code: def gen_foreach_derivativeinfo(
      foreach_function: NativeFunction,
      functional_info_by_signature: Dict[
          FunctionSchema, Dict[str, DifferentiabilityInfo]
      ],
      non_functional_info_by_signature: Dict[
          FunctionSchema, Dict[str, DifferentiabilityInfo]
      ],
      dispatch_key: str = "Default",
  ) -> Tuple[Optional[DifferentiabilityInfo], bool]:
      """Generate DifferentiabilityInfo for out-place foreach function, return the existing one for in-place.
  
      The second return value indicates whether the info is generated in this function.
      """
      ref_diff_info: Optional[DifferentiabilityInfo] = None
  
      for (
          function_schema,
          diff_info,
      ) in functional_info_by_signature.items():
          if not is_reference_for_foreach(
              foreach_function, function_schema
          ):
              continue
          ref_diff_info = diff_info[dispatch_key]
          if ref_diff_info is not None:
              break
      # note(crcrpar): It seems like `zero`'s info isn't available in functional_info_by_signature
      # while the info of `zero_` is in non_functional_info_by_signature
      if (
          ref_diff_info is None
          and foreach_function.func.kind() == SchemaKind.inplace
          and str(foreach_function.func.name)
          in _foreach_with_inplace_ref
      ):
          for (
              function_schema,
              diff_info,
          ) in non_functional_info_by_signature.items():
              if not is_reference_for_foreach(
                  foreach_function, function_schema
              ):
                  continue
              ref_diff_info = diff_info[dispatch_key]
              if ref_diff_info is not None:
                  break
      if ref_diff_info is None:
          return None, False
  
      # non out-place uses the existing Derivative.
      if foreach_function.func.kind() == SchemaKind.inplace:
          return ref_diff_info, False
  
      map_refarg2foreacharg, map_name2arg = {}, {}
      for i, (arg, ref_arg) in enumerate(
          zip(
              foreach_function.func.arguments.flat_non_out,
              function_schema.arguments.flat_non_out,
          )
      ):
          map_refarg2foreacharg[ref_arg.name] = arg.name
          map_name2arg[arg.name] = arg
  
      all_saved_inputs, all_saved_outputs, all_var_names = [], [], []
      modified_derivative_formulas = []
      for i, derivative in enumerate(ref_diff_info.derivatives):
          modified_formula = derivative.formula.replace(
              "grad", "grads[i]"
          ).replace("result", "result[i]")
          saved_inputs, saved_outputs = [], []
          # note(crcrpar): This context seems necessary to call `cpp.argument_type`
          with local.parametrize(
              use_const_ref_for_mutable_tensors=foreach_function.use_const_ref_for_mutable_tensors,
              use_ilistref_for_tensor_lists=foreach_function.part_of_structured_group,
          ):
              for ref_input in derivative.saved_inputs:
                  ref_input_jit_name = ref_input.expr.split(".")[0]
                  mapped_name = map_refarg2foreacharg[
                      ref_input_jit_name
                  ]
                  if isinstance(
                      map_name2arg[mapped_name].type, ListType
                  ):
                      mapped_expr = mapped_name + "[i]"
                  else:
                      mapped_expr = mapped_name
                  new_expr = ref_input.expr.replace(
                      ref_input_jit_name, mapped_expr
                  )
                  modified_formula = modified_formula.replace(
                      cast(str, ref_input.nctype.name), new_expr
                  )
  
                  nctype = cpp.argument_type(
                      map_name2arg[mapped_name], binds=mapped_name
                  )
                  canonical_nctype = NamedCType(
                      nctype.name, nctype.type.remove_const_ref()
                  )
                  saved_inputs.append(
                      SavedAttribute(
                          nctype=canonical_nctype, expr=mapped_name
                      )
                  )
              for ref_output in derivative.saved_outputs:
                  if ref_output.nctype.name == "result":
                      saved_outputs.append(
                          SavedAttribute(
                              nctype=NamedCType(
                                  name="result",
                                  type=BaseCType(tensorListT),
                              ),
                              expr="result",
                          )
                      )
                  else:
                      raise RuntimeError("")
          var_names = [
              map_refarg2foreacharg[var] for var in derivative.var_names
          ]
          all_var_names.extend(var_names)
          all_saved_inputs.extend(saved_inputs)
          all_saved_outputs.extend(saved_outputs)
          modified_derivative = Derivative(
              formula=modified_formula,
              original_formula=derivative.formula,
              var_names=tuple(var_names),
              saved_inputs=tuple(saved_inputs),
              saved_outputs=tuple(saved_outputs),
              named_gradients=set(),
          )
          modified_derivative_formulas.append(modified_derivative)
  
      with local.parametrize(
          use_const_ref_for_mutable_tensors=foreach_function.use_const_ref_for_mutable_tensors,
          use_ilistref_for_tensor_lists=foreach_function.part_of_structured_group,
      ):
          args_with_derivatives = [
              Binding(
                  name=arg.name,
                  nctype=cpp.argument_type(arg, binds=arg.name),
                  argument=arg,
                  default=None,
              )
              for arg in foreach_function.func.arguments.flat_non_out
              if arg.name in all_var_names
          ]
  
