refactor(dispatch): allow dynamic type creation

GitOrigin-RevId: 27dde05cff7e1e0bf61c652a3ae1fe4def829ada

imperative/python/src/grad.cpp

@@ -19,6 +19,7 @@
 
 #include "range/v3/all.hpp"
 
+#include "./helper.h"
 #include "./transformation.h"
 
 namespace py = pybind11;
@@ -30,9 +31,7 @@ namespace {
 std::unordered_map<std::shared_ptr<GradKey>, GradKeyWrapper*> grad_key_map;
 }
 
-GradKeyWrapper::GradKeyWrapper() : m_key(std::make_shared<GradKey>()) {
-    grad_key_map[m_key] = this;
-}
+GradKeyWrapper::GradKeyWrapper() {}
 
 void GradKeyWrapper::attach(PyObject* const* args, size_t nargs) {
     if (nargs != 2) {
@@ -77,8 +76,8 @@ pybind11::function GradKeyWrapper::get_backward_closure(
     for (auto&& tensor : tensors) {
         args.push_back(TensorWrapper::try_cast(tensor.ptr())->m_tensor->data());
     }
-    auto closure = imperative::apply(GetBackwardColsure(self->m_key), args)[0]
-                           .as<FunctionValue>();
+    auto closure_value = imperative::apply(GetBackwardColsure(self->m_key), args)[0];
+    auto closure = closure_value.as_ref<FunctionValue>();
     auto py_function = [closure](std::vector<TensorWrapper*> tensors) {
         std::vector<ValueRef> args;
         for (auto* tw : tensors) {
@@ -90,11 +89,14 @@ pybind11::function GradKeyWrapper::get_backward_closure(
 }
 
 PyObject* GradKeyWrapper::get_name() {
-    return py::cast(m_key->name()).release().ptr();
+    return py::cast(m_name).release().ptr();
 }
 
 void GradKeyWrapper::set_name(py::handle name) {
-    m_key->name(py::cast<std::string>(name));
+    m_name = py::cast<std::string>(name);
+    if (m_key) {
+        m_key->name(m_name);
+    }
 }
 
 PyObject* GradKeyWrapper::is_attached_to(PyObject* const* args, size_t nargs) {
@@ -115,7 +117,10 @@ PyObject* GradKeyWrapper::is_attached_to(PyObject* const* args, size_t nargs) {
 }
 
 void GradKeyWrapper::enter() {
-    m_transformation = std::make_shared<GradTransformation>(m_key);
+    m_transformation = std::make_shared<GradTransformation>();
+    m_key = m_transformation->key();
+    m_key->name(m_name);
+    grad_key_map[m_key] = this;
     TransformationManager::get_instance().register_at<TransformationManager::Grad>(
             m_transformation);
 }
@@ -123,6 +128,8 @@ void GradKeyWrapper::enter() {
 void GradKeyWrapper::exit() {
     TransformationManager::get_instance().unregister<TransformationManager::Grad>(
             m_transformation);
+    grad_key_map.erase(m_key);
+    m_key = {};
     m_transformation.reset();
 }
 
@@ -138,8 +145,6 @@ GradKeyWrapper* GradKeyWrapper::get(std::shared_ptr<GradKey> key) {
     return grad_key_map.at(key);
 }
 
-GradKeyWrapper::~GradKeyWrapper() {
-    grad_key_map.erase(m_key);
-}
+GradKeyWrapper::~GradKeyWrapper() {}
 
 }  // namespace mgb::imperative::python

imperative/python/src/grad.h

@@ -26,6 +26,7 @@ struct GradKeyWrapper : NonCopyableObj {
     using wrap_t = pyext17::wrap<GradKeyWrapper>;
     static constexpr auto tp_name = pybind11::detail::_("GradKey");
 
+    std::string m_name;
     std::shared_ptr<GradKey> m_key;
     std::shared_ptr<GradTransformation> m_transformation;
 

imperative/python/src/grad_override.cpp

@@ -117,7 +117,7 @@ std::optional<ValueRefList> elemwise_grad_rule(
     maker.backward([shapes = std::move(input_shapes)](Span<ValueRef> grads) {
         mgb_assert(grads.size() == 1);
         ValueRef grad = grads[0];
-        ValueRefList ret(2);
+        SmallVector<ValueRef> ret(2);
         if (!grad) {
             return ret;
         }
@@ -147,7 +147,7 @@ std::optional<ValueRefList> reshape_grad_rule(
     maker.backward([shapes = std::move(input_shapes)](Span<ValueRef> grads) {
         mgb_assert(grads.size() == 1);
         ValueRef grad = grads[0];
-        ValueRefList ret(2);
+        SmallVector<ValueRef> ret(2);
         if (!grad) {
             return ret;
         }
@@ -180,7 +180,7 @@ std::optional<ValueRefList> subtensor_grad_rule(
                     grad_op_ = std::move(grad_op)](Span<ValueRef> grads) {
         mgb_assert(grads.size() == 1);
         ValueRef grad = grads[0];
-        ValueRefList ret(1);
+        SmallVector<ValueRef> ret(1);
         if (grad && inputs[0]) {
             ValueRefList args_(inputs.size() + 1);
             auto&& zeros = make_empty_tensor(grad.device(), inputs[0], grad.dtype());
@@ -215,7 +215,7 @@ std::optional<ValueRefList> indexingMultiAxisVec_grad_rule(
                     grad_op_ = std::move(grad_op)](Span<ValueRef> grads) {
         mgb_assert(grads.size() == 1);
         ValueRef grad = grads[0];
-        ValueRefList ret(1);
+        SmallVector<ValueRef> ret(1);
         if (grad && inputs[0]) {
             ValueRefList args_(inputs.size() + 1);
             auto&& zeros = make_empty_tensor(grad.device(), inputs[0], grad.dtype());
@@ -251,7 +251,7 @@ std::optional<ValueRefList> reduce_grad_rule(
     maker.backward([shapes = std::move(input_shapes)](Span<ValueRef> grads) {
         mgb_assert(grads.size() == 1);
         ValueRef grad = grads[0];
-        ValueRefList ret(1);
+        SmallVector<ValueRef> ret(1);
         if (grad && shapes[0]) {
             ret[0] = broadcast_to(grad, shapes[0]);
         }
@@ -274,7 +274,7 @@ std::optional<ValueRefList> addAxis_grad_rule(
     maker.backward([grad_op_ = std::move(grad_op), flag_ = flag](Span<ValueRef> grads) {
         mgb_assert(grads.size() == 1);
         ValueRef grad = grads[0];
-        ValueRefList ret(1);
+        SmallVector<ValueRef> ret(1);
         if (grad && flag_) {
             ret[0] = imperative::apply(*grad_op_, grad)[0];
         }
@@ -297,7 +297,7 @@ std::optional<ValueRefList> removeAxis_grad_rule(
     maker.backward([grad_op_ = std::move(grad_op), flag_ = flag](Span<ValueRef> grads) {
         mgb_assert(grads.size() == 1);
         ValueRef grad = grads[0];
-        ValueRefList ret(1);
+        SmallVector<ValueRef> ret(1);
         if (grad && flag_) {
             ret[0] = imperative::apply(*grad_op_, grad)[0];
         }
@@ -316,7 +316,7 @@ std::optional<ValueRefList> fastpathcopy_grad_rule(
     maker.backward([](Span<ValueRef> grads) {
         mgb_assert(grads.size() == 1);
         ValueRef grad = grads[0];
-        ValueRefList ret(1);
+        SmallVector<ValueRef> ret(1);
         if (grad) {
             ret[0] = grad;
         }

imperative/python/src/tensor.cpp

@@ -56,42 +56,44 @@ WeakKeyMap<ValueWeakRef, py::object> module_trace_info_map;
 
 struct SymbolVarContext {
     TransformationContext context;
-    cg::ComputingGraph* graph;
+    std::shared_ptr<SymbolTransformation> symbol_tsf;
+    std::shared_ptr<ScalarTransformation> scalar_tsf;
 
-    SymbolVarContext(cg::ComputingGraph* graph) : graph(graph) {
+    SymbolVarContext(cg::ComputingGraph* graph) {
+        symbol_tsf = std::make_shared<SymbolTransformation>(graph);
+        scalar_tsf = std::make_shared<ScalarTransformation>();
         Transformation::swap_context(context);
     }
 
     void init() {
-        std::make_shared<SymbolTransformation>(graph)->register_at(
-                Transformation::top());
-        std::make_shared<ScalarTransformation>()->register_at(Transformation::top());
+        symbol_tsf->register_at(Transformation::top());
+        scalar_tsf->register_at(Transformation::top());
     }
 
-    ~SymbolVarContext() { Transformation::swap_context(context); }
-};
+    ValueRef symvar2val(py::handle py_symbol_var) {
+        auto* symbol_var = py_symbol_var.cast<PySymbolVar*>();
+        ValueRef value = symbol_tsf->value_type().make(symbol_var->m_node);
+        if (symbol_var->is_scalar) {
+            value = scalar_tsf->value_type().make(value);
+        }
+        return value;
+    }
 
-ValueRef symvar2val(py::handle py_symbol_var) {
-    auto* symbol_var = py_symbol_var.cast<PySymbolVar*>();
-    ValueRef value = SymbolValue::make(symbol_var->m_node);
-    if (symbol_var->is_scalar) {
-        value = ScalarValue::make(value);
+    py::object val2symvar(py::handle typeobj, ValueRef value) {
+        bool is_scalar = false;
+        if (auto* scalar_value = value.as(scalar_tsf->value_type())) {
+            value = scalar_value->value();
+            is_scalar = true;
+        }
+        auto* node = value.cast(symbol_tsf->value_type()).node();
+        auto py_symbol_var =
+                typeobj(pybind11::cast(node, pybind11::return_value_policy::automatic));
+        py_symbol_var.cast<PySymbolVar*>()->is_scalar = is_scalar;
+        return py_symbol_var;
     }
-    return value;
-}
 
-py::object val2symvar(py::handle typeobj, ValueRef value) {
-    bool is_scalar = false;
-    if (auto* scalar_value = value.as<ScalarValue>()) {
-        value = scalar_value->value();
-        is_scalar = true;
-    }
-    auto* node = value.cast<SymbolValue>().node();
-    auto py_symbol_var =
-            typeobj(pybind11::cast(node, pybind11::return_value_policy::automatic));
-    py_symbol_var.cast<PySymbolVar*>()->is_scalar = is_scalar;
-    return py_symbol_var;
-}
+    ~SymbolVarContext() { Transformation::swap_context(context); }
+};
 
 }  // namespace
 
@@ -130,19 +132,21 @@ PyObject* py_apply(
         auto op = py::handle(py_op).cast<std::shared_ptr<OpDef>>();
         SmallVector<ValueRef, 8> tensors(nargs);
 
-        if (py::isinstance<PySymbolVar>(py::handle(args[0]))) {
+        bool is_symbol_var = (!TensorWrapper::try_cast(args[0])) &&
+                             py::isinstance<PySymbolVar>(py::handle(args[0]));
+        if (is_symbol_var) {
             // swap to a special context to reuse scalar handle
             SymbolVarContext context(
                     py::handle(args[0]).cast<PySymbolVar*>()->m_node->owner_graph());
             context.init();
             for (size_t i = 0; i < nargs; ++i) {
-                tensors[i] = symvar2val(args[i]);
+                tensors[i] = context.symvar2val(args[i]);
             }
             auto outputs = imperative::apply(*op, tensors);
             auto ret = pybind11::tuple(outputs.size());
             auto typeobj = py::handle(args[0]).get_type();
             for (size_t i = 0; i < outputs.size(); ++i) {
-                ret[i] = val2symvar(typeobj, outputs[i]);
+                ret[i] = context.val2symvar(typeobj, outputs[i]);
             }
             return ret.release().ptr();
         }
@@ -161,7 +165,7 @@ PyObject* py_apply(
             }
         }
 
-        auto outputs = imperative::apply(*op, tensors);
+        auto outputs = [&] { return imperative::apply(*op, tensors); }();
         size_t nout = outputs.size();
         auto ret = py::tuple(nout);
         for (size_t i = 0; i < nout; ++i) {
@@ -1573,9 +1577,9 @@ void init_tensor(py::module m) {
             SymbolVarContext context(graph);
             context.init();
             auto output = reduce_to_scalar(
-                    *op.cast<std::shared_ptr<OpDef>>(), symvar2val(tensor));
+                    *op.cast<std::shared_ptr<OpDef>>(), context.symvar2val(tensor));
             auto typeobj = tensor.get_type();
-            return val2symvar(typeobj, output);
+            return context.val2symvar(typeobj, output);
         } else {
             auto* tw = TensorWrapper::try_cast(tensor.ptr());
             auto output = reduce_to_scalar(

imperative/python/src/transformation.h

@@ -67,10 +67,9 @@ struct TransformationManager {
     }
 };
 
-class PyValue final
-        : public MixinValueImpl<PyValue, ValueKind::Object, pybind11::object> {
+class PyValue final : public PrimitiveValue<PyValue, pybind11::object> {
 public:
-    using MixinValueImpl::MixinValueImpl;
+    using PrimitiveValue::PrimitiveValue;
 
     std::string to_string() const {
         return pybind11::str((const pybind11::object&)*this).cast<std::string>();

imperative/src/impl/basic_operators.cpp

@@ -63,7 +63,7 @@ auto CreateTensor::parse(Span<ValueRef> inputs) const -> Args {
                     MegBrainError,
                     "unknown input type, expects HostStorage or DeviceStorage, got "
                     "%s",
-                    input.name()->c_str());
+                    input.to_string().c_str());
         }
     }
     mgb_assert(

imperative/src/impl/basic_values.cpp

@@ -12,7 +12,7 @@ std::string CompNodeValue::to_string() const {
 }
 
 std::string BoolValue::to_string() const {
-    return (*m_value) ? "true" : "false";
+    return (*this) ? "true" : "false";
 }
 
 std::string HostStorage::to_string() const {
@@ -26,10 +26,10 @@ std::string DeviceStorage::to_string() const {
 std::string HostValue::to_string() const {
     return ssprintf(
             "HostValue{device=%s, dtype=%s, shape=%s}", device().to_string().c_str(),
-            m_dtype.name(), m_shape.to_string().c_str());
+            dtype().name(), shape().to_string().c_str());
 }
 
-HostTensorND HostValue::as_nd(bool allow_scalar) const {
+HostTensorND HostTensor::as_nd(bool allow_scalar) const {
     HostTensorND nd;
     TensorShape tensor_shape;
     if (m_shape.is_scalar()) {
@@ -45,10 +45,10 @@ HostTensorND HostValue::as_nd(bool allow_scalar) const {
 std::string DeviceValue::to_string() const {
     return ssprintf(
             "DeviceValue{device=%s, dtype=%s, shape=%s}", device().to_string().c_str(),
-            m_dtype.name(), m_shape.to_string().c_str());
+            dtype().name(), shape().to_string().c_str());
 }
 
