diff --git a/nac3artiq/src/lib.rs b/nac3artiq/src/lib.rs
index 0734aa5c..ac087994 100644
--- a/nac3artiq/src/lib.rs
+++ b/nac3artiq/src/lib.rs
@@ -100,10 +100,13 @@ impl Nac3 {
                     let val = id_fn.call1((member.get_item(1)?,))?.extract()?;
                     name_to_pyid.insert(key.into(), val);
                 }
+                let typings = PyModule::import(py, "typing")?;
                 let helper = PythonHelper {
                     id_fn: builtins.getattr("id").unwrap().to_object(py),
                     len_fn: builtins.getattr("len").unwrap().to_object(py),
                     type_fn: builtins.getattr("type").unwrap().to_object(py),
+                    origin_ty_fn: typings.getattr("get_origin").unwrap().to_object(py),
+                    args_ty_fn: typings.getattr("get_args").unwrap().to_object(py),
                 };
                 Ok((
                     module.getattr("__name__")?.extract()?,
@@ -442,10 +445,13 @@ impl Nac3 {
         };
         let mut synthesized = parse_program(&synthesized).unwrap();
         let builtins = PyModule::import(py, "builtins")?;
+        let typings = PyModule::import(py, "typing")?;
         let helper = PythonHelper {
             id_fn: builtins.getattr("id").unwrap().to_object(py),
             len_fn: builtins.getattr("len").unwrap().to_object(py),
             type_fn: builtins.getattr("type").unwrap().to_object(py),
+            origin_ty_fn: typings.getattr("get_origin").unwrap().to_object(py),
+            args_ty_fn: typings.getattr("get_args").unwrap().to_object(py),
         };
         let resolver = Arc::new(Resolver(Arc::new(InnerResolver {
             id_to_type: self.builtins_ty.clone().into(),
diff --git a/nac3artiq/src/symbol_resolver.rs b/nac3artiq/src/symbol_resolver.rs
index 5160b786..f36c146f 100644
--- a/nac3artiq/src/symbol_resolver.rs
+++ b/nac3artiq/src/symbol_resolver.rs
@@ -43,6 +43,8 @@ pub struct PythonHelper {
     pub type_fn: PyObject,
     pub len_fn: PyObject,
     pub id_fn: PyObject,
+    pub origin_ty_fn: PyObject,
+    pub args_ty_fn: PyObject,
 }
 
 struct PythonValue {
@@ -133,47 +135,46 @@ impl InnerResolver {
         }))
     }
 
-    fn get_obj_type(
+    // handle python objects that represent types themselves
+    // primitives and class types should be themselves, use `ty_id` to check,
+    // TypeVars and GenericAlias(`A[int, bool]`) should use `ty_ty_id` to check
+    // the `bool` value returned indicates whether they are instantiated or not
+    fn get_pyty_obj_type(
         &self,
         py: Python,
-        obj: &PyAny,
+        pyty: &PyAny,
         unifier: &mut Unifier,
         defs: &[Arc<RwLock<TopLevelDef>>],
         primitives: &PrimitiveStore,
-    ) -> PyResult<Option<Type>> {
+    ) -> PyResult<Result<(Type, bool), String>> {
         let ty_id: u64 = self
             .helper
             .id_fn
-            .call1(py, (self.helper.type_fn.call1(py, (obj,))?,))?
+            .call1(py, (pyty,))?
+            .extract(py)?;
+        let ty_ty_id: u64 = self
+            .helper
+            .id_fn
+            .call1(py, (self.helper.type_fn.call1(py, (pyty,))?,))?
