return fmt.Sprintf("%s -> %s", old, new)
	case trace.EventRegionBegin:
		return fmt.Sprintf("region %q begin", ev.Region().Type)
	case trace.EventRegionEnd:
		return fmt.Sprintf("region %q end", ev.Region().Type)
	case trace.EventTaskBegin:
		t := ev.Task()
		return fmt.Sprintf("task %q (D %d, parent %d) begin", t.Type, t.ID, t.Parent)
	case trace.EventTaskEnd:
		return "task end"
	case trace.EventLog:

    if (auto cast = dyn_cast<TF::CastOp>(op)) {
      this->join(results[0], *operands[0]);
    } else if (auto while_op = dyn_cast<TF::WhileRegionOp>(op)) {
      for (auto &region : while_op->getRegions()) {
        for (auto [arg, value] :
             llvm::zip(region.getArguments(), while_op->getOperands())) {
          this->join(getLatticeElement(arg), *getLatticeElement(value));
        }
      }

 public:
  QuantizeContext(func::FuncOp func, const DeviceTarget &spec);

  // Returns all the quant region ops.
  std::vector<quantfork::QuantizeRegionOp> GetAllOps();

  // For each quant region op, propagates its quantization parameters according
  // to the kernel specification and also returns the adjacent quant region ops
  // which get the new quantization parameters propagated.
  LogicalResult Handle(quantfork::QuantizeRegionOp op,

  }
  return success();
}

// Check if the specified region is a binary reduction function that takes 2
// inputs and returns the second input. Functions like this are used by update
// scatter like ops.
template <>
LogicalResult MatchBinaryReduceFunction<void>(mlir::Region& function) {
  Block& body = function.front();
  if (body.getNumArguments() != 2) return failure();

}

// -----

// Check that an empty graph is invalid (it needs a region).
func.func @empty_graph() {
 "tf_executor.graph" () ({
// expected-error@-1 {{'tf_executor.graph' op region #0 ('body') failed to verify constraint: region with 1 blocks}}
  }) : () -> ()
  func.return
}

// -----

// Check that an empty graph is invalid (it needs a region).
func.func @empty_graph() {
 "tf_executor.graph" () ({

  outlined_func.setPrivate();

  // Create function body.
  Block* outlined_func_block = outlined_func.addEntryBlock();

  // Replace uses of live-in values within cluster_op region with function
  // arguments.
  Region& op_region = op.getBody();
  for (auto p : llvm::zip(live_ins, outlined_func_block->getArguments())) {
    replaceAllUsesInRegionWith(std::get<0>(p), std::get<1>(p), op_region);
  }

</ul>

<h2>User-defined tasks and regions</h2>
<p>
  The trace API allows a target program to annotate a <a
  href='https://pkg.go.dev/runtime/trace#Region'>region</a> of code
  within a goroutine, such as a key function, so that its performance
  can be analyzed.

  <a href='https://pkg.go.dev/runtime/trace#Log'>Log events</a> may be
  associated with a region to record progress and relevant values.

	// Virtual Memory Map of process 53799 (gopls)
	// Output report format:  2.4  -64-bit process
	// VM page size:  16384 bytes
	//
	// ==== Non-writable regions for process 53799
	// REGION TYPE                    START END         [ VSIZE  RSDNT  DIRTY   SWAP] PRT/MAX SHRMOD PURGE    REGION DETAIL
	// __TEXT                      1029a0000-1033bc000    [ 10.1M  7360K     0K     0K] r-x/rwx SM=COW          /Users/USER/*/gopls

// set of unique IDs representing the possible resources it could alias.
//
// Note that this is not an inter-procedural or inter-regional analysis, i.e.,
// each function and region are handled separately and cross-function or cross-
// region aliasing cannot be checked by this analysis.
class ResourceAliasAnalysis : public detail::PerFunctionAggregateAnalysis<

func BenchmarkStartRegion(b *testing.B) {
	b.ReportAllocs()
	ctx, task := NewTask(context.Background(), "benchmark")
	defer task.End()

	b.RunParallel(func(pb *testing.PB) {
		for pb.Next() {
			StartRegion(ctx, "region").End()
		}
	})
}

func BenchmarkNewTask(b *testing.B) {
	b.ReportAllocs()
	pctx, task := NewTask(context.Background(), "benchmark")
	defer task.End()

	b.RunParallel(func(pb *testing.PB) {