diff --git a/paddle/fluid/ir/dialect/paddle_dialect/ir/pd_type.cc b/paddle/fluid/ir/dialect/paddle_dialect/ir/pd_type.cc
index ce0f393200c87c85245a340e15e474725a82e78c..31ba23b0e1bbc034776e96705e1aa8a35197b71c 100644
--- a/paddle/fluid/ir/dialect/paddle_dialect/ir/pd_type.cc
+++ b/paddle/fluid/ir/dialect/paddle_dialect/ir/pd_type.cc
@@ -16,18 +16,6 @@
 
 namespace paddle {
 namespace dialect {
-const ir::Type& DenseTensorType::dtype() const { return storage()->dtype_; }
-
-const phi::DDim& DenseTensorType::dims() const { return storage()->dims_; }
-
-const phi::DataLayout& DenseTensorType::data_layout() const {
-  return storage()->layout_;
-}
-
-const phi::LoD& DenseTensorType::lod() const { return storage()->lod_; }
-
-const size_t& DenseTensorType::offset() const { return storage()->offset_; }
-
 const ir::Type& SelectedRowsType::dtype() const { return storage()->dtype_; }
 
 const phi::DDim& SelectedRowsType::dims() const { return storage()->dims_; }
@@ -43,5 +31,4 @@ const size_t& SelectedRowsType::offset() const { return storage()->offset_; }
 }  // namespace dialect
 }  // namespace paddle
 
-IR_DEFINE_EXPLICIT_TYPE_ID(paddle::dialect::DenseTensorType)
 IR_DEFINE_EXPLICIT_TYPE_ID(paddle::dialect::SelectedRowsType)
diff --git a/paddle/fluid/ir/dialect/paddle_dialect/ir/pd_type.h b/paddle/fluid/ir/dialect/paddle_dialect/ir/pd_type.h
index 640e4ab2392385f956acd19ebda963adcd29600c..9525e1a88b346ed71ec565b5f0a9e40a6d1756b0 100644
--- a/paddle/fluid/ir/dialect/paddle_dialect/ir/pd_type.h
+++ b/paddle/fluid/ir/dialect/paddle_dialect/ir/pd_type.h
@@ -15,30 +15,12 @@
 #pragma once
 
 #include "paddle/fluid/ir/dialect/paddle_dialect/ir/pd_type_storage.h"
+#include "paddle/ir/core/builtin_type.h"
 #include "paddle/ir/core/type.h"
 
 namespace paddle {
 namespace dialect {
-///
-/// \brief Define built-in parametric types.
-///
-class DenseTensorType : public ir::Type {
- public:
-  using Type::Type;
-
-  DECLARE_TYPE_UTILITY_FUNCTOR(DenseTensorType, DenseTensorTypeStorage);
-
-  const ir::Type &dtype() const;
-
-  const phi::DDim &dims() const;
-
-  const phi::DataLayout &data_layout() const;
-
-  const phi::LoD &lod() const;
-
-  const size_t &offset() const;
-};
-
+using DenseTensorType = ir::DenseTensorType;
 class SelectedRowsType : public ir::Type {
  public:
   using Type::Type;
@@ -59,5 +41,4 @@ class SelectedRowsType : public ir::Type {
 }  // namespace dialect
 }  // namespace paddle
 
-IR_DECLARE_EXPLICIT_TYPE_ID(paddle::dialect::DenseTensorType)
 IR_DECLARE_EXPLICIT_TYPE_ID(paddle::dialect::SelectedRowsType)
diff --git a/paddle/fluid/ir/dialect/paddle_dialect/ir/pd_type_storage.h b/paddle/fluid/ir/dialect/paddle_dialect/ir/pd_type_storage.h
index fcfff1db5ae855d76ec69ea99c69c447a8d99fbb..1a74b6d6c105926a4a0e3f9b5ed9b62d6df286e1 100644
--- a/paddle/fluid/ir/dialect/paddle_dialect/ir/pd_type_storage.h
+++ b/paddle/fluid/ir/dialect/paddle_dialect/ir/pd_type_storage.h
@@ -16,117 +16,15 @@
 
 #include <type_traits>
 
+#include "paddle/ir/core/builtin_type_storage.h"
 #include "paddle/ir/core/type.h"
 #include "paddle/ir/core/type_base.h"
 #include "paddle/ir/core/utils.h"
 #include "paddle/phi/core/tensor_meta.h"
 
