# Copyright 2017 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
# pylint: disable=unidiomatic-typecheck
"""Defun decorator for defining graph-mode functions."""

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

import collections
import enum  # pylint: disable=g-bad-import-order
import functools
import itertools
import threading
import types as types_lib
import weakref

import numpy as np
import six

from tensorflow.core.framework import attr_value_pb2
from tensorflow.core.framework import function_pb2
from tensorflow.python import pywrap_tensorflow
from tensorflow.python.eager import context
from tensorflow.python.eager import execute
from tensorflow.python.eager import tape
from tensorflow.python.eager.graph_only_ops import graph_placeholder
from tensorflow.python.framework import c_api_util
from tensorflow.python.framework import composite_tensor
from tensorflow.python.framework import constant_op
from tensorflow.python.framework import device as pydev
from tensorflow.python.framework import dtypes
from tensorflow.python.framework import error_interpolation
from tensorflow.python.framework import errors
from tensorflow.python.framework import func_graph as func_graph_module
from tensorflow.python.framework import ops
from tensorflow.python.framework import tensor_shape
from tensorflow.python.framework import tensor_spec
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import custom_gradient
from tensorflow.python.ops import default_gradient
from tensorflow.python.ops import functional_ops
from tensorflow.python.ops import gradients_util
from tensorflow.python.ops import resource_variable_ops
from tensorflow.python.platform import tf_logging as logging
from tensorflow.python.util import compat
from tensorflow.python.util import function_utils
from tensorflow.python.util import lazy_loader
from tensorflow.python.util import memory
from tensorflow.python.util import nest
from tensorflow.python.util import object_identity
from tensorflow.python.util import tf_decorator
from tensorflow.python.util import tf_inspect

# Loaded lazily due to a circular dependency (roughly
# tf.function->autograph->->dataset->tf.function).
# TODO(b/133251390): Use a regular import.
ag_ctx = lazy_loader.LazyLoader(
    "ag_ctx", globals(),
    "tensorflow.python.autograph.core.ag_ctx")


FORWARD_FUNCTION_ATTRIBUTE_NAME = "forward_function_name"
BACKWARD_FUNCTION_ATTRIBUTE_NAME = "backward_function_name"


class CacheKey(
    collections.namedtuple("CacheKey", [
        "input_signature", "parent_graph", "device_functions",
        "colocation_stack", "in_cross_replica_context"
    ])):
  """Named tuple used to key the function cache."""

  def __hash__(self):
    """Provide a hash even if the input signature objects aren't hashable."""
    return hash(self._fields_safe)

  @property
  def _fields_safe(self):
    """Hash & equality-safe version of all the namedtuple fields."""
    return (self._hash_fix(self.input_signature), self.parent_graph,
            self.device_functions, self.colocation_stack,
            self.in_cross_replica_context)

  def _hash_fix(self, elem):
    """Ensure elem is hashable even if a Variable is nested in it."""
    # Descend into tuples
    if isinstance(elem, tuple):
      return tuple(self._hash_fix(i) for i in elem)

    if isinstance(elem, set):
      return {self._hash_fix(i) for i in elem}

    # If the element is not hashable, assume it is a weakref to a variable and
    # return the dtype & shape. Else, simply return the element
    try:
      hash(elem)
    except TypeError:
      v = elem()
      return (v.__class__, tensor_spec.TensorSpec(v.shape, v.dtype))

    return elem

  def __eq__(self, other):
    return self._fields_safe == other._fields_safe  # pylint: disable=protected-access


CacheKey.replace = CacheKey._replace  # pylint: disable=protected-access


def _flat_shape_list(*params):
  """Return a flat list of TensorShapes, one for each tensor[spec] in `*params`.

  If `params` contains `CompositeTensors`, then they are expanded to their
  components `Tensors`.

  Args:
    *params: Set of nested entries containing Tensors, TensorSpec, and
      non-tensors.

  Returns:
    A list of entries containing either `None` or `TensorShape`.
  """
  return [tensor_shape.TensorShape(x.shape)
          if isinstance(x, (ops.Tensor, tensor_spec.TensorSpec)) else None
          for x in nest.flatten(params, expand_composites=True)]


def _shape_less_specific_than(relaxed, to_check):
  """Checks if `relaxed` is less specific than `to_check`.

  This is an asymmetric check, unlike `TensorShape.is_compatible_with`. If
  `to_check` has a dimension with an undefined shape, `relaxed` must also have
  an undefined shape for that dimension.

  Args:
    relaxed: A `TensorShape` to check against.
    to_check: A second `TensorShape`.

  Returns:
    True if `to_check` represents a set of shapes which is a subset of
    `relaxed`'s shapes and False otherwise.
  """
  if to_check.dims is not None and relaxed.dims is not None:
    if to_check.rank != relaxed.rank:
      return False
    for check_dim, relaxed_dim in zip(to_check.dims, relaxed.dims):
      if check_dim.value is None and relaxed_dim.value is not None:
        return False
      if not relaxed_dim.is_compatible_with(check_dim):
        return False
  return True


def _compatible_shapes(flat_relaxed, flat_to_check):
  """Check if lists of TensorShapes contain compatible shapes.

  Checks that each `flat_relaxed` shape covers a superset of the shapes of the
  corresponding `flat_to_check` shape.

  Args:
    flat_relaxed: List of TensorShape or None.
    flat_to_check: List of TensorShape or None.

  Returns:
    A python bool.

  Raises:
    RuntimeError:
      if `len(flat_relaxed) != len(flat_to_check)`.
    RuntimeError:
      if `flat_relaxed[i] is None != flat_to_check[i] is None` for any `i`.
  """

  if len(flat_relaxed) != len(flat_to_check):
    raise RuntimeError("Expected shape lists of identical lengths, but saw: "
                       "%s and %s" % (flat_relaxed, flat_to_check))
  def is_compatible(relaxed, to_check):
    """Internal help function.

    Args:
      relaxed: TensorShape or None.
      to_check: TensorShape or None.

    Returns:
      Python bool.

    Raises:
      RuntimeError: If `relaxed is None != to_check is None`.
    """
    # If both x and y are None, there is no shape to compare.  Otherwise check
    # if they are compatible with each other.  Either way, both input signatures
    # must have have Tensors in the same entries.  If not, raise an assertion
    # error.
    if relaxed is None != to_check is None:
      raise RuntimeError(
          "Expected signature type matches between flattened input shapes "
          "%s and %s; but saw that (%s is None) != (%s is None)"
          % (flat_relaxed, flat_to_check, relaxed, to_check))
    return relaxed is None or _shape_less_specific_than(relaxed, to_check)
  return all(is_compatible(relaxed, to_check)
             for relaxed, to_check in zip(flat_relaxed, flat_to_check))


def common_shape(x, y):
  """Find a `TensorShape` that is compatible with both `x` and `y`."""
  if x is None != y is None:
    raise RuntimeError(
        "Cannot find a common shape when LHS shape is None but RHS shape "
        "is not (or vice versa): %s vs. %s" % (x, y))
  if x is None:
    return None  # The associated input was not a Tensor, no shape generated.
  if not isinstance(x, tensor_shape.TensorShape):
    raise TypeError("Expected x to be a TensorShape but saw %s" % (x,))
  if not isinstance(y, tensor_shape.TensorShape):
    raise TypeError("Expected y to be a TensorShape but saw %s" % (y,))
  if x.rank != y.rank or x.rank is None:
    return tensor_shape.TensorShape(None)
  dims = []
  for dim_x, dim_y in zip(x.dims, y.dims):
    if (dim_x != dim_y
        or tensor_shape.dimension_value(dim_x) is None
        or tensor_shape.dimension_value(dim_y) is None):
      dims.append(None)
    else:
      dims.append(tensor_shape.dimension_value(dim_x))
  return tensor_shape.TensorShape(dims)


def is_same_structure(structure1,
                      structure2,
                      check_values=False):
  """Check two structures for equality, optionally of types and of values."""
  try:
    nest.assert_same_structure(structure1, structure2, expand_composites=True)
  except (ValueError, TypeError):
    return False
  if check_values:
    flattened1 = nest.flatten(structure1, expand_composites=True)
    flattened2 = nest.flatten(structure2, expand_composites=True)
    # First check the types to avoid AttributeErrors.
    if any(type(f1) != type(f2) for f1, f2 in zip(flattened1, flattened2)):
      return False
    return flattened1 == flattened2
  return True


def _parse_func_attrs(attributes):
  """Convert the keyword arguments into function_def attributes.

  Currently only support primitive types: bool, int, float and string.

  Args:
    attributes: the dictionary of attributes.
  Returns:
    A dict of attributes where the key is the name of attribute and the value
      is the AttrValue proto.
  Raises:
    ValueError: If the kwargs contains unwhitelisted name or unsupported value
      types.
  """
  attrs = {}
  for key, value in attributes.items():
    if isinstance(value, attr_value_pb2.AttrValue):
      attrs[key] = value
    # bool type check has to happen before int since bool is a subclass of int.
    elif isinstance(value, bool):
      attrs[key] = attr_value_pb2.AttrValue(b=value)
    elif isinstance(value, int):
      attrs[key] = attr_value_pb2.AttrValue(i=value)
    elif isinstance(value, float):
      attrs[key] = attr_value_pb2.AttrValue(f=value)
    elif isinstance(value, (str, bytes, six.text_type)):
      attrs[key] = attr_value_pb2.AttrValue(s=compat.as_bytes(value))
    else:
      raise ValueError("Unsupported attribute type for %s with type %s" %
                       (key, type(value)))
  return attrs


class _InterpolateFunctionError(object):
  """Context Manager that interpolates the exception from 'top_level_func'."""

  def __init__(self, top_level_func):
    self._func = top_level_func

  def __enter__(self):
    pass

  def __exit__(self, typ, exc, tb):
    if not exc or not isinstance(exc, errors.OpError):
      return False
    message = compat.as_text(exc.message)
    _, tags = error_interpolation.parse_message(message)
    g = None
    func_stack = []
    for t in tags:
      if t.type == "function_node":
        # TODO(mdan): Tests should cover this.
        if t.name == compat.as_str(self._func.name):
          g = self._func.graph
        elif g:
          next_func = g._get_function(t.name)
          if next_func is not None and isinstance(next_func,
                                                  _EagerDefinedFunction):
            g = next_func.graph
        if g:
          func_stack.append(g.name)
        else:
          func_stack.append("<unknown>")
    if g:
      message = error_interpolation.interpolate(message, g)
      message += "\n\nFunction call stack:\n"
      message += " -> ".join(func_stack)
      message += "\n"
      exc._message = message  # pylint: disable=protected-access
    return False


def _forward_name(n):
  """The name of a generated forward defun named n."""
  return "__forward_%s_%s" % (n, ops.uid())


def _backward_name(n):
  """The name of a generated backward defun named n."""
  return "__backward_%s_%s" % (n, ops.uid())


def _inference_name(n):
  """The name of a forward-but-no-gradient defun named n."""
  return "__inference_%s_%s" % (n, ops.uid())


class _EagerDefinedFunctionDeleter(object):
  """Unregister function from eager context."""

  def __init__(self, name):
    self.name = name

  def __del__(self):
    try:
      context.remove_function(self.name)
    except TypeError:
      # Suppress some exceptions, mainly for the case when we're running on
      # module deletion. Things that can go wrong include the context module
      # already being unloaded, self._handle._handle_data no longer being
      # valid, and so on. Printing warnings in these cases is silly
      # (exceptions raised from __del__ are printed as warnings to stderr).
      pass  # 'NoneType' object is not callable when the handle has been
      # partially unloaded.
    except AttributeError:
      pass  # 'NoneType' object has no attribute 'eager_mode' when context has
      # been unloaded. Will catch other module unloads as well.


# TODO(apassos) get rid of this by splitting framework.function._DefinedFunction
# so it doesn't have the definition-generating logic and is just a container for
# an already-defined function.
class _EagerDefinedFunction(object):
  """Callable with the interface of `framework.function._DefinedFunction`.

  `_EagerDefinedFunction` encapsulates a function definition and its properties,
  and it provides a method for calling the encapsulated function. Some Ops
  take functions as attributes, which have type `func`; an instance of this
  class may be provided as the value of these `func` attributes.
  """

  def __init__(self, name, graph, inputs, outputs, attrs):
    """Initializes an eager defined function.

