*
     * @return an {@link Optional} containing the output stream, or empty if not applicable
     */
    @Nonnull
    Optional<OutputStream> out();

    /**
     * Returns the error stream for the Maven execution, if running in embedded mode.
     *
     * @return an {@link Optional} containing the error stream, or empty if not applicable
     */
    @Nonnull
    Optional<OutputStream> err();

    /**

  // +optional
  optional UserSubject user = 2;

  // `group` matches based on user group name.
  // +optional
  optional GroupSubject group = 3;

  // `serviceAccount` matches ServiceAccounts.
  // +optional
  optional ServiceAccountSubject serviceAccount = 4;
}

// UserSubject holds detailed information for user-kind subject.
message UserSubject {

  // +optional
  optional UserSubject user = 2;

  // `group` matches based on user group name.
  // +optional
  optional GroupSubject group = 3;

  // `serviceAccount` matches ServiceAccounts.
  // +optional
  optional ServiceAccountSubject serviceAccount = 4;
}

// UserSubject holds detailed information for user-kind subject.
message UserSubject {

			Key:         apiRequestsMax,
			Description: `set the maximum number of concurrent requests (default: auto)`,
			Optional:    true,
			Type:        "number",
		},
		config.HelpKV{
			Key:         apiClusterDeadline,
			Description: `set the deadline for cluster readiness check` + defaultHelpPostfix(apiClusterDeadline),
			Optional:    true,
			Type:        "duration",
		},
		config.HelpKV{
			Key:         apiCorsAllowOrigin,

   *
   * <p><b>Java 9 users:</b> use {@code optional.stream()} instead.
   */
  @Beta
  @InlineMe(replacement = "optional.stream()")
  @InlineMeValidationDisabled("Java 9+ API only")
  public static <T> Stream<T> stream(java.util.Optional<T> optional) {
    return optional.isPresent() ? Stream.of(optional.get()) : Stream.empty();
  }

  /**
   * If a value is present in {@code optional}, returns a stream containing only that element,

        // v1 == 0.
        .optional(defaultValue = 0),
      Adapters.INTEGER_AS_BIG_INTEGER,
      algorithmIdentifier,
      name,
      validity,
      name,
      subjectPublicKeyInfo,
      Adapters.BIT_STRING.withTag(tag = 1L).optional(),
      Adapters.BIT_STRING.withTag(tag = 2L).optional(),
      extension.asSequenceOf().withExplicitBox(tag = 3).optional(defaultValue = listOf()),
      decompose = {

  // name is allowed to be "" to represent the legacy, ungroupified resources.
  // More info: https://git.k8s.io/community/contributors/devel/sig-architecture/api-conventions.md#metadata
  // +optional
  optional k8s.io.apimachinery.pkg.apis.meta.v1.ObjectMeta metadata = 1;

  // versions are the versions supported in this group. They are sorted in descending order of preference,
  // with the preferred version being the first entry.

  // +optional
  optional k8s.io.apimachinery.pkg.apis.meta.v1.ObjectMeta metadata = 1;

  // provisioner indicates the type of the provisioner.
  optional string provisioner = 2;

  // parameters holds the parameters for the provisioner that should
  // create volumes of this storage class.
  // +optional
  map<string, string> parameters = 3;

            throw new LookupException(e);
        }
    }

    @Override
    public <T> Optional<T> lookupOptional(Class<T> type) {
        try {
            return Optional.of(container.lookup(type));
        } catch (ComponentLookupException e) {
            if (e.getCause() instanceof NoSuchElementException) {
                return Optional.empty();
            }
            throw new LookupException(e);
        }
    }

from typing import Optional

from fastapi import FastAPI
from fastapi.testclient import TestClient
from pydantic import BaseModel

app = FastAPI()


class SubModel(BaseModel):
    a: Optional[str] = "foo"


class Model(BaseModel):
    x: Optional[int] = None
    sub: SubModel


class ModelSubclass(Model):
    y: int
    z: int = 0
    w: Optional[int] = None


class ModelDefaults(BaseModel):