-namespace std {
-///
-/// \brief Enable hashing std::vector<T> instances.
-///
-template <typename T>
-struct hash<std::vector<T>> {
-  std::size_t operator()(const std::vector<T>& dim) const {
-    std::size_t seed = 0;
-    for (size_t i = 0; i < dim.size(); ++i) {
-      seed ^= std::hash<T>()(dim[i]) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
-    }
-    return seed;
-  }
-};
-
-}  // namespace std
-
 namespace paddle {
 namespace dialect {
-///
-/// \brief Define Parametric TypeStorage for DenseTensorType.
-///
-/// NOTE(zhangbo9674): The derived TypeStorage class needs to implement the
-/// following methods: (1)declare ParamKey, (2)define Construction method,
-/// (3)define HashValue method, (4)overload operator==.
-///
-struct DenseTensorTypeStorage : public ir::TypeStorage {
-  using DataLayout = phi::DataLayout;
-  using Dim = phi::DDim;
-  using LoD = std::vector<std::vector<size_t>>;
-  ///
-  /// \brief Declare ParamKey according to parameter type.
-  ///
-  using ParamKey =
-      std::tuple<ir::Type, phi::DDim, phi::DataLayout, phi::LoD, size_t>;
-
-  DenseTensorTypeStorage(const ir::Type& dtype,
-                         const phi::DDim& dims,
-                         const phi::DataLayout& layout,
-                         const phi::LoD& lod,
-                         size_t offset)
-      : dtype_(dtype),
-        dims_(dims),
-        layout_(layout),
-        lod_(lod),
-        offset_(offset) {}
-
-  ///
-  /// \brief Each derived TypeStorage must define a Construct method, which
-  /// StorageManager uses to construct a derived TypeStorage.
-  ///
-  static DenseTensorTypeStorage* Construct(const ParamKey& key) {
-    return new DenseTensorTypeStorage(std::get<0>(key),
-                                      std::get<1>(key),
-                                      std::get<2>(key),
-                                      std::get<3>(key),
-                                      std::get<4>(key));
-  }
-
-  ///
-  /// \brief Each derived TypeStorage must provide a HashValue method.
-  ///
-  static std::size_t HashValue(const ParamKey& key) {
-    std::size_t hash_value = 0;
-    // hash dtype
-    hash_value =
-        ir::hash_combine(hash_value, std::hash<ir::Type>()(std::get<0>(key)));
-    // hash dims
-    hash_value =
-        ir::hash_combine(hash_value, std::hash<phi::DDim>()(std::get<1>(key)));
-    // hash layout
-    hash_value = ir::hash_combine(
-        hash_value,
-        std::hash<std::underlying_type<phi::DataLayout>::type>()(
-            static_cast<std::underlying_type<phi::DataLayout>::type>(
-                std::get<2>(key))));
-    // hash lod
-    hash_value =
-        ir::hash_combine(hash_value, std::hash<phi::LoD>()(std::get<3>(key)));
-    // hash offset
-    hash_value =
-        ir::hash_combine(hash_value, std::hash<size_t>()(std::get<4>(key)));
-    return hash_value;
-  }
-
-  ///
-  /// \brief Each derived TypeStorage needs to overload operator==.
-  ///
-  bool operator==(const ParamKey& key) const {
-    return ParamKey(dtype_, dims_, layout_, lod_, offset_) == key;
-  }
-
-  ParamKey GetAsKey() const {
-    return ParamKey(dtype_, dims_, layout_, lod_, offset_);
-  }
-
-  ///
-  /// \brief DenseTensorTypeStorage include five parameters: dims, dtype,
-  /// layout, lod, offset.
-  ///
-  ir::Type dtype_;
-  phi::DDim dims_;
-  phi::DataLayout layout_;
-  phi::LoD lod_;
-  size_t offset_;
-};
+using DenseTensorTypeStorage = ir::DenseTensorTypeStorage;
 
 struct SelectedRowsTypeStorage : public ir::TypeStorage {
   using DataLayout = phi::DataLayout;
diff --git a/paddle/ir/core/CMakeLists.txt b/paddle/ir/core/CMakeLists.txt
index c35bc02b344fadc70a533a037930edd5ba758ed0..39a3d71b2712894877bfb51439133cce6c7678c8 100644
--- a/paddle/ir/core/CMakeLists.txt
+++ b/paddle/ir/core/CMakeLists.txt
@@ -3,4 +3,4 @@ set(NEWIR_BINARY_DIR "${PADDLE_BINARY_DIR}/paddle/ir")
 
 file(GLOB IR_SRCS "*.cc")
 
-ir_library(ir_core SRCS ${IR_SRCS})
+ir_library(ir_core SRCS ${IR_SRCS} DEPS ddim)
diff --git a/paddle/ir/core/builtin_type.cc b/paddle/ir/core/builtin_type.cc
index 8a0aea5745a5b2a3535fac5bbdd80d8a07adbd07..49a15484466b259fdfc9c0d795b1e7c4b3b37032 100644
--- a/paddle/ir/core/builtin_type.cc
+++ b/paddle/ir/core/builtin_type.cc
@@ -17,6 +17,21 @@
 namespace ir {
 std::vector<Type> VectorType::data() const { return storage()->GetAsKey(); }
 