    Args:
      name: str, the name for the created function.
      graph: Graph, the graph containing the operations in the function
      inputs: the tensors in the graph to be used as inputs to the function
      outputs: the tensors in the graph which will be outputs to the function
      attrs: dict mapping names of attributes to their AttrValue values
    """
    input_ops = set(arg.op for arg in inputs)
    operations = [op for op in graph.get_operations() if op not in input_ops]

    graph_output_names = graph._output_names  # pylint: disable=protected-access
    if (graph_output_names is not None and
        all(ops.tensor_id(t) in graph_output_names for t in outputs)):
      output_names = [
          compat.as_bytes(graph_output_names[ops.tensor_id(t)]) for t in outputs
      ]
      if len(set(output_names)) != len(output_names):
        # There are duplicate names for some reason, probably an invalid
        # signature. Revert to auto-naming.
        output_names = []
    else:
      output_names = []
    fn = pywrap_tensorflow.TF_GraphToFunction_wrapper(
        graph._c_graph,  # pylint: disable=protected-access
        compat.as_str(name),
        False,
        [o._c_op for o in operations],  # pylint: disable=protected-access
        [t._as_tf_output() for t in inputs],  # pylint: disable=protected-access
        [t._as_tf_output() for t in outputs],  # pylint: disable=protected-access
        output_names,
        [o._c_op for o in graph.control_outputs],  # pylint: disable=protected-access
        [],  # control_output_names
        None,
        compat.as_str(""))

    for name, attr_value in attrs.items():
      serialized = attr_value.SerializeToString()
      # TODO(iga): this creates and deletes a new TF_Status for every attr.
      # It might be worth creating a convenient way to re-use status.
      pywrap_tensorflow.TF_FunctionSetAttrValueProto(
          fn, compat.as_str(name), serialized)

    # TODO(apassos) avoid creating a FunctionDef (specially to grab the
    # signature, but also in general it's nice not to depend on it.
    with c_api_util.tf_buffer() as buffer_:
      pywrap_tensorflow.TF_FunctionToFunctionDef(fn, buffer_)
      proto_data = pywrap_tensorflow.TF_GetBuffer(buffer_)
    function_def = function_pb2.FunctionDef()
    function_def.ParseFromString(compat.as_bytes(proto_data))
    self.name = compat.as_bytes(function_def.signature.name)
    with ops.init_scope():
      if context.executing_eagerly():
        context.ensure_initialized()
        context.add_function(fn)
        self._function_deleter = _EagerDefinedFunctionDeleter(self.name)
        self._registered_on_context = True
    self.definition = function_def
    self.signature = function_def.signature
    self._num_outputs = len(self.signature.output_arg)
    self._output_types = [o.type for o in self.signature.output_arg]
    self._output_shapes = [o.shape for o in outputs]
    self._control_captures = graph.control_captures
    # Shallow copy outputs since ConcreteFunction may mutate it.
    self._func_graph_outputs = list(outputs)
    self.grad_func_name = None
    self.python_grad_func = None
    self._c_func = c_api_util.ScopedTFFunction(fn)
    self._grad_func = None
    self.graph = graph
    self._stateful_ops = tuple(op for op in operations if op._is_stateful)  # pylint: disable=protected-access

  def add_to_graph(self, g=None):
    # pylint: disable=protected-access
    if not g and context.executing_eagerly():
      context.context().add_function_def(self.definition)
    else:
      if self.name not in g._functions:
        g._add_function(self)
      for f in self.graph._functions.values():
        if f.name not in g._functions:
          g._add_function(f)
    # pylint: enable=protected-access

  @property
  def stateful_ops(self):
    return self._stateful_ops

  def call(self, ctx, args, cancellation_manager=None):
    """Calls this function with `args` as inputs.

    `ConcreteFunction` execution respects device annotations only if the
    function won't be compiled with xla.

    Args:
      ctx: a Context object
      args: a list of arguments to supply this function with.
      cancellation_manager: a `CancellationManager` object that can be used to
        cancel function execution.

    Returns:
      The outputs of the function call.

    Raises:
      ValueError: if the number of arguments is incorrect.
    """
    if len(args) != len(self.signature.input_arg):
      raise ValueError(
          "Arguments and signature arguments do not match. "
          "got: %s, expected: %s " %
          (len(args), len(list(self.signature.input_arg))))

    function_call_options = ctx.function_call_options
    if function_call_options.config_proto_serialized is None:
      config = function_utils.get_disabled_rewriter_config()
    else:
      config = function_call_options.config_proto_serialized
    executor_type = function_call_options.executor_type or ""

    executing_eagerly = ctx.executing_eagerly()
    if executing_eagerly:
      with _InterpolateFunctionError(self):
        if cancellation_manager is None:
          outputs = execute.execute(
              str(self.signature.name),
              num_outputs=self._num_outputs,
              inputs=args,
              attrs=("executor_type", executor_type, "config_proto", config),
              ctx=ctx)
        else:
          outputs = execute.execute_with_cancellation(
              str(self.signature.name),
              num_outputs=self._num_outputs,
              inputs=args,
              attrs=("executor_type", executor_type, "config_proto", config),
              ctx=ctx,
              cancellation_manager=cancellation_manager)
      # Replace empty list with None
      outputs = outputs or None
    else:
      # TODO(akshayka): Either remove this if the FunctionLibraryRuntime
      # creates `PartitionedCallOp` kernels by default, or remove the previous
      # branch if a TPU kernel is registered for `PartitionedCall`.
      with _InterpolateFunctionError(self):
        with ops.control_dependencies(self._control_captures):
          # The caller must use record_operation to record this operation in the
          # eager case, so we enforce the same requirement for the non-eager
          # case by explicitly pausing recording. We don't have a gradient
          # registered for PartitionedCall, so recording this operation confuses
          # forwardprop code (GradientTape manages to ignore it).
          with tape.stop_recording():
            outputs = functional_ops.partitioned_call(
                args=args,
                f=self,
                tout=self._output_types,
                executing_eagerly=executing_eagerly,
                config=config,
                executor_type=executor_type)

    if executing_eagerly:
      return outputs
    else:
      # TODO(b/128924522): This additional set_shape should not be
      # necessary. ShapeRefiner likely needs to inspect handle_data. Remove this
      # once that's done.
      for i, shape in enumerate(self._output_shapes):
        outputs[i].set_shape(shape)
      for i, func_graph_output in enumerate(self._func_graph_outputs):
        custom_gradient.copy_handle_data(func_graph_output, outputs[i])
      return outputs


class _DelayedRewriteGradientFunctions(object):
  """Caches forward/backward functions with a delayed forward rewrite."""

  def __init__(self, func_graph, attrs, func_graph_deleter):
    """Construct an inference function and initialize caches."""
    # A map from the number of forward function outputs with accepted gradients
    # to forward and backward functions, used to cache non-tape backward
    # function generation.
    self._cached_function_pairs = {}
    self._func_graph = func_graph
    self._inference_function = _EagerDefinedFunction(
        _inference_name(self._func_graph.name), self._func_graph,
        self._func_graph.inputs, self._func_graph.outputs, attrs)
    self._attrs = attrs
    self._gradient_name = None
    # Note that the FuncGraph is mutated later, so we need to inspect it now to
    # figure out the user-specified outputs of the inference function.
    self._num_inference_outputs = len(self._func_graph.outputs)
    self._func_graph_deleter = func_graph_deleter

  def forward_backward(self, num_doutputs=None):
    """A possibly-cached pair of forward and backward functions."""
    if num_doutputs is None:
      num_doutputs = self._num_inference_outputs
    forward_backward = self._cached_function_pairs.get(num_doutputs)
    if forward_backward is not None:
      return forward_backward
    forward, backward = self._construct_forward_backward(num_doutputs)
    self._cached_function_pairs[num_doutputs] = (forward, backward)
    return forward, backward

  def _construct_forward_backward(self, num_doutputs):
    """Constructs a pair of forward and backward functions.

    Args:
      num_doutputs: The constructed backprop function will take output gradients
        for the first `num_doutputs` outputs of the forward function. Defaults
        to the number of outputs for the inference function, but when
        higher-order gradients are computed this will increase to include side
        outputs.

    Returns:
      A pair of (forward_function, backward_function):
        forward_function: A re-generated inference function (an
          _EagerDefinedFunction) to account for new side outputs, if any extra
          were required when building the backward pass.
        backward_function: A ConcreteFunction that Takes `num_doutputs`
          arguments and returns gradients with respect to inputs of the forward
          function.
    """
    trainable_outputs = [
        output for output in self._func_graph.outputs[:num_doutputs]
        if gradients_util.IsTrainable(output)]

    signature = []
    for t in trainable_outputs:
      signature.append(
          tensor_spec.TensorSpec(*default_gradient.shape_and_dtype(t)))

    def _backprop_function(*grad_ys):
      return gradients_util._GradientsHelper(  # pylint: disable=protected-access
          trainable_outputs,
          self._func_graph.inputs,
          grad_ys=grad_ys,
          src_graph=self._func_graph)

    with self._func_graph.as_default():
      backwards_graph = func_graph_module.FuncGraph(
          _backward_name(self._func_graph.name))
      func_graph_module.func_graph_from_py_func(
          name=backwards_graph.name,
          python_func=_backprop_function,
          args=[], kwargs={},
          signature=signature,
          func_graph=backwards_graph)
      backwards_graph_captures = backwards_graph.external_captures
      captures_from_forward = [
          c for c in backwards_graph_captures if
          not isinstance(c, ops.EagerTensor) and c.graph is self._func_graph]

      forward_function_name = _forward_name(self._func_graph.name)

      existing_outputs = object_identity.ObjectIdentitySet(
          self._func_graph.outputs)
      for capture in captures_from_forward:
        if capture not in existing_outputs:
          existing_outputs.add(capture)
          self._func_graph.outputs.append(capture)
      backward_function_attr = _parse_func_attrs(
          {FORWARD_FUNCTION_ATTRIBUTE_NAME: forward_function_name})
      backward_function_attr.update(self._attrs)

      backward_function = ConcreteFunction(
          backwards_graph, attrs=backward_function_attr)
      forward_function_attr = _parse_func_attrs({
          BACKWARD_FUNCTION_ATTRIBUTE_NAME:
          backward_function.name})
      forward_function_attr.update(self._attrs)

      forward_function = _EagerDefinedFunction(
          forward_function_name, self._func_graph, self._func_graph.inputs,
          self._func_graph.outputs, forward_function_attr)
      return forward_function, backward_function

  def _rewrite_forward_and_call_backward(self, op, *doutputs):
    """Add outputs to the forward call and feed them to the grad function."""
    forward_function, backwards_function = self.forward_backward(len(doutputs))
    if not backwards_function.outputs:
      return []
    forward_function.add_to_graph(op.graph)

    # pylint: disable=protected-access
    # Rewrite an inference call op to be a forward call op
    op._set_func_attr("f", forward_function.name)
    op._set_type_list_attr("Tout", forward_function._output_types)
    op._add_outputs(
        forward_function._output_types[len(op.outputs):],
        forward_function._output_shapes[len(op.outputs):])
    for i in range(len(op.outputs)):
      func_graph_output = forward_function._func_graph_outputs[i]
      custom_gradient.copy_handle_data(func_graph_output, op.outputs[i])
    # pylint: enable=protected-access

    capture_mapping = dict(
        zip([ops.tensor_id(t) for t in self._func_graph.outputs], op.outputs))
    remapped_captures = [
        capture_mapping.get(ops.tensor_id(capture), capture)
        for capture in backwards_function.captured_inputs
    ]

    # Replace Nones with zeros since we're calling a graph function which
    # expects numeric inputs.
    cleaned_doutputs = []
    for doutput, placeholder in zip(doutputs, self._func_graph.outputs):
      if gradients_util.IsTrainable(placeholder):
        if doutput is not None:
          cleaned_doutputs.append(doutput)
        else:
          cleaned_doutputs.append(default_gradient.zeros_like(placeholder))

    # Compute the gradients using the side outputs
    return backwards_function._call_flat(  # pylint: disable=protected-access
        cleaned_doutputs, remapped_captures)

  def register(self):
    """Registers a delayed-rewrite gradient with a unique name (idempotent).