-DeviceTensorND DeviceValue::as_nd(bool allow_scalar) const {
+DeviceTensorND DeviceTensor::as_nd(bool allow_scalar) const {
     DeviceTensorND nd;
     TensorShape tensor_shape;
     if (m_shape.is_scalar()) {

imperative/src/impl/dispatch.cpp

@@ -19,46 +19,18 @@
 namespace mgb {
 namespace imperative {
 
-namespace {
-MGB_NOINLINE void copy_outputs(
-        ForwardAllocator<ValueRef>& allocator, ValueRefList& outputs) {
-    size_t nr_outputs = outputs.size();
-    if (mgb_likely(nr_outputs == 1)) {
-        ValueRef output_copy;
-        output_copy = outputs[0];
-        allocator.clear();
-        outputs = ValueRefList({output_copy});
-    } else if (!outputs.empty()) {
-        SmallVector<ValueRef> outputs_copy(nr_outputs);
-        for (size_t i = 0; i < nr_outputs; ++i) {
-            outputs_copy[i] = outputs[i];
-        }
-        outputs.clear();
-        allocator.clear();
-        outputs = {outputs_copy.begin(), outputs_copy.end()};
-    } else {
-        allocator.clear();
-    }
-}
-}  // namespace
-
 ValueRefList apply(const Operator& op, Span<ValueRef> inputs) {
     auto& context = Transformation::get_context();
     size_t& depth = context.next_transformation;
-    bool top = depth == 0;
-    auto outputs = ([&] {
-        if (mgb_unlikely(depth >= context.transformations.size())) {
-            return op.fallback(inputs);
-        } else {
-            auto& transformation = *context.transformations[depth++];
-            CleanupGuard _{[&] { --depth; }};
-            return transformation.apply_transformation(op, inputs);
-        }
-    })();
-    if (mgb_unlikely(top)) {
-        copy_outputs(context.allocator, outputs);
+    // TODO: add fallback transformation
+    bool fallback = depth >= context.transformations.size();
+    if (mgb_unlikely(fallback)) {
+        return op.fallback(inputs);
+    } else {
+        auto& transformation = *context.transformations[depth++];
+        CleanupGuard _{[&] { --depth; }};
+        return transformation.apply_transformation(op, inputs);
     }
-    return outputs;
 }
 
 ValueRefList apply(const OpDef& def, Span<ValueRef> inputs) {
@@ -66,12 +38,7 @@ ValueRefList apply(const OpDef& def, Span<ValueRef> inputs) {
 }
 
 ValueRefList apply(const Subgraph& graph, Span<ValueRef> inputs) {
-    SmallVector<ValueRef> inputs_storage;
-    for (size_t i = 0; i < inputs.size(); ++i) {
-        inputs_storage.push_back(inputs[i]);
-    }
-    auto apply_functor = [](std::shared_ptr<OpDef> op, SmallVector<ValueRef> inputs,
-                            size_t) {
+    auto apply_functor = [](std::shared_ptr<OpDef> op, Span<ValueRef> inputs, size_t) {
         auto outputs = imperative::apply(*op, inputs);
         return SmallVector<ValueRef>(outputs.begin(), outputs.end());
     };
@@ -93,7 +60,7 @@ ValueRefList apply(const Subgraph& graph, Span<ValueRef> inputs) {
                 HostStorage::make(host_value.storage()),
                 DeviceStorage::make(device_value.storage()))[0];
     };
-    auto outputs = graph.apply(inputs_storage, apply_functor, make_const);
+    auto outputs = graph.apply(inputs, apply_functor, make_const);
     return ValueRefList{outputs.begin(), outputs.end()};
 }
 

imperative/src/impl/interpreter/interpreter_impl.cpp

@@ -331,6 +331,7 @@ void ChannelImpl::dispatch_kernel(
     cmd.inputs = std::move(input_infos);
     cmd.outputs.reserve(output_descs.size());
     outputs->reserve(output_descs.size());
+
     for (int i = 0; i < output_descs.size(); ++i) {
         auto&& desc = output_descs[i];
         auto info = alloc();
@@ -730,7 +731,8 @@ void ChannelImpl::do_apply_op(const ApplyOp& cmd, std::string reason) {
                 input_descs.push_back({{{}, input->dtype()}, input->comp_node()});
             }
             auto forward_graph = OpDef::make_forward_graph(def, input_descs);
-            auto outputs = forward_graph.apply(inputs, apply_functor, const_functor);
+            auto outputs = forward_graph.apply<TensorPtr>(
+                    inputs, apply_functor, const_functor);
             return outputs;
         }
         return OpDef::apply_on_physical_tensor(def, inputs);

imperative/src/impl/ops/elemwise.cpp

@@ -11,6 +11,7 @@
 
 #include "megbrain/imperative/opr_utility.h"
 #include "megbrain/imperative/ops/autogen.h"
+#include "megbrain/imperative/utils/stats.h"
 #include "megbrain/opr/basic_arith.h"
 #include "megbrain/opr/utility.h"
 
@@ -101,7 +102,7 @@ void apply_on_device_tensornd(
         const OpDef& def, const SmallVector<DeviceTensorND>& inputs,
         SmallVector<DeviceTensorND>* outputs) {
     auto&& op_def = def.cast_final_safe<Elemwise>();
-    auto trait = megdnn::Elemwise::ModeTrait::from_mode(op_def.mode);
+    auto&& trait = megdnn::Elemwise::ModeTrait::from_mode(op_def.mode);
     mgb_assert(
             inputs.size() == trait.arity, "%s expects %u inputs; got %zu actually",
             trait.name, trait.arity, inputs.size());

imperative/src/impl/subgraph_detail.cpp

@@ -36,7 +36,7 @@ VarNodeArray apply_on_var_node(const OpDef& def, const VarNodeArray& inputs) {
                 .node();
     };
     auto subgraph = def.trait()->make_forward_graph(def, input_descs);
-    auto outputs = subgraph.apply(inputs, apply_functor, const_functor);
+    auto outputs = subgraph.apply<VarNode*>(inputs, apply_functor, const_functor);
     return outputs;
 }
 
@@ -56,7 +56,8 @@ std::tuple<SmallVector<LogicalTensorDesc>, bool> infer_output_attrs_fallible(
                 value->layout(), value->comp_node(),
                 value->get_value().proxy_to_default_cpu()};
     };
-    auto outputs = subgraph.apply(inputs, apply_functor, const_functor);
+    auto outputs =
+            subgraph.apply<LogicalTensorDesc>(inputs, apply_functor, const_functor);
     return {outputs, all_validated};
 }
 
@@ -72,7 +73,7 @@ SmallVector<TensorPtr> apply_on_physical_tensor(
         return OpDef::apply_on_physical_tensor(*op, inputs);
     };
     auto const_functor = [&](const TensorPtr& value) { return value; };
-    auto outputs = subgraph.apply(inputs, apply_functor, const_functor);
+    auto outputs = subgraph.apply<TensorPtr>(inputs, apply_functor, const_functor);
     return outputs;
 }
 
@@ -94,7 +95,7 @@ static EncodedSubgraph make_backward_graph_from_forward(
     };
     GradContext<var_t> grad_context{accum_grad};
     auto input_vars = builder.write_inputs(inputs);
-    auto outputs = forward_graph.apply(
+    auto outputs = forward_graph.apply<var_t>(
             input_vars, std::bind(&decltype(builder)::write_expr, &builder, _1, _2, _3),
             [&](TensorPtr constant) {
                 return builder.write_constant(
@@ -102,7 +103,7 @@ static EncodedSubgraph make_backward_graph_from_forward(
             });
     size_t nr_outputs = outputs.size();
     auto apply_mask = [](auto&& values, SmallVector<bool> mask) {
-        mgb_assert(mask.size() == values.size(), "");
+        mgb_assert(mask.size() == values.size());
         std::decay_t<decltype(values)> results;
         for (size_t i = 0; i < mask.size(); ++i) {
             if (mask[i]) {
@@ -143,7 +144,7 @@ static EncodedSubgraph make_backward_graph_from_forward(
                     return builder.write_constant(
                             constant, {constant->layout(), constant->comp_node()});
                 };
-                return bg.apply(grad_inputs, apply_functor, const_functor);
+                return bg.apply<var_t>(grad_inputs, apply_functor, const_functor);
             });
     builder.add_outputs(grad_context.get_grads(input_vars));
     for (size_t i = 0; i < nr_outputs; ++i) {

imperative/src/impl/transformations/eval.cpp

@@ -10,20 +10,19 @@
  */
 
 #include "megbrain/imperative/transformations/eval.h"
-#include "megbrain/imperative/transformations/grad.h"
 #include "megbrain/imperative/utils/stats.h"
 
 namespace mgb {
 namespace imperative {
 
-DTypeValue::ref_t InterpreterInfo::dtype() const {
+DTypeValue::ref_t InterpreterValue::dtype() const {
     if (!m_dtype) {
         m_dtype = DTypeValue::make(handle()->channel()->get_dtype(handle()->handle()));
     }
     return m_dtype;
 }
 
-CompNodeValue::ref_t InterpreterInfo::comp_node() const {
+CompNodeValue::ref_t InterpreterValue::comp_node() const {
     if (!m_comp_node) {
         m_comp_node = CompNodeValue::make(
                 handle()->channel()->get_device(handle()->handle()));
@@ -31,7 +30,7 @@ CompNodeValue::ref_t InterpreterInfo::comp_node() const {
     return m_comp_node;
 }
 
-ShapeValue::ref_t InterpreterInfo::shape() const {
+ShapeValue::ref_t InterpreterValue::shape() const {
     if (!m_shape) {
         m_shape = ShapeValue::make(
                 ValueShape::from(handle()->channel()->get_shape(handle()->handle())));
@@ -51,21 +50,22 @@ ValueRefList InterpreterTransformation::apply_op(
         }
     }};
     for (auto input : inputs) {
-        input_handles.push_back(input.cast<InterpreterValue>().handle()->handle());
+        input_handles.push_back(input.cast(m_value_type).handle()->handle());
     }
     output_handles =
             m_channel->apply_op(apply_op.op().shared_from_this(), input_handles);
     ValueRefList outputs(output_handles.size());
     for (size_t i = 0; i < output_handles.size(); ++i) {
-        outputs[i] = InterpreterValue::make(share_handle(output_handles[i]));
+        outputs[i] = m_value_type.make(share_handle(output_handles[i]));
         output_handles[i] = nullptr;
     }
+    output_handles.clear();
     return outputs;
 }
 
 ValueRefList InterpreterTransformation::apply_get_attr(
         const GetAttr& get_attr, Span<ValueRef> inputs) {
-    auto& input = inputs.item().cast<InterpreterValue>();
+    auto& input = inputs.item().cast(m_value_type);
     ValueRef output;
     switch (get_attr.attr()) {
         case GetAttr::DType:
@@ -98,10 +98,10 @@ ValueRefList InterpreterTransformation::apply_create_tensor(
     if (!args.device) {
         // implies H2D
         mgb_assert(args.host, "neither host and device value is valid");
-        return {InterpreterValue::make(share_handle(
+        return {m_value_type.make(share_handle(
                 m_channel->put(*args.host, args.kind == CreateTensor::Unique)))};
     } else {
-        return {InterpreterValue::make(share_handle(m_channel->put(
+        return {m_value_type.make(share_handle(m_channel->put(
                 *args.device, args.host ? *args.host : HostTensorND())))};
     }
 }
@@ -119,7 +119,7 @@ ValueRefList InterpreterTransformation::apply_transformation(
     } else if (auto* create_tensor = op.as<CreateTensor>()) {
         return apply_create_tensor(*create_tensor, inputs);
     } else if (auto* dtr_command = op.as<DTRCommand>()) {
-        auto handle = inputs[0].cast<InterpreterValue>().handle()->handle();
+        auto handle = inputs[0].cast(m_value_type).handle()->handle();
         switch (dtr_command->kind()) {
             case DTRCommand::Drop:
                 m_channel->drop(handle);
@@ -129,10 +129,10 @@ ValueRefList InterpreterTransformation::apply_transformation(
         }
         return {};
     } else if (auto* rename_value = op.as<RenameValue>()) {
-        auto& input = inputs[0].cast<InterpreterValue>();
-        return {InterpreterValue::make(input.handle(), rename_value->name())};
+        auto& input = inputs[0].cast(m_value_type);
+        return {m_value_type.make(input.handle(), rename_value->name())};
     } else if (op.is<GetName>()) {
-        auto name = inputs[0].cast<InterpreterValue>().name();
+        auto name = inputs[0].cast(m_value_type).name();
         if (!name.empty()) {
             return {StringValue::make(name)};
         } else {

imperative/src/impl/transformations/grad.cpp

@@ -68,7 +68,7 @@ BackwardGraphWithClosure::BackwardGraphWithClosure(
     size_t count = std::count_if(
             save_for_backward.begin(), save_for_backward.end(), ranges::identity{});
     if (!backward_graph->precomp.empty()) {
-        ValueRefList inputs_and_outputs(inputs.size() + outputs.size());
+        SmallVector<ValueRef> inputs_and_outputs(inputs.size() + outputs.size());
         auto it = inputs_and_outputs.begin();
         for (auto&& input : inputs) {
             *it++ = input;
@@ -94,7 +94,7 @@ BackwardGraphWithClosure::BackwardGraphWithClosure(
     }
 }
 void BackwardGraphWithClosure::operator()(
-        ValueRefList grads, std::function<void(size_t, ValueRef)> receiver) {
+        Span<ValueRef> grads, std::function<void(size_t, ValueRef)> receiver) {
     ValueRef args[closure.size() + grads.size()];
     size_t nargs = 0;
     for (auto&& value : closure) {
@@ -114,7 +114,9 @@ void BackwardGraphWithClosure::operator()(
     if (null_grad) {
         return;
     }
-    auto igrads = imperative::apply(backward_graph->backward, Span(args, nargs));
+    auto igrads_ = imperative::apply(backward_graph->backward, Span(args, nargs));
+    SmallVector<ValueRef> igrads = {igrads_.begin(), igrads_.end()};
+    igrads_.clear();
     auto&& iter = igrads.begin();
     for (auto [i, p] : ranges::views::enumerate(backward_graph->input_has_grad)) {
         if (p) {
@@ -125,7 +127,7 @@ void BackwardGraphWithClosure::operator()(
 }
 
 void CustomBackward::operator()(
-        ValueRefList grads, std::function<void(size_t, ValueRef)> receiver) {
+        Span<ValueRef> grads, std::function<void(size_t, ValueRef)> receiver) {
     size_t nargs = grads.size();
     ValueRef args[nargs];
     for (size_t i = 0; i < nargs; ++i) {
@@ -206,7 +208,7 @@ void GradKey::backward() {
                 mgb_throw(AssertionError, "invalid backward");
             } else {
                 mgb_assert(grad_fn->m_slots.size() > 0);
-                ValueRefList grads (grad_fn->m_slots.size());
+                SmallVector<ValueRef> grads (grad_fn->m_slots.size());
                 auto iter = grads.begin();
                 for (auto&& slot : grad_fn->m_slots) {
                     *iter++ = slot.m_grad;
@@ -231,11 +233,9 @@ void GradKey::backward() {
 