             .extract(py)?;
 
         if ty_id == self.primitive_ids.int || ty_id == self.primitive_ids.int32 {
-            Ok(Some(primitives.int32))
+            Ok(Ok((primitives.int32, true)))
         } else if ty_id == self.primitive_ids.int64 {
-            Ok(Some(primitives.int64))
+            Ok(Ok((primitives.int64, true)))
         } else if ty_id == self.primitive_ids.bool {
-            Ok(Some(primitives.bool))
+            Ok(Ok((primitives.bool, true)))
         } else if ty_id == self.primitive_ids.float {
-            Ok(Some(primitives.float))
+            Ok(Ok((primitives.float, true)))
         } else if ty_id == self.primitive_ids.list {
-            let len: usize = self.helper.len_fn.call1(py, (obj,))?.extract(py)?;
-            if len == 0 {
-                let var = unifier.get_fresh_var().0;
-                let list = unifier.add_ty(TypeEnum::TList { ty: var });
-                Ok(Some(list))
-            } else {
-                let ty = self.get_list_elem_type(py, obj, len, unifier, defs, primitives)?;
-                Ok(ty.map(|ty| unifier.add_ty(TypeEnum::TList { ty })))
-            }
+            // do not handle type var param and concrete check here
+            let var = unifier.get_fresh_var().0;
+            let list = unifier.add_ty(TypeEnum::TList { ty: var });
+            Ok(Ok((list, false)))
         } else if ty_id == self.primitive_ids.tuple {
-            let elements: &PyTuple = obj.cast_as()?;
-            let types: Result<Option<Vec<_>>, _> = elements
-                .iter()
-                .map(|elem| self.get_obj_type(py, elem, unifier, defs, primitives))
-                .collect();
-            let types = types?;
-            Ok(types.map(|types| unifier.add_ty(TypeEnum::TTuple { ty: types })))
-        } else if let Some(def_id) = self.pyid_to_def.read().get(&ty_id) {
+            // do not handle type var param and concrete check here
+            Ok(Ok((unifier.add_ty(TypeEnum::TTuple { ty: vec![] }), false)))
+        } else if let Some(def_id) = self.pyid_to_def.read().get(&ty_id).cloned() {
             let def = defs[def_id.0].read();
             if let TopLevelDef::Class {
                 object_id,
@@ -183,54 +184,275 @@ impl InnerResolver {
                 ..
             } = &*def
             {
-                let var_map: HashMap<_, _> = type_vars
-                    .iter()
-                    .map(|var| {
-                        (
-                            if let TypeEnum::TVar { id, .. } = &*unifier.get_ty(*var) {
-                                *id
-                            } else {
-                                unreachable!()
-                            },
-                            unifier.get_fresh_var().0,
-                        )
-                    })
-                    .collect();
-                let mut fields_ty = HashMap::new();
-                for method in methods.iter() {
-                    fields_ty.insert(method.0, (method.1, false));
-                }
-                for field in fields.iter() {
-                    let name: String = field.0.into();
-                    let field_data = obj.getattr(&name)?;
-                    let ty = self
-                        .get_obj_type(py, field_data, unifier, defs, primitives)?
-                        .unwrap_or(primitives.none);
-                    let field_ty = unifier.subst(field.1, &var_map).unwrap_or(field.1);
-                    if unifier.unify(ty, field_ty).is_err() {
-                        // field type mismatch
-                        return Ok(None);
+                // do not handle type var param and concrete check here, and no subst
+                Ok(Ok({
+                    let ty = TypeEnum::TObj {
+                        obj_id: *object_id,
+                        params: RefCell::new({
+                            type_vars
+                                .iter()
+                                .map(|x| {
+                                    if let TypeEnum::TVar { id, .. } = &*unifier.get_ty(*x) {
+                                        (*id, *x)
+                                    } else {
+                                        println!("{}", unifier.default_stringify(*x));
+                                        unreachable!()
+                                    }
+                                }).collect()
+                        }),
+                        fields: RefCell::new({
+                            let mut res = methods
+                                .iter()
+                                .map(|(iden, ty, _)| (*iden, (*ty, false)))
+                                .collect::<HashMap<_, _>>();
+                            res.extend(fields.clone().into_iter().map(|x| (x.0, (x.1, x.2))));
+                            res
+                        })
+                    };
+                    // here also false, later instantiation use python object to check compatible
+                    (unifier.add_ty(ty), false)
+                }))
+            } else {
+                // only object is supported, functions are not supported
+                unreachable!("function type is not supported, should not be queried")
+            }
+        } else if ty_ty_id == self.primitive_ids.typevar {
+            let constraint_types = {
+                let constraints = pyty.getattr("__constraints__").unwrap();
+                let mut result: Vec<Type> = vec![];
+                for i in 0.. {
+                    if let Ok(constr) = constraints.get_item(i) {
+                        result.push({
+                            match self.get_pyty_obj_type(py, constr, unifier, defs, primitives)? {
+                                Ok((ty, _)) => {
+                                    if unifier.is_concrete(ty, &[]) {
+                                        ty
+                                    } else {
+                                        return Ok(Err(format!(
+                                            "the {}th constraint of TypeVar `{}` is not concrete",
+                                            i + 1,
+                                            pyty.getattr("__name__")?.extract::<String>()?