    The gradient rewrites an inference call op to a forward call op, but does
    not modify a pre-existing forward call op. It then computes the gradient
    from the output's gradients and the side outputs of the forward op.

    Returns:
      The name under which gradient was registered.
    """
    if self._gradient_name:
      return self._gradient_name
    self._gradient_name = "PartitionedCall-%s" % ops.uid()

    @ops.RegisterGradient(self._gradient_name)
    def _registered_grad_fn(op, *doutputs):  # pylint: disable=unused-variable
      return self._rewrite_forward_and_call_backward(op, *doutputs)
    return self._gradient_name

  @property
  def forward(self):
    """A forward function with only user-specified outputs.

    The call operation for the returned inference function can be rewritten into
    a forward function. This only happens if the backward function (from the
    `backward` method) ends up being used to compute gradients.

    This approach avoids constructing unnecessary graphs, but it only works if
    we are calling this function when not executing eagerly.

    Returns:
      An _EagerDefinedFunction.
    """
    return self._inference_function

  def backward(self, outputs):
    """Fetch a backward function for `outputs` from the forward function."""
    def _backward_function(*args):
      call_op = outputs[0].op
      return self._rewrite_forward_and_call_backward(call_op, *args)
    return _backward_function, outputs


class _TapeGradientFunctions(object):
  """Caches forward and backward functions compatible with eager gradients.

  In contrast to the delayed-rewrite approach in
  `_DelayedRewriteGradientFunctions` which only works with delayed execution,
  the forward function generated by this class has a fixed set of outputs which
  may be preserved by a tape in order to compute gradients later.

  This class is abstract; its child classes differ in how many side outputs of
  the forward function their backward function accepts gradients for, which
  determines whether higher-order tape gradients are possible.
  """

  def __init__(self, func_graph, attrs, func_graph_deleter):
    self._func_graph = func_graph
    self._attrs = attrs
    self._forward = None
    self._backward = None
    self._num_outputs = len(func_graph.outputs)
    self._func_graph_deleter = func_graph_deleter

  def _build_functions_for_outputs(self, outputs):
    """Forward+backward functions where the backward function sees `outputs`."""
    # First figure out which of `outputs` are trainable. We'll accept gradients
    # for each of these in the backward function.
    handles_to_variables = self._func_graph.variable_captures
    trainable_outputs = []
    for output in outputs:
      if gradients_util.IsTrainable(output):
        # Swap in the Variable object for resource handles if we can so
        # sparse gradients work.
        output = handles_to_variables.get(ops.tensor_id(output), output)
        trainable_outputs.append(output)

    backwards_graph = func_graph_module.FuncGraph(
        _backward_name(self._func_graph.name))
    # Keep track of the forward graph so that if the backwards graph
    # tries to capture tensors those will be correctly captured first in
    # the forward graph. This is an edge case that can only happen with
    # tf.custom_gradient.
    backwards_graph._forward_func_graph = self._func_graph  # pylint: disable=protected-access
    with backwards_graph.as_default():
      gradients_wrt_outputs = []
      for output in trainable_outputs:
        gradient_shape, gradient_dtype = default_gradient.shape_and_dtype(
            output)
        gradients_wrt_outputs.append(
            graph_placeholder(gradient_dtype, gradient_shape))
      gradients_wrt_inputs = gradients_util._GradientsHelper(  # pylint: disable=protected-access
          trainable_outputs,
          self._func_graph.inputs,
          grad_ys=gradients_wrt_outputs,
          src_graph=self._func_graph)

      captures_from_forward = [
          c for c in backwards_graph.external_captures
          if not isinstance(c, ops.EagerTensor) and c.graph is self._func_graph
      ]
      existing_outputs = object_identity.ObjectIdentitySet(
          self._func_graph.outputs)
      for capture in captures_from_forward:
        if capture not in existing_outputs:
          existing_outputs.add(capture)
          self._func_graph.outputs.append(capture)

    forward_function_name = _forward_name(self._func_graph.name)
    backward_function_attr = _parse_func_attrs(
        {FORWARD_FUNCTION_ATTRIBUTE_NAME: forward_function_name})
    backward_function_attr.update(self._attrs)

    # The ordering of `backwards_graph.inputs` is important: inputs of
    # `backward_function` correspond to outputs (including
    # side outputs) of `self._tape_forward_function`.
    backwards_graph.inputs = (
        gradients_wrt_outputs + backwards_graph.internal_captures)
    backwards_graph.outputs.extend(
        grad
        for grad in nest.flatten(gradients_wrt_inputs, expand_composites=True)
        if grad is not None)
    backwards_graph.structured_outputs = gradients_wrt_inputs
    backward_function = ConcreteFunction(
        backwards_graph, attrs=backward_function_attr)

    forward_function_attr = _parse_func_attrs({
        BACKWARD_FUNCTION_ATTRIBUTE_NAME:
            backward_function.name})
    forward_function_attr.update(self._attrs)

    forward_function = _EagerDefinedFunction(
        forward_function_name, self._func_graph, self._func_graph.inputs,
        self._func_graph.outputs,
        forward_function_attr)
    return forward_function, backward_function

  @property
  def forward(self):
    """Construct or fetch a forward function with side-outputs.

    When graph building without a tape active, symbolic gradients rely on
    regenerating the backward function for higher-order gradients (to account
    for new side outputs of the rewritten forward function call). Thus there is
    no fixed backward function for this case. However, when a tape is active
    (eager or graph building), we generate fixed backward and forward functions
    at forward function call time.

    This difference between the tape and non-tape cases is to avoid building
    unneeded backward functions while graph building (where we may or may not
    eventually need gradients).

    Returns:
      A forward _EagerDefinedFunction.
    """
    if self._forward is None:
      self._forward, self._backward = (
          self._forward_and_backward_functions())
    return self._forward

  def backward(self, outputs):
    """Create a backward function given `outputs` from the forward function."""
    capture_mapping = dict(
        zip([ops.tensor_id(t) for t in self._func_graph.outputs], outputs))
    remapped_captures = [
        capture_mapping.get(ops.tensor_id(capture), capture)
        for capture in self._backward.captured_inputs
    ]
    # We may need to use zeros_like to get a zero for variant Tensors with
    # unconnected gradients. We do that in advance so we don't have to hold on
    # to the outputs themselves, which may not be needed otherwise.
    variant_zeros_like = {}
    backward_function_inputs = (
        len(self._backward.inputs) - len(self._backward.captured_inputs))
    recorded_outputs = []
    trainable_recorded_outputs = 0
    skip_positions = []
    for output_index, output in enumerate(outputs):
      if trainable_recorded_outputs < backward_function_inputs:
        recorded_outputs.append(output)
      if gradients_util.IsTrainable(output):
        trainable_recorded_outputs += 1
      else:
        skip_positions.append(output_index)
      if output.dtype == dtypes.variant:
        variant_zeros_like[output_index] = default_gradient.zeros_like(output)

    def _backward_function_wrapper(*args):
      """Process output gradients and call the backward function."""
      if not self._backward.outputs:
        return []
      processed_args = []
      input_index = 0
      for output_index, arg in enumerate(args):
        if output_index in skip_positions:
          continue
        if arg is None:
          # We're calling a (non-polymorphic) ConcreteFunction, so we need to
          # have a Tensor value for each Tensor we thought would be trainable
          # based on its dtype, even if it ended up being unconnected.
          input_placeholder = self._backward.inputs[
              input_index]
          if input_placeholder.dtype == dtypes.variant:
            arg = variant_zeros_like[output_index]
          else:
            arg = array_ops.zeros(
                *default_gradient.shape_and_dtype(input_placeholder))
        processed_args.append(arg)
        input_index += 1
        if input_index >= backward_function_inputs:
          break
      return self._backward._call_flat(  # pylint: disable=protected-access
          processed_args, remapped_captures)

    return _backward_function_wrapper, recorded_outputs


class _FirstOrderTapeGradientFunctions(_TapeGradientFunctions):
  """Caches tape-friendly functions for first-order gradients."""

  def __init__(self, func_graph, attrs, func_graph_deleter):
    super(_FirstOrderTapeGradientFunctions, self).__init__(
        func_graph, attrs, func_graph_deleter)
    self._num_inference_outputs = len(func_graph.outputs)
    self._func_graph_deleter = func_graph_deleter

  def _forward_and_backward_functions(self):
    """Shortcut for when only first-order gradients are required.

    The returned backward function does not accept gradients with respect to
    side output of forward_function. This is fine as long as the user can't
    possibly request second order tape gradients, as when they've used a single
    non-persistent GradientTape. Since we don't need the backward function to
    take gradients with respect to side outputs, we can skip some potentially
    slow graph building.

    Returns:
      A tuple of (forward_function, backward_function):
        forward_function: Takes the same inputs as the inference function, but
          returns side outputs used by backward_function in addition to the
          inference function's outputs.
        backward_function: Takes side outputs from forward_function and
          gradients with respect to the "real" outputs of forward_function and
          returns gradients with respect to the inputs.
    """
    outputs = self._func_graph.outputs[:self._num_inference_outputs]
    return self._build_functions_for_outputs(outputs)


class _HigherOrderTapeGradientFunctions(_TapeGradientFunctions):
  """Caches tape-friendly functions for higher-order gradients."""

  # TODO(b/136189779): Cond/while under a tape may need similar logic. Consider
  # generalizing if so.
  def _forward_and_backward_functions(self):
    """Forward and backward functions suitable for higher-order gradients.

    Unlike in `_FirstOrderTapeGradientFunctions`, the backward function built by
    this method accepts gradients for all of the outputs of the returned forward
    function, including side outputs.

    Returns:
      A tuple of (forward_function, backward_function):
        forward_function: Takes the same inputs as the inference function, but
          returns side outputs used by backward_function in addition to the
          inference function's outputs.
        backward_function: Takes side outputs from forward_function and
          gradients with respect to all of its outputs, real and side. Returns
          gradients with respect to the inputs.
    """
    outputs = []
    # First we need to figure out how many side outputs from the forward pass
    # will be required. We do this in a temporary graph to avoid actually
    # running multiple copies of the backward pass (one per _GradientsHelper
    # call).
    #
    # While computing gradients, the backward function captures Tensors from
    # the forward function. We add these as side outputs of the original
    # function. However, we then need to accept output gradients with respect
    # to these side outputs for higher order gradients to work. Thus we loop
    # until the number of outputs of the function stabilizes. Note that this
    # is only required for tape gradients, where we need to declare in advance
    # all of the forward op's outputs: symbolic gradients with tf.gradients
    # instead rely on regenerating backward functions when higher-order
    # gradients are requested.
    while len(outputs) < len(self._func_graph.outputs):
      new_outputs = self._func_graph.outputs[len(outputs):]
      outputs = list(self._func_graph.outputs)
      self._build_functions_for_outputs(new_outputs)
    forward_function, backward_function = (
        self._build_functions_for_outputs(outputs))
    if len(self._func_graph.outputs) != len(outputs):
      raise AssertionError(
          ("Unexpectedly added new outputs to the forward function when "
           "building the backward function: {}").format(
               self._func_graph.outputs[len(outputs):]))
    return forward_function, backward_function


class _PossibleTapeGradientTypes(enum.Enum):
  """Represents the output of TFE_Py_TapeSetPossibleGradientTypes."""
  NONE = 0
  FIRST_ORDER = 1
  HIGHER_ORDER = 2


class ConcreteFunction(object):
  """Callable object encapsulating a function definition and its gradient.

  `ConcreteFunction` is a callable that encapsulates a function definition and
  is differentiable under `tf.GradientTape` objects.
  """

  def __init__(self, func_graph, attrs=None, signature=None,
               shared_func_graph=True):
    """Initialize a `ConcreteFunction`.

    Args:
      func_graph: An instance of FuncGraph: the function body to wrap.
      attrs: (optional) dict mapping names of attributes to their AttrValue
        values. Attributes in `attrs` will be included in this function's
        definition.
     signature: a nested sequence of `TensorSpec` objects specifying the input
       signature of this function.
     shared_func_graph: If False, the ConcreteFunction takes ownership of
       `func_graph` and will break reference cycles when it is deleted. This
       makes the FuncGraph inoperable.