 GradValue::ref_t GradKey::attach(
         ValueRef tensor, std::function<void(ValueRef)> callback) {
-    auto grad_value = tensor.as_ref<GradValue>();
-    if (grad_value && grad_value->has_key(shared_from_this())) {
-        mgb_assert(
-                !tensor.cast<GradValue>().slot_for(shared_from_this())->callback,
-                "callback exists");
+    auto grad_value = tensor.as_ref(m_value_type);
+    if (grad_value) {
+        mgb_assert(!tensor.cast(m_value_type).slot()->callback, "callback exists");
     } else {
         GradSlotPtr grad_slot;
         auto& grad_fn = grad_slot.m_fn;
@@ -243,9 +243,9 @@ GradValue::ref_t GradKey::attach(
         grad_fn->m_key = shared_from_this();
         grad_fn->m_slots.resize(1);
         grad_slot.m_index = 0;
-        grad_value = GradValue::make(tensor, shared_from_this(), grad_slot);
+        grad_value = m_value_type.make(tensor, shared_from_this(), grad_slot);
     }
-    grad_value->slot_for(shared_from_this()).m_fn->m_slots[0].callback = callback;
+    grad_value->slot().m_fn->m_slots[0].callback = callback;
     return grad_value;
 }
 
@@ -263,7 +263,7 @@ void GradKey::freeze() {
 ValueRefList GradTransformation::apply_transformation(
         const Operator& op, Span<ValueRef> inputs) {
     auto fallback = [&] {
-        ValueRefList unwrapped_inputs(inputs.size());
+        SmallVector<ValueRef> unwrapped_inputs(inputs.size());
         {
             // overhead
             for (size_t i = 0; i < inputs.size(); ++i) {
@@ -367,7 +367,7 @@ ValueRefList GradTransformation::apply_transformation(
                 for (size_t i = 0; i < inputs.size(); ++i) {
                     if (backward.input_has_grad(i) && require_grads[i]) {
                         auto& input_grad_slot =
-                                inputs[i].cast<GradValue>().slot_for(m_key);
+                                inputs[i].cast(m_value_type).slot();
                         grad_fn->m_dests.emplace_back(input_grad_slot);
                         grad_fn->m_dests.back().m_producer_record.insert_after(
                                 input_grad_slot->m_producer_head);
@@ -378,7 +378,7 @@ ValueRefList GradTransformation::apply_transformation(
                 for (size_t i = 0; i < outputs.size(); ++i) {
                     if (backward.output_requires_grad(i)) {
                         // little overhead: Value::make
-                        auto grad_value = GradValue::make(outputs[i], m_key, GradSlotPtr{grad_fn, i});
+                        auto grad_value = m_value_type.make(outputs[i], m_key, GradSlotPtr{grad_fn, i});
                         outputs[i] = record_grad(grad_value);
                     }
                 }
@@ -435,7 +435,10 @@ ValueRefList GradTransformation::apply_transformation(
         backward.m_input_has_grad = SmallVector(nr_inputs, true);
         backward.m_output_attrs =
                 SmallVector(nr_outputs, CustomBackward::OutputAttr{true, true});
-        backward.m_backward = set_grad->grad_fn();
+        backward.m_backward = [fn = set_grad->grad_fn()](Span<ValueRef> inputs) {
+            auto result = fn(inputs);
+            return SmallVector<ValueRef>(result.begin(), result.end());
+        };
         ValueRefList outputs(nr_outputs);
         grad_fn->m_key = m_key;
         grad_fn->m_slots.resize(nr_outputs);
@@ -454,10 +457,10 @@ ValueRefList GradTransformation::apply_transformation(
             auto& output = outputs_[i];
             auto grad_value = as_grad_value(output);
             if (grad_value) {
-                grad_value = GradValue::make(
+                grad_value = m_value_type.make(
                         grad_value->m_value, m_key, GradSlotPtr(grad_fn, i));
             } else {
-                grad_value = GradValue::make(output, m_key, GradSlotPtr(grad_fn, i));
+                grad_value = m_value_type.make(output, m_key, GradSlotPtr(grad_fn, i));
             }
             outputs[i] = record_grad(grad_value);
         }
@@ -485,8 +488,7 @@ ValueRefList GradTransformation::apply_transformation(
         mgb_assert(inputs.size() == 1);
         if (auto&& grad_value = as_grad_value(inputs[0])) {
             auto output = imperative::apply(op, grad_value->m_value)[0];
-            auto grad_output = GradValue::make(
-                    output, grad_value->key(), grad_value->slot_for(m_key));
+            auto grad_output = m_value_type.make(output, m_key, grad_value->slot());
             return {record_grad(grad_output)};
         } else {
             return imperative::apply(op, inputs);
@@ -502,7 +504,7 @@ GenericFunction GradTransformation::make_backward_closure(Span<ValueRef> ys) {
     std::vector<GradSlotPtr> y_slots;
     for (auto&& y : ys) {
         if (auto&& grad_value = as_grad_value(y)) {
-            y_slots.push_back(grad_value->slot_for(grad_key));
+            y_slots.push_back(grad_value->slot());
         } else {
             y_slots.emplace_back();
         }

imperative/src/impl/transformations/lazy.cpp

@@ -32,7 +32,7 @@ ValueRefList LazyEvalTransformation::apply_transformation(
         bool require_link = mm_io_ops.count(op_val->op().dyn_typeinfo());
         VarNodeArray input_nodes;
         for (auto&& input : inputs) {
-            if (auto* input_node = input.as<LazyEvalValue>()) {
+            if (auto* input_node = input.as(m_value_type)) {
                 input_nodes.push_back(input_node->node());
             } else {
                 // ImmutableTensor has empty shape issues
@@ -112,7 +112,7 @@ ValueRefList LazyEvalTransformation::apply_transformation(
             return {record_var(node)};
         }
     } else if (auto* get_attr = op.as<GetAttr>()) {
-        if (auto* lazy_val = inputs.item().as<LazyEvalValue>()) {
+        if (auto* lazy_val = inputs.item().as(m_value_type)) {
             switch (get_attr->attr()) {
                 case GetAttr::DType:
                     return {DTypeValue::make(lazy_val->node()->dtype())};
@@ -167,14 +167,14 @@ ValueRefList LazyEvalTransformation::apply_transformation(
             return imperative::apply(op, inputs);
         }
     } else if (auto* rename_value = op.as<RenameValue>()) {
-        if (auto* lazy_val = inputs.item().as<LazyEvalValue>()) {
+        if (auto* lazy_val = inputs.item().as(m_value_type)) {
             return {record_var(
                     lazy_val->node(), lazy_val->bound_data(), rename_value->name())};
         } else {
             return imperative::apply(op, inputs);
         }
     } else if (op.is<GetName>()) {
-        if (auto* lazy_val = inputs.item().as<LazyEvalValue>()) {
+        if (auto* lazy_val = inputs.item().as(m_value_type)) {
             auto name = lazy_val->name();
             if (!name.empty()) {
                 return {StringValue::make(lazy_val->name())};
@@ -255,7 +255,7 @@ void LazyEvalTransformation::on_unregister() noexcept {
                 DeviceStorage::make(data.storage()))[0]);
     }
     for (auto&& lazy_val : lazy_vals) {
-        if (lazy_val.is<LazyEvalValue>()) {
+        if (lazy_val.is(m_value_type)) {
             std::string repr =
                     ssprintf("lazy eval failed for %s", lazy_val->to_string().c_str());
             mgb_log_debug("%s", repr.c_str());

imperative/src/impl/transformations/scalar.cpp

@@ -20,7 +20,8 @@ namespace imperative {
 
 namespace {
 
-using ScalarRule = ValueRefList (*)(const OpDef&, Span<ValueRef>, Span<bool>);
+using ScalarRule = ValueRefList (*)(
+        const OpDef&, Span<ValueRef>, Span<bool>, const Type<ScalarValue>&);
 static std::unordered_map<Typeinfo*, ScalarRule> scalar_rules;
 
 ValueRef make_scalar_shape(CompNode device) {
@@ -41,17 +42,22 @@ bool is_scalar_shape(ValueRef shape) {
     return *shape_of_shape == ValueShape{0};
 }
 
-template <typename T, ValueRefList (*rule)(const T&, Span<ValueRef>, Span<bool>)>
+template <
+        typename T,
+        ValueRefList (*rule)(
+                const T&, Span<ValueRef>, Span<bool>, const Type<ScalarValue>&)>
 void register_scalar_rule() {
     scalar_rules[T::typeinfo()] = [](const OpDef& def, Span<ValueRef> inputs,
-                                     Span<bool> inputs_mask) {
-        return (*rule)(def.cast_final_safe<T>(), inputs, inputs_mask);
+                                     Span<bool> inputs_mask,
+                                     const Type<ScalarValue>& value_type) {
+        return (*rule)(def.cast_final_safe<T>(), inputs, inputs_mask, value_type);
     };
 }
 
 template <typename TOpDef, size_t nr_inputs>
 ValueRefList elemwise_rule(
-        const TOpDef& op_def, Span<ValueRef> inputs, Span<bool> inputs_mask) {
+        const TOpDef& op_def, Span<ValueRef> inputs, Span<bool> inputs_mask,
+        const Type<ScalarValue>& scalar_type) {
     if constexpr (nr_inputs != 0) {
         mgb_assert(inputs.size() == inputs.size(), "inputs size mismatch");
     }
@@ -63,27 +69,29 @@ ValueRefList elemwise_rule(
     }
     auto outputs = imperative::apply(op_def, inputs);
     if (all_scalar) {
-        outputs[0] = ScalarValue::make(outputs[0]);
+        outputs[0] = scalar_type.make(outputs[0]);
     }
     return outputs;
 }
 
 ValueRefList remove_axis_rule(
-        const RemoveAxis& remove_axis, Span<ValueRef> inputs, Span<bool> inputs_mask) {
+        const RemoveAxis& remove_axis, Span<ValueRef> inputs, Span<bool> inputs_mask,
+        const Type<ScalarValue>& scalar_type) {
     mgb_assert(!inputs_mask.item());
     bool is_scalar = inputs.item().shape()->ndim == remove_axis.axis.size();
     if (is_scalar && remove_axis.axis.size() == 1) {
-        return {ScalarValue::make(inputs.item())};
+        return {scalar_type.make(inputs.item())};
     }
     auto outputs = imperative::apply(remove_axis, inputs);
     if (is_scalar) {
-        outputs[0] = ScalarValue::make(outputs[0]);
+        outputs[0] = scalar_type.make(outputs[0]);
     }
     return outputs;
 }
 
 ValueRefList reduce_rule(
-        const Reduce& reduce, Span<ValueRef> inputs, Span<bool> inputs_mask) {
+        const Reduce& reduce, Span<ValueRef> inputs, Span<bool> inputs_mask,
+        const Type<ScalarValue>& scalar_type) {
     if (inputs.size() == 1) {
         return imperative::apply(reduce, inputs);
     }
@@ -91,7 +99,7 @@ ValueRefList reduce_rule(
     bool is_scalar = is_scalar_shape(inputs[1]);
     if (is_scalar) {
         CompNode device = *inputs[0].device();
-        return {ScalarValue::make(
+        return {scalar_type.make(
                 imperative::apply(reduce, inputs[0], make_scalar_shape(device))[0])};
     }
     return imperative::apply(reduce, inputs);
@@ -99,7 +107,7 @@ ValueRefList reduce_rule(
 
 ValueRefList collective_comm_rule(
         const CollectiveComm& collective_comm, Span<ValueRef> inputs,
-        Span<bool> inputs_mask) {
+        Span<bool> inputs_mask, const Type<ScalarValue>& scalar_type) {
     mgb_assert(inputs.size() == 1);
     static std::unordered_set<CollectiveComm::Mode> modes = {
             CollectiveComm::Mode::ALL_REDUCE_MAX, CollectiveComm::Mode::ALL_REDUCE_MIN,
@@ -110,7 +118,7 @@ ValueRefList collective_comm_rule(
         return imperative::apply(collective_comm, inputs);
     }
     if (inputs_mask.item()) {
-        return {ScalarValue::make(imperative::apply(collective_comm, inputs[0])[0])};
+        return {scalar_type.make(imperative::apply(collective_comm, inputs[0])[0])};
     } else {
         return imperative::apply(collective_comm, inputs);
     }
@@ -118,24 +126,27 @@ ValueRefList collective_comm_rule(
 
 ValueRefList param_pack_split_rule(
         const ParamPackSplit& param_pack_split, Span<ValueRef> inputs,
-        Span<bool> inputs_mask) {
+        Span<bool> inputs_mask, const Type<ScalarValue>& scalar_type) {
     auto outputs = imperative::apply(param_pack_split, inputs);
     size_t nr_outputs = outputs.size();
     mgb_assert(nr_outputs == param_pack_split.shapes.size());
     for (size_t i = 0; i < nr_outputs; ++i) {
         if (param_pack_split.shapes[i].empty()) {
-            outputs[i] = ScalarValue::make(outputs[i]);
+            outputs[i] = scalar_type.make(outputs[i]);
         }
     }
     return outputs;
 }
 
-ValueRefList dot_rule(const Dot& dot, Span<ValueRef> inputs, Span<bool> inputs_mask) {
-    return {ScalarValue::make(imperative::apply(dot, inputs)[0])};
+ValueRefList dot_rule(
+        const Dot& dot, Span<ValueRef> inputs, Span<bool> inputs_mask,
+        const Type<ScalarValue>& scalar_type) {
+    return {scalar_type.make(imperative::apply(dot, inputs)[0])};
 }
 
 ValueRefList add_axis_rule(
-        const AddAxis& add_axis, Span<ValueRef> inputs, Span<bool> inputs_mask) {
+        const AddAxis& add_axis, Span<ValueRef> inputs, Span<bool> inputs_mask,
+        const Type<ScalarValue>& scalar_type) {
     mgb_assert(inputs.size() == 1);
     if (inputs_mask.item()) {
         mgb_assert(add_axis.axis[0] == 0);
@@ -151,7 +162,8 @@ ValueRefList add_axis_rule(
 }
 
