
                   args: Tuple['Argument', ...], kwargs: Dict[str, 'Argument'],
                   type : Optional[Any] = None) -> None:
          self.graph = graph
          self.name = name  # unique name of value being created
          assert op in ['placeholder', 'call_method', 'call_module', 'call_function', 'get_attr', 'output', 'root']
          self.op = op  # the kind of operation = placeholder|call_method|call_module|call_function|get_attr
          if op in ['call_method', 'call_module']:
              assert isinstance(target, str)
          self.target = target  # for method/module/function, the name of the method/module/function/attr
          # being invoked, e.g add, layer1, or torch.add
  
          # All `Node`-valued inputs. Key is the Node, value is don't-care.
          # The public API for this is `all_input_nodes`, this private attribute
          # should not be accessed directly.
          self._input_nodes : Dict[Node, None] = {}
          self.__update_args_kwargs(map_arg(args, lambda x: x), map_arg(kwargs, lambda x: x))  # type: ignore
  
          # All of the nodes that use the value produced by this Node
          # Note one user may correspond to several uses, e.g. the node fo ``x + x``
          # would appear once here, but represents two uses.
          #
          # Is a dict to act as an "ordered set". Keys are significant, value dont-care
          self.users : Dict['Node', None] = {}
          # Type expression representing the output value of this node.
          # This should contain the same class of Type objects that would appear
          # as type annotations for function inputs/outputs.
          #
          # For placeholder nodes, this value will be used to type-annotate the
          # generated function parameters.
          # For the return ndoe, this value will be used to type-annotate the
          # generated function return type. (Note this is a special case. ``return``
          # does not produce a value, it's more of a notation. Thus, this value
          # describes the type of args[0] in the ``return`` node.
          self.type : Optional[Any] = type
          self._prev = self
          self._next = self
          self._erased = False
  
      @property
      def next(self) -> 'Node':
          """
          Returns the next ``Node`` in the linked list of Nodes.
  
          Returns:
  
              The next ``Node`` in the linked list of Nodes.
          """
          return self._next
  
      @property
      def prev(self) -> 'Node':
          """
          Returns the previous ``Node`` in the linked list of Nodes.
  
          Returns:
  
              The previous ``Node`` in the linked list of Nodes.
          """
          return self._prev
  
      def prepend(self, x: 'Node') -> None:
          """
          Insert x before this node in the list of nodes in the graph. Example::
  
              Before: p -> self
                      bx -> x -> ax
              After:  p -> x -> self
                      bx -> ax
  
          Args:
              x (Node): The node to put before this node. Must be a member of the same graph.
          """
          assert self.graph == x.graph, "Attempting to move a Node into a different Graph"
          x._remove_from_list()
          p = self._prev
          p._next, x._prev = x, p
          x._next, self._prev = self, x
  
      def append(self, x: 'Node') -> None:
          """
          Insert x after this node in the list of nodes in the graph.
          Equvalent to ``self.next.prepend(x)``
  
          Args:
              x (Node): The node to put after this node. Must be a member of the same graph.
          """
          self._next.prepend(x)
  
      def _remove_from_list(self):
          p, n = self._prev, self._next
          p._next, n._prev = n, p
  
      @property
      def args(self) -> Tuple[Argument, ...]:
          """
          The tuple of arguments to this ``Node``. The interpretation of arguments
          depends on the node's opcode. See the :class:`Node` docstring for more
          information.
  
          Assignment to this property is allowed. All accounting of uses and users
          is updated automatically on assignment.
          """
          return self._args
  
      @args.setter
      def args(self, a : Tuple[Argument, ...]):
          """
          Set the tuple of arguments to this Node. The interpretation of arguments
          depends on the node's opcode. See the ``fx.Graph`` docstring for more
          information.
          """
          # DO NOT CALL `__update_args_kwargs` directly. The correct way to
          # set `args` is via direct assignment, i.e. `node.args = new_args`
          self.__update_args_kwargs(map_arg(a, lambda x: x), self._kwargs)  # type: ignore
  
      @property
      def kwargs(self) -> Dict[str, Argument]:
          """
          The dict of keyword arguments to this ``Node``. The interpretation of arguments
          depends on the node's opcode. See the :class:`Node` docstring for more
          information.
  
          Assignment to this property is allowed. All accounting of uses and users
          is updated automatically on assignment.
          """
          return self._kwargs
  
      @kwargs.setter
      def kwargs(self, k : Dict[str, Argument]):
          """
          Set the dict of kwargs to this Node. The interpretation of arguments
          depends on the node's opcode. See the ``fx.Graph`` docstring for more
          information.
          """
          # DO NOT CALL `__update_args_kwargs` directly. The correct way to
          # set `args` is via direct assignment, i.e. `node.kwargs = new_kwargs`
          self.__update_args_kwargs(self._args, map_arg(k, lambda x: x))  # type: ignore
  
      @property
      def all_input_nodes(self) -> List['Node']:
          """
          Return all Nodes that are inputs to this Node. This is equivalent to
          iterating over ``args`` and ``kwargs`` and only collecting the values that
          are Nodes.
  
          Returns:
  
              List of ``Nodes`` that appear in the ``args`` and ``kwargs`` of this
              ``Node``, in that order.
          """
          return list(self._input_nodes.keys())
  
      def __update_args_kwargs(self, new_args : Tuple['Argument', ...], new_kwargs : Dict[str, 'Argument']):
          """
          This API is internal. Do *not* call it directly.
          """
          self._args = new_args
          self._kwargs = new_kwargs
  
          for old_use in self._input_nodes.keys():
              old_use.users.pop(self)
  
          self._input_nodes = {}
          map_arg(self._args, lambda n: self._input_nodes.setdefault(n))
          map_arg(self._kwargs, lambda n: self._input_nodes.setdefault(n))
  
          for new_use in self._input_nodes.keys():
              new_use.users.setdefault(self)
  
      def __repr__(self) -> str:
          return self.name
  
      def replace_all_uses_with(self, replace_with : 'Node') -> List['Node']:
          """
          Replace all uses of ``self`` in the Graph with the Node ``replace_with``.
  
          Args:
  
              replace_with (Node): The node to replace all uses of ``self`` with.
  
          Returns:
  
              The list of Nodes on which this change was made.
          """
          to_process = list(self.users)
          for use_node in to_process:
              def maybe_replace_node(n : Node) -> Node:
                  if n == self:
                      return replace_with
                  else:
                      return n
  
              new_args = map_arg(use_node.args, maybe_replace_node)
              new_kwargs = map_arg(use_node.kwargs, maybe_replace_node)
              assert isinstance(new_args, tuple)
              assert isinstance(new_kwargs, dict)
              use_node.__update_args_kwargs(new_args, new_kwargs)
  
          assert len(self.users) == 0
          return to_process
  
  def map_arg(a: Argument, fn: Callable[[Node], Argument]) -> Argument:
      """ Apply fn to each Node appearing arg. arg may be a list, tuple, slice, or dict with string keys. """
      if isinstance(a, tuple):
          return tuple(map_arg(elem, fn) for elem in a)
      elif isinstance(a, list):
          return immutable_list(map_arg(elem, fn) for elem in a)
      elif isinstance(a, dict):
          return immutable_dict((k, map_arg(v, fn)) for k, v in a.items())
      elif isinstance(a, slice):
          return slice(map_arg(a.start, fn), map_arg(a.stop, fn), map_arg(a.step, fn))
      elif isinstance(a, Node):
          return fn(a)
      else:
          return a
  