    Raises:
      ValueError: If number of input_placeholders is not equal to the number
        of function inputs.
    """
    self._arg_keywords = None
    self._num_positional_args = None
    self._func_graph = func_graph
    self._captured_inputs = self._func_graph.external_captures
    self._captured_closures = self._func_graph.deferred_external_captures
    self._output_shapes = tuple(
        output.shape for output in self._func_graph.outputs)
    attrs = _parse_func_attrs(attrs or {})
    self._signature = signature

    if shared_func_graph:
      self._garbage_collector = None
    else:
      self._garbage_collector = ConcreteFunctionGarbageCollector(
          func_graph)

    # Pairs of forward and backward functions used for computing gradients.
    #
    # These each get a reference to the FuncGraph deleter since they use the
    # FuncGraph directly.
    self._delayed_rewrite_functions = _DelayedRewriteGradientFunctions(
        func_graph, attrs, self._garbage_collector)
    self._first_order_tape_functions = _FirstOrderTapeGradientFunctions(
        func_graph, attrs, self._garbage_collector)
    self._higher_order_tape_functions = _HigherOrderTapeGradientFunctions(
        func_graph, attrs, self._garbage_collector)

  def __call__(self, *args, **kwargs):
    """Executes the wrapped function.

    Args:
      *args: Tensors or Variables. Positional arguments are only accepted when
        they correspond one-to-one with arguments of the traced Python function.
      **kwargs: Tensors or Variables specified by name. When
        `get_concrete_function` was called to create this `ConcreteFunction`,
        each Tensor input was given a name, defaulting to the name of the Python
        function's argument but possibly overridden by the `name=` argument to
        `tf.TensorSpec`. These names become the argument names for the concrete
        function.

    Returns:
      The result of applying the TF function on the given Tensors.

    Raises:
      AssertionError: If this `ConcreteFunction` was not created through
        `get_concrete_function`.
      ValueError: If arguments contains anything other than Tensors or
        Variables.
      TypeError: For invalid positional/keyword argument combinations.
    """
    return self._call_impl(args, kwargs)

  def _call_impl(self, args, kwargs, cancellation_manager=None):
    """See `__call__` for details."""
    if self._arg_keywords is None or self._num_positional_args is None:
      if self._signature is not None:
        if kwargs:
          raise NotImplementedError(
              "Keyword arguments not supported when calling a "
              "wrap_function-decorated function.")
        return self._call_flat(args, self.captured_inputs)
      raise AssertionError(
          "Tried to call a concrete function obtained from an internal API "
          "through the public interface. Use get_concrete_function instead.")
    if len(args) > self._num_positional_args:
      raise TypeError(
          ("Expected at most {} positional arguments (and the rest keywords, "
           "of {}), got {}. When calling a concrete function, positional "
           "arguments may not be bound to Tensors within nested structures."
          ).format(self._num_positional_args, self._arg_keywords, args))
    args = list(args)
    for keyword in self._arg_keywords[len(args):]:
      try:
        args.append(kwargs.pop(compat.as_str(keyword)))
      except KeyError:
        specified_keywords = (list(self._arg_keywords[:len(args)])
                              + list(kwargs.keys()))
        raise TypeError(
            "Expected argument names {} but got values for {}. Missing: {}."
            .format(
                list(self._arg_keywords),
                specified_keywords,
                list(set(self._arg_keywords) - set(specified_keywords))))
    if kwargs:
      positional_arg_keywords = set(self._arg_keywords[:len(args)])
      for unused_key in kwargs:
        if unused_key in positional_arg_keywords:
          raise TypeError("Got two values for keyword '{}'.".format(unused_key))
      raise TypeError("Keyword arguments {} unknown. Expected {}.".format(
          list(kwargs.keys()), list(self._arg_keywords)))
    return self._call_flat(args, self.captured_inputs, cancellation_manager)

  def _filtered_call(self, args, kwargs):
    """Executes the function, filtering arguments from the Python function.

    Objects aside from Tensors, CompositeTensors, and Variables are ignored.
    CompositeTensors are expanded into their components.

    Args:
      args: Canonicalized positional arguments of the Python function.
      kwargs: Canonicalized keyword arguments of the Python function.

    Returns:
      The result of applying the function on the Tensors/Variables contained in
      `args` and `kwargs`.
    """
    return self._call_flat(
        (t for t in nest.flatten((args, kwargs), expand_composites=True)
         if isinstance(t, (ops.Tensor,
                           resource_variable_ops.BaseResourceVariable))),
        self.captured_inputs)

  def _call_flat(self, args, captured_inputs, cancellation_manager=None):
    """Executes the wrapped function.

    Args:
      args: a list of Tensors or Variables.  Any CompositeTensors should be
        expanded before calling this method.
      captured_inputs: the captured inputs that are also part of the input args
        to the actual execution. By default, it should be self._captured_inputs.
      cancellation_manager: (Optional.) A `CancellationManager` that can be
        used to cancel function invocation.

    Returns:
      The result of applying the TF function to `args`.

    Raises:
      ValueError: If `args` contains anything other than Tensors or Variables.
    """
    args = list(args)
    ctx = context.context()
    executing_eagerly = ctx.executing_eagerly()

    # Copy saveable status of function's graph to current FuncGraph.
    default_graph = ops.get_default_graph()
    if default_graph.building_function and not self._func_graph.saveable:
      default_graph.mark_as_unsaveable(self._func_graph.saving_errors)

    if any(isinstance(a, composite_tensor.CompositeTensor) for a in args):
      raise AssertionError("Expected all args to be Tensors or Variables; "
                           "but got CompositeTensor: %r" % args)

    if (tape.could_possibly_record() or
        hasattr(ops.get_default_graph(), "watch_variable")):
      for v in self._func_graph.variables:
        resource_variable_ops.variable_accessed(v)

    tensor_inputs = []
    variables_used = object_identity.ObjectIdentitySet([])
    for i, arg in enumerate(args):
      if isinstance(arg, resource_variable_ops.BaseResourceVariable):
        # We can pass a variable more than once, and in this case we need to
        # pass its handle only once.
        if arg.handle in variables_used:
          continue
        resource_variable_ops.variable_accessed(arg)
        tensor_inputs.append(arg.handle)
        variables_used.add(arg.handle)
      elif isinstance(arg, ops.Tensor):
        tensor_inputs.append(arg)
        if not executing_eagerly:
          # If we're graph building, shape inference is on. We check for input
          # compatibility up front to avoid hard to debug incompatibilities
          # later.
          graph_input_shape = tensor_shape.TensorShape(
              self._func_graph.inputs[i].shape)
          if not graph_input_shape.is_compatible_with(arg.shape):
            if self._arg_keywords:
              arg_name = "'{}'".format(self._arg_keywords[i])
            else:
              arg_name = "with index {}".format(i)
            raise ValueError(
                ("The argument {} (value {}) is not compatible with the shape "
                 "this function was traced with. Expected shape {}, but got "
                 "shape {}.\n\nIf you called get_concrete_function, you may "
                 "need to pass a tf.TensorSpec(..., shape=...) with a less "
                 "specific shape, having None on axes which can vary.").format(
                     arg_name, arg,
                     self._func_graph.inputs[i].shape,
                     arg.shape))
      elif (self._signature is not None and
            isinstance(self._signature[i], tensor_spec.TensorSpec)):
        tensor_inputs.append(
            ops.convert_to_tensor(arg, self._signature[i].dtype))
      else:
        raise ValueError("All inputs to `ConcreteFunction`s must be Tensors; "
                         "on invocation of %s, the %d-th input (%s) was not a "
                         "Tensor." % (self._func_graph.name, i, str(arg)))
    args = tensor_inputs + captured_inputs
    forward_backward = self._select_forward_and_backward_functions(args)
    forward_function = forward_backward.forward
    if executing_eagerly:
      flat_outputs = forward_function.call(
          ctx, args, cancellation_manager=cancellation_manager)
    else:
      gradient_name = self._delayed_rewrite_functions.register()
      with ops.get_default_graph().gradient_override_map(
          {"PartitionedCall": gradient_name,
           "StatefulPartitionedCall": gradient_name}):
        flat_outputs = forward_function.call(ctx, args)
    if isinstance(flat_outputs, ops.Operation) or flat_outputs is None:
      # We only record function calls which have outputs.
      return self._build_call_outputs(flat_outputs)
    backward_function, to_record = forward_backward.backward(flat_outputs)
    tape.record_operation(forward_function.signature.name,
                          to_record, args, backward_function)
    return self._build_call_outputs(flat_outputs)

  def _experimental_with_cancellation_manager(self, cancellation_manager):
    """Returns a callable that invokes a cancelable version of this function.

    Args:
      cancellation_manager: A `CancellationManager` object that can be used to
        cancel function invocation.

    Returns:
      A callable with the same signature as this concrete function.
    """

    def cancellable_call(*args, **kwargs):
      return self._call_impl(
          args, kwargs, cancellation_manager=cancellation_manager)

    return cancellable_call

  @property
  def name(self):
    """`ConcreteFunction` name."""
    return self._delayed_rewrite_functions.forward.name

  @property
  def graph(self):
    """Returns the graph from which this function was constructed."""
    return self._func_graph

  @property
  def inputs(self):
    """Returns tensors in `self.graph` corresponding to arguments."""
    return self._func_graph.inputs

  @property
  def structured_input_signature(self):
    """Returns structured signature of the original function."""
    return self._func_graph.structured_input_signature

  @property
  def outputs(self):
    """Returns tensors in `self.graph` corresponding to returned tensors."""
    return self._func_graph.outputs

  @property
  def structured_outputs(self):
    """Returns outputs in `self.graph` as returned by the original function."""
    return self._func_graph.structured_outputs

  @property
  def captured_inputs(self):
    """Returns external Tensors captured by this function.

    self.__call__(*args) passes `args + self.captured_inputs` to the function.
    """
    from_closures = nest.flatten([x() for x in self._captured_closures],
                                 expand_composites=True)
    return self._captured_inputs + from_closures

  @property
  def function_def(self):
    """Returns a `FunctionDef` object representing this function."""
    return self._delayed_rewrite_functions.forward.definition

  @property
  def output_shapes(self):
    """The function's output shapes."""
    return nest.map_structure(
        lambda x: getattr(x, "shape", tensor_shape.TensorShape(None)),
        composite_tensor.replace_composites_with_components(
            self._func_graph.structured_outputs),
        expand_composites=False)

  @property
  def output_dtypes(self):
    # TODO(akshayka): Consider removing this.
    return nest.map_structure(
        lambda x: x.dtype if x is not None else None,
        composite_tensor.replace_composites_with_components(
            self._func_graph.structured_outputs),
        expand_composites=False)

  def add_to_graph(self, g=None):
    """Registers the function, adds it to the graph g or default graph.

    Args:
      g: If specified, registers the function with this graph. Defaults to the
        current context (either the default graph or the eager context).
    """
    # If we are not executing eagerly, adds the function to default graph if no
    # graph is specified.
    # In case of eager execution, function definition gets added to context
    # during construction itself.

    if not context.executing_eagerly() and not g:
      g = ops.get_default_graph()
    self._delayed_rewrite_functions.forward.add_to_graph(g)

  def add_gradient_functions_to_graph(self, g=None):
    """Add forward/backward functions to graph `g` or the current context."""
    if not context.executing_eagerly() and not g:
      g = ops.get_default_graph()
    self._delayed_rewrite_functions.forward.add_to_graph(g)
    forward_function, backward_function = (
        self._delayed_rewrite_functions.forward_backward())
    forward_function.add_to_graph(g)
    backward_function.add_to_graph(g)

  def _register_delayed_rewrite_gradient(self):
    """Registers a delayed-rewrite gradient function and returns the name."""
    return self._delayed_rewrite_functions.register()

  def _select_forward_and_backward_functions(self, args):
    """Selects forward and backward functions based on the calling context.

    The forward function computes the "real" function outputs, `self._outputs`,
    and any extra values needed by the corresponding backward function.

    Args:
      args: A flat list of Tensors with all of the inputs to the forward
        function (including user-specified and captured inputs).

