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/runtime.sx

@@ -135,6 +135,56 @@
         (dict-set! s :next-ref (+ n 1))
         (er-mk-ref n)))))
 
+;; ── logical clock + timer wheel ──────────────────────────────────
+;; The scheduler runs a synchronous model: logical time advances only
+;; when the runnable queue drains (see `er-sched-advance-time!`). The
+;; clock is in milliseconds, monotonic, never derived from wall time
+;; — deterministic and time-travel-safe. `send_after` schedules a
+;; message-delivery event at an absolute deadline; `receive after Ms`
+;; schedules a timeout event the same way. When no process is runnable
+;; the scheduler jumps the clock to the earliest pending deadline and
+;; fires that single event, then re-runs.
+(define er-clock (fn () (get (er-sched) :clock)))
+
+;; Advance the clock to `ms`, but never backwards (monotonicity).
+(define
+  er-clock-set!
+  (fn (ms) (dict-set! (er-sched) :clock (max (er-clock) ms))))
+
+(define er-sched-timers (fn () (get (er-sched) :timers)))
+
+;; Register a timer event. `dest` is a pid or registered-atom value,
+;; resolved to a live process at fire time. Returns the timer ref.
+(define
+  er-timer-add!
+  (fn
+    (deadline dest msg ref)
+    (append!
+      (er-sched-timers)
+      {:ref ref :deadline deadline :dest dest :msg msg :alive true})
+    ref))
+
+;; Find the live timer with the given ref, or nil.
+(define
+  er-timer-find-alive
+  (fn
+    (ref)
+    (let
+      ((ts (er-sched-timers)) (found (list nil)))
+      (for-each
+        (fn
+          (i)
+          (let
+            ((t (nth ts i)))
+            (when
+              (and
+                (= (nth found 0) nil)
+                (get t :alive)
+                (er-ref-equal? (get t :ref) ref))
+              (set-nth! found 0 t))))
+        (range 0 (len ts)))
+      (nth found 0))))
+
 ;; ── scheduler state ──────────────────────────────────────────────
 (define er-scheduler (list nil))
 
@@ -151,6 +201,8 @@
         :processes {}
         :registered {}
         :ets {}
+        :clock 0
+        :timers (list)
         :runnable (er-q-new)})))
 
 (define er-sched (fn () (nth er-scheduler 0)))
@@ -217,6 +269,7 @@
             :trap-exit false
             :has-timeout false
             :timed-out false
+            :timeout-deadline nil
             :exit-reason nil}))
         (dict-set! (er-sched-processes) (er-pid-key pid) proc)
         (er-sched-enqueue! pid)
@@ -456,6 +509,69 @@
       (error "Erlang: make_ref/0: arity")
       (er-ref-new!))))
 
+;; ── timer BIFs ───────────────────────────────────────────────────
+;; erlang:send_after(Time, Dest, Msg) -> Ref
+;;   Schedules Msg to be delivered to Dest after Time ms (logical).
+;;   Time must be a non-negative integer; Dest a pid or registered
+;;   atom name. Returns a fresh timer reference.
+(define
+  er-bif-send-after
+  (fn
+    (vs)
+    (let
+      ((time (nth vs 0)) (dest (nth vs 1)) (msg (nth vs 2)))
+      (cond
+        (not (and (= (type-of time) "number") (>= time 0)))
+        (raise (er-mk-error-marker (er-mk-atom "badarg")))
+        (not (or (er-pid? dest) (er-atom? dest)))
+        (raise (er-mk-error-marker (er-mk-atom "badarg")))
+        :else
+        (er-timer-add!
+          (+ (er-clock) (truncate time))
+          dest
+          msg
+          (er-ref-new!))))))
+
+;; erlang:cancel_timer(Ref) -> RemainingMs | false
+;;   For a live (not-yet-fired) timer, marks it cancelled and returns
+;;   the milliseconds left until its deadline. For an already-fired,
+;;   already-cancelled, or unknown ref, returns the atom `false`.
+(define
+  er-bif-cancel-timer
+  (fn
+    (vs)
+    (let
+      ((ref (nth vs 0)))
+      (cond
+        (not (er-ref? ref))
+        (raise (er-mk-error-marker (er-mk-atom "badarg")))
+        :else
+        (let
+          ((t (er-timer-find-alive ref)))
+          (cond
+            (= t nil) (er-mk-atom "false")
+            :else (do
+              (dict-set! t :alive false)
+              (max 0 (- (get t :deadline) (er-clock))))))))))
+
+;; erlang:monotonic_time() | erlang:monotonic_time(Unit) -> Integer
+;;   Returns the scheduler's logical monotonic clock in milliseconds.
+;;   Unit (millisecond / second / native) is accepted for API
+;;   compatibility; all units report from the same ms-resolution clock.
+(define
+  er-bif-monotonic-time
+  (fn
+    (vs)
+    (cond
+      (= (len vs) 0) (er-clock)
+      (and (= (len vs) 1) (er-atom? (nth vs 0)))
+      (let
+        ((unit (get (nth vs 0) :name)))
+        (cond
+          (= unit "second") (truncate (/ (er-clock) 1000))
+          :else (er-clock)))
+      :else (raise (er-mk-error-marker (er-mk-atom "badarg"))))))
+
 ;; Add `target` to `pid`'s :links list if not already there.
 (define
   er-link-add-one!
@@ -664,37 +780,122 @@
       (cond
         (not (= pid nil))
         (do (er-sched-step! pid) (er-sched-run-all!))
-        ;; Queue empty — fire one pending receive-with-timeout and go again.
-        (er-sched-fire-one-timeout!) (er-sched-run-all!)
+        ;; Queue empty — advance logical time to the next pending
+        ;; deadline (timer delivery or receive-timeout) and go again.
+        (er-sched-advance-time!) (er-sched-run-all!)
         :else nil))))
 