 ValueRefList remote_recv_rule(
-        const RemoteRecv& remote_recv, Span<ValueRef> inputs, Span<bool> inputs_mask) {
+        const RemoteRecv& remote_recv, Span<ValueRef> inputs, Span<bool> inputs_mask,
+        const Type<ScalarValue>& scalar_type) {
     if (remote_recv.shape.empty()) {
         std::vector<int32_t> shape = {1};
         auto remote_recv_no_scalar = RemoteRecv::make(
@@ -167,20 +179,21 @@ ValueRefList remote_recv_rule(
 
 ValueRefList check_no_finite_rule(
         const CheckNonFinite& check_no_finite, Span<ValueRef> inputs,
-        Span<bool> inputs_mask) {
+        Span<bool> inputs_mask, const Type<ScalarValue>& scalar_type) {
     auto outputs = imperative::apply(check_no_finite, inputs);
     mgb_assert(outputs.size() == inputs.size() + 1, "output size mismatch");
-    outputs.back() = ScalarValue::make(outputs.back());
+    outputs.back() = scalar_type.make(outputs.back());
     for (size_t i = 0; i < inputs.size(); ++i) {
         if (inputs_mask[i]) {
-            outputs[i] = ScalarValue::make(outputs[i]);
+            outputs[i] = scalar_type.make(outputs[i]);
         }
     }
     return outputs;
 }
 
 ValueRefList subtensor_rule(
-        const Subtensor& subtensor, Span<ValueRef> inputs, Span<bool> inputs_mask) {
+        const Subtensor& subtensor, Span<ValueRef> inputs, Span<bool> inputs_mask,
+        const Type<ScalarValue>& scalar_type) {
     mgb_assert(inputs.size() >= 1);
     auto input = inputs[0];
     bool is_scalar;
@@ -199,14 +212,14 @@ ValueRefList subtensor_rule(
     }
     auto outputs = imperative::apply(subtensor, inputs);
     if (is_scalar) {
-        outputs[0] = ScalarValue::make(outputs[0]);
+        outputs[0] = scalar_type.make(outputs[0]);
     }
     return outputs;
 }
 
 ValueRefList get_var_shape_rule(
-        const GetVarShape& get_var_shape, Span<ValueRef> inputs,
-        Span<bool> inputs_mask) {
+        const GetVarShape& get_var_shape, Span<ValueRef> inputs, Span<bool> inputs_mask,
+        const Type<ScalarValue>& scalar_type) {
     bool all_scalar = true;
     mgb_assert(inputs.size() >= 1);
     for (auto&& input_mask : inputs_mask) {
@@ -228,11 +241,12 @@ ValueRefList get_var_shape_rule(
 }
 
 ValueRefList reshape_rule(
-        const Reshape& reshape, Span<ValueRef> inputs, Span<bool> inputs_mask) {
+        const Reshape& reshape, Span<ValueRef> inputs, Span<bool> inputs_mask,
+        const Type<ScalarValue>& scalar_type) {
     mgb_assert(inputs.size() == 2);
     bool is_scalar = is_scalar_shape(inputs[1]);
     if (is_scalar) {
-        return {ScalarValue::make(imperative::apply(
+        return {scalar_type.make(imperative::apply(
                 reshape, inputs[0], make_scalar_shape(*inputs[0].device()))[0])};
     } else {
         return imperative::apply(reshape, inputs);
@@ -240,11 +254,12 @@ ValueRefList reshape_rule(
 }
 
 ValueRefList broadcast_rule(
-        const Broadcast& broadcast, Span<ValueRef> inputs, Span<bool> inputs_mask) {
+        const Broadcast& broadcast, Span<ValueRef> inputs, Span<bool> inputs_mask,
+        const Type<ScalarValue>& scalar_type) {
     mgb_assert(inputs.size() == 2);
     bool is_scalar = is_scalar_shape(inputs[1]);
     if (is_scalar) {
-        return {ScalarValue::make(imperative::apply(
+        return {scalar_type.make(imperative::apply(
                 broadcast, inputs[0], make_scalar_shape(*inputs[0].device()))[0])};
     } else {
         return imperative::apply(broadcast, inputs);
@@ -299,11 +314,11 @@ struct ScalarRuleRegistry {
 ValueRefList ScalarTransformation::apply_get_attr(
         const GetAttr& get_attr, Span<ValueRef> inputs) {
     auto&& input = inputs.item();
-    bool is_scalar = input.is<ScalarValue>();
+    bool is_scalar = input.is(m_value_type);
     if (!is_scalar) {
         return imperative::apply(get_attr, input);
     }
-    auto unwrapped_input = input.cast<ScalarValue>().value();
+    auto unwrapped_input = input.cast(m_value_type).value();
     if (get_attr.attr() == GetAttr::Shape) {
         if (!m_empty_shape) {
             m_empty_shape = ShapeValue::make();
@@ -352,7 +367,7 @@ ValueRefList ScalarTransformation::apply_transformation(
     ValueRefList unwrapped_inputs(nr_inputs);
     SmallVector<bool> inputs_mask(nr_inputs);
     for (size_t i = 0; i < inputs.size(); ++i) {
-        if (auto&& scalar_value = inputs[i].as_ref<ScalarValue>()) {
+        if (auto&& scalar_value = inputs[i].as_ref(m_value_type)) {
             unwrapped_inputs[i] = scalar_value->value();
             inputs_mask[i] = true;
         } else {
@@ -364,7 +379,8 @@ ValueRefList ScalarTransformation::apply_transformation(
     if (auto apply_op = op.as<ApplyOp>()) {
         auto iter = scalar_rules.find(apply_op->op().dyn_typeinfo());
         if (iter != scalar_rules.end()) {
-            return iter->second(apply_op->op(), unwrapped_inputs, inputs_mask);
+            return iter->second(
+                    apply_op->op(), unwrapped_inputs, inputs_mask, m_value_type);
         } else {
             // TODO: repeat op
             return fallback();
@@ -375,7 +391,7 @@ ValueRefList ScalarTransformation::apply_transformation(
             CreateTensor scalar_op(
                     create_tensor->kind(), create_tensor->device(),
                     create_tensor->dtype(), scalar_shape);
-            return {ScalarValue::make(imperative::apply(scalar_op, inputs)[0])};
+            return {m_value_type.make(imperative::apply(scalar_op, inputs)[0])};
         } else {
             return imperative::apply(op, inputs);
         }
@@ -387,7 +403,7 @@ ValueRefList ScalarTransformation::apply_transformation(
         bool is_scalar = inputs_mask[0];
         auto outputs = fallback();
         if (is_scalar) {
-            outputs[0] = ScalarValue::make(outputs[0]);
+            outputs[0] = m_value_type.make(outputs[0]);
         }
         return outputs;
     } else {

imperative/src/impl/transformations/trace.cpp

@@ -160,7 +160,7 @@ ValueRefList TracingTransformation::apply_transformation(
         SmallVector<TracingValue::ref_t> wrapped_inputs;
         SmallVector<size_t> input_ids;
         for (auto input : inputs) {
-            auto tracing_value = input.as_ref<TracingValue>();
+            auto tracing_value = input.as_ref(m_value_type);
             if (!tracing_value) {
                 tracing_value =
                         record_var(input, m_capture_as_const, VarKind::External);
@@ -208,7 +208,7 @@ ValueRefList TracingTransformation::apply_transformation(
     } else if (auto* get_attr = op.as<GetAttr>()) {
         auto unwrapped_input = unwrap_var(inputs[0]);
         auto outputs = imperative::apply(op, unwrapped_input);
-        if (auto* tracing_value = inputs[0].as<TracingValue>()) {
+        if (auto* tracing_value = inputs[0].as(m_value_type)) {
             auto& var_info = m_vars[tracing_value->id()];
             switch (get_attr->attr()) {
                 case GetAttr::Shape:
@@ -228,7 +228,7 @@ ValueRefList TracingTransformation::apply_transformation(
     } else if (auto* trace_mark_var = op.as<TraceMarkVar>()) {
         mgb_assert(inputs.size() == 1, "TraceMarkVar expects exactly one input");
         auto input = inputs[0];
-        auto tracing_var = input.as_ref<TracingValue>();
+        auto tracing_var = input.as_ref(m_value_type);
         if (!tracing_var) {
             bool is_input = trace_mark_var->mark().substr(0, 4) == "arg_" ||
                             trace_mark_var->mark().substr(0, 6) == "kwarg_";
@@ -247,7 +247,7 @@ ValueRefList TracingTransformation::apply_transformation(
     } else if (auto* trace_name_var = op.as<RenameValue>()) {
         mgb_assert(inputs.size() == 1, "RenameValue expects exactly one input");
         auto input = inputs[0];
-        auto tracing_var = input.as_ref<TracingValue>();
+        auto tracing_var = input.as_ref(m_value_type);
         if (!tracing_var) {
             tracing_var = record_var(input, m_capture_as_const, VarKind::External);
         } else {
@@ -260,7 +260,7 @@ ValueRefList TracingTransformation::apply_transformation(
     } else if (op.is<GetName>()) {
         mgb_assert(inputs.size() == 1, "GetName expects exactly one input");
         auto input = inputs[0];
-        if (auto tracing_var = input.as_ref<TracingValue>()) {
+        if (auto tracing_var = input.as_ref(m_value_type)) {
             auto name = m_vars[tracing_var->id()].name;
             if (!name.empty()) {
                 return {StringValue::make(name)};
@@ -425,26 +425,12 @@ void CompiledTransformation::compile() {
             }
             auto& node = var_accessors[input].node;
             if (input_vars.empty() && require_link && mm_io_link.node()) {
-                /*mgb_assert(
-                        !input_vars.empty(),
-                        "io-mm operator should have at least one input");*/
                 auto comp_node = mm_io_link.node()->comp_node();
-                // auto comp_node = input_vars[0]->comp_node();
                 node = opr::VirtualDep::make({SymbolVar(node), mm_io_link}, comp_node)
                                .node();
             }
             input_vars.push_back(node);
         }
-        /*if (require_link && mm_io_link.node()) {
-            mgb_assert(
-                    !input_vars.empty(),
-                    "io-mm operator should have at least one input");
-            auto comp_node = mm_io_link.node()->comp_node();
-            // auto comp_node = input_vars[0]->comp_node();
-            input_vars[0] = opr::VirtualDep::make(
-                                    {SymbolVar(input_vars[0]), mm_io_link}, comp_node)
-                                    .node();
-        }*/
         VarNodeArray output_vars;
         if (item.op) {
             output_vars = OpDef::apply_on_var_node(*item.op, input_vars);
@@ -520,7 +506,7 @@ void CompiledTransformation::trace_input(size_t id, ValueRef value) {
         switch (var.kind) {
             case VarKind::External: {
                 trace_assert(
-                        !value.is<TracedValue>(), "expect external node, got internal");
+                        !value.is(m_value_type), "expect external node, got internal");
                 if (var.bound_data) {
                     assert_tensor_equal(var.bound_data, value);
                 } else {
@@ -545,8 +531,8 @@ void CompiledTransformation::trace_input(size_t id, ValueRef value) {
             }
             case VarKind::Internal: {
                 trace_assert(
-                        value.is<TracedValue>(), "expect internal node, got external");
-                auto& traced_value = value.cast<TracedValue>();
+                        value.is(m_value_type), "expect internal node, got external");
+                auto& traced_value = value.cast(m_value_type);
                 trace_assert(traced_value.id() == id, "input id mismatch");
                 break;
             }
@@ -559,7 +545,7 @@ void CompiledTransformation::trace_input(size_t id, ValueRef value) {
 }
 
 auto CompiledTransformation::trace_output(size_t id) -> TracedValue::ref_t {
-    auto traced_value = TracedValue::make(id, &m_vars[id], &m_var_accessors[id]);
+    auto traced_value = m_value_type.make(id, &m_vars[id], &m_var_accessors[id]);
     m_weak_values.push_back(traced_value);
     return traced_value;
 }
@@ -569,7 +555,7 @@ TraceResult::SeqItem& CompiledTransformation::next_instruction() {
     return m_seq[m_pc++];
 }
 
-ShapeValue::ref_t CompiledTransformation::TracedInfo::shape() const {
+ShapeValue::ref_t CompiledTransformation::TracedValue::shape() const {
     if (!m_shape) {
         trace_assert(m_accessor->shape_getter, "shape unreadable");
         m_shape = ShapeValue::make(ValueShape::from(m_accessor->shape_getter()));
@@ -577,14 +563,14 @@ ShapeValue::ref_t CompiledTransformation::TracedInfo::shape() const {
     return m_shape;
 }
 
-DTypeValue::ref_t CompiledTransformation::TracedInfo::dtype() const {
+DTypeValue::ref_t CompiledTransformation::TracedValue::dtype() const {
     return m_var->dtype;
 }
 
-CompNodeValue::ref_t CompiledTransformation::TracedInfo::comp_node() const {
+CompNodeValue::ref_t CompiledTransformation::TracedValue::comp_node() const {
     return m_var->device;
 }
-auto CompiledTransformation::TracedInfo::accessor() const -> const VarAccessor& {
+auto CompiledTransformation::TracedValue::accessor() const -> const VarAccessor& {
     return *m_accessor;
 }
 
@@ -605,7 +591,7 @@ ValueRefList CompiledTransformation::apply_op(
 
 ValueRefList CompiledTransformation::apply_get_attr(
         const GetAttr& get_attr, Span<ValueRef> inputs) {
-    if (auto* traced_value = inputs[0].as<TracedValue>()) {
+    if (auto* traced_value = inputs[0].as(m_value_type)) {
         ValueRef output;
         auto& var_accessor = traced_value->accessor();
         switch (get_attr.attr()) {
@@ -718,15 +704,11 @@ void CompiledTransformation::on_unregister() noexcept {
 
 void CompiledTransformation::execute() {
     mgb_assert(m_executable != nullptr);
-    m_graph_executor = std::thread([&] {
-        try {
-            m_executable->execute();
-            m_executable->wait();
-        } catch (...) {
-            auto exc = std::current_exception();
-            set_exception(exc);
-        }
-    });
+    {
+        MGB_LOCK_GUARD(m_mutex);
+        m_graph_status = 1;
+    }
+    m_cv.notify_all();
 }
 
 void CompiledTransformation::wait() {
@@ -735,8 +717,9 @@ void CompiledTransformation::wait() {
     } catch (...) {
     }
     mgb_assert(m_executable != nullptr);
-    m_graph_executor.join();
-    m_graph_executor = {};
+    std::unique_lock lock{m_mutex};
+    m_cv.wait(lock, [&] { return m_graph_status == 0; });
+    lock.unlock();
     for (auto&& box : m_boxes) {
         box->reset();
     }

imperative/src/impl/value.cpp

@@ -25,16 +25,16 @@ ValueRef::storage_t& ValueRef::storage() const {
     return m_storage;
 }
 