    Returns:
      An object with a `forward` property containing an _EagerDefinedFunction,
      and a corresponding `backward` method which takes outputs from the forward
      function and returns a backward function.
    """
    possible_gradient_type = _PossibleTapeGradientTypes(
        pywrap_tensorflow.TFE_Py_TapeSetPossibleGradientTypes(args))
    if possible_gradient_type == _PossibleTapeGradientTypes.FIRST_ORDER:
      if context.executing_eagerly():
        # There is a single non-persistent tape active, so the user can only
        # request first-order gradients from a tape. We can spend less time
        # graph building since we know this.
        #
        # We may still end up computing higher-order gradients, but that'd be
        # through `tf.gradients`, which can re-write the forward pass and so
        # needs no preparation here.
        return self._first_order_tape_functions
      else:
        # We can avoid computing second-order gradients in some cases by doing a
        # delayed rewrite when graph building. Since we know we'll only compute
        # first-order tape gradients, the delayed rewrite is safe: we won't need
        # to tell the tape about side outputs.
        #
        # TODO(allenl): This case is really dirty. It would be better if we
        # could temporarily pop all of the current tapes to avoid
        # accidentally taking second-order gradients.
        return self._delayed_rewrite_functions
    elif possible_gradient_type == _PossibleTapeGradientTypes.HIGHER_ORDER:
      # Either there's a persistent tape watching, or there are multiple nested
      # tapes. Either way, the user may request higher-order gradients. We'll
      # spend a bit more time and make sure higher-order gradients are correct.
      return self._higher_order_tape_functions
    # else possible_gradient_type == _PossibleTapeGradientTypes.NONE, meaning no
    # tape is recording.
    return self._delayed_rewrite_functions

  def _build_call_outputs(self, result):
    """Maps the fdef output list to actual output structure.

    Args:
      result: Output lists defined by FunctionDef.
    Returns:
      The actual call output.
    """
    if self._func_graph.structured_outputs is None:
      return result

    # Replace outputs with results, skipping over any 'None' values.
    outputs_list = nest.flatten(self._func_graph.structured_outputs,
                                expand_composites=True)
    j = 0
    for i, o in enumerate(outputs_list):
      if o is not None:
        outputs_list[i] = result[j]
        j += 1
    ret = nest.pack_sequence_as(self._func_graph.structured_outputs,
                                outputs_list, expand_composites=True)
    return ret


pywrap_tensorflow.RegisterType("Tensor", ops.Tensor)
pywrap_tensorflow.RegisterType("IndexedSlices", ops.IndexedSlices)


def _deterministic_dict_values(dictionary):
  return tuple(dictionary[key] for key in sorted(dictionary))


class FunctionSpec(object):
  """Specification of how to bind arguments to a function."""

  @staticmethod
  def from_function_and_signature(python_function, input_signature):
    """Create a FunctionSpec instance given a python function and signature."""
    fullargspec = tf_inspect.getfullargspec(python_function)
    # Treat a wrapped partial function as a special case. For all arguments that
    # were overridden with keywords in the partial:
    #   - remove the corresponding arguments,
    #   - remove the corresponding keywords.
    _, unwrapped = tf_decorator.unwrap(python_function)
    # TODO(b/131153379): Consider Python3's fullargspec.kwonlyargs and
    # fullargspec.kwonlydefaults.
    if isinstance(unwrapped, functools.partial):
      # Also consider the Python3 case with kwonlydefaults.
      if fullargspec.defaults or fullargspec.kwonlydefaults:
        new_defaults = fullargspec.defaults
        new_args = fullargspec.args
        if fullargspec.defaults:
          # To be able to canonicalize the function properly, we want to ignore
          # default values that are overridden via a partial kwarg. For example:
          #
          #   def func(a, b, c, d=5, e=7):
          #     return a, b, c, d, e
          #   p_func = functools.partial(tf.function(func, 10, e=9))
          #
          # Here we want to drop from the defaults the parameter `e`. If we
          # forwarded the call to the partial function with a default for `e`
          # we would get an error for passing two values for one parameter.
          #
          # Note that this has a limitation: we can only override parameters at
          # the end of the parameter list.
          #
          # In this case we want to end up with 3 arguments (b, c, d) and 1
          # default value (5). We do this by constructing a mask where 0 stands
          # for a value that was overridden by a partial kwarg. The seemingly
          # complicated logic below does just that - for arguments (b, c, d, e)
          # we would get a mask (1, 1, 1, 0).
          old_args = fullargspec.args
          old_defaults = fullargspec.defaults

          no_default = object()
          num_args_without_defaults = len(old_args) - len(old_defaults)
          left_padding = tuple([no_default] * num_args_without_defaults)

          args_with_defaults = zip(old_args, left_padding + old_defaults)

          # Create a mask where 0 stands for args that had a partial kwarg
          # defined.
          non_keyword_defaults_mask = [
              0 if key in unwrapped.keywords else 1 for key in old_args
          ]
          # Keep only arguments and defaults that were not kwargs of partial.
          new_args_with_defaults = list(
              itertools.compress(args_with_defaults, non_keyword_defaults_mask))
          # Keep all args.
          new_args = [arg for arg, _ in new_args_with_defaults]
          # Keep only real default values.
          new_defaults = [
              default for _, default in new_args_with_defaults
              if default is not no_default
          ]
        fullargspec = tf_inspect.FullArgSpec(
            args=new_args,
            varargs=fullargspec.varargs,
            varkw=fullargspec.varkw,
            defaults=new_defaults,
            kwonlyargs=[],
            kwonlydefaults={},
            annotations=fullargspec.annotations)
    is_method = tf_inspect.ismethod(python_function)
    return FunctionSpec(fullargspec, is_method, [], {}, input_signature)

  def __init__(self, fullargspec, is_method, args_to_prepend, kwargs_to_include,
               input_signature):
    self._fullargspec = fullargspec
    self._is_method = is_method
    del args_to_prepend
    del kwargs_to_include
    self._default_values = fullargspec.defaults

    if self._is_method:
      # Remove `self`: default arguments shouldn't be matched to it.
      # TODO(b/127938157): Should this error out if there is no arg to
      # be removed?
      args = fullargspec.args[1:]
    else:
      args = fullargspec.args

    # A cache mapping from argument name to index, for canonicalizing
    # arguments that are called in a keyword-like fashion.
    self._args_to_indices = {arg: i for i, arg in enumerate(args)}
    self.arg_names = args
    self.vararg_name = fullargspec.varargs

    # A cache mapping from arg index to default value, for canonicalization.
    offset = len(args) - len(self._default_values or [])
    self._arg_indices_to_default_values = {
        offset + index: default
        for index, default in enumerate(self._default_values or [])
    }
    if input_signature is None:
      self._input_signature = None
    else:
      if fullargspec.kwonlyargs:
        raise ValueError("Cannot define a TensorFlow function from a Python "
                         "function with keyword arguments when "
                         "input_signature is provided.")

      if not isinstance(input_signature, (tuple, list)):
        raise TypeError("input_signature must be either a tuple or a "
                        "list, received " + str(type(input_signature)))

      self._input_signature = tuple(input_signature)
      self._flat_input_signature = tuple(nest.flatten(input_signature,
                                                      expand_composites=True))

  @property
  def fullargspec(self):
    return self._fullargspec

  @property
  def is_method(self):
    return self._is_method

  @property
  def args_to_prepend(self):
    return self._args_to_prepend

  @property
  def kwargs_to_include(self):
    return self._kwargs_to_include

  @property
  def input_signature(self):
    return self._input_signature

  @property
  def flat_input_signature(self):
    return self._flat_input_signature

  def canonicalize_function_inputs(self, *args, **kwargs):
    """Canonicalizes `args` and `kwargs`.

    Canonicalize the inputs to the Python function using a `FunctionSpec`
    instance. In particular, we parse the varags and kwargs that the
    original function was called with into a tuple corresponding to the
    Python function's positional (named) arguments and a dictionary
    corresponding to its kwargs.

    Args:
      *args: The varargs this object was called with.
      **kwargs: The keyword args this function was called with.

    Returns:
      A canonicalized ordering of the inputs representened by a tuple in the
      form (args, kwargs). Here: `args` is a full list of bound arguments, and
      `kwargs` contains only true keyword arguments, as opposed to named
      arguments called in a keyword-like fashion.

    Raises:
      ValueError: If a keyword in `kwargs` cannot be matched with a positional
        argument when an input signature is specified, or when the inputs
        do not conform to the input signature.
    """
    if self._input_signature is not None:
      if len(args) > len(self._input_signature):
        raise TypeError(
            "When input_signature is provided, only pass arguments "
            "covered by it. Received %d argument(s)." % len(args))
      for arg in six.iterkeys(kwargs):
        index = self._args_to_indices.get(arg, None)
        if index is None:
          raise TypeError(
              "Function got an unexpected keyword argument %s" % arg)
        if index >= len(self._input_signature):
          raise TypeError(
              "When input_signature is provided, only pass arguments "
              "covered by it. Received argument %s." % arg)

    if not kwargs:
      inputs = args
      default_keys = sorted(self._arg_indices_to_default_values.keys())
      if default_keys:
        assert min(default_keys) <= len(
            args), "Not enough arguments (%s, %s, %s)" % (args, default_keys,
                                                          self.arg_names)
      for index in default_keys:
        if index >= len(args):
          inputs += (self._arg_indices_to_default_values[index],)
    else:
      # Maps from index of arg to its corresponding value, according to `args`
      # and `kwargs`; seeded with the default values for the named args that
      # aren't in `args`.
      arg_indices_to_values = {
          index: default for index, default in six.iteritems(
              self._arg_indices_to_default_values) if index >= len(args)
      }
      consumed_args = []
      for arg, value in six.iteritems(kwargs):
        index = self._args_to_indices.get(arg, None)
        if index is not None:
          arg_indices_to_values[index] = value
          consumed_args.append(arg)
        elif self._input_signature is not None:
          raise ValueError("Cannot define a TensorFlow function from a Python "
                           "function with keyword arguments when "
                           "input_signature is provided.")
      for arg in consumed_args:
        # After this loop, `kwargs` will only contain true keyword arguments, as
        # opposed to named arguments called in a keyword-like fashion.
        kwargs.pop(arg)
      inputs = args + _deterministic_dict_values(arg_indices_to_values)

    if self._input_signature is None:
      inputs = _convert_numpy_inputs(inputs)
      return inputs, kwargs
    else:
      assert not kwargs
      inputs = _convert_inputs_to_signature(
          inputs,
          self._input_signature,
          self._flat_input_signature)
      return inputs, {}


def _convert_numpy_inputs(inputs):
  """Convert numpy array inputs to tensors."""
  # We assume that any CompositeTensors have already converted their components
  # from numpy arrays to Tensors, so we don't need to expand composites here.
  flat_inputs = nest.flatten(inputs, expand_composites=False)

  # Check for NumPy arrays in arguments and convert them to Tensors.
  # TODO(nareshmodi): Skip ndarray conversion to tensor altogether, perhaps
  # finding a way to store them directly in the cache key (currently not
  # possible since ndarrays are not hashable).
  need_packing = False
  for index, value in enumerate(flat_inputs):
    if type(value) == np.ndarray:
      flat_inputs[index] = constant_op.constant(value)
      need_packing = True
  if need_packing:
    return nest.pack_sequence_as(
        structure=inputs, flat_sequence=flat_inputs, expand_composites=False)
  else:
    return inputs


def _convert_inputs_to_signature(inputs, input_signature, flat_input_signature):
  """Convert inputs to pass into a function with an explicit signature."""