+const ir::Type& DenseTensorType::dtype() const { return storage()->dtype_; }
+
+const DenseTensorTypeStorage::Dim& DenseTensorType::dims() const {
+  return storage()->dims_;
+}
+
+const DenseTensorTypeStorage::DataLayout& DenseTensorType::data_layout() const {
+  return storage()->layout_;
+}
+
+const DenseTensorTypeStorage::LoD& DenseTensorType::lod() const {
+  return storage()->lod_;
+}
+
+const size_t& DenseTensorType::offset() const { return storage()->offset_; }
 }  // namespace ir
 
 IR_DEFINE_EXPLICIT_TYPE_ID(ir::UInt8Type)
@@ -33,3 +48,4 @@ IR_DEFINE_EXPLICIT_TYPE_ID(ir::IndexType)
 IR_DEFINE_EXPLICIT_TYPE_ID(ir::BoolType)
 IR_DEFINE_EXPLICIT_TYPE_ID(ir::Complex64Type)
 IR_DEFINE_EXPLICIT_TYPE_ID(ir::Complex128Type)
+IR_DEFINE_EXPLICIT_TYPE_ID(ir::DenseTensorType)
diff --git a/paddle/ir/core/builtin_type.h b/paddle/ir/core/builtin_type.h
index 9a2939110deaca170db1cb6618e3d2e2ab9327ab..a660f065376b2e90ee615da1436c95de88233bec 100644
--- a/paddle/ir/core/builtin_type.h
+++ b/paddle/ir/core/builtin_type.h
@@ -1,3 +1,4 @@
+
 // Copyright (c) 2023 PaddlePaddle Authors. All Rights Reserved.
 //
 // Licensed under the Apache License, Version 2.0 (the "License");
@@ -53,6 +54,23 @@ class IR_API VectorType : public Type {
   Type operator[](size_t index) const { return data()[index]; }
 };
 
+class DenseTensorType : public ir::Type {
+ public:
+  using Type::Type;
+
+  DECLARE_TYPE_UTILITY_FUNCTOR(DenseTensorType, DenseTensorTypeStorage);
+
+  const ir::Type &dtype() const;
+
+  const DenseTensorTypeStorage::Dim &dims() const;
+
+  const DenseTensorTypeStorage::DataLayout &data_layout() const;
+
+  const DenseTensorTypeStorage::LoD &lod() const;
+
+  const size_t &offset() const;
+};
+
 #define DECLARE_BUILTIN_TYPE(__name)                   \
   class IR_API __name : public Type {                  \
    public:                                             \
@@ -99,3 +117,4 @@ IR_EXPORT_DECLARE_EXPLICIT_TYPE_ID(ir::BoolType)
 IR_EXPORT_DECLARE_EXPLICIT_TYPE_ID(ir::IndexType)
 IR_EXPORT_DECLARE_EXPLICIT_TYPE_ID(ir::Complex64Type)
 IR_EXPORT_DECLARE_EXPLICIT_TYPE_ID(ir::Complex128Type)
+IR_EXPORT_DECLARE_EXPLICIT_TYPE_ID(ir::DenseTensorType)
diff --git a/paddle/ir/core/builtin_type_storage.h b/paddle/ir/core/builtin_type_storage.h
index 64d0c4284aa7f1a602307ca098379da678ca270a..4488b28b07fa22b76e1d501e56dc2aa56efbd497 100644
--- a/paddle/ir/core/builtin_type_storage.h
+++ b/paddle/ir/core/builtin_type_storage.h
@@ -17,15 +17,122 @@
 #include "paddle/ir/core/type.h"
 #include "paddle/ir/core/type_base.h"
 #include "paddle/ir/core/utils.h"
+#include "paddle/phi/common/layout.h"
+#include "paddle/phi/core/ddim.h"
+
+namespace std {
+///
+/// \brief Enable hashing std::vector<T> instances.
+///
+template <typename T>
+struct hash<std::vector<T>> {
+  std::size_t operator()(const std::vector<T>& dim) const {
+    std::size_t seed = 0;
+    for (size_t i = 0; i < dim.size(); ++i) {
+      seed ^= std::hash<T>()(dim[i]) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
+    }
+    return seed;
+  }
+};
+
+}  // namespace std
 