-const Value* ValueRef::as(size_t typecode) const {
+const Value* ValueRef::as(const IType& type) const {
     auto&& storage = this->storage();
-    if (storage->m_typecode != typecode) {
+    if (storage->type() != type) {
         return nullptr;
     }
     return static_cast<Value*>(storage.get());
 }
 
-bool ValueRef::is(size_t typecode) const {
-    return this->storage()->m_typecode == typecode;
+bool ValueRef::is(const IType& type) const {
+    return this->storage()->type() == type;
 }
 
 TypedValueRef<DeviceValue> ValueRef::dev_tensor() const {
@@ -106,9 +106,7 @@ std::string ValueRef::raw_type() const {
     if (!m_storage) {
         return "null";
     }
-    auto& types = Value::registered_types();
-    mgb_assert(types.size() > m_storage->m_typecode);
-    return types[m_storage->m_typecode].name();
+    return m_storage->type().name();
 }
 
 bool ValueRef::watching() const {
@@ -137,7 +135,7 @@ ValueRef ValueWeakRef::lock() {
     return {strong_storage};
 }
 
-Value::Value(size_t typecode) : m_typecode{typecode} {
+Value::Value() {
     m_id = nr_values++;
 }
 
@@ -147,17 +145,6 @@ Value::~Value() {
     }
 }
 
-size_t Value::register_type(std::type_index type) {
-    auto& types = const_cast<std::vector<std::type_index>&>(registered_types());
-    types.push_back(type);
-    return types.size() - 1;
-}
-
-const std::vector<std::type_index>& Value::registered_types() {
-    static std::vector<std::type_index> sm_registered_types;
-    return sm_registered_types;
-}
-
 void Value::register_value(ValueRef value) {
     registered_values[value.id()] = ValueWeakRef(value);
 }
@@ -188,7 +175,7 @@ std::vector<ValueRef> Value::end_record_values() {
 }
 
 void Value::try_rethrow() {
-    if (m_typecode == ErrorValue::TYPE_CODE) {
+    if (type() == PrimitiveType<ErrorValue>::instance) {
         auto message = static_cast<ErrorValue*>(this)->message();
         mgb_throw(MegBrainError, "invalid value: %s", message.c_str());
     }
@@ -198,13 +185,9 @@ inline void ValueRefList::init(size_t nr_elems) {
     m_size = nr_elems;
     if (m_size > 0) {
         if (m_size == 1) {
-            m_data = inline_storage();
+            m_data = new (inline_storage()) ValueRef();
         } else {
-            auto& context = Transformation::get_context();
-            m_data = context.allocator.allocate(m_size);
-        }
-        for (size_t i = 0; i < m_size; ++i) {
-            new (m_data + i) ValueRef();
+            m_data = new ValueRef[m_size];
         }
     } else {
         m_data = nullptr;
@@ -215,9 +198,6 @@ ValueRefList::ValueRefList(size_t nr_elems) {
     init(nr_elems);
 }
 
-/*ValueRefList::ValueRefList(std::initializer_list<ValueRef> values)
-        : ValueRefList(values.begin(), values.end()) {}*/
-
 ValueRefList::ValueRefList(const ValueRefList& rhs)
         : ValueRefList(rhs.cbegin(), rhs.cend()) {}
 
@@ -271,14 +251,12 @@ ValueRefList::~ValueRefList() {
 }
 
 void ValueRefList::clear() {
-    for (size_t i = 0; i < m_size; ++i) {
-        m_data[i].~ValueRef();
-    }
     if (m_data) {
         if (m_size != 1) {
-            Transformation::get_context().allocator.deallocate(m_data, m_size);
+            delete[] m_data;
         } else {
             mgb_assert(m_data == inline_storage());
+            m_data->~ValueRef();
         }
     }
     m_data = nullptr;

imperative/src/include/megbrain/imperative/basic_values.h

@@ -25,79 +25,68 @@ class GradKey;
 
 using GenericFunction = std::function<ValueRefList(Span<ValueRef>)>;
 
-class ShapeValue final
-        : public MixinValueImpl<ShapeValue, ValueKind::Primitive, ValueShape> {
+class ShapeValue final : public PrimitiveValue<ShapeValue, ValueShape> {
 public:
-    using MixinValueImpl::MixinValueImpl;
+    using PrimitiveValue::PrimitiveValue;
 
     std::string to_string() const override;
 };
 
-class CompNodeValue final
-        : public MixinValueImpl<CompNodeValue, ValueKind::Primitive, CompNode> {
+class CompNodeValue final : public PrimitiveValue<CompNodeValue, CompNode> {
 public:
-    using MixinValueImpl::MixinValueImpl;
+    using PrimitiveValue::PrimitiveValue;
 
     std::string to_string() const override;
 };
 
-// TODO: override factory method
-class BoolValue final : public ValueImpl<BoolValue, ValueKind::Primitive> {
+class Boolean {
 private:
-    std::optional<bool> m_value;
+    bool m_value;
 
 public:
-    BoolValue(bool value) : m_value{value} {}
-    operator bool() const { return *m_value; }
+    Boolean() = default;
+    Boolean(bool value) : m_value(value) {}
 
-    std::string to_string() const override;
+    operator bool() const { return m_value; }
+};
 
-    void clear() override { m_value.reset(); }
+// TODO: override factory method
+class BoolValue final : public PrimitiveValue<BoolValue, Boolean> {
+public:
+    using PrimitiveValue::PrimitiveValue;
+
+    std::string to_string() const override;
 };
 
-class HostStorage final
-        : public MixinValueImpl<HostStorage, ValueKind::Primitive, HostTensorStorage> {
+class HostStorage final : public PrimitiveValue<HostStorage, HostTensorStorage> {
 public:
-    using MixinValueImpl::MixinValueImpl;
+    using PrimitiveValue::PrimitiveValue;
 
     std::string to_string() const override;
 };
 
-class DeviceStorage final
-        : public MixinValueImpl<
-                  DeviceStorage, ValueKind::Primitive, DeviceTensorStorage> {
+class DeviceStorage final : public PrimitiveValue<DeviceStorage, DeviceTensorStorage> {
 public:
-    using MixinValueImpl::MixinValueImpl;
+    using PrimitiveValue::PrimitiveValue;
 
     std::string to_string() const override;
 };
 
-/**
- * \brief like HostTensorND mixin, but allow scalar value
- *
- */
-class HostValue final : public ValueImpl<HostValue, ValueKind::Primitive> {
+class HostTensor {
 private:
     DType m_dtype;
     ValueShape m_shape;
     HostTensorStorage m_storage;
 
 public:
-    HostValue(DType dtype, ValueShape shape, HostTensorStorage storage)
+    HostTensor() = default;
+    HostTensor(DType dtype, ValueShape shape, HostTensorStorage storage)
             : m_dtype(dtype), m_shape(shape), m_storage(storage) {}
-    HostValue(HostTensorND value)
-            : HostValue(
+    HostTensor(HostTensorND value)
+            : HostTensor(
                       value.dtype(), ValueShape::from(value.shape()), value.storage()) {
     }
 
-    std::string to_string() const override;
-
-    void clear() override {
-        m_dtype = {};
-        m_shape = {};
-        m_storage = {};
-    }
-
     DType dtype() const { return m_dtype; }
     const ValueShape& shape() const { return m_shape; }
     CompNode device() const { return m_storage.comp_node(); }
@@ -112,31 +101,31 @@ public:
 };
 
 /**
- * \brief like DeviceTensorND mixin, but allow scalar value
+ * \brief like HostTensorND mixin, but allow scalar value
  *
  */
-class DeviceValue final : public ValueImpl<DeviceValue, ValueKind::Primitive> {
+class HostValue final : public PrimitiveValue<HostValue, HostTensor> {
+public:
+    using PrimitiveValue::PrimitiveValue;
+
+    std::string to_string() const override;
+};
+
+class DeviceTensor {
 private:
     DType m_dtype;
     ValueShape m_shape;
     DeviceTensorStorage m_storage;
 
 public:
-    DeviceValue(DType dtype, ValueShape shape, DeviceTensorStorage storage)
+    DeviceTensor() = default;
+    DeviceTensor(DType dtype, ValueShape shape, DeviceTensorStorage storage)
             : m_dtype(dtype), m_shape(shape), m_storage(std::move(storage)) {}
-    DeviceValue(const DeviceTensorND& value)
-            : DeviceValue(
+    DeviceTensor(const DeviceTensorND& value)
+            : DeviceTensor(
                       value.dtype(), ValueShape::from(value.shape()), value.storage()) {
     }
 
-    std::string to_string() const override;
-
-    void clear() override {
-        m_dtype = {};
-        m_shape = {};
-        m_storage = {};
-    }
-
     DType dtype() const { return m_dtype; }
     const ValueShape& shape() const { return m_shape; }
     CompNode device() const { return m_storage.comp_node(); }
@@ -145,26 +134,34 @@ public:
     DeviceTensorND as_nd(bool allow_scalar = false) const;
 };
 
-class FunctionValue final
-        : public MixinValueImpl<FunctionValue, ValueKind::Primitive, GenericFunction> {
+/**
+ * \brief like DeviceTensorND mixin, but allow scalar value
+ *
+ */
+class DeviceValue final : public PrimitiveValue<DeviceValue, DeviceTensor> {
+public:
+    using PrimitiveValue::PrimitiveValue;
+
+    std::string to_string() const override;
+};
+
+class FunctionValue final : public PrimitiveValue<FunctionValue, GenericFunction> {
 public:
-    using MixinValueImpl::MixinValueImpl;
+    using PrimitiveValue::PrimitiveValue;
 
     std::string to_string() const override;
 };
 
-class DTypeValue final
-        : public MixinValueImpl<DTypeValue, ValueKind::Primitive, DType> {
+class DTypeValue final : public PrimitiveValue<DTypeValue, DType> {
 public:
-    using MixinValueImpl::MixinValueImpl;
+    using PrimitiveValue::PrimitiveValue;
 
     std::string to_string() const override;
 };
 
-class StringValue final
-        : public MixinValueImpl<StringValue, ValueKind::Primitive, std::string> {
+class StringValue final : public PrimitiveValue<StringValue, std::string> {
 public:
-    using MixinValueImpl::MixinValueImpl;
+    using PrimitiveValue::PrimitiveValue;
 
     std::string to_string() const override;
 };
@@ -180,10 +177,9 @@ public:
     std::string message() const { return m_message; }
 };
 
-class ErrorValue final
-        : public MixinValueImpl<ErrorValue, ValueKind::Primitive, Error> {
+class ErrorValue final : public PrimitiveValue<ErrorValue, Error> {
 public:
-    using MixinValueImpl::MixinValueImpl;
+    using PrimitiveValue::PrimitiveValue;
 
     std::string to_string() const override;
 };

imperative/src/include/megbrain/imperative/subgraph.h

@@ -57,7 +57,7 @@ struct Subgraph {
     SmallVector<expr_t> exprs;
 
     template <typename T, typename F, typename C>
-    SmallVector<T> apply(SmallVector<T> input_vars, F&& f, C&& c) const {
+    SmallVector<T> apply(Span<T> input_vars, F&& f, C&& c) const {
         std::unordered_map<size_t, T> idx2var;
         mgb_assert(inputs.size() == input_vars.size(), "input size mismatch");
         for (size_t i = 0; i < inputs.size(); ++i) {
@@ -71,8 +71,7 @@ struct Subgraph {
             for (auto idx : expr.inputs) {
                 expr_inputs.push_back(idx2var[idx]);
             }
-            SmallVector<T> expr_outputs =
-                    f(expr.op, std::move(expr_inputs), expr.outputs.size());
+            SmallVector<T> expr_outputs = f(expr.op, expr_inputs, expr.outputs.size());
             mgb_assert(
                     expr_outputs.size() == expr.outputs.size(), "output size mismatch");
             for (size_t i = 0; i < expr_outputs.size(); ++i) {
@@ -102,9 +101,9 @@ struct EncodedSubgraph {
     SmallVector<bool> input_mask;
     SmallVector<bool> output_mask;
 
-    template <typename TContainer>
-    TContainer encode_inputs(TContainer inputs) const {
-        TContainer encoded_inputs;
+    template <typename T>
+    SmallVector<T> encode_inputs(Span<T> inputs) const {
+        SmallVector<T> encoded_inputs;
         size_t index = 0;
         for (auto&& input : inputs) {
             mgb_assert(index < input_mask.size(), "index out of range");
@@ -116,9 +115,9 @@ struct EncodedSubgraph {
         return encoded_inputs;
     }
 
-    template <typename TContainer>
-    TContainer encode_outputs(TContainer outputs) const {
-        TContainer encoded_outputs;
+    template <typename T>
+    SmallVector<T> encode_outputs(Span<T> outputs) const {
+        SmallVector<T> encoded_outputs;
         size_t index = 0;
         for (auto&& output : outputs) {
             mgb_assert(index < output_mask.size(), "index out of range");
@@ -130,9 +129,9 @@ struct EncodedSubgraph {
         return encoded_outputs;
     }
 
-    template <typename TContainer>
-    TContainer decode_outputs(TContainer outputs) const {
-        TContainer decoded_outputs;
+    template <typename T>
+    SmallVector<T> decode_outputs(Span<T> outputs) const {
+        SmallVector<T> decoded_outputs;
         size_t index = 0;
         for (size_t i = 0; i < output_mask.size(); i++) {
             mgb_assert(index < output_mask.size(), "index out of range");
@@ -150,8 +149,8 @@ struct EncodedSubgraph {
         EncodedSubgraph result;
         result.input_mask = graph.gen_input_mask();
         result.output_mask = graph.gen_output_mask();
-        graph.inputs = result.encode_inputs(graph.inputs);
-        graph.outputs = result.encode_outputs(graph.outputs);
+        graph.inputs = result.encode_inputs<Subgraph::var_t>(graph.inputs);
+        graph.outputs = result.encode_outputs<Subgraph::var_t>(graph.outputs);
         result.graph = graph;
         return result;
     }
@@ -179,11 +178,11 @@ struct EncodedSubgraph {
     }
 
     template <typename T, typename F, typename C>
-    SmallVector<T> apply(SmallVector<T> input_vars, F&& f, C&& c) const {
-        auto encoded_inputs = encode_inputs(input_vars);
+    SmallVector<T> apply(Span<T> input_vars, F&& f, C&& c) const {
+        auto encoded_inputs = encode_inputs<T>(input_vars);
         auto encoded_outputs =
-                graph.apply(encoded_inputs, std::forward<F>(f), std::forward<C>(c));
-        return decode_outputs(encoded_outputs);
+                graph.apply<T>(encoded_inputs, std::forward<F>(f), std::forward<C>(c));
+        return decode_outputs<T>(encoded_outputs);
     }
 
     std::string repr() const;
@@ -280,4 +279,4 @@ public:
 };
 