  def format_error_message(inputs, input_signature):
    return ("  inputs: (\n" + "    " +
            ",\n    ".join([str(i) for i in inputs]) + ")\n" +
            "  input_signature: (\n" + "    " +
            ",\n    ".join([str(i) for i in input_signature]) + ")")

  try:
    # TODO(b/124370185): Use all elements as inputs to throw an error if there
    # are ignored arguments. Calling with arguments that are not part of the
    # signature should throw an error.
    flatten_inputs = nest.flatten_up_to(
        input_signature,
        inputs[:len(input_signature)],
        expand_composites=True)
  except ValueError:
    raise ValueError("Structure of Python function inputs does not match "
                     "input_signature:\n%s" %
                     format_error_message(inputs, input_signature))

  need_packing = False
  for index, (value, spec) in enumerate(zip(flatten_inputs,
                                            flat_input_signature)):
    if not pywrap_tensorflow.IsTensor(value):
      try:
        flatten_inputs[index] = ops.convert_to_tensor(
            value, dtype_hint=spec.dtype)
        need_packing = True
      except ValueError:
        raise ValueError("When input_signature is provided, all inputs to "
                         "the Python function must be convertible to "
                         "tensors:\n%s" %
                         format_error_message(inputs, input_signature))

  if any(not spec.is_compatible_with(other) for spec, other in zip(
      flat_input_signature,
      flatten_inputs)):
    raise ValueError("Python inputs incompatible with input_signature:\n%s" %
                     format_error_message(inputs, input_signature))

  if need_packing:
    inputs = nest.pack_sequence_as(
        structure=input_signature,
        flat_sequence=flatten_inputs,
        expand_composites=True)

  return inputs


class FunctionCache(object):
  """A lightweight container for cached functions.
  """

  def __init__(self):
    # The set of functions that have been missed; entries are CacheKey with
    # input_signature `None` (e.g. a "call context key")
    self.missed = set()
    # The primary cache, mapping a fully shaped CacheKey to a function.
    self.primary = collections.OrderedDict()
    # A cache key lookup, mapping a CacheKey generated without shape info to a
    # flat list of relaxed shapes (one for each argument).  Arguments that are
    # not Tensors contain a `None` for the corresponding relaxed shape.
    self.arg_relaxed_shapes = collections.OrderedDict()
    # The secondary cache, mapping a CacheKey generated without shape info to a
    # function.
    self.arg_relaxed = collections.OrderedDict()
    # All OrderedDicts require manual garbage collection.
    self._garbage_collectors = [
        _FunctionGarbageCollector(self.primary),
        _FunctionGarbageCollector(self.arg_relaxed),
        _FunctionGarbageCollector(self.arg_relaxed_shapes)]

  def all_values(self):
    """A set of all `ConcreteFunction` instances held by this cache."""
    return set(self.primary.values()) | set(self.arg_relaxed.values())


class Function(object):
  """Wrapper class for the graph functions defined for a Python function.

  See the documentation for `defun` for more information on the semantics of
  defined functions.

  `Function` class is thread-compatible meaning that minimal usage of defuns
  (defining and calling) is thread-safe, but if users call other methods or
  invoke the base `python_function` themselves, external synchronization is
  necessary.
  """

  def __init__(self,
               python_function,
               name,
               input_signature=None,
               attributes=None,
               autograph=True,
               autograph_options=None,
               experimental_relax_shapes=False,
               capture_by_value=None):
    """Initializes a `Function`.

    Args:
      python_function: the function to be wrapped.
      name: the name given to it.
      input_signature: a possibly nested sequence of `TensorSpec` objects
        specifying the input signature of this function. If `None`, a separate
        function is instantiated for each inferred input signature.
      attributes: dict, extra keyword arguments that will be added as attribute
        of the function.
      autograph: whether to use autograph to compile
        `python_function`. See https://www.tensorflow.org/guide/autograph for
        more information.
      autograph_options: Experimental knobs to control behavior
        `when autograph=True`. See https://www.tensorflow.org/guide/autograph
        for more information.
      experimental_relax_shapes: When true, argument shapes may be relaxed to
        avoid unecessary retracing.
      capture_by_value: Experimental. Whether to capture resource variables by
        value or reference. If None, will inherit from a parent context or
        default to False.

    Raises:
      ValueError: if `input_signature` is not None and the `python_function`'s
        argspec has keyword arguments.
    """
    self._python_function = python_function
    self._function_spec = FunctionSpec.from_function_and_signature(
        python_function, input_signature)
    self._name = name
    self._autograph = autograph
    self._autograph_options = autograph_options
    self._experimental_relax_shapes = experimental_relax_shapes
    self._function_cache = FunctionCache()
    self._function_attributes = attributes or {}
    self._capture_by_value = capture_by_value

    self._lock = threading.RLock()
    # _descriptor_cache is a of instance of a class to an instance-specific
    # `Function`, used to make sure defun-decorated methods create different
    # functions for each instance.
    self._descriptor_cache = weakref.WeakKeyDictionary()

  def __call__(self, *args, **kwargs):
    """Calls a graph function specialized to the inputs."""
    graph_function, args, kwargs = self._maybe_define_function(args, kwargs)
    return graph_function._filtered_call(args, kwargs)  # pylint: disable=protected-access

  @property
  def python_function(self):
    """Returns the wrapped Python function."""
    return self._python_function  # pylint: disable=protected-access

  @property
  def function_spec(self):
    return self._function_spec

  @property
  def input_signature(self):
    """Returns the input signature."""
    return self._function_spec.input_signature

  @property
  def flat_input_signature(self):
    """Returns the flattened input signature."""
    return self._function_spec.flat_input_signature

  def _get_concrete_function_internal_garbage_collected(self, *args, **kwargs):
    """Returns a concrete function which cleans up its graph function."""
    if self.input_signature:
      args, kwargs = None, None
    graph_function, _, _ = self._maybe_define_function(args, kwargs)
    return graph_function

  def _get_concrete_function_internal(self, *args, **kwargs):
    """Bypasses error checking when getting a graph function."""
    graph_function = self._get_concrete_function_internal_garbage_collected(
        *args, **kwargs)
    # We're returning this concrete function to someone, and they may keep a
    # reference to the FuncGraph without keeping a reference to the
    # ConcreteFunction object. So we won't clean up the reference cycles
    # manually and instead will leave them to Python's garbage collector.
    graph_function._garbage_collector.release()  # pylint: disable=protected-access
    return graph_function

  def get_concrete_function(self, *args, **kwargs):
    """Returns a `ConcreteFunction` specialized to inputs and execution context.

    Args:
      *args: inputs to specialize on.
      **kwargs: inputs to specialize on.
    """
    if self.input_signature:
      if kwargs:
        raise ValueError("Cannot define a TensorFlow function from a Python "
                         "function with keyword arguments when "
                         "input_signature is provided.")
      if args:
        # If args are provided, they must match the input signature.
        if not is_same_structure(self.input_signature, args):
          raise ValueError("Structure of Python function inputs does not match "
                           "input_signature.")
        flat_inputs = nest.flatten(args, expand_composites=True)
        if any(not isinstance(arg, (ops.Tensor, tensor_spec.TensorSpec))
               for arg in flat_inputs):
          raise ValueError("When input_signature is provided, all inputs to "
                           "the Python function must be Tensors or "
                           "tf.TensorSpec objects.")
        if any(not spec.is_compatible_with(other)
               for spec, other in zip(self.flat_input_signature, flat_inputs)):
          raise ValueError("Python inputs incompatible with input_signature: "
                           "inputs (%s), input_signature (%s)" %
                           (str(args), str(self.input_signature)))
      args, kwargs = None, None
    graph_function, args, kwargs = self._maybe_define_function(args, kwargs)
    if self.input_signature:
      args = self.input_signature
      kwargs = {}
    seen_names = set()
    captured = object_identity.ObjectIdentitySet(
        graph_function.graph.internal_captures)
    # pylint: disable=protected-access
    graph_function._arg_keywords = []
    prefix_counts = {}
    # pylint: enable=protected-access
    num_positional = 0
    for arg in graph_function.graph.inputs:
      if arg in captured:
        break
      num_positional += 1
      user_arg_name = compat.as_str(arg.op.get_attr("_user_specified_name"))
      proposal = user_arg_name
      while proposal in seen_names:
        index = prefix_counts.get(user_arg_name, 1)
        proposal = "{}_{}".format(user_arg_name, index)
        prefix_counts[user_arg_name] = index + 1
      seen_names.add(proposal)
      graph_function._arg_keywords.append(proposal)  # pylint: disable=protected-access
    # Anything can be a positional argument, in the same order as .inputs
    graph_function._num_positional_args = num_positional  # pylint: disable=protected-access
    return graph_function

  def __get__(self, instance, owner):
    """Makes it possible to defun instance methods."""
    del owner
    # `instance` here is the instance that this `Function` was accessed through
    # e.g., for
    #
    #   class Foo(object):
    #
    #     @function.defun
    #     def bar(self):
    #       ...
    #
    #   foo = Foo()
    #   foo.bar()  # `foo.bar` is a `Function` instance
    #
    # then `instance` will be `foo` (and `owner` will be `Foo`).  We create a
    # new instance of `Function` here to allow different instances each
    # to create variables once, thereby allowing methods to be decorated with
    # defun. Keeps a cache to avoid retracing the function every time the
    # descriptor is accessed.
    if instance not in self._descriptor_cache:
      if instance is None:
        return self
      # If there is no instance-specific `Function` in the cache, we construct
      # an instance-specific `Function` that uses a weak reference to the
      # instance (so that the instance will be correctly gc'd).

      # And finally add the wrapped function to the description cache
      self._descriptor_cache[instance] = class_method_to_instance_method(
          self, instance)

    # Return the cached `Function` for the instance
    return self._descriptor_cache[instance]

  def _cache_key(self, args, kwargs, include_tensor_ranks_only=False):
    """Computes the cache key given inputs and execution context."""
    if self.input_signature is None:
      inputs = (args, kwargs) if kwargs else args
      input_signature = pywrap_tensorflow.TFE_Py_EncodeArg(
          inputs, include_tensor_ranks_only)
    else:
      del args, kwargs
      assert not include_tensor_ranks_only
      input_signature = self.flat_input_signature

    ctx = context.context()

    # Don't need to open an init_scope if the _cache_key call is in eager mode
    # already.
    executing_eagerly = ctx.executing_eagerly()
    parent_graph = None
    if not executing_eagerly:
      with ops.init_scope():
        # The graph, or whether we're executing eagerly, should be a part of the
        # cache key so we don't improperly capture tensors such as variables.
        executing_eagerly = ctx.executing_eagerly()
        parent_graph = None if executing_eagerly else ops.get_default_graph()

    # pylint: disable=protected-access
    default_graph = ops.get_default_graph()
    # TODO(b/117617952): The current distribution strategy will affect graph
    # building (e.g. accessing different variables from different devices) and
    # so requires retracing for each device.
    strategy_stack = default_graph._distribution_strategy_stack
    uses_distribution_strategy = (
        strategy_stack and
        strategy_stack[-1].strategy.extended._retrace_functions_for_each_device
    )
    if executing_eagerly:
      colocation_stack = ()
      if uses_distribution_strategy:
        device_functions = (pydev.merge_device(ctx.device_name),)
      else:
        device_functions = ()
    else:
      colocation_stack = tuple(default_graph._colocation_stack.peek_objs())
      if (uses_distribution_strategy
          or func_graph_module.device_stack_has_callable(
              default_graph._device_function_stack)):
        # Putting the device in the cache key ensures that call-site device
        # annotations are respected.
        device_functions = tuple(default_graph._device_functions_outer_to_inner)
      else:
        device_functions = ()

    in_cross_replica_context = False
    try:
      in_cross_replica_context = (strategy_stack[-1].replica_context is None)  # pylint: disable=protected-access
    except (AttributeError, IndexError):
      pass

    return CacheKey(input_signature, parent_graph, device_functions,
                    colocation_stack, in_cross_replica_context)

  def _create_graph_function(self, args, kwargs, override_flat_arg_shapes=None):
    """Create a `ConcreteFunction` from `args` and `kwargs`."""
    if self.input_signature is None:
      arglen = len(args)
    else:
      arglen = len(self.input_signature)
    base_arg_names = self._function_spec.arg_names[:arglen]
    num_missing_args = arglen - len(self._function_spec.arg_names)
    missing_arg_names = [self._function_spec.vararg_name] * num_missing_args
    # Produce a list of missing args of the form ["arg_0", "arg_1", ...],
    # where arg is based on the self._function_spec.vararg_name.
    missing_arg_names = [
        "%s_%d" % (arg, i) for i, arg in enumerate(missing_arg_names)
    ]
    arg_names = base_arg_names + missing_arg_names
    graph_function = ConcreteFunction(
        func_graph_module.func_graph_from_py_func(
            self._name,
            self._python_function,
            args,
            kwargs,
            self.input_signature,
            autograph=self._autograph,
            autograph_options=self._autograph_options,
            arg_names=arg_names,
            override_flat_arg_shapes=override_flat_arg_shapes,
            capture_by_value=self._capture_by_value),
        self._function_attributes,
        # Tell the ConcreteFunction to clean up its graph once it goes out of
        # scope. This is not the default behavior since it gets used in some
        # places (like Keras) where the FuncGraph lives longer than the
        # ConcreteFunction.
        shared_func_graph=False)
    return graph_function

  def _define_function_with_shape_relaxation(self, args, kwargs):
    """Define a function, relaxing arg shapes to avoid unecessary retracing."""