 namespace ir {
+///
+/// \brief Define Parametric TypeStorage for DenseTensorType.
+///
+/// NOTE(zhangbo9674): The derived TypeStorage class needs to implement the
+/// following methods: (1)declare ParamKey, (2)define Construction method,
+/// (3)define HashValue method, (4)overload operator==.
+///
+
+struct DenseTensorTypeStorage : public ir::TypeStorage {
+  ///
+  /// \brief Declare ParamKey according to parameter type.
+  ///
+  using DataLayout = phi::DataLayout;
+  using Dim = phi::DDim;
+  using LoD = std::vector<std::vector<size_t>>;
+  using ParamKey = std::tuple<ir::Type, Dim, DataLayout, LoD, size_t>;
+
+  DenseTensorTypeStorage(const ir::Type& dtype,
+                         const Dim& dims,
+                         const DataLayout& layout,
+                         const LoD& lod,
+                         size_t offset)
+      : dtype_(dtype),
+        dims_(dims),
+        layout_(layout),
+        lod_(lod),
+        offset_(offset) {}
+
+  ///
+  /// \brief Each derived TypeStorage must define a Construct method, which
+  /// StorageManager uses to construct a derived TypeStorage.
+  ///
+  static DenseTensorTypeStorage* Construct(const ParamKey& key) {
+    return new DenseTensorTypeStorage(std::get<0>(key),
+                                      std::get<1>(key),
+                                      std::get<2>(key),
+                                      std::get<3>(key),
+                                      std::get<4>(key));
+  }
+
+  ///
+  /// \brief Each derived TypeStorage must provide a HashValue method.
+  ///
+  static std::size_t HashValue(const ParamKey& key) {
+    std::size_t hash_value = 0;
+    // hash dtype
+    hash_value =
+        ir::hash_combine(hash_value, std::hash<ir::Type>()(std::get<0>(key)));
+    // hash dims
+    hash_value =
+        ir::hash_combine(hash_value, std::hash<Dim>()(std::get<1>(key)));
+    // hash layout
+    hash_value = ir::hash_combine(
+        hash_value,
+        std::hash<std::underlying_type<DataLayout>::type>()(
+            static_cast<std::underlying_type<DataLayout>::type>(
+                std::get<2>(key))));
+    // hash lod
+    hash_value =
+        ir::hash_combine(hash_value, std::hash<LoD>()(std::get<3>(key)));
+    // hash offset
+    hash_value =
+        ir::hash_combine(hash_value, std::hash<size_t>()(std::get<4>(key)));
+    return hash_value;
+  }
+
+  ///
+  /// \brief Each derived TypeStorage needs to overload operator==.
+  ///
+  bool operator==(const ParamKey& key) const {
+    return ParamKey(dtype_, dims_, layout_, lod_, offset_) == key;
+  }
+
+  ParamKey GetAsKey() const {
+    return ParamKey(dtype_, dims_, layout_, lod_, offset_);
+  }
+
+  ///
+  /// \brief DenseTensorTypeStorage include five parameters: dims, dtype,
+  /// layout, lod, offset.
+  ///
+  ir::Type dtype_;
+  Dim dims_;
+  DataLayout layout_;
+  LoD lod_;
+  size_t offset_;
+};
+
 struct VectorTypeStorage : public TypeStorage {
   using ParamKey = std::vector<Type>;
 
-  explicit VectorTypeStorage(const ParamKey &key) {
-    data_ = reinterpret_cast<Type *>(malloc(key.size() * sizeof(Type)));
-    memcpy(reinterpret_cast<void *>(data_),
-           reinterpret_cast<const void *>(key.data()),
+  explicit VectorTypeStorage(const ParamKey& key) {
+    data_ = reinterpret_cast<Type*>(malloc(key.size() * sizeof(Type)));
+    memcpy(reinterpret_cast<void*>(data_),
+           reinterpret_cast<const void*>(key.data()),
            key.size() * sizeof(Type));
     size_ = key.size();
   }
@@ -36,14 +143,14 @@ struct VectorTypeStorage : public TypeStorage {
   /// \brief Each derived TypeStorage must define a Construc method, which
   /// StorageManager uses to construct a derived TypeStorage.
   ///
-  static VectorTypeStorage *Construct(const ParamKey &key) {
+  static VectorTypeStorage* Construct(const ParamKey& key) {
     return new VectorTypeStorage(key);
   }
 