+                                        )))
+                                    }
+                                },
+                                Err(err) => return Ok(Err(err))
+                            }
+                        })
+                    } else {
+                        break;
+                    }
+                }
+                result
+            };
+            let res = unifier.get_fresh_var_with_range(&constraint_types).0;
+            Ok(Ok((res, true)))
+        } else if ty_ty_id == self.primitive_ids.generic_alias.0 || ty_ty_id == self.primitive_ids.generic_alias.1 {
+            let origin = self.helper.origin_ty_fn.call1(py, (pyty,))?;
+            let args = self.helper.args_ty_fn.call1(py, (pyty,))?;
+            let args: &PyTuple = args.cast_as(py)?;
+            let origin_ty = match self.get_pyty_obj_type(py, origin.as_ref(py), unifier, defs, primitives)? {
+                Ok((ty, false)) => ty,
+                Ok((_, true)) => return Ok(Err("instantiated type does not take type parameters".into())),
+                Err(err) => return Ok(Err(err))
+            };
+
+            match &*unifier.get_ty(origin_ty) {
+                TypeEnum::TList { .. } => {
+                    if args.len() == 1 {
+                        let ty = match self.get_pyty_obj_type(py, args.get_item(0), unifier, defs, primitives)? {
+                            Ok(ty) => ty,
+                            Err(err) => return Ok(Err(err))
+                        };
+                        if !unifier.is_concrete(ty.0, &[]) && !ty.1 {
+                            panic!("type list should take concrete parameters in type var ranges")
+                        }
+                        Ok(Ok((unifier.add_ty(TypeEnum::TList { ty: ty.0 }), true)))
+                    } else {
+                        return Ok(Err(format!("type list needs exactly 1 type parameters, found {}", args.len())))
+                    }
+                 },
+                TypeEnum::TTuple { .. } => {
+                    let args = match args
+                        .iter()
+                        .map(|x| self.get_pyty_obj_type(py, x, unifier, defs, primitives))
+                        .collect::<Result<Vec<_>, _>>()?
+                        .into_iter()
+                        .collect::<Result<Vec<_>, _>>() {
+                            Ok(args) if !args.is_empty() => args
+                                .into_iter()
+                                .map(|(x, check)| if !unifier.is_concrete(x, &[]) && !check {
+                                        panic!("type tuple should take concrete parameters in type var ranges")
+                                    } else {
+                                        x
+                                    }
+                                )
+                                .collect::<Vec<_>>(),
+                            Err(err) => return Ok(Err(err)),
+                            _ => return Ok(Err("tuple type needs at least 1 type parameters".to_string()))
+                        };
+                    Ok(Ok((unifier.add_ty(TypeEnum::TTuple { ty: args }), true)))
+                },
+                TypeEnum::TObj { params, obj_id, .. } => {
+                    let subst = {
+                        let params = &*params.borrow();
+                        if params.len() != args.len() {
+                            return Ok(Err(format!(
+                                "for class #{}, expect {} type parameters, got {}.",
+                                obj_id.0,
+                                params.len(),
+                                args.len(),
+                            )))
+                        }
+                        let args = match args
+                            .iter()
+                            .map(|x| self.get_pyty_obj_type(py, x, unifier, defs, primitives))
+                            .collect::<Result<Vec<_>, _>>()?
+                            .into_iter()
+                            .collect::<Result<Vec<_>, _>>() {
+                                Ok(args) => args
+                                .into_iter()
+                                .map(|(x, check)| if !unifier.is_concrete(x, &[]) && !check {
+                                        panic!("type class should take concrete parameters in type var ranges")
+                                    } else {
+                                        x
+                                    }
+                                )
+                                .collect::<Vec<_>>(),
+                                Err(err) => return Ok(Err(err)),
+                            };
+                        params
+                            .iter()
+                            .zip(args.iter())
+                            .map(|((id, _), ty)| (*id, *ty))
+                            .collect::<HashMap<_, _>>()
+                    };
+                    Ok(Ok((unifier.subst(origin_ty, &subst).unwrap_or(origin_ty), true)))
+                },
+                TypeEnum::TVirtual { .. } => {
+                    if args.len() == 1 {
+                        let ty = match self.get_pyty_obj_type(py, args.get_item(0), unifier, defs, primitives)? {
+                            Ok(ty) => ty,
+                            Err(err) => return Ok(Err(err))
+                        };
+                        if !unifier.is_concrete(ty.0, &[]) && !ty.1 {
+                            panic!("virtual class should take concrete parameters in type var ranges")
+                        }
