"array",
        ["string", "null"],
        None,
    ],
)
def test_allowed_schema_type(
    type_value: Optional[Union[SchemaType, list[SchemaType]]],
) -> None:
    """Test that Schema accepts SchemaType, List[SchemaType] and None for type field."""
    schema = Schema(type=type_value)
    assert schema.type == type_value


def test_invalid_type_value() -> None:

from fastapi import FastAPI
from pydantic import BaseModel

app = FastAPI()


class Item(BaseModel):
    name: str
    description: str | None = None
    price: float
    tax: float | None = None
    tags: set[str] = set()


@app.post("/items/", response_model=Item, summary="Create an item")
async def create_item(item: Item):
    """
    Create an item with all the information:

    - **name**: each item must have a name

# Without aliases


@app.get("/optional-str")
async def read_optional_str(p: Annotated[Optional[str], Cookie()] = None):
    return {"p": p}


class CookieModelOptionalStr(BaseModel):
    p: Optional[str] = None


@app.get("/model-optional-str")
async def read_model_optional_str(p: Annotated[CookieModelOptionalStr, Cookie()]):
    return {"p": p.p}

app = FastAPI()


class Item(BaseModel):
    name: str | None = None
    description: str | None = None
    price: float | None = None
    tax: float = 10.5
    tags: list[str] = []


items = {
    "foo": {"name": "Foo", "price": 50.2},
    "bar": {"name": "Bar", "description": "The bartenders", "price": 62, "tax": 20.2},
    "baz": {"name": "Baz", "description": None, "price": 50.2, "tax": 10.5, "tags": []},
}

from typing import Union

from fastapi import FastAPI
from pydantic import BaseModel

app = FastAPI()


class Item(BaseModel):
    name: str
    description: Union[str, None] = None
    price: float
    tax: Union[float, None] = None
    tags: set[str] = set()


@app.post("/items/", response_model=Item, summary="Create an item")
async def create_item(item: Item):
    """
    Create an item with all the information:

# Without aliases


@app.get("/optional-list-str")
async def read_optional_list_str(
    p: Annotated[Optional[list[str]], Header()] = None,
):
    return {"p": p}


class HeaderModelOptionalListStr(BaseModel):
    p: Optional[list[str]] = None


@app.get("/model-optional-list-str")
async def read_model_optional_list_str(
    p: Annotated[HeaderModelOptionalListStr, Header()],
):

from fastapi import FastAPI
from pydantic import BaseModel


class Item(BaseModel):
    name: str
    description: str | None = None
    price: float
    tax: float | None = None


app = FastAPI()


@app.put("/items/{item_id}")
async def update_item(item_id: int, item: Item, q: str | None = None):
    result = {"item_id": item_id, **item.model_dump()}
    if q:
        result.update({"q": q})

from typing import Annotated

from fastapi import Body, FastAPI
from pydantic import BaseModel

app = FastAPI()


class Item(BaseModel):
    name: str
    description: str | None = None
    price: float
    tax: float | None = None


@app.put("/items/{item_id}")
async def update_item(
    *,
    item_id: int,
    item: Annotated[
        Item,
        Body(
            openapi_examples={

from typing import Union

from fastapi import Body, FastAPI
from pydantic import BaseModel

app = FastAPI()


class Item(BaseModel):
    name: str
    description: Union[str, None] = None
    price: float
    tax: Union[float, None] = None


@app.put("/items/{item_id}")
async def update_item(
    *,
    item_id: int,
    item: Item = Body(
        openapi_examples={
            "normal": {

app = FastAPI()


@app.get("/hidden_cookie")
async def hidden_cookie(
    hidden_cookie: Optional[str] = Cookie(default=None, include_in_schema=False),
):
    return {"hidden_cookie": hidden_cookie}


@app.get("/hidden_header")
async def hidden_header(
    hidden_header: Optional[str] = Header(default=None, include_in_schema=False),
):
    return {"hidden_header": hidden_header}


@app.get("/hidden_path/{hidden_path}")