-;; Wake one waiting process whose receive had an `after Ms` clause.
-;; Returns true if one fired. In our synchronous model "time passes"
-;; once the runnable queue drains — timeouts only fire then.
+;; ── time advance ─────────────────────────────────────────────────
+;; Called when the runnable queue is empty. Two kinds of pending event
+;; carry a deadline: live `send_after` timers and waiting processes in
+;; a `receive ... after Ms` block. Find the single earliest deadline
+;; across both, jump the clock to it, and fire just that one event
+;; (timer wins ties — a message delivered exactly at the timeout
+;; arrives "first"). Returns true if an event fired, false when there
+;; is nothing left to wake (genuine idle / termination).
 (define
-  er-sched-fire-one-timeout!
+  er-sched-advance-time!
   (fn
     ()
     (let
-      ((ks (keys (er-sched-processes))) (fired (list false)))
+      ((best (er-sched-next-event)))
+      (cond
+        (= best nil) false
+        :else (do
+          (er-clock-set! (get best :deadline))
+          (cond
+            (= (get best :kind) "timer")
+            (er-timer-fire! (get best :timer))
+            :else (er-recv-timeout-fire! (get best :proc)))
+          true)))))
+
+;; Scan timers and waiting-with-timeout processes for the earliest
+;; deadline. Returns {:kind "timer"|"recv" :deadline D ...} or nil.
+(define
+  er-sched-next-event
+  (fn
+    ()
+    (let
+      ((best (list nil)))
+      (for-each
+        (fn
+          (i)
+          (let
+            ((t (nth (er-sched-timers) i)))
+            (when
+              (get t :alive)
+              (er-event-consider!
+                best
+                {:kind "timer" :deadline (get t :deadline) :timer t}))))
+        (range 0 (len (er-sched-timers))))
       (for-each
         (fn
           (k)
-          (when
-            (not (nth fired 0))
-            (let
-              ((p (get (er-sched-processes) k)))
-              (when
-                (and
-                  (= (get p :state) "waiting")
-                  (get p :has-timeout))
-                (dict-set! p :timed-out true)
-                (dict-set! p :has-timeout false)
-                (dict-set! p :state "runnable")
-                (er-sched-enqueue! (get p :pid))
-                (set-nth! fired 0 true)))))
-        ks)
-      (nth fired 0))))
+          (let
+            ((p (get (er-sched-processes) k)))
+            (when
+              (and (= (get p :state) "waiting") (get p :has-timeout))
+              (er-event-consider!
+                best
+                {:kind "recv"
+                  :deadline (get p :timeout-deadline)
+                  :proc p}))))
+        (keys (er-sched-processes)))
+      (nth best 0))))
+
+;; Keep the earlier-deadline candidate in the single-cell `best`.
+;; Strictly-earlier replaces; equal deadlines keep the incumbent so a
+;; timer registered first (and timers over recv-timeouts) win ties.
+(define
+  er-event-consider!
+  (fn
+    (best cand)
+    (when
+      (or
+        (= (nth best 0) nil)
+        (< (get cand :deadline) (get (nth best 0) :deadline)))
+      (set-nth! best 0 cand))))
+
+;; Deliver a fired timer's message to its destination and retire it.
+;; Destination is resolved at fire time; a dead/missing target (or an
+;; unregistered name) silently drops the message, as in real Erlang.
+(define
+  er-timer-fire!
+  (fn
+    (t)
+    (dict-set! t :alive false)
+    (let
+      ((pid (er-timer-resolve-dest (get t :dest))))
+      (when
+        (and (not (= pid nil)) (er-proc-exists? pid))
+        (er-proc-mailbox-push! pid (get t :msg))
+        (when
+          (= (er-proc-field pid :state) "waiting")
+          (er-proc-set! pid :state "runnable")
+          (er-sched-enqueue! pid))))))
+
+;; Non-raising destination resolver for timer delivery.
+(define
+  er-timer-resolve-dest
+  (fn
+    (v)
+    (cond
+      (er-pid? v) v
+      (er-atom? v)
+      (let
+        ((name (get v :name)))
+        (if (dict-has? (er-registered) name) (get (er-registered) name) nil))
+      :else nil)))
+
+;; Wake a process whose `receive ... after Ms` deadline elapsed.
+(define
+  er-recv-timeout-fire!
+  (fn
+    (p)
+    (dict-set! p :timed-out true)
+    (dict-set! p :has-timeout false)
+    (dict-set! p :state "runnable")
+    (er-sched-enqueue! (get p :pid))))
 
 (define
   er-sched-step!
@@ -1506,6 +1707,10 @@
     (er-register-bif! "erlang" "exit" 1 er-bif-exit)
     (er-register-bif! "erlang" "exit" 2 er-bif-exit)
     (er-register-bif! "erlang" "make_ref" 0 er-bif-make-ref)
+    (er-register-bif! "erlang" "send_after" 3 er-bif-send-after)
+    (er-register-bif! "erlang" "cancel_timer" 1 er-bif-cancel-timer)
+    (er-register-bif! "erlang" "monotonic_time" 0 er-bif-monotonic-time)
+    (er-register-bif! "erlang" "monotonic_time" 1 er-bif-monotonic-time)
     (er-register-bif! "erlang" "link" 1 er-bif-link)
     (er-register-bif! "erlang" "unlink" 1 er-bif-unlink)
     (er-register-bif! "erlang" "monitor" 2 er-bif-monitor)