   ///
   /// \brief Each derived TypeStorage must provide a HashValue method.
   ///
-  static std::size_t HashValue(const ParamKey &key) {
+  static std::size_t HashValue(const ParamKey& key) {
     std::size_t hash_value = 0;
     for (size_t i = 0; i < key.size(); ++i) {
       hash_value = hash_combine(hash_value, std::hash<Type>()(key[i]));
@@ -54,7 +161,7 @@ struct VectorTypeStorage : public TypeStorage {
   ///
   /// \brief Each derived TypeStorage needs to overload operator==.
   ///
-  bool operator==(const ParamKey &key) const {
+  bool operator==(const ParamKey& key) const {
     if (key.size() != size_) {
       return false;
     }
@@ -72,7 +179,7 @@ struct VectorTypeStorage : public TypeStorage {
   /// \brief DenseTensorTypeStorage include five parameters: dims, dtype,
   /// layout, lod, offset.
   ///
-  Type *data_;
+  Type* data_;
   size_t size_;
 };
 
diff --git a/paddle/ir/dialect/shape/CMakeLists.txt b/paddle/ir/dialect/shape/CMakeLists.txt
index e0356f14345f474d879d137b421193bffa167e85..62d7c0d42c85c8a78814851fd838dd8179259e61 100644
--- a/paddle/ir/dialect/shape/CMakeLists.txt
+++ b/paddle/ir/dialect/shape/CMakeLists.txt
@@ -1,9 +1,2 @@
 file(GLOB_RECURSE SHAPE_SRCS "*.cc")
-ir_library(
-  ir_shape
-  SRCS
-  ${SHAPE_SRCS}
-  ${PADDLE_SOURCE_DIR}/paddle/fluid/ir/dialect/paddle_dialect/ir/pd_type.cc
-  DEPS
-  ddim
-  ir_core)
+ir_library(ir_shape SRCS ${SHAPE_SRCS} DEPS ir_core)
diff --git a/paddle/ir/dialect/shape/ir/shape_dialect.cc b/paddle/ir/dialect/shape/ir/shape_dialect.cc
index c2fd60d88a4783c14bd02909f5effe0ee449b340..d058924511bcd59b76d32b86a09b51deec19c09d 100644
--- a/paddle/ir/dialect/shape/ir/shape_dialect.cc
+++ b/paddle/ir/dialect/shape/ir/shape_dialect.cc
@@ -22,7 +22,9 @@ ShapeDialect::ShapeDialect(IrContext *context)
   initialize();
 }
 
-void ShapeDialect::initialize() { RegisterOps<SymbolicDim>(); }
+void ShapeDialect::initialize() {
+  RegisterOps<SymbolicDim, DimOp, TieProductEqualOp>();
+}
 
 }  // namespace dialect
 }  // namespace ir
diff --git a/paddle/ir/dialect/shape/ir/shape_op.cc b/paddle/ir/dialect/shape/ir/shape_op.cc
index 4d418403d60a34ff02ab41c82dab6bca5396632a..3681aafa36520bea1665d3b1d068853f2a44fa8e 100644
--- a/paddle/ir/dialect/shape/ir/shape_op.cc
+++ b/paddle/ir/dialect/shape/ir/shape_op.cc
@@ -14,6 +14,7 @@
 
 #include "paddle/ir/dialect/shape/ir/shape_op.h"
 #include "paddle/ir/core/builtin_attribute.h"
+#include "paddle/ir/core/builtin_type.h"
 
 namespace ir {
 namespace dialect {
@@ -132,7 +133,65 @@ bool SymbolicDim::merge(SymbolicDim other) {
   return true;
 }
 
+const char *DimOp::attributes_name[attributes_num] = {"name"};  // NOLINT
+
+void DimOp::Build(Builder &builder,
+                  OperationArgument &argument,
+                  const std::string &name) {
+  ir::Attribute attr_name =
+      ir::StrAttribute::get(ir::IrContext::Instance(), name);
+  argument.AddAttribute("name", attr_name);
+  argument.output_types.emplace_back(
+      ir::IndexType::get(ir::IrContext::Instance()));
+}
+
+const std::string DimOp::getName() {
+  return attribute<ir::StrAttribute>("name").AsString();
+}
+
+void DimOp::setName(std::string attrName) {
+  operation()->set_attribute(
+      "name", ir::StrAttribute::get(ir::IrContext::Instance(), attrName));
+}
+
+const char *TieProductEqualOp::attributes_name[attributes_num] = {
+    "lhs_len", "rhs_len"};  // NOLINT
+
+void TieProductEqualOp::Build(Builder &builder,
+                              OperationArgument &argument,
+                              int64_t lhs_len,
+                              int64_t rhs_len,
+                              const std::vector<ir::OpResult> &inputs) {
+  ir::Attribute attr_lhs_len =
+      ir::Int64Attribute::get(ir::IrContext::Instance(), lhs_len);
+  argument.AddAttribute("lhs_len", attr_lhs_len);
+  ir::Attribute attr_rhs_len =
+      ir::Int64Attribute::get(ir::IrContext::Instance(), rhs_len);
+  argument.AddAttribute("rhs_len", attr_rhs_len);
+  argument.inputs = inputs;
+}
+
+std::vector<ir::Value> TieProductEqualOp::getLhs() {
+  int64_t lhs_len = attribute<ir::Int64Attribute>("lhs_len").data();
+  std::vector<ir::Value> res;
+  for (uint32_t idx = 0; idx < lhs_len; idx++) {
+    res.push_back(operand_source(idx));
+  }
+  return res;
+}
+std::vector<ir::Value> TieProductEqualOp::getRhs() {
+  int64_t lhs_len = attribute<ir::Int64Attribute>("lhs_len").data();
+  int64_t rhs_len = attribute<ir::Int64Attribute>("rhs_len").data();
+  std::vector<ir::Value> res;
+  for (uint32_t idx = 0; idx < rhs_len; idx++) {
+    res.push_back(operand_source(lhs_len + idx));
+  }
+  return res;
+}
+
 }  // namespace dialect
 }  // namespace ir
 
