[&](Operation* op) -> llvm::SmallVector<mlir::Operation*, 4> const& {
    if (extraDependencies) {
      return extraDependencies(op, /*incoming=*/true);
    } else {
      return empty_op_set;
    }
  };
  auto ctrlSuccessors =
      [&](Operation* op) -> llvm::SmallVector<mlir::Operation*, 4> const& {
    if (extraDependencies) {
      return extraDependencies(op, /*incoming=*/false);
    } else {
      return empty_op_set;
    }

// op should be returned. If "incoming" is false, the list of successors.
// The algorithm assumes that these are consistent which each other. So
// if (and only if) op1 is in extra_dependencies(op2, true), then op2
// must also be in extra_dependencies(op1, false).
// This function is called multiple times during the topological sort,
// so the implementation should preferably be constant-time.

  for (func::FuncOp func : module.getOps<func::FuncOp>()) {
    std::vector<std::pair<Operation*, Operation*>> side_effect_data;
    const detail::SideEffectAnalysisInfo* info = nullptr;
    auto extra_dependencies =
        [&](Operation* op,
            bool incoming) -> llvm::SmallVector<Operation*, 4> const& {
      return incoming ? info->DirectControlPredecessors(op)
                      : info->DirectControlSuccessors(op);