docs: fix expression index's document again

sql-statements/sql-statement-create-index.md

@@ -106,28 +106,28 @@ Query OK, 0 rows affected (0.31 sec)
 
 In some scenarios, the filtering condition of a query is based on a certain expression. In these scenarios, the query performance is relatively poor because ordinary indexes cannot take effect, the query can only be executed by scanning the entire table. The expression index is a type of special index that can be created on an expression. Once an expression index is created, TiDB can use the index for the expression-based query, which significantly improves the query performance.
 
-For example, if you want to create an index based on `col1+cols2`, execute the following SQL statement:
+For example, if you want to create an index based on `lower(col1)`, execute the following SQL statement:
 
 {{< copyable "sql" >}}
 
 ```sql
-CREATE INDEX idx1 ON t1 ((col1 + col2));
+CREATE INDEX idx1 ON t1 (lower(col1));
 ```
 
 Or you can execute the following equivalent statement:
 
 {{< copyable "sql" >}}
 
 ```sql
-ALTER TABLE t1 ADD INDEX idx1((col1 + col2));
+ALTER TABLE t1 ADD INDEX idx1(lower(col1));
 ```
 
 You can also specify the expression index when you create the table:
 
 {{< copyable "sql" >}}
 
 ```sql
-CREATE TABLE t1(col1 char(10), col2 char(10), key index((col1 + col2)));
+CREATE TABLE t1(col1 char(10), col2 char(10), key index(lower(col1)));
 ```
 
 You can drop an expression index in the same way as dropping an ordinary index:
@@ -139,6 +139,28 @@ DROP INDEX idx1 ON t1;
 ```
 
 > **Note:**
+> 
+> Expression index involves various kinds of expressions. To ensure correctness, only some fully tested functions are allowed for creating an expression index. This means that only these functions are allowed in expressions in a production environment. You can get these functions by querying `tidb_allow_function_for_expression_index` variable. In future versions, more functions might be added to the list.
+> 
+> {{< copyable "sql" >}}
+>
+> ```sql
+> mysql> select @@tidb_allow_function_for_expression_index;
+> +--------------------------------------------+
+> | @@tidb_allow_function_for_expression_index |
+> +--------------------------------------------+
+> | lower, md5, reverse, upper, vitess_hash    |
+> +--------------------------------------------+
+> 1 row in set (0.00 sec)
+> ```
+> 
+> For the functions that are not included in the returned result above, those functions are not fully tested and not recommended for a production environment, which can be seen as experimental. Other expressions such as operators, `cast`, and `case when` are also seen as experimental and not recommended for production. However, if you still want to use those expressions, you can make the following configuration in the [TiDB configuration file](/tidb-configuration-file.md#allow-expression-index-new-in-v400):
+> 
+> {{< copyable "sql" >}}
+> 
+> ```sql
+> allow-expression-index = true
+> ```
 >
 > An expression index cannot be created on a primary key.
 >

system-variables.md

@@ -253,6 +253,11 @@ mysql> SELECT * FROM t1;
 - Default value: ""
 - This variable is used to specify a list of storage engines that might fall back to TiKV. If the execution of a SQL statement fails due to a failure of the specified storage engine in the list, TiDB retries executing this SQL statement with TiKV. This variable can be set to "" or "tiflash". When this variable is set to "tiflash", if the execution of a SQL statement fails due to a failure of TiFlash, TiDB retries executing this SQL statement with TiKV.
 
+### tidb_allow_function_for_expression_index <span class="version-mark">New in v5.2.0</span>
+
+- Scope: NONE
+- This variable is used to show the functions that are allowed to be used for creating expression indexes.
+
 ### tidb_allow_mpp <span class="version-mark">New in v5.0</span>
 
 - Scope: SESSION | GLOBAL

tidb-configuration-file.md

@@ -642,3 +642,12 @@ For pessimistic transaction usage, refer to [TiDB Pessimistic Transaction Mode](
 
 + Controls whether the [`INFORMATION_SCHEMA.DEADLOCKS`](/information-schema/information-schema-deadlocks.md) table collects the information of retryable deadlock errors. For the description of retryable deadlock errors, see [Retryable deadlock errors](/information-schema/information-schema-deadlocks.md#retryable-deadlock-errors).
 + Default value: `false`
+
+## experimental
+
+The `experimental` section, introduced in v3.1.0, describes the configurations related to the experimental features of TiDB.
+
+### `allow-expression-index` <span class="version-mark">New in v4.0.0</span>
+
++ Controls whether an expression index can be created. Since TiDB v5.2.0, if the function in an expression is safe, you can create an expression index directly based on this function without enabling this configuration. If you want to create an expression index based on other functions, you can enable this configuration, but correctness issues might exist. By querying the `tidb_allow_function_for_expression_index` variable, you can get the functions that are safe to be directly used for creating an expression.
++ Default value: `false`