docs: replace asyncio.create_task pattern with ctx.run() in all examples

example/backend/routes/chat.py

@@ -7,7 +7,8 @@
 
 Pattern:
 1. Create a ``StreamContext`` at the start of the request.
-2. Spin up a background asyncio task that calls llm_service.chat().
+2. Call ``await ctx.run(...)`` to schedule the background work with
+   automatic finish/error handling.
 3. Return ``StreamingResponse(ctx.stream(), ...)`` immediately so the
    client starts receiving SSE events as they are produced.
 
@@ -18,8 +19,6 @@
 
 from __future__ import annotations
 
-import asyncio
-
 from fastapi import APIRouter
 from fastapi.responses import StreamingResponse
 from pydantic import BaseModel
@@ -29,7 +28,6 @@
 from ..services import llm_service
 
 router = APIRouter()
-_background_tasks: set[asyncio.Task] = set()
 
 
 class ChatMessage(BaseModel):
@@ -51,19 +49,11 @@ async def chat(request: ChatRequest) -> StreamingResponse:
     """
     ctx = StreamContext()
 
-    async def _work() -> None:
-        try:
-            messages = [m.model_dump() for m in request.messages]
-            await llm_service.chat(messages, ctx=ctx)
-        except Exception as exc:
-            await ctx.write_text(f"\n\n_(Error: {exc})_")
-        finally:
-            await ctx.finish()
-
-    _task = asyncio.create_task(_work())
-    _background_tasks.add(_task)
-    _task.add_done_callback(_background_tasks.discard)
+    async def _work(c: StreamContext) -> None:
+        messages = [m.model_dump() for m in request.messages]
+        await llm_service.chat(messages, ctx=c)
 
+    await ctx.run(_work)
     return StreamingResponse(
         ctx.stream(),
         media_type="text/event-stream",

src/ai_sdk_stream_python/__init__.py

@@ -18,7 +18,6 @@
     from fastapi import FastAPI
     from fastapi.responses import StreamingResponse
     from ai_sdk_stream_python import StreamContext
-    import asyncio
 
     app = FastAPI()
 
@@ -27,14 +26,11 @@
     async def chat():
         ctx = StreamContext()
 
-        async def _work():
-            try:
-                await ctx.write_text("Hello ")
-                await ctx.write_text("world!")
-            finally:
-                await ctx.finish()
+        async def _work(c: StreamContext) -> None:
+            await c.write_text("Hello ")
+            await c.write_text("world!")
 
-        asyncio.create_task(_work())
+        await ctx.run(_work)
         return StreamingResponse(
             ctx.stream(),
             media_type="text/event-stream",

src/ai_sdk_stream_python/context.py

@@ -34,15 +34,12 @@
     async def chat(request: ChatRequest):
         ctx = StreamContext()
 
-        async def _work():
-            try:
-                await ctx.store.set("query", request.message)
-                async for chunk in my_llm.stream(request.message):
-                    await ctx.write_text(chunk)
-            finally:
-                await ctx.finish()
+        async def _work(c: StreamContext) -> None:
+            await c.store.set("query", request.message)
+            async for chunk in my_llm.stream(request.message):
+                await c.write_text(chunk)
 
-        asyncio.create_task(_work())
+        await ctx.run(_work)
         return StreamingResponse(
             ctx.stream(),
             media_type="text/event-stream",
@@ -117,8 +114,8 @@ class StreamContext(Generic[_InfoT]):
     A stateful context for producing a Vercel AI SDK v6 UIMessageStream.
 
     One ``StreamContext`` maps to one assistant message.  Create it at the
-    start of a request, spin up a background task that writes events through
-    the helpers, and pass ``ctx.stream()`` to ``StreamingResponse``.
+    start of a request, use ``ctx.run()`` to schedule the background work,
+    and pass ``ctx.stream()`` to ``StreamingResponse``.
 
     Attributes
     ----------