erlang: erlang:send_after/3 + cancel_timer/1 + monotonic_time (T1+T2, 766/766)

Logical-clock timer wheel in the scheduler. send_after schedules a
message-delivery event at an absolute deadline (clock + Time ms);
cancel_timer marks a live timer cancelled and reports remaining ms,
or false. Time advances only when the runnable queue drains, jumping
to the earliest pending deadline (deterministic, no wall clock).

monotonic_time/0,1 exposes the logical ms clock.

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

lib/erlang/tests/send_after.sx

@@ -0,0 +1,80 @@
+;; erlang:send_after / cancel_timer — timer primitives.
+;;
+;; A process schedules a message to itself (or another pid / registered
+;; name) after N logical milliseconds. `cancel_timer` removes a pending
+;; timer and reports the time left. These are the same primitives the
+;; gen_server library uses to implement `{noreply, State, Timeout}`.
+;;
+;; The scheduler runs a synchronous logical clock (see runtime.sx
+;; `er-sched-advance-time!`): time advances only when the runnable
+;; queue drains, jumping to the earliest pending deadline. That makes
+;; delivery deterministic and time-travel-safe — no wall clock.
+
+(define er-sa-test-count 0)
+(define er-sa-test-pass 0)
+(define er-sa-test-fails (list))
+
+(define
+  er-sa-test
+  (fn
+    (name actual expected)
+    (set! er-sa-test-count (+ er-sa-test-count 1))
+    (if
+      (= actual expected)
+      (set! er-sa-test-pass (+ er-sa-test-pass 1))
+      (append!
+        er-sa-test-fails
+        {:actual actual :expected expected :name name}))))
+
+(define er-sa-pred
+  (fn (name actual) (er-sa-test name (if actual true false) true)))
+
+(define sa-ev erlang-eval-ast)
+
+;; ── T1 — schedule a self-message, receive it after the deadline ──
+;; send_after returns a reference handle.
+(er-sa-pred
+  "T1 send_after returns a ref"
+  (er-ref?
+    (sa-ev "erlang:send_after(50, self(), hello)")))
+
+;; The scheduled message lands and a plain receive picks it up.
+(er-sa-test
+  "T1 delivered message received"
+  (get
+    (sa-ev
+      "erlang:send_after(50, self(), hello),
+       receive M -> M end")
+    :name)
+  "hello")
+
+;; Logical time advances exactly to the timer deadline (50ms) by the
+;; time the message is received — round-trip latency well under 100ms.
+(er-sa-test
+  "T1 clock at deadline on receipt"
+  (sa-ev
+    "erlang:send_after(50, self(), hello),
+     receive hello -> erlang:monotonic_time() end")
+  50)
+
+;; ── T2 — cancel_timer returns remaining ms; message never arrives ──
+;; Cancel immediately after scheduling: clock has not advanced, so the
+;; full duration (~1000ms) is reported as remaining.
+(er-sa-test
+  "T2 cancel returns remaining ms"
+  (sa-ev
+    "Ref = erlang:send_after(1000, self(), late),
+     erlang:cancel_timer(Ref)")
+  1000)
+
+;; The cancelled timer never delivers — the receive falls through to
+;; its `after` clause and returns `none`.
+(er-sa-test
+  "T2 cancelled message never arrives"
+  (get
+    (sa-ev
+      "Ref = erlang:send_after(1000, self(), late),
+       erlang:cancel_timer(Ref),
+       receive late -> got after 50 -> none end")
+    :name)
+  "none")