 }  // namespace imperative
-}  // namespace mgb
+}  // namespace mgb
\ No newline at end of file

imperative/src/include/megbrain/imperative/transformations/eval.h

@@ -18,7 +18,7 @@
 
 namespace mgb::imperative {
 
-struct InterpreterInfo {
+class InterpreterValue final : public ObjectValue<InterpreterValue> {
 public:
     using Handle = interpreter::Interpreter::Handle;
     using Channel = interpreter::Interpreter::Channel;
@@ -46,8 +46,7 @@ private:
     mutable ShapeValue::ref_t m_shape;
 
 public:
-    InterpreterInfo() = default;
-    InterpreterInfo(LocalPtr<RAIIHandle> handle, std::string name = {})
+    InterpreterValue(LocalPtr<RAIIHandle> handle, std::string name = {})
             : m_handle(handle), m_name(name) {}
 
     const LocalPtr<RAIIHandle>& handle() const { return m_handle; }
@@ -57,18 +56,14 @@ public:
     ShapeValue::ref_t shape() const;
 
     std::string name() const { return m_name; }
-};
-
-class InterpreterValue final
-        : public MixinValueImpl<InterpreterValue, ValueKind::Object, InterpreterInfo> {
-public:
-    using MixinValueImpl::MixinValueImpl;
 
     std::string to_string() const override {
         return ssprintf(
                 "Handle{ptr=%p, name=%s}", handle().get(),
                 imperative::quoted(name()).c_str());
     }
+
+    void clear() override { m_handle = {}; }
 };
 
 /**
@@ -82,11 +77,12 @@ class InterpreterTransformation final : public Transformation {
 public:
     using Interpreter = interpreter::Interpreter;
     using Handle = Interpreter::Handle;
-    using SharedHandle = LocalPtr<InterpreterInfo::RAIIHandle>;
+    using SharedHandle = LocalPtr<InterpreterValue::RAIIHandle>;
     using Channel = Interpreter::Channel;
 
 private:
     std::shared_ptr<Channel> m_channel;
+    ObjectType<InterpreterValue> m_value_type{"InterpreterValue"};
 
 public:
     explicit InterpreterTransformation(std::shared_ptr<Channel> channel)
@@ -105,7 +101,7 @@ public:
             const Operator& op, Span<ValueRef> inputs) override;
 
     ValueRef unwrap(ValueRef value) override {
-        mgb_assert(!value.is<InterpreterValue>());
+        mgb_assert(!value.is(m_value_type));
         return value;
     }
 

imperative/src/include/megbrain/imperative/transformations/grad.h

@@ -34,7 +34,8 @@ struct BackwardGraphWithClosure {
             std::shared_ptr<OptimizedBackwardGraphResult> backward_graph,
             std::shared_ptr<OpDef> op, Span<ValueRef> inputs, Span<ValueRef> outputs);
 
-    void operator()(ValueRefList grads, std::function<void(size_t, ValueRef)> receiver);
+    void operator()(
+            Span<ValueRef> grads, std::function<void(size_t, ValueRef)> receiver);
 
     bool input_has_grad(size_t i) { return backward_graph->input_has_grad[i]; }
 
@@ -51,7 +52,7 @@ struct CustomBackward;
 using GradRuleFn = std::function<ValueRefList(Span<ValueRef> inputs, CustomBackward&)>;
 
 struct CustomBackward {
-    using BackwardFn = std::function<ValueRefList(Span<ValueRef>)>;
+    using BackwardFn = std::function<SmallVector<ValueRef>(Span<ValueRef>)>;
     using BackwardRule = std::function<std::optional<ValueRefList>(
             const OpDef&, Span<ValueRef>, Span<bool>, CustomBackward&)>;
     BackwardFn m_backward;
@@ -62,7 +63,8 @@ struct CustomBackward {
     SmallVector<OutputAttr> m_output_attrs;
 
 public:
-    void operator()(ValueRefList grads, std::function<void(size_t, ValueRef)> receiver);
+    void operator()(
+            Span<ValueRef> grads, std::function<void(size_t, ValueRef)> receiver);
 
     bool input_has_grad(size_t i) { return m_input_has_grad[i]; }
     bool output_requires_grad(size_t i) { return m_output_attrs[i].requires_grad; }
@@ -175,7 +177,7 @@ inline GradSlot* GradSlotPtr::operator->() const {
     return &m_fn->m_slots[m_index];
 }
 
-class GradValue final : public ValueImpl<GradValue, ValueKind::Object> {
+class GradValue final : public ObjectValue<GradValue> {
 private:
     ValueRef m_value;
     std::shared_ptr<GradKey> m_key;
@@ -187,14 +189,9 @@ public:
 
     std::string to_string() const override;
 
-    bool has_key(const std::shared_ptr<GradKey>& key) const { return m_key == key; }
+    const GradSlotPtr& slot() const { return m_slot; }
 
-    const GradSlotPtr& slot_for(std::shared_ptr<GradKey> key) const {
-        mgb_assert(m_key == key);
-        return m_slot;
-    }
-
-    std::shared_ptr<GradKey> key() const { return m_key; }
+    // std::shared_ptr<GradKey> key() const { return m_key; }
 
     void clear() override {
         m_slot = {};
@@ -216,9 +213,12 @@ private:
     std::vector<std::pair<LocalWeakPtr<GradFn>, std::shared_ptr<OpDef>>> m_tape;
     std::vector<std::pair<LocalPtr<GradFn>, std::shared_ptr<OpDef>>> m_frozen_tape;
     bool m_frozen = false;
+    const Type<GradValue>& m_value_type;
 
 public:
-    GradKey() { m_tape.reserve(4 * 1024); }
+    GradKey(const Type<GradValue>& value_type) : m_value_type(value_type) {
+        m_tape.reserve(4 * 1024);
+    }
 
     void backward();
     GradValue::ref_t attach(ValueRef tensor, std::function<void(ValueRef)> callback);
@@ -230,10 +230,9 @@ public:
 };
 
 class GradKeyValue final
-        : public MixinValueImpl<
-                  GradKeyValue, ValueKind::Primitive, std::shared_ptr<GradKey>> {
+        : public PrimitiveValue<GradKeyValue, std::shared_ptr<GradKey>> {
 public:
-    using MixinValueImpl::MixinValueImpl;
+    using PrimitiveValue::PrimitiveValue;
 
     std::string to_string() const override {
         return ssprintf("GradKey{%s}", (*this)->name().c_str());
@@ -242,26 +241,20 @@ public:
 
 class GradTransformation final : public Transformation {
 private:
+    ObjectType<GradValue> m_value_type{"GradValue"};
     std::shared_ptr<GradKey> m_key;
     std::vector<GradValue::weak_ref_t> m_weak_values;
     size_t m_suppressed = 0;
 
 public:
-    GradTransformation(std::shared_ptr<GradKey> key) : m_key(key) {}
+    GradTransformation() { m_key = std::make_shared<GradKey>(m_value_type); }
 
     auto record_grad(GradValue::ref_t tensor) {
         m_weak_values.push_back(tensor);
         return tensor;
     }
 
-    bool is_grad_value(const ValueRef& value) {
-        if (auto* grad_value = value.as<GradValue>()) {
-            if (grad_value->has_key(m_key)) {
-                return true;
-            }
-        }
-        return false;
-    }
+    bool is_grad_value(const ValueRef& value) { return value.is(m_value_type); }
 
     /**
      * \brief test whether value is related to this GradTransformation
@@ -273,13 +266,7 @@ public:
      * \return GradValue::ref_t
      */
     const GradValue::ref_t& as_grad_value(const ValueRef& value) {
-        auto&& grad_value = value.as_ref<GradValue>();
-        if (grad_value) {
-            if (grad_value->has_key(m_key)) {
-                return grad_value;
-            }
-        }
-        return GradValue::ref_t::nil;
+        return value.as_ref(m_value_type);
     }
 
     bool has_key(std::shared_ptr<GradKey> key) {
@@ -299,6 +286,8 @@ public:
         return value;
     }
 
+    const std::shared_ptr<GradKey>& key() const { return m_key; }
+
     std::string name() const override { return "GradTransformation"; }
 
     GenericFunction make_backward_closure(Span<ValueRef> ys);

imperative/src/include/megbrain/imperative/transformations/lazy.h

@@ -22,32 +22,27 @@
 
 namespace mgb::imperative {
 
-class LazyEvalInfo {
+class LazyEvalValue final : public ObjectValue<LazyEvalValue> {
 private:
     VarNode* m_node = nullptr;
     ValueRef m_bound_data;
     std::string m_name;
 
 public:
-    LazyEvalInfo() = default;
-    LazyEvalInfo(VarNode* node, ValueRef bound_data, std::string name)
+    LazyEvalValue(VarNode* node, ValueRef bound_data, std::string name)
             : m_node(node), m_bound_data(bound_data), m_name(name) {}
     VarNode* node() const { return m_node; }
 
     ValueRef bound_data() const { return m_bound_data; }
 
     std::string name() const { return m_name; }
-};
-
-class LazyEvalValue final
-        : public MixinValueImpl<LazyEvalValue, ValueKind::Object, LazyEvalInfo> {
-public:
-    using MixinValueImpl::MixinValueImpl;
 
     std::string to_string() const override {
         return ssprintf(
                 "LazyEvalValue{node=%p, name=%s}", node(), node()->name().c_str());
     }
+
+    void clear() override {}
 };
 
 /**
@@ -67,6 +62,7 @@ private:
     std::vector<LazyEvalValue::weak_ref_t> m_weak_vars;
     SymbolVar m_io_link = nullptr;
     std::exception_ptr m_graph_exc;
+    ObjectType<LazyEvalValue> m_value_type{"LazyEvalValue"};
 
 public:
     LazyEvalTransformation(bool no_exec) : m_no_exec(no_exec) {
@@ -75,7 +71,7 @@ public:
 
     LazyEvalValue::ref_t record_var(
             VarNode* node, ValueRef bound_data = {}, std::string name = {}) {
-        auto lazy_eval_val = LazyEvalValue::make(node, bound_data, name);
+        auto lazy_eval_val = m_value_type.make(node, bound_data, name);
         m_weak_vars.push_back(lazy_eval_val);
         return lazy_eval_val;
     }
@@ -86,7 +82,7 @@ public:
             const Operator& op, Span<ValueRef> inputs) override;
 
     ValueRef unwrap(ValueRef value) override {
-        mgb_assert(!value.is<LazyEvalValue>());
+        mgb_assert(!value.is(m_value_type));
         return value;
     }
 

imperative/src/include/megbrain/imperative/transformations/scalar.h

@@ -17,7 +17,7 @@
 
 namespace mgb::imperative {
 
-class ScalarValue final : public ValueImpl<ScalarValue, ValueKind::Object> {
+class ScalarValue final : public ObjectValue<ScalarValue> {
 private:
     ValueRef m_value;
 
@@ -47,17 +47,21 @@ public:
 class ScalarTransformation final : public Transformation {
 private:
     ShapeValue::ref_t m_empty_shape;  // []
+    ObjectType<ScalarValue> m_value_type{"ScalarValue"};
+
 public:
     ValueRefList apply_get_attr(const GetAttr& get_attr, Span<ValueRef> inputs);
     ValueRefList apply_transformation(
             const Operator& op, Span<ValueRef> inputs) override;
 
     ValueRef unwrap(ValueRef value) override {
-        mgb_assert(!value.is<ScalarValue>());
+        mgb_assert(!value.is(m_value_type));
         return value;
     }
 
     std::string name() const override { return "ScalarTransformation"; }
+
+    const Type<ScalarValue>& value_type() const { return m_value_type; }
 };
 
 }  // namespace mgb::imperative

imperative/src/include/megbrain/imperative/transformations/symbol.h

@@ -22,7 +22,7 @@
 
 namespace mgb::imperative {
 
-class SymbolValue final : public ValueImpl<SymbolValue, ValueKind::Object> {
+class SymbolValue final : public ObjectValue<SymbolValue> {
 private:
     VarNode* m_node = nullptr;
 
@@ -47,6 +47,7 @@ public:
 class SymbolTransformation final : public Transformation {
 private:
     ComputingGraph* m_graph = nullptr;
+    ObjectType<SymbolValue> m_value_type{"SymbolValue"};
 
 public:
     SymbolTransformation(ComputingGraph* graph) : m_graph(graph) {}
@@ -55,12 +56,12 @@ public:
         if (auto* apply_op = op.as<ApplyOp>()) {
             SmallVector<VarNode*> input_nodes;
             for (auto&& input : inputs) {
-                input_nodes.push_back(input.cast<SymbolValue>().node());
+                input_nodes.push_back(input.cast(m_value_type).node());
             }
             auto output_nodes = OpDef::apply_on_var_node(apply_op->op(), input_nodes);
             ValueRefList outputs(output_nodes.size());
             for (size_t i = 0; i < output_nodes.size(); ++i) {
-                outputs[i] = SymbolValue::make(output_nodes[i]);
+                outputs[i] = m_value_type.make(output_nodes[i]);
             }
             return outputs;
         } else if (auto* create_tensor = op.as<CreateTensor>()) {
@@ -69,9 +70,9 @@ public:
                     args.kind == CreateTensor::Const,
                     "only const value is allowed here");
             auto* node = opr::ImmutableTensor::make(*m_graph, *args.host, {}).node();
-            return {SymbolValue::make(node)};
+            return {m_value_type.make(node)};
         } else if (auto* get_attr = op.as<GetAttr>()) {
-            auto* node = inputs.as_array<1>()[0].cast<SymbolValue>().node();
+            auto* node = inputs.item().cast(m_value_type).node();
             switch (get_attr->attr()) {
                 case GetAttr::DType:
                     return {DTypeValue::make(node->dtype())};
@@ -121,11 +122,13 @@ public:
     }
 
     ValueRef unwrap(ValueRef value) override {
-        mgb_assert(!value.is<SymbolValue>(), "SymbolValue doesn't support unwrap");
+        mgb_assert(!value.is(m_value_type), "SymbolValue doesn't support unwrap");
         return value;
     }
 
     std::string name() const override { return "SymbolTransformation"; }
+
+    const Type<SymbolValue>& value_type() const { return m_value_type; }
 };
 
 }  // namespace mgb::imperative

imperative/src/include/megbrain/imperative/transformations/trace.h

@@ -100,22 +100,15 @@ public:
     }
 };
 
-class TracingInfo {
+class TracingValue final : public ObjectValue<TracingValue> {
 private:
     ValueRef m_value = {};
     size_t m_id = 0;
 
 public:
-    TracingInfo() = default;
-    TracingInfo(ValueRef value, size_t id) : m_value(value), m_id(id) {}
+    TracingValue(ValueRef value, size_t id) : m_value(value), m_id(id) {}
     ValueRef value() const { return m_value; }
     size_t id() const { return m_id; }
-};
-
-class TracingValue final
-        : public MixinValueImpl<TracingValue, ValueKind::Object, TracingInfo> {
-public:
-    using MixinValueImpl::MixinValueImpl;
 
     std::string to_string() const override {
         return ssprintf(
@@ -126,6 +119,8 @@ public:
     void on_watch() override { value().watch(); }
 
     void on_unwatch() override { value().unwatch(); }
+
+    void clear() override { m_value = {}; }
 };
 