+                        Ok(Ok((unifier.add_ty(TypeEnum::TVirtual { ty: ty.0 }), true)))
+                    } else {
+                        return Ok(Err(format!("virtual class needs exactly 1 type parameters, found {}", args.len())))
+                    }
+                }
+                _ => unimplemented!()
+            }
+        } else if ty_id == self.primitive_ids.virtual_id {
+            Ok(Ok(({
+                let ty = TypeEnum::TVirtual { ty: unifier.get_fresh_var().0 };
+                unifier.add_ty(ty)
+            }, false)))
+        } else {
+            Ok(Err("unknown type".into()))
+        }
+    }
+
+    fn get_obj_type(
+        &self,
+        py: Python,
+        obj: &PyAny,
+        unifier: &mut Unifier,
+        defs: &[Arc<RwLock<TopLevelDef>>],
+        primitives: &PrimitiveStore,
+    ) -> PyResult<Option<Type>> {
+        let ty = self.helper.type_fn.call1(py, (obj,)).unwrap();
+        let (extracted_ty, inst_check) = match self.get_pyty_obj_type(
+            py,
+            {
+                if [self.primitive_ids.typevar,
+                    self.primitive_ids.generic_alias.0,
+                    self.primitive_ids.generic_alias.1
+                ].contains(&self.helper.id_fn.call1(py, (ty.clone(),))?.extract::<u64>(py)?) {
+                    obj
+                } else {
+                    ty.as_ref(py)
+                }
+            },
+            unifier,
+            defs,
+            primitives
+        )? {
+            Ok(s) => s,
+            Err(_) => return Ok(None)
+        };
+        return match (&*unifier.get_ty(extracted_ty), inst_check) {
+            // do the instantiation for these three types
+            (TypeEnum::TList { ty }, false) => {
+                let len: usize = self.helper.len_fn.call1(py, (obj,))?.extract(py)?;
+                if len == 0 {
+                    assert!(matches!(
+                        &*unifier.get_ty(extracted_ty),
+                        TypeEnum::TVar { meta: nac3core::typecheck::typedef::TypeVarMeta::Generic, range, .. }
+                            if range.borrow().is_empty()
+                    ));
+                    Ok(Some(extracted_ty))
+                } else {
+                    let actual_ty = self
+                        .get_list_elem_type(py, obj, len, unifier, defs, primitives)?;
+                    if let Some(actual_ty) = actual_ty {
+                        unifier.unify(*ty, actual_ty).unwrap();
+                        Ok(Some(extracted_ty))
+                    } else {
+                        Ok(None)
+                    }
+                }
+            }
+            (TypeEnum::TTuple { .. }, false) => {
+                let elements: &PyTuple = obj.cast_as()?;
+                let types: Result<Option<Vec<_>>, _> = elements
+                    .iter()
+                    .map(|elem| self.get_obj_type(py, elem, unifier, defs, primitives))
+                    .collect();
+                let types = types?;
+                Ok(types.map(|types| unifier.add_ty(TypeEnum::TTuple { ty: types })))
+            }
+            (TypeEnum::TObj { params, fields, .. }, false) => {
+                let var_map = params
+                    .borrow()
+                    .iter()
+                    .map(|(id_var, ty)| {
+                        if let TypeEnum::TVar { id, range, .. } = &*unifier.get_ty(*ty) {
+                            assert_eq!(*id, *id_var);
+                            (*id, unifier.get_fresh_var_with_range(&range.borrow()).0)
+                        } else {
+                            unreachable!()
+                        }
+                    })
+                    .collect::<HashMap<_, _>>();
+                // loop through non-function fields of the class to get the instantiated value
+                for field in fields.borrow().iter() {
+                    let name: String = (*field.0).into();
+                    if let TypeEnum::TFunc( .. ) = &*unifier.get_ty(field.1.0) {
+                        continue;
+                    } else {
+                        let field_data = obj.getattr(&name)?;
+                        let ty = self
+                            .get_obj_type(py, field_data, unifier, defs, primitives)?
+                            .unwrap_or(primitives.none);
+                        let field_ty = unifier.subst(field.1.0, &var_map).unwrap_or(field.1.0);
+                        if unifier.unify(ty, field_ty).is_err() {
+                            // field type mismatch
+                            return Ok(None);
+                        }
                     }
-                    fields_ty.insert(field.0, (ty, field.2));
                 }
                 for (_, ty) in var_map.iter() {
                     // must be concrete type
                     if !unifier.is_concrete(*ty, &[]) {
-                        return Ok(None);
+                        return Ok(None)
                     }
                 }
-                Ok(Some(unifier.add_ty(TypeEnum::TObj {
-                    obj_id: *object_id,
-                    fields: RefCell::new(fields_ty),
-                    params: RefCell::new(var_map),
-                })))
-            } else {
-                // only object is supported, functions are not supported
-                Ok(None)
+                return Ok(Some(unifier.subst(extracted_ty, &var_map).unwrap_or(extracted_ty)));
             }
-        } else {
-            Ok(None)
-        }
+            _ => Ok(Some(extracted_ty))
+        };
     }
 
     fn get_obj_value<'ctx, 'a>(