 IR_DEFINE_EXPLICIT_TYPE_ID(ir::dialect::SymbolicDim)
+IR_DEFINE_EXPLICIT_TYPE_ID(ir::dialect::DimOp)
+IR_DEFINE_EXPLICIT_TYPE_ID(ir::dialect::TieProductEqualOp)
diff --git a/paddle/ir/dialect/shape/ir/shape_op.h b/paddle/ir/dialect/shape/ir/shape_op.h
index d04f0002da536a55b68c44374f712dedf262e1c7..af61393a24c9b3d22028ec256f06afb936bd5b2a 100644
--- a/paddle/ir/dialect/shape/ir/shape_op.h
+++ b/paddle/ir/dialect/shape/ir/shape_op.h
@@ -57,7 +57,45 @@ class IR_API SymbolicDim : public Op<SymbolicDim> {
   void Verify() {}
 };
 
+class IR_API DimOp : public Op<DimOp> {
+ public:
+  using Op::Op;
+  static const char *name() { return "shape.dim"; }
+
+  static constexpr uint32_t attributes_num = 1;
+  static const char *attributes_name[attributes_num];
+
+  static void Build(Builder &builder,             // NOLINT
+                    OperationArgument &argument,  // NOLINT
+                    const std::string &name);
+
+  const std::string getName();
+  void setName(std::string attrValue);
+  ir::OpResult out() { return result(0); }
+  void Verify() {}
+};
+
+class IR_API TieProductEqualOp : public Op<TieProductEqualOp> {
+ public:
+  using Op::Op;
+  static const char *name() { return "shape.tie_product_equal"; }
+
+  static constexpr uint32_t attributes_num = 2;
+  static const char *attributes_name[attributes_num];
+  // attr operand_segment_sizes
+  static void Build(Builder &builder,             // NOLINT
+                    OperationArgument &argument,  // NOLINT
+                    int64_t lhs_len,
+                    int64_t rhs_len,
+                    const std::vector<ir::OpResult> &inputs);
+  std::vector<ir::Value> getLhs();
+  std::vector<ir::Value> getRhs();
+  void Verify() {}
+};
+
 }  // namespace dialect
 }  // namespace ir
 
 IR_EXPORT_DECLARE_EXPLICIT_TYPE_ID(ir::dialect::SymbolicDim);
+IR_EXPORT_DECLARE_EXPLICIT_TYPE_ID(ir::dialect::DimOp);
+IR_EXPORT_DECLARE_EXPLICIT_TYPE_ID(ir::dialect::TieProductEqualOp);
diff --git a/paddle/ir/dialect/shape/utils/shape_utils.cc b/paddle/ir/dialect/shape/utils/shape_utils.cc
index d9676ad5a78b3b24fffa9d351c1860a41ffc75d7..182d335f71c3d4cf3f845ff92b53f78d216625c6 100644
--- a/paddle/ir/dialect/shape/utils/shape_utils.cc
+++ b/paddle/ir/dialect/shape/utils/shape_utils.cc
@@ -18,8 +18,8 @@
 namespace ir {
 
 bool compareSymbolicDimNames(const std::string& lhs, const std::string& rhs) {
-  if (lhs.size() < 1 || lhs[0] != 'S' && lhs[0] != 'C') return lhs < rhs;
-  if (rhs.size() < 1 || rhs[0] != 'S' && rhs[0] != 'C') return lhs < rhs;
+  if (lhs.size() < 1 || (lhs[0] != 'S' && lhs[0] != 'C')) return lhs < rhs;
+  if (rhs.size() < 1 || (rhs[0] != 'S' && rhs[0] != 'C')) return lhs < rhs;
   int64_t lhsIdx = 0, rhsIdx = 0;
   try {
     lhsIdx = stol(lhs.substr(1));
@@ -30,18 +30,19 @@ bool compareSymbolicDimNames(const std::string& lhs, const std::string& rhs) {
   return (lhs[0] < rhs[0]) || (lhs[0] == rhs[0] && lhsIdx < rhsIdx);
 }
 
