erlang: send_after to registered name + gen_server timeout returns (T5+T6, 771/771)

T5 — send_after addresses a registered atom name; the delayed message
lands in that process's mailbox (destination resolved at fire time,
dead/unregistered targets drop silently).

T6 — gen_server loop now handles the {reply,R,S,T} / {noreply,S,T}
timeout-bearing callback returns by scheduling {timeout} to itself via
send_after; handle_info({timeout}, S) fires when no other message
arrives first. Sanity-checks the library hookup.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

lib/erlang/runtime.sx

@@ -1265,8 +1265,15 @@
            {reply, Reply, NewState} ->
              From ! {Ref, Reply},
              gen_server:loop(Mod, NewState);
+           {reply, Reply, NewState, Timeout} ->
+             From ! {Ref, Reply},
+             erlang:send_after(Timeout, self(), {timeout}),
+             gen_server:loop(Mod, NewState);
            {noreply, NewState} ->
              gen_server:loop(Mod, NewState);
+           {noreply, NewState, Timeout} ->
+             erlang:send_after(Timeout, self(), {timeout}),
+             gen_server:loop(Mod, NewState);
            {stop, Reason, Reply, NewState} ->
              From ! {Ref, Reply},
              exit(Reason)
@@ -1274,11 +1281,17 @@
        {'$gen_cast', Msg} ->
          case Mod:handle_cast(Msg, State) of
            {noreply, NewState} -> gen_server:loop(Mod, NewState);
+           {noreply, NewState, Timeout} ->
+             erlang:send_after(Timeout, self(), {timeout}),
+             gen_server:loop(Mod, NewState);
            {stop, Reason, NewState} -> exit(Reason)
          end;
        Other ->
          case Mod:handle_info(Other, State) of
            {noreply, NewState} -> gen_server:loop(Mod, NewState);
+           {noreply, NewState, Timeout} ->
+             erlang:send_after(Timeout, self(), {timeout}),
+             gen_server:loop(Mod, NewState);
            {stop, Reason, NewState} -> exit(Reason)
          end
      end.")

lib/erlang/scoreboard.json

@@ -1,7 +1,7 @@
 {
   "language": "erlang",
-  "total_pass": 769,
-  "total": 769,
+  "total_pass": 771,
+  "total": 771,
   "suites": [
     {"name":"tokenize","pass":62,"total":62,"status":"ok"},
     {"name":"parse","pass":52,"total":52,"status":"ok"},
@@ -14,6 +14,6 @@
     {"name":"fib","pass":8,"total":8,"status":"ok"},
     {"name":"ffi","pass":37,"total":37,"status":"ok"},
     {"name":"vm","pass":78,"total":78,"status":"ok"},
-    {"name":"send_after","pass":8,"total":8,"status":"ok"}
+    {"name":"send_after","pass":10,"total":10,"status":"ok"}
   ]
 }

lib/erlang/scoreboard.md

@@ -1,6 +1,6 @@
 # Erlang-on-SX Scoreboard
 
-**Total: 769 / 769 tests passing**
+**Total: 771 / 771 tests passing**
 
 |  | Suite | Pass | Total |
 |---|---|---|---|
@@ -15,7 +15,7 @@
 | ✅ | fib | 8 | 8 |
 | ✅ | ffi | 37 | 37 |
 | ✅ | vm | 78 | 78 |
-| ✅ | send_after | 8 | 8 |
+| ✅ | send_after | 10 | 10 |
 
 
 Generated by `lib/erlang/conformance.sh`.

lib/erlang/tests/send_after.sx

@@ -118,3 +118,46 @@
        erlang:cancel_timer(Ref)")
     :name)
   "false")
+
+;; ── T5 — send_after to a registered atom name ──────────────────────
+;; A second process registers itself as `srv`; the timer addresses it
+;; by name, and the delayed message lands in that process's mailbox.
+;; The server forwards what it got back to the parent for inspection.
+(er-sa-test
+  "T5 timer delivers to registered name"
+  (get
+    (sa-ev
+      "Me = self(),
+       Pid = spawn(fun () -> receive M -> Me ! {got, M} end end),
+       register(srv, Pid),
+       erlang:send_after(20, srv, ping),
+       receive {got, X} -> X end")
+    :name)
+  "ping")
+
+;; ── T6 — gen_server {noreply, State, Timeout} hookup ───────────────
+;; A gen_server that, on the `arm` cast, returns {noreply, S, 100}.
+;; The library schedules {timeout} to itself via send_after; when no
+;; other message arrives first, handle_info({timeout}, S) fires. The
+;; handler signals the parent so we can confirm the timeout landed.
+(do
+  (er-load-gen-server!)
+  (erlang-load-module
+    "-module(sa_tmo).
+     init(Me) -> {ok, Me}.
+     handle_call(_R, _F, S) -> {reply, ok, S}.
+     handle_cast(arm, Me) -> {noreply, Me, 100}.
+     handle_info({timeout}, Me) -> Me ! fired, {noreply, Me};
+     handle_info(_M, S) -> {noreply, S}.")
+  nil)
+
+(er-sa-test
+  "T6 gen_server timeout fires handle_info"
+  (get
+    (sa-ev
+      "Me = self(),
+       P = gen_server:start_link(sa_tmo, Me),
+       gen_server:cast(P, arm),
+       receive fired -> ok after 5000 -> timeout end")
+    :name)
+  "ok")