 /**
@@ -146,6 +141,7 @@ private:
     std::vector<TracingValue::weak_ref_t> m_weak_vars;
     bool m_capture_as_const = false;
     bool m_record_input_shapes = false;
+    ObjectType<TracingValue> m_value_type{"TracingValue"};
 
 public:
     TracingTransformation(bool capture_as_const, bool record_input_shapes)
@@ -162,7 +158,7 @@ public:
      */
     TypedValueRef<TracingValue> record_var(ValueRef value, bool capture, VarKind kind) {
         size_t id = m_vars.size();
-        auto wrapped_value = TracingValue::make(value, id);
+        auto wrapped_value = m_value_type.make(value, id);
         m_vars.push_back({id, value.dtype(), value.device()});
         auto& var = m_vars.back();
         if (capture) {
@@ -179,7 +175,7 @@ public:
         return wrapped_value;
     }
     ValueRef unwrap_var(ValueRef value) {
-        if (auto* tracing_value = value.as<TracingValue>()) {
+        if (auto* tracing_value = value.as(m_value_type)) {
             return tracing_value->value();
         }
         return value;
@@ -189,7 +185,7 @@ public:
             const Operator& op, Span<ValueRef> inputs) override;
 
     ValueRef unwrap(ValueRef value) override {
-        if (auto* tracing_value = value.as<TracingValue>()) {
+        if (auto* tracing_value = value.as(m_value_type)) {
             return tracing_value->value();
         }
         return value;
@@ -234,7 +230,7 @@ public:
         std::function<void(std::exception_ptr)> exc_setter;
     };
 
-    class TracedInfo {
+    class TracedValue final : public ObjectValue<TracedValue> {
     private:
         size_t m_id = 0;
         VarInfo* m_var = nullptr;
@@ -244,8 +240,7 @@ public:
         mutable CompNodeValue::ref_t m_comp_node;
 
     public:
-        TracedInfo() = default;
-        TracedInfo(size_t id, VarInfo* var, VarAccessor* accessor)
+        TracedValue(size_t id, VarInfo* var, VarAccessor* accessor)
                 : m_id(id), m_var(var), m_accessor(accessor) {}
         size_t id() const { return m_id; }
         ShapeValue::ref_t shape() const;
@@ -256,16 +251,12 @@ public:
         void set_exception(std::exception_ptr exc) const {
             m_accessor->exc_setter(exc);
         }
-    };
-
-    class TracedValue final
-            : public MixinValueImpl<TracedValue, ValueKind::Object, TracedInfo> {
-    public:
-        using MixinValueImpl::MixinValueImpl;
 
         std::string to_string() const override {
             return ssprintf("TracedValue{\"id\"=%zu}", id());
         }
+
+        void clear() override {}
     };
 
 private:
@@ -280,9 +271,12 @@ private:
     std::function<bool(ValueRef, ValueRef)> m_value_comparator;
     bool m_input_shape_static;
     std::mutex m_mutex;
+    std::condition_variable m_cv;
     std::exception_ptr m_graph_exc;
+    int m_graph_status = 0;  // 0 = stop, 1 = running, 2 = finalizing
     std::vector<std::shared_ptr<BoxBase>> m_boxes;
     ComputingGraph::OutputSpec m_output_spec;
+    ObjectType<TracedValue> m_value_type{"TracedValue"};
 
 public:
     CompiledTransformation(TraceResult result, bool input_shape_static)
@@ -292,6 +286,27 @@ public:
         m_graph = ComputingGraph::make();
         options().no_force_inplace = true;
         options().async_exec_level = 0b100;
+        m_graph_executor = std::thread([&] {
+            while (true) {
+                std::unique_lock lock{m_mutex};
+                m_cv.wait(lock, [&] { return m_graph_status != 0; });
+                lock.unlock();
+                if (m_graph_status == 2) {
+                    break;
+                }
+                try {
+                    m_executable->execute();
+                    m_executable->wait();
+                } catch (...) {
+                    auto exc = std::current_exception();
+                    set_exception(exc);
+                }
+                lock.lock();
+                m_graph_status = 0;
+                lock.unlock();
+                m_cv.notify_all();
+            }
+        });
     }
 
     ComputingGraph& graph() { return *m_graph; }
@@ -350,7 +365,7 @@ public:
     void on_unregister() noexcept override;
 
     ValueRef unwrap(ValueRef value) override {
-        mgb_assert(!value.is<TracedValue>());
+        mgb_assert(!value.is(m_value_type));
         return value;
     }
 
@@ -368,6 +383,15 @@ public:
         m_boxes.push_back(box);
         return box;
     }
+
+    ~CompiledTransformation() {
+        {
+            MGB_LOCK_GUARD(m_mutex);
+            m_graph_status = 2;
+        }
+        m_cv.notify_all();
+        m_graph_executor.join();
+    }
 };
 
 }  // namespace mgb::imperative

imperative/src/include/megbrain/imperative/utils/allocator.h

@@ -11,7 +11,9 @@
 
 #pragma once
 
+#include <optional>
 #include <typeindex>
+#include <vector>
 
 #include "megbrain/utils/mempool.h"
 #include "megbrain/utils/metahelper.h"

imperative/src/include/megbrain/imperative/utils/span.h

@@ -34,7 +34,7 @@ public:
     Span(const T* begin, const T* end) : m_begin{begin}, m_end{end} {}
     Span(const T* begin, size_t size) : Span(begin, begin + size) {}
     template <typename TContainer>
-    Span(TContainer& container) : Span(container.data(), container.size()) {}
+    Span(const TContainer& container) : Span(container.data(), container.size()) {}
     const T* begin() const { return m_begin; }
     const T* end() const { return m_end; }
     const T* data() const { return m_begin; }

imperative/src/include/megbrain/imperative/utils/stats.h

@@ -2,7 +2,10 @@
 
 #include <chrono>
 #include <iostream>
+#include <map>
+#include <memory>
 #include <string>
+#include <unordered_map>
 #include <vector>
 
 namespace mgb {
@@ -18,7 +21,7 @@ public:
 private:
     clock_t::duration m_duration = clock_t::duration{0};
     size_t m_timing = 0;
-    const char* m_name = nullptr;
+    std::string m_name;
     uint64_t m_count = 0;
     size_t m_enabled = 1;
     bool m_default_enabled = true;
@@ -42,7 +45,8 @@ private:
             }
             if (timer.m_enabled) {
                 if (!--timer.m_timing) {
-                    timer.m_duration += (clock_t::now() - start);
+                    auto duration = (clock_t::now() - start);
+                    timer.m_duration += duration;
                 }
                 timer.m_count++;
             }
@@ -67,13 +71,10 @@ private:
         }
     };
 
-    using TimeScope = TimeScopeRecursive;
-
 public:
-    Timer(const char* name, bool default_enabled);
+    Timer(std::string name, bool default_enabled = true);
 
-    const char* name() { return m_name; }
-    auto time_scope() { return TimeScope(*this); }
+    std::string name() { return m_name; }
     auto time_scope_recursive() { return TimeScopeRecursive(*this); };
     auto enable_scope() { return EnableScope(*this); }
     void reset() {
@@ -88,7 +89,14 @@ public:
 }  // namespace stats
 
 struct Stats {
-    static inline std::vector<stats::Timer*> sm_timers;
+    struct TimerNode {
+        std::map<std::string, std::unique_ptr<TimerNode>> children;
+        stats::Timer* timer = nullptr;
+
+        TimerNode() {}
+    };
+
+    static inline TimerNode sm_root;
 
     // register your timers here
     // for example:
@@ -97,33 +105,84 @@ struct Stats {
     //
     // then use MGE_TIMER_SCOPE(mytimer) to collect durations in your code
 
-    static void print() {
-        std::vector<const char*> unused_timers;
-
-        for (auto* timer : sm_timers) {
-            if (timer->count() == 0) {
-                unused_timers.push_back(timer->name());
-            } else {
-                printf("%s costs %ld ns, happens %ld times\n", timer->name(),
-                       timer->get().count(), timer->count());
+    static std::pair<long, long> print_node(
+            std::string name, TimerNode& node, size_t indent = 0) {
+        auto print_indent = [&] {
+            for (size_t i = 0; i < indent; ++i) {
+                printf(" ");
+            }
+        };
+        long ns = 0, count = 0;
+        if (auto* timer = node.timer) {
+            print_indent();
+            printf("%s costs %'ld ns, hits %'ld times\n", name.c_str(),
+                   (long)timer->get().count(), (long)timer->count());
+            ns = timer->get().count();
+            count = timer->count();
+        }
+        if (!node.children.empty()) {
+            bool collect_children = node.timer == nullptr;
+            if (collect_children) {
+                print_indent();
+                printf("%s:\n", name.c_str());
+            }
+            long ns = 0, count = 0;
+            for (auto&& child : node.children) {
+                auto [child_ns, child_count] =
+                        print_node(child.first, *child.second, indent + 4);
+                if (collect_children) {
+                    ns += child_ns;
+                    count += child_count;
+                }
+            }
+            if (collect_children) {
+                print_indent();
+                printf("total costs %'ld ns, hits %'ld times\n", ns, count);
             }
         }
+        return {ns, count};
+    }
 
-        if (!unused_timers.empty()) {
-            printf("%zu timers unused\n", unused_timers.size());
+    static void print() {
+        for (auto&& child : sm_root.children) {
+            print_node(child.first, *child.second);
         }
     }
 
     static void reset() {
-        for (auto* timer : sm_timers) {
-            timer->reset();
-        }
+        auto reset_node = [](TimerNode& node, auto&& reset_node) -> void {
+            if (auto* timer = node.timer) {
+                timer->reset();
+            }
+            for (auto&& child : node.children) {
+                reset_node(*child.second, reset_node);
+            }
+        };
+        reset_node(sm_root, reset_node);
     }
 };
 
-inline stats::Timer::Timer(const char* name, bool default_enabled)
+inline stats::Timer::Timer(std::string name, bool default_enabled)
         : m_name(name), m_default_enabled(default_enabled) {
-    Stats::sm_timers.push_back(this);
+    std::vector<std::string> terms;
+    Stats::TimerNode* node = &Stats::sm_root;
+    while (true) {
+        auto pos = name.find(".");
+        if (pos == std::string::npos) {
+            auto& child = node->children[name];
+            child = std::make_unique<Stats::TimerNode>();
+            node = child.get();
+            node->timer = this;
+            break;
+        } else {
+            auto& child = node->children[name.substr(0, pos)];
+            if (!child) {
+                child = std::make_unique<Stats::TimerNode>();
+            }
+            node = child.get();
+            name = name.substr(pos + 1);
+        }
+    }
 }
 
 #if MGE_ENABLE_STATS

imperative/src/include/megbrain/imperative/value.h

@@ -50,18 +50,70 @@ class Operator;
 
 class ValueRefList;
 
+/**
+ * \brief base class of all value types
+ */
+class IType : public NonCopyableObj {
+private:
+    std::string m_name;
+    // TODO: count values, or make an linkedlist
+
+public:
+    IType(std::string name) : m_name(std::move(name)) {}
+
+    const std::string& name() const { return m_name; }
+
+    bool operator==(const IType& rhs) const { return this == &rhs; }
+
+    bool operator!=(const IType& rhs) const { return this != &rhs; }
+};
+
+/**
+ * \brief type of values.
+ *
+ * \tparam T ctype of value
+ */
+template <typename T>
+class Type : public IType {
+protected:
+    Type(std::string name) : IType(std::move(name)) {}
+    // TODO: each type owns an allocator
+
+public:
+    /**
+     * \brief helper function for construct a value
+     *
+     * \tparam TArgs types of arguments
+     * \param args arguments
+     * \return TypedValueRef<T> reference of value
+     */
+    template <typename... TArgs>
+    TypedValueRef<T> make(TArgs&&... args) const;
+};
+
+/**
+ * \brief type of primitive values.
+ *
+ * \tparam T ctype of value
+ */
 template <typename T>
-class Type {
+class PrimitiveType : public Type<T> {
 private:
-    const size_t m_code = T::TYPE_CODE;
+    PrimitiveType();
 
 public:
-    inline size_t code() const { return m_code; }
+    static inline PrimitiveType instance;
 };
 
-enum class ValueKind {
-    Primitive,
-    Object,
+/**
+ * \brief type of object values.
+ *
+ * \tparam T ctype of value
+ */
+template <typename T>
+class ObjectType : public Type<T> {
+public:
+    ObjectType(std::string name) : Type<T>(name) {}
 };
 
 /**
@@ -71,9 +123,8 @@ enum class ValueKind {
  * and only the tail node is valid. ValueRef stores a value node, and it may be
  * an invalid internal node. When you dereference it, it will check its successor,
  * automatically find the tail node and return. This list would be modified to reduce
- * list length by change value's successor, but a ValueRef always has steady m_storage
- * when not explicitly modified.
- * So we use m_storage to identify a ValueRef ( hash / equility / id ).
+ * list length by change value's successor, but a steady id was kept in ValueRef
+ * so we can use it for identify a ValueRef ( hash / equility / id ).
  */
 class ValueRef {
 public:
@@ -93,9 +144,7 @@ private:
      */
     storage_t& storage() const;
 
-    const Value* as(size_t typecode) const;
-
-    bool is(size_t typecode) const;
+    const Value* as(const IType& type) const;
 
 public:
     ValueRef() = default;
@@ -103,45 +152,76 @@ public:
     /**
      * \brief whether value is instance of target type or not
      *
-     * \tparam TValue target type
-     * \return true if type of value is TValue
-     * \return false if empty or type of value is not TValue
+     * \param type target type
+     * \return true if type of value is instance of type
+     * \return false if empty or type of value is not instance of type
      */
-    template <typename TValue>
-    inline bool is(Type<TValue> type = {}) const;
+    bool is(const IType& type) const;
 
     /**
      * \brief try cast value as target type
      *
-     * \tparam TValue target type
+     * \tparam type target type
      * \return TValue* raw pointer if success, otherwise nullptr
      */
     template <typename TValue>
-    inline const TValue* as(Type<TValue> type = {}) const;
+    inline const TValue* as(const Type<TValue>& type) const;
 
     /**
      * \brief cast value to target type
      *
-     * \tparam TValue target type
+     * \param type target type
      * \return TValue& reference of value
      */
     template <typename TValue>
-    inline const TValue& cast(Type<TValue> type = {}) const;
+    inline const TValue& cast(const Type<TValue>& type) const;
 