-ir::Operation* SymbolTable::lookup(const std::string& name) const {
-  auto it = symbolTableMap_.find(name);
-  return it != symbolTableMap_.end() ? it->second : nullptr;
-}
-
 const std::string SymbolTable::insert(ir::Operation* symbol) {
   std::string name;
-  if (symbol->HasAttribute("sym_name")) {
+  if (symbol->name() == "shape.SymbolicDim") {
     name = symbol->dyn_cast<SymbolicDim>().getSymName();
+    symbolTableMap_.insert({name, symbol});
   }
-  // TODO(liujinnan): add constraint_func name branch.
-  symbolTableMap_.insert({name, symbol});
+
+  // TODO(liujinnan): add more constraint_func name branch.
+  if (symbol->name() == "shape.tie_product_equal") {
+    name = "tie_product_equal";
+    symbolFuncMap_[name].emplace_back(symbol);
+  }
+
   return name;
 }
 
diff --git a/paddle/ir/dialect/shape/utils/shape_utils.h b/paddle/ir/dialect/shape/utils/shape_utils.h
index 1f9736f7d3e8b54acb5428e14013212745897120..70f2a16c4481e8c30564983249f59210410291e4 100644
--- a/paddle/ir/dialect/shape/utils/shape_utils.h
+++ b/paddle/ir/dialect/shape/utils/shape_utils.h
@@ -15,6 +15,7 @@
 #pragma once
 
 #include <functional>
+#include <type_traits>
 #include <unordered_map>
 #include <unordered_set>
 #include "paddle/ir/core/builtin_op.h"
@@ -29,29 +30,51 @@ struct SymbolicDimProduct {
   std::vector<SymbolicDim> symbols;
   int64_t factor = 1;
   bool empty() { return factor == 1 && symbols.empty(); }
-};
-
-inline bool operator==(const SymbolicDimProduct& lhs,
-                       const SymbolicDimProduct& rhs) {
-  return lhs.factor == rhs.factor && lhs.symbols == rhs.symbols;
-}
+  friend inline bool operator==(const SymbolicDimProduct& lhs,
+                                const SymbolicDimProduct& rhs) {
+    return lhs.factor == rhs.factor && lhs.symbols == rhs.symbols;
+  }
 
-inline bool operator!=(const SymbolicDimProduct& lhs,
-                       const SymbolicDimProduct& rhs) {
-  return !(lhs == rhs);
-}
+  friend inline bool operator!=(const SymbolicDimProduct& lhs,
+                                const SymbolicDimProduct& rhs) {
+    return !(lhs == rhs);
+  }
+};
 
 class SymbolTable {
  public:
   explicit SymbolTable(ir::Operation* symbolTableOp)
       : symbolTableOp_(symbolTableOp) {}
-  ir::Operation* lookup(const std::string& name) const;
+
+  template <typename T>
+  typename std::enable_if<std::is_same<T, SymbolicDim>::value,
+                          SymbolicDim>::type
+  lookup(const std::string& name) const {
+    auto it = symbolTableMap_.find(name);
+    return it != symbolTableMap_.end() ? it->second->dyn_cast<SymbolicDim>()
+                                       : SymbolicDim(nullptr);
+  }
+  template <typename T>
+  typename std::enable_if<!std::is_same<T, SymbolicDim>::value,
+                          std::vector<T>>::type
+  lookup(const std::string& name) const {
+    std::vector<T> res;
+    auto it = symbolFuncMap_.find(name);
+    if (it != symbolFuncMap_.end()) {
+      for (auto& p : it->second) {
+        res.push_back(p->dyn_cast<T>());
+      }
+    }
+    return res;
+  }
+
   const std::string insert(Operation* symbol);
   ir::Operation* getOp() const { return symbolTableOp_; }
 
  private:
   ir::Operation* symbolTableOp_;
   std::unordered_map<std::string, ir::Operation*> symbolTableMap_;
+  std::unordered_map<std::string, std::vector<ir::Operation*>> symbolFuncMap_;
 };
 
 struct SymDimHasher {
diff --git a/test/cpp/ir/shape_dialect/symbolic_op_test.cc b/test/cpp/ir/shape_dialect/symbolic_op_test.cc
index 5dfcf19c22f34df240c309660c0ed0c5968e4449..7b0751d17ac138666947f353f6e6dbbea5b6536f 100644
--- a/test/cpp/ir/shape_dialect/symbolic_op_test.cc
+++ b/test/cpp/ir/shape_dialect/symbolic_op_test.cc
@@ -88,10 +88,9 @@ TEST(assist_struct_test, symbolic_dim_table) {
 
   ir::SymbolTable symbolTable(program.module_op());
   EXPECT_EQ(symbolTable.insert(symDim), "S0");
-  EXPECT_EQ(symbolTable.lookup("S0")->dyn_cast<ir::dialect::SymbolicDim>(),
-            symDim);
-  EXPECT_EQ(symbolTable.lookup("S1"), nullptr);
+  EXPECT_EQ(symbolTable.lookup<ir::dialect::SymbolicDim>("S0"), symDim);
   EXPECT_EQ(symbolTable.getOp(), program.module_op());
+  EXPECT_FALSE(symbolTable.lookup<ir::dialect::SymbolicDim>("S1"));
 }
 
