diff --git a/paddle/cinn/adt/arithmetic.h b/paddle/cinn/adt/arithmetic.h
index 5bebcfba657376..904b5c63358164 100644
--- a/paddle/cinn/adt/arithmetic.h
+++ b/paddle/cinn/adt/arithmetic.h
@@ -19,8 +19,6 @@
 namespace cinn::adt {
 
 DEFINE_ADT_UNARY(Negative);
-template <typename T>
-using Neg = Negative<T>;
 DEFINE_ADT_UNARY(Reciprocal);
 DEFINE_ADT_BINARY(Add);
 DEFINE_ADT_BINARY(Sub);
@@ -28,7 +26,7 @@ DEFINE_ADT_BINARY(Mul);
 DEFINE_ADT_BINARY(Div);
 DEFINE_ADT_BINARY(Mod);
 
-// Arithmetic T = Neg T
+// Arithmetic T = Negative T
 //              | Add T T
 //              | Sub T T
 //              | Mul T T
@@ -36,7 +34,7 @@ DEFINE_ADT_BINARY(Mod);
 //              | Mod T T
 template <typename ValueT>
 DEFINE_ADT_UNION(Arithmetic,
-                 Neg<ValueT>,
+                 Negative<ValueT>,
                  Add<ValueT, ValueT>,
                  Sub<ValueT, ValueT>,
                  Mul<ValueT, ValueT>,
diff --git a/paddle/cinn/adt/ast.h b/paddle/cinn/adt/ast.h
new file mode 100644
index 00000000000000..5423964773830f
--- /dev/null
+++ b/paddle/cinn/adt/ast.h
@@ -0,0 +1,22 @@
+#pragma once
+
+#include <optional>
+#include "paddle/cinn/adt/adt.h"
+#include "paddle/cinn/adt/arithmetic.h"
+
+namespace cinn::adt {
+
+template<typename VarT, typename ValueT, typename BodyT>
+struct Let final {
+  List<std::pair<VarT, ValueT>> var2value;
+  BodyT body;
+};
+
+template<typename ConditionT, typename TrueValueT, typename FalseValueT>
+struct If final {
+  ConditionT condition;
+  TrueValueT true_value;
+  std::optional<FalseValueT> false_value;
+};
+
+}
diff --git a/paddle/cinn/adt/map_expr.h b/paddle/cinn/adt/map_expr.h
index de7ebe39acbdb6..37a4c091e3b207 100644
--- a/paddle/cinn/adt/map_expr.h
+++ b/paddle/cinn/adt/map_expr.h
@@ -19,6 +19,7 @@
 #include "paddle/cinn/adt/adapter_dynamic_tensor.h"
 #include "paddle/cinn/adt/adapter_tensor.h"
 #include "paddle/cinn/adt/adt.h"
+#include "paddle/cinn/adt/ast.h"
 #include "paddle/cinn/adt/arithmetic.h"
 #include "paddle/cinn/adt/equation_value.h"
 #include "paddle/cinn/adt/logical.h"
@@ -181,29 +182,42 @@ class AnchoredMapStmt final : public Tuple<MapStmt<Stmt>,
   }
 };
 
-DEFINE_ADT_UNION(GenericDim, SymbolicDim, std::int64_t);
-using KernelCondition = Logical<Tree<Arithmetic, GenericDim>>;
+using CppVar = tVar<UniqueId>;
 
-template <typename T>
-class ConditionalAnchoredMapStmt
-    : public Tuple<List<KernelCondition>, tTrue<T>, tFalse<T>> {
- public:
-  using Tuple<List<KernelCondition>, tTrue<T>, tFalse<T>>::Tuple;
-};
-
-using KernelBody = Tree<ConditionalAnchoredMapStmt, AnchoredMapStmt>;
 
-// Kernel = (KernelBody, In [Tensor], Out [Tensor])
+// Kernel = (AnchoredMapStmt, In [Tensor], Out [Tensor], [SymbolicDim])
 class Kernel final : public Tuple<List<AnchoredMapStmt>,
                                   tIn<List<Tensor>>,
-                                  tOut<List<Tensor>>> {
+                                  tOut<List<Tensor>>,
+                                  List<std::pair<CppVar, DimExpr>>> {
  public:
-  using Tuple<List<AnchoredMapStmt>, tIn<List<Tensor>>, tOut<List<Tensor>>>::
+  using Tuple<List<AnchoredMapStmt>, tIn<List<Tensor>>, tOut<List<Tensor>>, List<SymbolicDim>>::
       Tuple;
 };
 
-// MapExpr = Kernel;
-using MapExpr = Kernel;
+template <typename T>
+struct ConditionalEntries {
+  List<If<Logical<DimExpr>, T, T>> conditional_entries;
+};
+
+struct ShapeInferExpr final {
+  List<List<DimExpr>> output_shape_expr;
+  ConditionalEntries<DimExpr> temp_storage_expr;
+};
+
+struct GetTensorShapeDim final {
+  Tensor tensor;
+  std::int64_t aixs;
+  DimExpr symbolic_dim_expr;
+};
+
+template <typename T>
+using WithRuntimeTensorShapeDim = Let<CppVar, GetTensorShapeDim, T>;
+
+struct MapExpr final {
+  WithRuntimeTensorShapeDim<ShapeInferExpr> shape_infer_expr;
+  WithRuntimeTensorShapeDim<ConditionalEntries<Kernel>> host_kernel_expr;
+};
 
 }  // namespace adt
 }  // namespace cinn
diff --git a/paddle/cinn/adt/tags.h b/paddle/cinn/adt/tags.h
index 641d7cad316b2d..a6b707075ea392 100644
--- a/paddle/cinn/adt/tags.h
+++ b/paddle/cinn/adt/tags.h
@@ -39,4 +39,6 @@ DEFINE_ADT_TAG(tHasNoConflictValue);
 DEFINE_ADT_TAG(tReduceInit);
 DEFINE_ADT_TAG(tReduceAcc);
 
+DEFINE_ADT_TAG(tVar);
+
 }  // namespace cinn::adt