      forward_derivatives: List[ForwardDerivative] = []
      fw_derivative: ForwardDerivative
      for fw_derivative in ref_diff_info.forward_derivatives:
          var_names: List[str] = list(fw_derivative.var_names)  # type: ignore[no-redef]
          var_types: List[Type] = list(fw_derivative.var_types)
          required_inputs_fw_grad: List[str] = []
          required_inputs_primal: List[str] = []
          if fw_derivative.required_inputs_fw_grad is not None:
              required_inputs_fw_grad = list(
                  fw_derivative.required_inputs_fw_grad
              )
          if fw_derivative.required_inputs_primal:
              required_inputs_primal = list(
                  fw_derivative.required_inputs_primal
              )
          modified_formula = fw_derivative.formula
  
          # Foreach's result is TensorList
          if "result" in modified_formula:
              modified_formula = fw_derivative.formula.replace(
                  "result", "result[i]"
              )
  
          for foreach_arg, ref_arg in zip(
              foreach_function.func.arguments.flat_non_out,
              ref_diff_info.func.func.arguments.flat_non_out,
          ):
              # Modify reference forward formula
              if (
                  isinstance(foreach_arg.type, ListType)
                  and not foreach_arg.type.is_tensor_like()
              ):
                  # Assuming ScalarList
                  modified_formula = modified_formula.replace(
                      ref_arg.name, foreach_arg.name + "[i]"
                  )
              elif foreach_arg.type.is_tensor_like():
                  # Assuming TensorList / Tensor
                  # assert isinstance(foreach_arg.type, ListType), f"{foreach_function.func.name}, {foreach_arg.type}"
                  assert isinstance(foreach_arg.type, ListType) or (
                      foreach_arg.type == BaseType(BaseTy.Tensor)
                      and str(foreach_function.func.name)
                      in _foreach_with_tensor_overload
                  ), f"{foreach_function.func.name}, {foreach_arg.type}"
                  for suffix in ("_p", "_t"):
                      curr_expr = ref_arg.name + suffix
                      if curr_expr in modified_formula:
                          new_expr = foreach_arg.name + suffix
                          modified_formula = modified_formula.replace(
                              curr_expr, new_expr
                          )
              else:
                  # Assuming Scalar
                  if foreach_arg.name != ref_arg.name:
                      modified_formula = modified_formula.replace(
                          ref_arg.name, foreach_arg.name
                      )
  
              # note(crcrpar): there should exist a cooler way...
              for i, name in enumerate(var_names):
                  if name == ref_arg.name:
                      var_names[i] = foreach_arg.name
                      var_types[i] = foreach_arg.type
              for i, name in enumerate(required_inputs_fw_grad):
                  if name == ref_arg.name:
                      required_inputs_fw_grad[i] = foreach_arg.name
              for i, name in enumerate(required_inputs_primal):
                  if name == ref_arg.name:
                      required_inputs_primal[i] = foreach_arg.name
          forward_derivatives.append(
              ForwardDerivative(
                  formula=modified_formula,
                  var_names=tuple(var_names),
                  var_types=tuple(var_types),
                  required_inputs_fw_grad=tuple(
                      required_inputs_fw_grad
                  ),
                  required_inputs_primal=tuple(required_inputs_primal),
                  required_original_self_value=fw_derivative.required_original_self_value,
                  is_reusing_outplace_formula=fw_derivative.is_reusing_outplace_formula,
              )
          )
  
      return (
          DifferentiabilityInfo(
              name=foreach_function.func.name.name.base,
              func=foreach_function,
              op=f"Foreach{ref_diff_info.op}{foreach_function.func.name.overload_name}",
              derivatives=modified_derivative_formulas,
              forward_derivatives=forward_derivatives,
              all_saved_inputs=tuple(set(all_saved_inputs)),
              all_saved_outputs=tuple(set(all_saved_outputs)),
              available_named_gradients=(),
              used_named_gradients=set(),
              args_with_derivatives=args_with_derivatives,
              non_differentiable_arg_names=[],
              output_differentiability=None,
              output_differentiability_conditions=None,
          ),
          True,
      )
  
imports: import re
  from dataclasses import dataclass
  from typing import cast, Dict, List, Match, Optional, Sequence, Set, Tuple
  from torchgen import local
  from torchgen.api import cpp
  from torchgen.api.types import BaseCType, Binding, NamedCType, tensorListT
  from torchgen.model import BaseTy, BaseType, FunctionSchema, ListType, NativeFunction, NativeFunctionsViewGroup, SchemaKind, Type
  from torchgen.utils import IDENT_REGEX
label_desc: Use image node_id 7 for calling a global function with example usage: gen_foreach_derivativeinfo(foreach_function, functional_info_by_signature, non_functional_info_by_signature, dispatch_key) and returns: DifferentiabilityInfo,  True, None,  False, ref_diff_info,  False