     /**
      * \brief like as(), but returns TypedValueRef instead
      *
-     * \tparam TValue target type
+     * \param type target type
      * \return TypedValueRef<TValue> reference if success, otherwise empty reference
      */
     template <typename TValue>
-    inline const TypedValueRef<TValue>& as_ref(Type<TValue> type = {}) const;
+    inline const TypedValueRef<TValue>& as_ref(const Type<TValue>& type) const;
+
+    /**
+     * \brief like cast(), but allow empty value and returns TypedValueRef instead
+     *
+     * \param type target type
+     * \return TypedValueRef<TValue> reference if success, otherwise empty reference
+     */
+    template <typename TValue>
+    inline const TypedValueRef<TValue>& cast_ref(const Type<TValue>& type) const;
+
+    template <typename TValue>
+    inline std::enable_if_t<TValue::is_primitive, bool> is() const {
+        return is(PrimitiveType<TValue>::instance);
+    }
+
+    template <typename TValue>
+    inline std::enable_if_t<TValue::is_primitive, const TValue*> as() const {
+        return as(PrimitiveType<TValue>::instance);
+    }
+
+    template <typename TValue>
+    inline std::enable_if_t<TValue::is_primitive, const TValue&> cast() const {
+        return cast(PrimitiveType<TValue>::instance);
+    }
 
     template <typename TValue>
-    inline const TypedValueRef<TValue>& cast_ref(Type<TValue> type = {}) const;
+    inline std::enable_if_t<TValue::is_primitive, const TypedValueRef<TValue>&> as_ref()
+            const {
+        return as_ref(PrimitiveType<TValue>::instance);
+    }
 
     template <typename TValue>
-    void on_cast_failure() const;
+    inline std::enable_if_t<TValue::is_primitive, const TypedValueRef<TValue>&>
+    cast_ref() const {
+        return cast_ref(PrimitiveType<TValue>::instance);
+    }
+
+    void on_cast_failure(const IType& type) const;
 
     operator bool() const { return bool(m_storage); }
 
@@ -172,8 +252,6 @@ public:
     friend class ValueWeakRef;
     template <typename>
     friend class TypedValueRef;
-    template <typename, ValueKind>
-    friend class ValueImpl;
     friend ValueRefList apply(const Operator& op, Span<ValueRef> inputs);
 };
 
@@ -195,7 +273,8 @@ protected:
 
 public:
     ValueWeakRef() = default;
-    ValueWeakRef(ValueRef value) : m_id(value.id()), m_storage(value.m_storage) {}
+    ValueWeakRef(const ValueRef& value)
+            : m_id(value.id()), m_storage(value.m_storage) {}
 
     /**
      * \brief try promote to ValueRef
@@ -218,19 +297,15 @@ public:
 class Value : public NonCopyableObj {
 private:
     uint64_t m_id = std::numeric_limits<uint64_t>::max();
-    size_t m_typecode = 0;
+    const IType* m_type = nullptr;
     ValueRef m_successor;
     size_t m_watching = 0;
 
 protected:
-    Value(size_t typecode);
+    Value();
 
 public:
-    size_t typecode() const { return m_typecode; }
-    const std::type_index type() const { return registered_types()[m_typecode]; }
-
-    static size_t register_type(std::type_index type);
-    static const std::vector<std::type_index>& registered_types();
+    const IType& type() const { return *m_type; }
 
     static void register_value(ValueRef value);
     static ValueRef get_value_by_id(uint64_t id);
@@ -251,11 +326,12 @@ public:
     friend class ValueRef;
     friend class ValueWeakRef;
 
-    template <typename, ValueKind>
-    friend class ValueImpl;
     template <typename T>
     friend class TypedValueRef;
 
+    template <typename T>
+    friend class Type;
+
     ~Value();
 
 private:
@@ -267,30 +343,17 @@ private:
  *
  * \tparam T type of value
  */
-template <typename T, ValueKind Kind>
-class ValueImpl : public Value {
+template <typename T>
+class ObjectValue : public Value {
 protected:
-    ValueImpl() : Value(TYPE_CODE) {}
+    ObjectValue() {}
 
 public:
     using ref_t = TypedValueRef<T>;
     using weak_ref_t = TypedValueWeakRef<T>;
 
-    static inline const size_t TYPE_CODE = [] { return register_type(typeid(T)); }();
-    static constexpr ValueKind KIND = Kind;
-
-    /**
-     * \brief helper function for construct a value
-     *
-     * \tparam TArgs types of arguments
-     * \param args arguments
-     * \return TypedValueRef<T> reference of value
-     */
-    template <typename... TArgs>
-    static MGB_NOINLINE TypedValueRef<T> make(TArgs&&... args) {
-        static_assert(std::is_final_v<T>);
-        return ValueRef::make(LocalPtr<Value>::make<T>(std::forward<TArgs&&>(args)...));
-    }
+    static constexpr bool is_primitive = false;
+    static constexpr bool is_object = true;
 };
 
 /**
@@ -299,74 +362,89 @@ public:
  * \tparam T type of value
  * \tparam TMixin type of mixin class
  */
-template <typename T, ValueKind Kind, typename TMixin>
-class MixinValueImpl : public ValueImpl<T, Kind>, public TMixin {
+template <typename T, typename TMixin>
+class PrimitiveValue : public Value, public TMixin {
 public:
+    using ref_t = TypedValueRef<T>;
+    using weak_ref_t = TypedValueWeakRef<T>;
+
     using TMixin::TMixin;
 
-    MixinValueImpl(TMixin mixin) : TMixin(std::move(mixin)) {}
+    PrimitiveValue(TMixin&& mixin) : TMixin(std::move(mixin)) {}
+    PrimitiveValue(const TMixin& mixin) : TMixin(mixin) {}
 
 public:
     void clear() override final { ((TMixin&)*this) = {}; }
 
     bool eq(const TMixin& value) const { return ((const TMixin&)*this) == value; }
+
+    /**
+     * \brief helper function for construct a value
+     *
+     * \tparam TArgs types of arguments
+     * \param args arguments
+     * \return TypedValueRef<T> reference of value
+     */
+    template <typename... TArgs>
+    static TypedValueRef<T> make(TArgs&&... args) {
+        return PrimitiveType<T>::instance.make(std::forward<TArgs&&>(args)...);
+    }
+
+    static constexpr bool is_primitive = true;
+    static constexpr bool is_object = false;
 };
 
+template <typename T>
+PrimitiveType<T>::PrimitiveType() : Type<T>(typeid(T).name()) {
+    static_assert(std::is_base_of_v<Value, T>);
+    static_assert(!std::is_base_of_v<ObjectValue<T>, T>);
+}
+
 inline ValueRef::ValueRef(storage_t storage) {
-    // mgb_assert(storage);
     m_storage = storage;
     m_id = m_storage->m_id;
 }
 
 template <typename TValue>
-inline const TValue* ValueRef::as(Type<TValue> type) const {
-    // auto _ = Stats::time_value_as.time_scope();
+inline const TValue* ValueRef::as(const Type<TValue>& type) const {
     static_assert(std::is_base_of_v<Value, TValue>);
-    return static_cast<const TValue*>(as(type.code()));
+    return static_cast<const TValue*>(as((const IType&)type));
 }
 
 template <typename TValue>
-inline const TValue& ValueRef::cast(Type<TValue> type) const {
-    // auto _ = Stats::time_value_cast.time_scope();
+inline const TValue& ValueRef::cast(const Type<TValue>& type) const {
     auto* ptr = as<TValue>(type);
     if (mgb_unlikely(!ptr)) {
-        on_cast_failure<TValue>();
+        on_cast_failure(type);
     }
     return static_cast<const TValue&>(*ptr);
 }
 
 template <typename TValue>
-inline bool ValueRef::is(Type<TValue> type) const {
-    // auto _ = Stats::time_value_is.time_scope();
-    return is(type.code());
-}
-
-template <typename TValue>
-inline const TypedValueRef<TValue>& ValueRef::as_ref(Type<TValue> type) const {
-    if (!is<TValue>(type)) {
+inline const TypedValueRef<TValue>& ValueRef::as_ref(const Type<TValue>& type) const {
+    if (!is(type)) {
         return TypedValueRef<TValue>::nil;
     }
     return *reinterpret_cast<const TypedValueRef<TValue>*>(this);
 }
 
 template <typename TValue>
-inline const TypedValueRef<TValue>& ValueRef::cast_ref(Type<TValue> type) const {
+inline const TypedValueRef<TValue>& ValueRef::cast_ref(const Type<TValue>& type) const {
     if (!m_storage) {
         return TypedValueRef<TValue>::nil;
     }
-    if (mgb_unlikely(!is<TValue>(type))) {
-        on_cast_failure<TValue>();
+    if (mgb_unlikely(!is(type))) {
+        on_cast_failure(type);
     }
     return *reinterpret_cast<const TypedValueRef<TValue>*>(this);
 }
 
-template <typename TValue>
-void ValueRef::on_cast_failure() const {
+inline void ValueRef::on_cast_failure(const IType& type) const {
     // if this is ErrorValue, rethrow directly
     storage()->try_rethrow();
     mgb_assert(
-            storage()->m_typecode != TValue::TYPE_CODE, "expect type %s, got %s",
-            typeid(TValue).name(), to_string().c_str());
+            storage()->type() != type, "expect type %s, got %s", type.name().c_str(),
+            to_string().c_str());
 }
 
 /**
@@ -382,26 +460,10 @@ private:
 public:
     TypedValueRef() = default;
     const T& operator*() const {
-        if constexpr (T::KIND == ValueKind::Object) {
-            return this->template cast<T>();
-        } else if constexpr (T::KIND == ValueKind::Primitive) {
-            if (!m_storage) {
-                on_cast_failure<T>();
-            }
-            return static_cast<const T&>(*m_storage);
-        } else {
-            static_assert(!std::is_same_v<T, T>);
-        }
-    }
-    const T* operator->() const {
-        if constexpr (T::KIND == ValueKind::Object) {
-            return this->template as<T>();
-        } else if constexpr (T::KIND == ValueKind::Primitive) {
-            return static_cast<const T*>(m_storage.get());
-        } else {
-            static_assert(!std::is_same_v<T, T>);
-        }
+        mgb_assert(m_storage, "empty storage");
+        return static_cast<const T&>(*m_storage);
     }
+    const T* operator->() const { return static_cast<const T*>(m_storage.get()); }
 
     /**
      * \brief reset underlying value to another value
@@ -409,7 +471,7 @@ public:
      * \param successor new value
      */
     inline void reset(ValueRef successor) {
-        static_assert(T::KIND == ValueKind::Object);
+        static_assert(std::is_base_of_v<ObjectValue<T>, T>);
         mgb_assert(m_storage);
         mgb_assert(!m_storage->m_successor);
         if (m_storage->m_watching) {
@@ -422,25 +484,19 @@ public:
     static inline const TypedValueRef nil;
 
     friend class ValueRef;
-
-    template <typename, ValueKind>
-    friend class ValueImpl;
+    friend class Type<T>;
+    friend class TypedValueWeakRef<T>;
 };
 
 template <typename T>
 class TypedValueWeakRef : public ValueWeakRef {
 private:
+    TypedValueWeakRef(const ValueRef& value) : ValueWeakRef(value) {}
+    TypedValueWeakRef(const ValueWeakRef& value) : ValueWeakRef(value) {}
+
 public:
-    TypedValueWeakRef(ValueRef value) : ValueWeakRef(value) {}
-    TypedValueWeakRef(ValueWeakRef value) : ValueWeakRef(value) {}
-    TypedValueRef<T> lock() {
-        auto value = ValueWeakRef::lock();
-        if (value) {
-            return value.template as_ref<T>();
-        } else {
-            return {};
-        }
-    }
+    TypedValueWeakRef(const TypedValueRef<T>& value) : ValueWeakRef(value) {}
+    TypedValueRef<T> lock() { return (TypedValueRef<T>)ValueWeakRef::lock(); }
 };
 
 // TODO: add proxy value type, which is meant to be reset in the end
@@ -509,10 +565,14 @@ inline ValueRefList::ValueRefList(ValueRef item) : m_data(inline_storage()), m_s
     m_data[0] = std::move(item);
 }
 
-/*class ValueRefList : public SmallVector<ValueRef, 1> {
-public:
-    using SmallVector::SmallVector;
-};*/
+template <typename T>
+template <typename... TArgs>
+TypedValueRef<T> Type<T>::make(TArgs&&... args) const {
+    static_assert(std::is_final_v<T>);
+    auto storage = LocalPtr<Value>::make<T>(std::forward<TArgs&&>(args)...);
+    storage->m_type = this;
+    return ValueRef::make(std::move(storage));
+}
 
 }  // namespace imperative
 }  // namespace mgb

imperative/src/test/backward_graph.cpp

@@ -123,7 +123,7 @@ TEST(TestImperative, BackwardGraphBasic) {
         }
     }
     inputs.clear();
-    auto input_grads = result.graph.apply(
+    auto input_grads = result.graph.apply<TensorPtr>(
             backward_graph_inputs, apply_shared_on_physical_tensor,
             [&](auto&& x) { return x; });
     mgb_assert(input_grads.size() == input_has_grad.size());
@@ -177,7 +177,7 @@ TEST(TestImperative, BackwardGraphIdentity) {
         }
     }
     inputs.clear();
-    auto input_grads = result.graph.apply(
+    auto input_grads = result.graph.apply<TensorPtr>(
             backward_graph_inputs, apply_shared_on_physical_tensor,
             [&](auto&& x) { return x; });
     mgb_assert(input_grads.size() == input_has_grad.size());
@@ -244,11 +244,11 @@ TEST(TestImperative, OptimizedBackwardGraphBasic) {
             bg, {a_tn, b_tn}, {c_tn}, {dc_tn});
     auto grads = expand_grads(
             bg.output_mask,
-            bg.graph.apply(
+            bg.graph.apply<TensorPtr>(
                     backward_graph_inputs, apply_shared_on_physical_tensor,
                     [&](auto&& x) { return x; }));
 
-    auto precomp = obg.precomp.apply(
+    auto precomp = obg.precomp.apply<TensorPtr>(
             SmallVector<TensorPtr>{a_tn, b_tn, c_tn}, apply_shared_on_physical_tensor,
             [&](auto&& x) { return x; });
     ASSERT_EQ(precomp.size(), 2);
@@ -261,7 +261,7 @@ TEST(TestImperative, OptimizedBackwardGraphBasic) {
             obg, precomp, {a_tn, b_tn}, {c_tn}, {dc_tn});
     auto grads2 = expand_grads(
             obg.input_has_grad,
-            obg.backward.apply(
+            obg.backward.apply<TensorPtr>(
                     backward_inputs, apply_shared_on_physical_tensor,
                     [&](auto&& x) { return x; }));