diff --git a/include/tvm/tir/function.h b/include/tvm/tir/function.h
index 97ee7f7211d4..25ed2f9ae8d1 100644
--- a/include/tvm/tir/function.h
+++ b/include/tvm/tir/function.h
@@ -187,6 +187,44 @@ class LinkedParam : public ObjectRef {
   TVM_DEFINE_OBJECT_REF_COW_METHOD(LinkedParamNode);
 };
 
+/*!
+ * \brief Specialize parameters of PrimFunc.
+ * \param func The PrimFunc to be specialized.
+ * \param param_map The mapping from function params to the instance.
+ * \return The new function with parameter specialized.
+ * \note We can define a Meta TIR function with symbolic shape:
+ *
+ * \code
+ *  @tvm.script.tir
+ *  def mem_copy(a: ty.handle, b: ty.handle, m: ty.int32, n: ty.int32) -> None:
+ *      A = tir.match_buffer(a, (m, n), "float32")
+ *      B = tir.match_buffer(b, (m, n), "float32")
+ *
+ *      with tir.block([m, n], "") as [vi, vj]:
+ *          B[vi, vj] = A[vi, vj]
+ * \endcode
+ *
+ * Then we can make it specialized with given shapes or buffers.
+ *
+ * \code
+ *  a, _, m, n = mem_copy.params
+ *  func = mem_copy.specialize({a: tir.decl_buffer((16, 16))})
+ *  # or
+ *  func = mem_copy.specialize({n: 16, m: 16})
+ * \endcode
+ *
+ * \code {.language-id}
+ *  @tvm.script.tir
+ *  def mem_copy_16_16(a: ty.handle, b: ty.handle) -> None:
+ *      A = tir.match_buffer(a, (16, 16), "float32")
+ *      B = tir.match_buffer(b, (16, 16), "float32")
+ *
+ *      with tir.block([16, 16], "") as [vi, vj]:
+ *          B[vi, vj] = A[vi, vj]
+ * \endcode
+ */
+PrimFunc Specialize(PrimFunc func, const Map<Var, ObjectRef>& param_map);
+
 /*!
  * \brief PrimFunc specific attribute names.
  *
diff --git a/python/tvm/tir/function.py b/python/tvm/tir/function.py
index f75e61c8859e..b1081d436150 100644
--- a/python/tvm/tir/function.py
+++ b/python/tvm/tir/function.py
@@ -89,7 +89,7 @@ def with_body(self, new_body, span=None):
         return PrimFunc(self.params, new_body, self.ret_type, self.buffer_map, self.attrs, span)
 
     def specialize(self, param_map: Mapping[Var, Union[PrimExpr, Buffer]]):
-        """Metaprogramming usage: specialize parameters of PrimFunc
+        """Specialize parameters of PrimFunc
 
         Parameters
         ----------
diff --git a/src/tir/ir/specialize.cc b/src/tir/ir/specialize.cc
index c6d21ca70760..aa5f271c20c2 100644
--- a/src/tir/ir/specialize.cc
+++ b/src/tir/ir/specialize.cc
@@ -218,6 +218,23 @@ class PrimFuncSpecializer : public StmtExprMutator {
   std::unordered_map<Buffer, Buffer, ObjectPtrHash, ObjectPtrEqual> buffer_map_;
 };
 
+/*!
+ * \brief Update Specialize var map with buffer matching.
+ * \param func The function to be specialized.
+ * \param param The given function parameter
+ * \param specific_buf The matching buffer.
+ * \param var_map The var mapping to be updated.
+ * \note This function will match target buffer's shape, strides and element_offset
+ *   For example, we define a buffer in PrimFunc:
+ *   A = tir.match_buffer(a, [m, n])
+ *
+ *   Then we match it with a buffer B =  tir.decl_buffer((8, 16))
+ *
+ *   It means we have two var mappings here: m = 8 and n = 16
+ *
+ *   If the buffer signature is not a Var, the mapping will fail.
+ *   e.g. A = tir.match_buffer(a, [m * 2, n + 1])
+ */
 void UpdateSpecializeVarMap(const PrimFunc& func, const Var& param, const Buffer& specific_buf,
                             VarMap* var_map) {
   // preliminaries
@@ -275,6 +292,13 @@ void UpdateSpecializeVarMap(const PrimFunc& func, const Var& param, const Buffer
       << " vs. " << specific_buf->offset_factor << ".";
 }
 
+/*!
+ * \brief Update Specialize var map with parameter value.
+ * \param func The function to be specialized.
+ * \param param The given function parameter
+ * \param specific_expr The parameter value.
+ * \param var_map The var mapping to be updated.
+ */
 void UpdateSpecializeVarMap(const PrimFunc& func, const Var& param, const PrimExpr& specific_expr,
                             VarMap* var_map) {
   // check param is in PrimFunc's parameters
@@ -286,26 +310,28 @@ void UpdateSpecializeVarMap(const PrimFunc& func, const Var& param, const PrimEx
   (*var_map)[param] = specific_expr;
 }
 