 TEST(assist_struct_test, symbolic_dim_mgr) {
@@ -133,15 +132,63 @@ TEST(assist_struct_test, symbolic_dim_mgr) {
   EXPECT_EQ(symDimC10.getValue(), 10);
   EXPECT_EQ(symDimVec[0].getSymName(), "S2");
   EXPECT_EQ(symDimVec[1].getSymName(), "C2");
-  EXPECT_EQ(symDimMgr.symbolTable()
-                .lookup("S0")
-                ->dyn_cast<ir::dialect::SymbolicDim>(),
+  EXPECT_EQ(symDimMgr.symbolTable().lookup<ir::dialect::SymbolicDim>("S0"),
             symDimS0);
-  EXPECT_EQ(symDimMgr.symbolTable()
-                .lookup("C10")
-                ->dyn_cast<ir::dialect::SymbolicDim>(),
+  EXPECT_EQ(symDimMgr.symbolTable().lookup<ir::dialect::SymbolicDim>("C10"),
             symDimC10);
   EXPECT_EQ(symDimMgr.getRootSymbolicDim(symDimS1), symDimS0);
   EXPECT_TRUE(symDimMgr.isSymbolicDimEqual(symDimS0, symDimS1));
   EXPECT_FALSE(symDimMgr.isSymbolicDimEqual(symDimS0, symDimC10));
 }
+
+TEST(assist_struct_test, dim) {
+  ir::IrContext *ctx = ir::IrContext::Instance();
+  ir::Program program(ctx);
+  ctx->GetOrRegisterDialect<ir::dialect::ShapeDialect>();
+  ir::Builder builder = ir::Builder(ctx, program.block());
+
+  ir::dialect::DimOp dimOp = builder.Build<ir::dialect::DimOp>("S0");
+  ir::OpResult res = dimOp.out();
+  EXPECT_EQ(dimOp.getName(), "S0");
+  dimOp.setName("S1");
+  EXPECT_EQ(dimOp.getName(), "S1");
+  EXPECT_EQ(res.GetDefiningOp(), dimOp.operation());
+  EXPECT_EQ(res.type(), ir::IndexType::get(ctx));
+}
+
+TEST(assist_struct_test, tie_product_equal) {
+  ir::IrContext *ctx = ir::IrContext::Instance();
+  ir::Program program(ctx);
+  ctx->GetOrRegisterDialect<ir::dialect::ShapeDialect>();
+  ir::Builder builder = ir::Builder(ctx, program.block());
+  ir::SymbolTable symbolTable(program.module_op());
+
+  ir::OpResult dimOp0 = builder.Build<ir::dialect::DimOp>("S0").out();
+  ir::OpResult dimOp1 = builder.Build<ir::dialect::DimOp>("S1").out();
+  ir::OpResult dimOp2 = builder.Build<ir::dialect::DimOp>("S2").out();
+  ir::OpResult dimOp3 = builder.Build<ir::dialect::DimOp>("S3").out();
+  ir::OpResult dimOp4 = builder.Build<ir::dialect::DimOp>("S4").out();
+
+  ir::dialect::TieProductEqualOp tie_product_equal =
+      builder.Build<ir::dialect::TieProductEqualOp>(
+          2,
+          3,
+          std::vector<ir::OpResult>{dimOp0, dimOp1, dimOp2, dimOp3, dimOp4});
+
+  std::vector<ir::Value> lhs = tie_product_equal.getLhs();
+  std::vector<ir::Value> rhs = tie_product_equal.getRhs();
+
+  std::vector<ir::Value> lhs_ref{dimOp0, dimOp1};
+  std::vector<ir::Value> rhs_ref{dimOp2, dimOp3, dimOp4};
+
+  EXPECT_EQ(symbolTable.insert(tie_product_equal), "tie_product_equal");
+  EXPECT_EQ(
+      symbolTable.lookup<ir::dialect::TieProductEqualOp>("tie_product_equal")
+          .size(),
+      static_cast<size_t>(1));
+  EXPECT_EQ(symbolTable.lookup<ir::dialect::TieProductEqualOp>(
+                "tie_product_equal")[0],
+            tie_product_equal);
+  EXPECT_EQ(lhs, lhs_ref);
+  EXPECT_EQ(rhs, rhs_ref);
+}