また、数値のバリデーションを宣言することもできます:

* `gt`: より大きい（`g`reater `t`han）
* `ge`: 以上（`g`reater than or `e`qual）
* `lt`: より小さい（`l`ess `t`han）
* `le`: 以下（`l`ess than or `e`qual）

!!! info "情報"
    `Query`、`Path`などは後に共通の`Param`クラスのサブクラスを見ることになります。（使う必要はありません）

    そして、それらすべては、これまで見てきた追加のバリデーションとメタデータと同じパラメータを共有しています。

!!! note "技術詳細"

    Because of that, versions of FastAPI previous to 0.99.0 still used versions of OpenAPI lower than 3.1.0.

### Pydantic and FastAPI `examples`

When you add `examples` inside a Pydantic model, using `schema_extra` or `Field(examples=["something"])` that example is added to the **JSON Schema** for that Pydantic model.

You send it a token and it returns an authenticated user.

This provider might be charging you per request, and calling it might take some extra time than if you had a fixed mock user for tests.

You probably want to test the external provider once, but not necessarily call it for every test that runs.

Vas con la persona que te gusta 😍 por comida rápida paralela 🍔.

Haces la cola mientras varios cajeros (digamos 8) que a la vez son cocineros 👨‍🍳👨‍🍳👨‍🍳👨‍🍳👨‍🍳👨‍🍳👨‍🍳👨‍🍳 toman los pedidos de las personas que están delante de ti.

You can define those cases using a list in the type declaration.

You will receive all the values from the duplicate header as a Python `list`.

For example, to declare a header of `X-Token` that can appear more than once, you can write:

=== "Python 3.10+"

    ```Python hl_lines="9"
    {!> ../../../docs_src/header_params/tutorial003_an_py310.py!}
    ```

=== "Python 3.9+"

    ```Python hl_lines="9"

```Python hl_lines="8"
{!../../../docs_src/events/tutorial001.py!}
```

In this case, the `startup` event handler function will initialize the items "database" (just a `dict`) with some values.

You can add more than one event handler function.

And your application won't start receiving requests until all the `startup` event handlers have completed.

### `shutdown` event

# Separate OpenAPI Schemas for Input and Output or Not

When using **Pydantic v2**, the generated OpenAPI is a bit more exact and **correct** than before. 😎

In fact, in some cases, it will even have **two JSON Schemas** in OpenAPI for the same Pydantic model, for input and output, depending on if they have **default values**.

Let's see how that works and how to change it if you need to do that.

## Pydantic Models for Input and Output

    ```Python hl_lines="19"
    {!> ../../../docs_src/dependencies/tutorial004.py!}
    ```

...and **FastAPI** will know what to do.

!!! tip
    If that seems more confusing than helpful, disregard it, you don't *need* it.

# SQL (Relational) Databases

!!! info
    These docs are about to be updated. 🎉

    The current version assumes Pydantic v1, and SQLAlchemy versions less than 2.0.

    The new docs will include Pydantic v2 and will use <a href="https://sqlmodel.tiangolo.com/" class="external-link" target="_blank">SQLModel</a> (which is also based on SQLAlchemy) once it is updated to use Pydantic v2 as well.

**FastAPI** doesn't require you to use a SQL (relational) database.