+/**************** Implementation ****************/
+
+PrimFunc Specialize(PrimFunc func, const Map<Var, ObjectRef>& param_map) {
+  VarMap var_map;
+  for (const auto& kv : param_map) {
+    const Var& param = kv.first;
+    const ObjectRef& instance = kv.second;
+    if (instance->IsInstance<BufferNode>()) {
+      UpdateSpecializeVarMap(func, param, Downcast<Buffer>(instance), &var_map);
+    } else if (instance->IsInstance<PrimExprNode>()) {
+      UpdateSpecializeVarMap(func, param, Downcast<PrimExpr>(instance), &var_map);
+    } else {
+      LOG(FATAL) << "TypeError: specialize expected instance to be Buffer or PrimExpr, but got "
+                 << instance->GetTypeKey();
+    }
+  }
+  return PrimFuncSpecializer::Specialize(func, std::move(var_map));
+}
+
 /**************** FFI ****************/
 
-TVM_REGISTER_GLOBAL("tir.Specialize")
-    .set_body_typed<PrimFunc(PrimFunc, Map<Var, ObjectRef>)>([](PrimFunc func,
-                                                                Map<Var, ObjectRef> param_map) {
-      VarMap var_map;
-      for (const auto& kv : param_map) {
-        const Var& param = kv.first;
-        const ObjectRef& instance = kv.second;
-        if (instance->IsInstance<BufferNode>()) {
-          UpdateSpecializeVarMap(func, param, Downcast<Buffer>(instance), &var_map);
-        } else if (instance->IsInstance<PrimExprNode>()) {
-          UpdateSpecializeVarMap(func, param, Downcast<PrimExpr>(instance), &var_map);
-        } else {
-          LOG(FATAL) << "TypeError: specialize expected instance to be Buffer or PrimExpr, but got "
-                     << instance->GetTypeKey();
-        }
-      }
-      return PrimFuncSpecializer::Specialize(std::move(func), std::move(var_map));
-    });
+TVM_REGISTER_GLOBAL("tir.Specialize").set_body_typed(Specialize);
 
 }  // namespace tir
 }  // namespace tvm
diff --git a/tests/python/unittest/test_tvmscript_meta_programming.py b/tests/python/unittest/test_tir_specialize.py
similarity index 94%
rename from tests/python/unittest/test_tvmscript_meta_programming.py
rename to tests/python/unittest/test_tir_specialize.py
index 5b304d42d785..2e9f1110732a 100644
--- a/tests/python/unittest/test_tvmscript_meta_programming.py
+++ b/tests/python/unittest/test_tir_specialize.py
@@ -150,7 +150,7 @@ def test_specialize_nothing():
     assert func.same_as(matmul)  # Pointer the same
 
 
-def test_tensor_dimension_invariant_code_matmul():
+def test_specialize_matmul():
     a, _, _, n = matmul.params
     # fully specialized
     func = matmul.specialize({a: tir.decl_buffer((128, 128))})
@@ -163,7 +163,7 @@ def test_tensor_dimension_invariant_code_matmul():
     tvm.ir.assert_structural_equal(func, matmul_m_8x)
 
 
-def test_tensor_dimension_invariant_code_elemwise():
+def test_specialize_elemwise():
     a, c = element_wise.params
     C = element_wise.buffer_map[c]
     # fully specialized
@@ -174,7 +174,7 @@ def test_tensor_dimension_invariant_code_elemwise():
     tvm.ir.assert_structural_equal(func, element_wise_128_n)
 
 
-def test_tensor_dimension_invariant_code_mem_copy():
+def test_specialize_mem_copy():
     a, _, m, n, p, q = mem_copy.params
     # fully specialized
     func = mem_copy.specialize({a: tir.decl_buffer((16, 16), strides=[8, 1], elem_offset=4)})
@@ -186,8 +186,14 @@ def test_tensor_dimension_invariant_code_mem_copy():
     tvm.ir.assert_structural_equal(func, mem_copy_m_n_p_n)
 
 
+def test_specialize_recursive_load():
+    # TODO(Siyuan): add recursive Load testcase, e.g. A[C[i]]
+    pass
+
+
 if __name__ == "__main__":
     test_specialize_nothing()
-    test_tensor_dimension_invariant_code_matmul()
-    test_tensor_dimension_invariant_code_elemwise()
-    test_tensor_dimension_invariant_code_mem_copy()
+    test_specialize_matmul()
+    test_specialize_elemwise()
+    test_specialize_mem_copy()
+    test_specialize_recursive_load()