📝 document async library facade composition apis

docs/api/library-async-logger-child.md

@@ -0,0 +1,82 @@
+---
+name: library-async-logger-child
+group: api
+category: facade
+update-time: 20260613
+description: Derive a child LibraryAsyncLogger facade by composing the current target with a child segment.
+key-word:
+    - async
+    - library
+    - child
+    - public
+---
+
+## Library-async-logger-child
+
+Create a child `LibraryAsyncLogger[S]` by composing the current target with another target segment. This is the library-facing hierarchical naming helper for async targets such as `sdk.cache` or `plugin.worker.io`.
+
+### Interface
+
+```moonbit
+pub fn[S] LibraryAsyncLogger::child(
+  self : LibraryAsyncLogger[S],
+  target : String,
+) -> LibraryAsyncLogger[S] {
+```
+
+#### input
+
+- `self : LibraryAsyncLogger[S]` - Parent facade whose target should be extended.
+- `target : String` - Child target segment or suffix.
+
+#### output
+
+- `LibraryAsyncLogger[S]` - New library-facing async facade whose target is the composed child path.
+
+### Explanation
+
+Detailed rules explaining key parameters and behaviors
+
+- This API delegates to the wrapped async logger's `child(...)` behavior and then re-wraps the result.
+- If the parent target is empty, the child target becomes the full target.
+- If the child target is empty, the parent target is preserved.
+- If both are non-empty, they are joined with `.`.
+
+### How to Use
+
+Here are some specific examples provided.
+
+#### When Need Hierarchical Async Naming In A Library API
+
+When a package wants stable namespace composition without exposing `AsyncLogger[S]`:
+```moonbit
+let worker = LibraryAsyncLogger::new(@bitlogger.console_sink())
+  .with_target("plugin")
+  .child("worker")
+```
+
+In this example, the final target becomes `plugin.worker`.
+
+#### When Build Scoped Async Facades Step By Step
+
+When deeper target composition should stay readable:
+```moonbit
+let client = LibraryAsyncLogger::new(@bitlogger.console_sink(), target="sdk")
+  .child("http")
+  .child("client")
+```
+
+In this example, the final facade emits under `sdk.http.client`.
+
+### Error Case
+
+e.g.:
+- If `target` is empty, the returned facade keeps the original parent target.
+
+- If callers need complete replacement instead of composition, `with_target(...)` should be used instead.
+
+### Notes
+
+1. This is the preferred library-facing API for hierarchical async target naming.
+
+2. Composition changes the target only and does not rebuild the queue or sink.