    rank_only_cache_key = self._cache_key(
        args, kwargs, include_tensor_ranks_only=True)

    arg_shapes = _flat_shape_list(args, kwargs)
    relaxed_arg_shapes = self._function_cache.arg_relaxed_shapes.get(
        rank_only_cache_key, None)
    relaxed_arg_function = self._function_cache.arg_relaxed.get(
        rank_only_cache_key, None)

    if (relaxed_arg_function is not None
        and _compatible_shapes(flat_relaxed=relaxed_arg_shapes,
                               flat_to_check=arg_shapes)):
      return relaxed_arg_function, args, kwargs

    if relaxed_arg_shapes is None:
      relaxed_arg_shapes = arg_shapes
    else:
      if len(arg_shapes) != len(relaxed_arg_shapes):
        raise RuntimeError("Expected arg_shapes len to match "
                           "relaxed_arg_shapes len: %d vs. %d"
                           % (len(arg_shapes), len(relaxed_arg_shapes)))
      relaxed_arg_shapes = [
          common_shape(x, y) for (x, y) in zip(
              arg_shapes, relaxed_arg_shapes)]
    self._function_cache.arg_relaxed_shapes[rank_only_cache_key] = (
        relaxed_arg_shapes)
    graph_function = self._create_graph_function(
        args, kwargs, override_flat_arg_shapes=relaxed_arg_shapes)
    self._function_cache.arg_relaxed[rank_only_cache_key] = graph_function

    return graph_function, args, kwargs

  def _maybe_define_function(self, args, kwargs):
    """Gets a function for these inputs, defining it if necessary.

    `args` and `kwargs` can be None if this `Function` was created with an
    `input_signature`.

    Args:
      args: The varargs for the Python function.
      kwargs: The keyword args for the Python function.

    Returns:
      A graph function corresponding to the input signature implied by args and
      kwargs, as well as the inputs that the object should be called with.

    Raises:
      ValueError: If inputs are incompatible with the input signature.
      TypeError: If the function inputs include non-hashable objects
      RuntimeError: If there's an internal bug (inconsistency) in handling
        shape relaxation retracing.
    """
    if self.input_signature is None or args is not None or kwargs is not None:
      args, kwargs = self._function_spec.canonicalize_function_inputs(
          *args, **kwargs)

    cache_key = self._cache_key(args, kwargs)

    try:
      hash(cache_key)
    except TypeError as e:
      raise TypeError(
          "Arguments supplied to `defun`-generated functions must be"
          " hashable.  Original error: %s" % e)

    with self._lock:
      graph_function = self._function_cache.primary.get(cache_key, None)
      if graph_function is not None:
        return graph_function, args, kwargs

      logging.vlog(1,
                   "Creating new FuncGraph for Python function %r (key: %r)",
                   self._python_function, cache_key)
      logging.vlog(2,
                   "Python function signature [args: %s] [kwargs: %s]",
                   args,
                   kwargs)

      call_context_key = cache_key.replace(input_signature=None)

      ag_status = (
          ag_ctx.Status.ENABLED if self._autograph else ag_ctx.Status.DISABLED)
      with ag_ctx.ControlStatusCtx(
          status=ag_status, options=self._autograph_options):

        # Build a function with shape relaxation retracing if:
        # 1. shape relaxation is explicitly enabled
        # and 2. there's no provided input signature
        # and 3. there's been a cache miss for this calling context
        if (self._experimental_relax_shapes
            and self.input_signature is None
            and call_context_key in self._function_cache.missed):
          return self._define_function_with_shape_relaxation(args, kwargs)

        self._function_cache.missed.add(call_context_key)
        graph_function = self._function_cache.primary.get(cache_key, None)
        if graph_function is None:
          graph_function = self._create_graph_function(args, kwargs)
          self._function_cache.primary[cache_key] = graph_function
        return graph_function, args, kwargs


def register(func, *args, **kwargs):
  """Register a specialization of a `Function` into the graph.

  This won't actually call the function with the inputs, and only put the
  function definition into graph. Register function with different input param
  will result into multiple version of functions registered in graph.

  Args:
    func: the `Function` instance that generated by a @defun
    *args: input arguments for the Python function.
    **kwargs: input keyword arguments for the Python function.

  Returns:
    a `ConcreteFunction` object specialized to inputs and execution context.

  Raises:
    ValueError: When the input function is not a defun wrapped python function.
  """
  if not isinstance(func, Function):
    raise ValueError("Only defun function is allowed to be registered. "
                     "Got type: %s" % type(func))
  concrete_func = func.get_concrete_function(*args, **kwargs)
  concrete_func.add_to_graph()
  concrete_func.add_gradient_functions_to_graph()
  return concrete_func


def validate_signature(signature):
  if any(not isinstance(arg, tensor_spec.TensorSpec)
         for arg in nest.flatten(signature, expand_composites=True)):
    raise TypeError("Invalid input_signature {}; input_signature must be "
                    "a possibly nested sequence of TensorSpec objects."
                    .format(signature))


def defun(func=None,
          input_signature=None,
          autograph=True,
          experimental_autograph_options=None,
          experimental_relax_shapes=False):
  """Compiles a Python function into a callable TensorFlow graph.

  `defun` (short for "define function") compiles a Python function
  composed of TensorFlow operations into a callable that executes a `tf.Graph`
  containing those operations. The callable produced by `defun` contains only
  the subgraph of TensorFlow operations that were executed when the Python
  function was called with a particular input signature, defined as a list
  of the shapes and dtypes of the Python function's Tensor-valued arguments and
  the values of its non-Tensor Python objects.

  When eager execution is enabled, the ability to create graphs from Python
  functions makes it possible to incrementally trade off debugability and
  interactivity for performance.  Functions compiled with `defun` cannot be
  inspected with `pdb`; however, executing a graph
  generated by `defun` sometimes takes less time and memory than eagerly
  executing the corresponding Python function, since specifying computations as
  graphs allows for optimizations like automatic buffer reuse and
  parallelization among ops. Note that executing a `defun`-compiled function
  incurs a small constant overhead, so eagerly executing sufficiently small
  Python functions might take less time than executing their corresponding
  `defun`-generated graphs.

  For a Python function to be compatible with `defun`, all of its arguments must
  be hashable Python objects or lists thereof. The function itself may not
  modify the list/map structure of its arguments. Additionally, it must return
  zero or more `tf.Tensor` objects. If the Python function returns
  a `tf.Variable`, its compiled version will return the value of that variable
  as a `tf.Tensor`.

  Executing a graph generated by `defun` respects device annotations (i.e.,
  all `with tf.device` directives present in a Python function will also be
  present in its corresponding graph), but it is not yet possible to execute the
  generated graphs across multiple machines.

  _Example Usage_

  ```python
  import tensorflow as tf

  tf.compat.v1.enable_eager_execution()

  # A simple example.
  def f(x, y):
    return tf.reduce_mean(tf.multiply(x ** 2, 3) + y)

  g = tf.contrib.eager.defun(f)

  x = tf.constant([[2.0, 3.0]])
  y = tf.constant([[3.0, -2.0]])

  # `f` and `g` will return the same value, but `g` will be executed as a
  # TensorFlow graph.
  assert f(x, y).numpy() == g(x, y).numpy()

  # `defun` is capable of compiling Python functions that close over Python
  # objects, including Tensors and Variables.
  @tf.contrib.eager.defun
  def h():
    return f(x, y)

  assert (h().numpy() == f(x, y).numpy()).all()

  # `defun` automatically lifts variables out of the graphs it creates,
  # allowing you to compile the `call` methods of `tf.keras.layers.Layer` and
  # `tf.keras.Model` objects.
  class MyModel(tf.keras.Model):

    def __init__(self, keep_probability=0.2):
      super(MyModel, self).__init__()
      self.dense1 = tf.keras.layers.Dense(4, activation=tf.nn.relu)
      self.dense2 = tf.keras.layers.Dense(5, activation=tf.nn.softmax)
      self.keep_probability = keep_probability

    @tf.contrib.eager.defun
    def call(self, inputs, training=True):
      x = self.dense2(self.dense1(inputs))
      if training:
        return tf.nn.dropout(x, self.keep_probability)
      else:
        return x

  model = MyModel()
  model(x, training=True)  # executes a graph, with dropout
  model(x, training=False) # executes a graph, without dropout

  # `defun`-compiled functions are differentiable.
  optimizer = tf.compat.v1.train.GradientDescentOptimizer(learning_rate=0.01)
  with tf.GradientTape() as tape:
    outputs = model(x)
  gradient = tape.gradient(outputs, model.trainable_variables)
  optimizer.apply_gradients((grad, var) for grad, var in zip(gradient,
                            model.trainable_variables))
  ```

  When using `defun`, there are subtleties regarding inputs, Python control
  flow, and variable creation that one should be aware of. For concreteness, let
  `f` be a Python function that returns zero or more `tf.Tensor` objects and
  let `F = defun(f)`. `F` builds a graph for each unique input signature it
  sees, Python control flow is baked into graphs, and operations related to
  variable initialization are automatically lifted out of the graphs that `F`
  generates and placed in the eager context if executing eagerly or into an
  outer graph otherwise.

  _Input Signatures_

  By default, `F = tf.contrib.eager.defun(f)` instantiates a separate graph
  for every unique sequence of the shapes and dtypes of Tensor arguments and
  the values of Python objects it is invoked with. For example, calling
  `F(tf.random.uniform([2])` will execute a different graph than
  `F(tf.random.uniform([3])` because the two inputs have different shapes.
  The first time that `F(*args, **kwargs)` is called with a particular sequence
  of Tensor shapes and dtypes and Python values, it constructs a graph by
  tracing the execution of `f(*args, **kwargs)`; this graph is bound to an
  input signature inferred from `(*args, **kwargs)` and cached for future reuse.

  NumPy arrays passed as inputs to `F` are converted to `tf.Tensor` objects
  before being passed to `f`, and are treated as Tensors for caching. This
  allows a function to be called multiple times with NumPy arrays having
  different values but the same shape and dtype without re-tracing each time.

  `tf.contrib.eager.defun` caches graphs for your convenience, letting you
  define TensorFlow functions without explicitly specifying their signatures.
  However, this policy is conservative and potentially expensive; for example,
  when different invocations of your function have differently-shaped Tensor
  inputs, this policy might generate more graph functions than necessary. To
  eliminate such costs, `tf.contrib.eager.defun` allows you to supply an
  optional `input_signature` argument specifying the shapes and dtypes of the
  inputs. In particular, the shapes may be partially unspecified, with `None`s
  in the unknown dimensions.  When an input signature is provided,
  `tf.contrib.eager.defun` will only instantiate a single graph for the
  decorated Python function. The following is an example:

  ```python
  import tensorflow as tf

  # The first `TensorSpec` below describes the shape and dtype of `words`,
  # and the second describes the shape and dtype of `another_tensor`. Note that
  # the last dimension of the `words` `TensorSpec` is left unspecified.
  @tf.contrib.eager.defun(input_signature=[
    tf.contrib.eager.TensorSpec(shape=[50, 300, None], dtype=tf.float32),
    tf.contrib.eager.TensorSpec(shape=[300, 100], dtype=tf.float32)
  ])
  def my_sequence_model(words, another_tensor):
    ...

  # Note how the third dimension of the first input can vary freely.
  words = tf.random.uniform(([50, 300, 10])
  second_input = tf.random.uniform([300, 100])
  my_sequence_model(words, second_input)

  words = tf.random.uniform(([50, 300, 20])
  my_sequence_model(words, second_input)

  # Passing an input with an incompatible shape will raise an error.
  words = tf.random.uniform(([50, 100, 20])
  my_sequence_model(words, second_input)  # <---- This will raise an error.

  ```

  Python functions that are compiled with an `input_signature` must only accept
  Tensors as arguments and must not take unnamed keyword arguments (**kwargs).

  _Tracing_

  Be aware that because `F` only logs TensorFlow operations, all the other
  Python code that `f` executes will only shape the _construction_ of the graphs
  that `F` executes: the Python code won't be executed when the graphs
  themselves are executed, though it will be executed every time the Python
  function is traced (and a given Python function might be traced multiple
  times, once for each input signature it is invoked with). For example, whereas
  the Python function

  ```python
  import tensorflow as tf
  import numpy as np

  tf.compat.v1.enable_eager_execution()

  def add_noise():
    return tf.eye(5) + np.random.randn(5, 5)
  ```

  will return a different output everytime it is invoked, the compiled function
  `compiled = tf.contrib.eager.defun(add_noise)` will return the same value
  every time it is called, since a particular random offset generated by NumPy
  will be inserted into the graph as a TensorFlow constant. The solution is to
  replace the call to `np.random.randn` with `tf.random.normal((5, 5))`.

  _Python Side-Effects_

  A corollary of the previous discussion on tracing is the following: If a
  Python function `f` has Python side-effects, then executing `f` multiple times
  will not necessarily be semantically equivalent to executing `F =
  tf.contrib.eager.defun(f)` multiple times; this difference is due to the fact
  that `defun` only captures the subgraph of TensorFlow operations that is
  constructed when `f` is called in a graph-building context.

  _Python Control Flow_

  The structure of many machine learning computations depend upon whether one is
  training or validating, and it is common to nest specialized logic under `if
  training:` blocks. By mapping each input signature to a unique graph, `defun`
  lets users transparently compile such code, as the following code snippet
  demonstrates:

  ```python
  import tensorflow as tf

  tf.compat.v1.enable_eager_execution()

  @tf.contrib.eager.defun
  def lossy_matmul(W, x, training=True):
    outputs = tf.matmul(W, x)
    if training:
      outputs = tf.nn.dropout(outputs, keep_probability=0.2)
    return outputs

  W = tf.random.normal((3, 5))
  x = tf.random.normal((5, 1))

  # Executes a graph that applies dropout.
  lossy_outputs = lossy_matmul(W, x, training=True)

  # Executes a graph that does not apply dropout.
  exact_outputs = lossy_matmul(W, x, training=False)
  ```

  _TensorFlow Control Flow_

  When `autograph` is `True`, data-dependent control flow is allowed as well.
  Control flow statements that depend on `Tensor` values are staged into
  corresponding TensorFlow ops. For example, the following code will work as
  expected:

  ```python
  @tf.contrib.eager.defun
  def dynamic_rnn_loop(cell, seq):
    state, output = cell.zero_state()
    for input in seq:
      state, output = cell(input, state)
    return output
  ```

  For more information see `tf.autograph`.

  _Variables_

  TensorFlow operations related to variable creation and initialization are
  automatically lifted out of the graphs generated by `defun`. In practice, this
  implies that variable creation and initialization only happen the first time
  `F` is called, and that variables are reused every time thereafter. Many
  TensorFlow APIs, like `tf.keras.layers.Layer` objects, create variables the
  first time they are called and reuse them thereafter. Automatic variable
  lifting makes it possible to compile these APIs without extra effort, at the
  cost of introducing a discrepancy between the semantics of executing Python
  functions and their corresponding compiled functions. For example:

  ```python
  import tensorflow as tf

  tf.compat.v1.enable_eager_execution()

  def fn():
    x = tf.Variable(0.0)
    x.assign_add(1.0)
    return x.read_value()

  # `fn` is a Python function, so x is created, initialized, and destroyed upon
  # every invocation
  assert fn().numpy() == fn().numpy() == 1.0

  compiled = tf.contrib.eager.defun(fn)

  # Compiling `fn` with `defun` hoists all variables outside of the generated
  # graph, so initialization happens exactly once.
  assert compiled().numpy() == 1.0
  assert compiled().numpy() == 2.0
  ```

  Finally, because each input signature is bound to a unique graph, if your
  Python function constructs `tf.Variable` objects, then each graph constructed
  for that Python function will reference a unique set of variables. To
  circumvent this problem, we recommend against compiling Python functions that
  create `tf.Variable` objects. Instead, Python functions should either
  lexically close over `tf.Variable` objects or accept them as arguments,
  preferably encapsulated in an object-oriented container. If you must create
  variables inside your Python function and you want each graph generated for it
  to reference the same set of variables, add logic to your Python function that
  ensures that variables are only created the first time it is called and are
  reused for every subsequent invocation; note that this is precisely what
  `tf.keras.layers.Layer` objects do, so we recommend using them to represent
  variable-bearing computations whenever possible.

  Args:
    func: function to be compiled. If `func` is None, returns a
      decorator that can be invoked with a single argument - `func`. The
      end result is equivalent to providing all the arguments up front.
      In other words, defun(input_signature=...)(func) is equivalent to
      defun(func, input_signature=...). The former allows
      the following use case:
        @tf.contrib.eager.defun(input_signature=...)
        def foo(...):
          ...

    input_signature: A possibly nested sequence of
      `tf.contrib.eager.TensorSpec` objects specifying the shapes and dtypes of
      the Tensors that will be supplied to this function. If `None`, a separate
      function is instantiated for each inferred input signature.  If a
      signature is specified, every input to `func` must be a `Tensor`, and
      `func` cannot accept `**kwargs`.
    autograph: Whether `func` should be compiled before
      constructing the graph. See https://www.tensorflow.org/guide/autograph
      for more information.
    experimental_autograph_options: Experimental knobs (in the form of a tuple
      of tensorflow.autograph.Feature values) to control behavior when
      autograph=True.
    experimental_relax_shapes: When true, argument shapes may be relaxed to
      avoid unecessary retracing.

  Returns:
     If `func` is not None, returns a callable that will execute the compiled
     function (and return zero or more `tf.Tensor` objects).
     If `func` is None, returns a decorator that, when invoked with a single
     `func` argument, returns a callable equivalent to the case above.

  Raises:
    TypeError: If `input_signature` is neither `None` nor a sequence of
      `tf.contrib.eager.TensorSpec` objects.
  """
  return defun_with_attributes(
      func=func,
      input_signature=input_signature,
      autograph=autograph,
      experimental_autograph_options=experimental_autograph_options,
      experimental_relax_shapes=experimental_relax_shapes)


def defun_with_attributes(func=None,
                          input_signature=None,
                          attributes=None,
                          autograph=True,
                          experimental_autograph_options=None,
                          experimental_relax_shapes=False):
  """Compiles a Python function into a callable TensorFlow graph.

  This function supports adding extra function attributes. See detailed
  documentation in defun(). Currently this is not exposed in public API since we
  don't expect user to directly use attributes, and attribute won't work by
  itself. This assumption might change in future.

  Args:
    func: function to be compiled.
    input_signature: same as defun()'s input_signature.
    attributes: A dictionary of arguments which will be added to function def as
      attributes. Currently only support primitive types as value, and only
      whitelisted attribute name is allowed. Unwhitelisted attribute name or
      unsupported value will result into ValueError. `func_name` is also one of
      the whitelisted argument which is a python string, and sets the name for
      this `ConcreteFunction` in the graph.
    autograph: same as defun()'s autograph.
    experimental_autograph_options: same as defun()'s
      experimental_autograph_options.
    experimental_relax_shapes: same as defun()'s experimental_relax_shapes

  Returns:
    Same as the return value of defun, with attributes added to the function in
    graph.
  """
  if input_signature is not None:
    validate_signature(input_signature)

  # TODO(apassos): deal with captured global state. Deal with control flow.
  def decorated(function):
    try:
      if attributes:
        name = attributes.pop("func_name", function.__name__)
      else:
        name = function.__name__
    except AttributeError:
      name = "function"
    return tf_decorator.make_decorator(
        function,
        Function(
            function,
            name,
            input_signature=input_signature,
            attributes=attributes,
            autograph=autograph,
            autograph_options=experimental_autograph_options,
            experimental_relax_shapes=experimental_relax_shapes))

  # This code path is for the `foo = tfe.defun(foo, ...)` use case
  if func is not None:
    return decorated(func)

  # This code path is for the
  #
  # @tfe.defun(...)
  # def foo(...):
  #    ...
  #
  # use case, which is equivalent to `foo = tfe.defun(...)(foo)`
  return decorated


# When a method is bound to objects of this type, it allows AutoGraph to
# recover a weak reference the original method's self pointer, so that it can
# execute it consistent with class_method_to_instance_method's
# bound_method_wrapper.
# TODO(b/119246461): This is not pretty. Use a descriptor instead?
class TfMethodTarget(object):
  """Binding target for methods replaced by function and defun."""

  def __init__(self, target, original_python_function):
    self.weakrefself_target__ = target
    self.weakrefself_func__ = weakref.ref(original_python_function)

  @property
  def target(self):
    return self.weakrefself_target__()

  def call(self, args, kwargs):
    wrapped_fn = self.weakrefself_func__()
    if tf_inspect.ismethod(wrapped_fn):
      wrapped_fn = six.get_unbound_function(wrapped_fn)
    return wrapped_fn(self.weakrefself_target__(), *args, **kwargs)


def class_method_to_instance_method(original_function, instance):
  """Constructs a new `Function` with `self` bound."""
  weak_instance = weakref.ref(instance)

  # Note: while we could bind to a weakref proxy instead, that causes the
  # bound method to be unhashable.
  bound_method = types_lib.MethodType(
      original_function.python_function,
      TfMethodTarget(weak_instance, original_function.python_function))

  # original_function is expected to be of one of the two `Function` types
  # (defined either in function.py or def_function.py).
  assert hasattr(original_function, "_name")
  assert hasattr(original_function, "_autograph")
  assert hasattr(original_function, "_function_spec")
  assert hasattr(original_function, "python_function")

  weak_bound_method_wrapper = None
  def bound_method_wrapper(*args, **kwargs):
    """Wraps either a dummy MethodType or a converted AutoGraph function."""
    # __wrapped__ allows AutoGraph to swap in a converted function.
    strong_bound_method_wrapper = weak_bound_method_wrapper()
    wrapped_fn = strong_bound_method_wrapper.__wrapped__

    if wrapped_fn is strong_bound_method_wrapper.__original_wrapped__:
      # If __wrapped__ was not replaced, then call original_function.
      # TODO(mdan): For better consistency, use the wrapper's call().
      wrapped_fn = original_function.python_function
      if tf_inspect.ismethod(wrapped_fn):
        wrapped_fn = six.get_unbound_function(wrapped_fn)
      return wrapped_fn(weak_instance(), *args, **kwargs)

    # If __wrapped__ was replaced, then it is always an unbound function.
    # However, the replacer is still responsible for attaching self properly.
    # TODO(mdan): Is it possible to do it here instead?
    return wrapped_fn(*args, **kwargs)
  weak_bound_method_wrapper = weakref.ref(bound_method_wrapper)

  # pylint: disable=protected-access
  # We make a dummy MethodType object to generate the correct bound method
  # signature. The actual call is to a function with a weak reference to
  # `instance`.
  instance_func = type(original_function)(
      tf_decorator.make_decorator(bound_method, bound_method_wrapper),
      name=original_function._name,
      autograph=original_function._autograph,
      input_signature=original_function.input_signature)
  # pylint: enable=protected-access

  # And we wrap the function with tf_decorator so inspection works correctly
  wrapped_instance_func = tf_decorator.make_decorator(
      original_function.python_function, instance_func)
  return wrapped_instance_func


class _FunctionGarbageCollector(object):
  """Cleans up cycles when a defun goes out of scope."""

  def __init__(self, cache):
    self._cache = cache

  def __del__(self):
    if func_graph_module is None or memory is None:
      return
    try:
      while self._cache:
        self._cache.popitem()
      memory.dismantle_ordered_dict(self._cache)
    except:  # pylint: disable=bare-except
      pass


class ConcreteFunctionGarbageCollector(object):
  """Cleans up reference cycles when a `ConcreteFunction` goes out of scope."""

  def __init__(self, func_graph):
    self._func_graph = func_graph

  def release(self):
    """Call off the FuncGraph deletion."""
    self._func_graph = None

  def __del__(self):
    if func_graph_module is None or memory is None or self._func_graph is None:
      return
    try:
      func_graph_module.dismantle_func_graph(self._func_graph)
    except:  # pylint: disable=bare-except
      pass
