feat: add Std.Notify type (#10368)

This PR adds `Notify` that is a structure that is similar to `CondVar`
but it's used for concurrency. The main difference between
`Std.Sync.Notify` and `Std.Condvar` is that depends on a `Std.Mutex` and
blocks the entire thread that the `Task` is using while waiting. If I
try to use it with async and a lot of `Task`s like this:

```lean
def condvar : Async Unit := do
  let condvar ← Std.Condvar.new
  let mutex ← Std.Mutex.new false

  for i in [0:threads] do
    background do
      IO.println s!"start {i + 1}"
      await =<< (show IO (ETask _ _) from IO.asTask (mutex.atomically (condvar.wait mutex)))
      IO.println s!"end {i + 1}"

  IO.sleep 2000
  condvar.notifyAll
```

It causes some weird behavior because some tasks start running and get
notified, while others don’t, because `condvar.wait` blocks the `Task`
entire task and right now afaik it blocks an entire thread and cannot be
paused while doing blocking operations like that.

`Notify` uses `Promise`s so it’s better suited for concurrency. The
`Task` is not blocked while waiting for a notification which makes it
simpler for use cases that just involve notifying:

```lean
def notify : Async Unit := do
  let notify ← Std.Notify.new

  for i in [0:threads] do
    background do
      IO.println s!"start {i}"
      notify.wait
      IO.println s!"end {i}"

  IO.sleep 2000
  notify.notify
```

This PR depends on: #10366, #10367 and #10370.

src/Std/Sync.lean

@@ -12,5 +12,6 @@ public import Std.Sync.Mutex
 public import Std.Sync.RecursiveMutex
 public import Std.Sync.Barrier
 public import Std.Sync.SharedMutex
+public import Std.Sync.Notify
 
 @[expose] public section

src/Std/Sync/Notify.lean

@@ -0,0 +1,140 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Sofia Rodrigues
+-/
+module
+
+prelude
+public import Init.System.Promise
+public import Init.Data.Queue
+public import Std.Sync.Mutex
+public import Std.Internal.Async.Select
+
+public section
+
+/-!
+This module contains the implementation of `Std.Notify`. `Std.Notify` provides a lightweight
+notification primitive for signaling between tasks or threads. It supports both synchronous
+and asynchronous waiting, and is useful for cases where you want to notify one or more waiters
+that an event has occurred.
+
+Unlike a channel, `Std.Notify` does not buffer messages or carry data. It's simply a trigger.
+If no one is waiting, notifications are lost. If one or more waiters are present, exactly one
+will be woken up per notification.
+-/
+
+namespace Std
+open Std.Internal.IO.Async
+
+inductive Notify.Consumer (α : Type) where
+  | normal (promise : IO.Promise α)
+  | select (finished : Waiter α)
+
+def Notify.Consumer.resolve (c : Consumer α) (x : α) : BaseIO Bool := do
+  match c with
+  | .normal promise =>
+    promise.resolve x
+    return true
+  | .select waiter =>
+    let lose := return false
+    let win promise := do
+      promise.resolve (.ok x)
+      return true
+    waiter.race lose win
+
+/--
+The central state structure for an a `Notify`.
+-/
+structure Notify.State where
+
+  /--
+  Consumers that are blocked waiting for a notification.
+  --/
+  consumers : Std.Queue (Notify.Consumer Unit)
+
+/--
+A notify is a synchronization primitive that allows multiple consumers to wait
+until notify is called.
+-/
+structure Notify where
+  state : Std.Mutex Notify.State
+
+namespace Notify
+
+/--
+Create a new notify.
+-/
+def new : BaseIO Notify := do
+  return { state := ← Std.Mutex.new { consumers := ∅ } }
+
+/--
+Notify all currently waiting consumers.
+-/
+def notify (x : Notify) : BaseIO Unit := do
+  x.state.atomically do
+    let mut st ← get
+
+    let mut remainingConsumers := st.consumers
+    st := { st with consumers := ∅ }
+
+    while true do
+      if let some (consumer, rest) := remainingConsumers.dequeue? then
+        remainingConsumers := rest
+        discard <| consumer.resolve ()
+      else
+        break
+
+    set st
+
+/--
+Notify exactly one waiting consumer (if any). Returns true if a consumer
+was notified, false if no consumers were waiting.
+-/
+def notifyOne (x : Notify) : BaseIO Bool := do
+  x.state.atomically do
+    let mut st ← get
+
+    if let some (consumer, rest) := st.consumers.dequeue? then
+      st := { st with consumers := rest }
+      set st
+      consumer.resolve ()
+    else
+      return false
+
+/--
+Wait to be notified. Returns a task that completes when notify is called.
+Note: if notify was called before wait, this will wait for the next notify call.
+-/
+def wait (x : Notify) : IO (AsyncTask Unit) :=
+  x.state.atomically do
+    let promise ← IO.Promise.new
+    modify fun st => { st with consumers := st.consumers.enqueue (.normal promise) }
+    IO.bindTask promise.result? fun
+      | some res => pure <| Task.pure (.ok res)
+      | none => throw (IO.userError "notify dropped")
+
+/--
+Creates a selector that waits for notifications
+-/
+def selector (notify : Notify) : Selector Unit := {
+  tryFn := do
+    return none
+
+  registerFn := fun waiter => do
+    notify.state.atomically do
+      modify fun st => { st with consumers := st.consumers.enqueue (.select waiter) }
+
+  unregisterFn := do
+    notify.state.atomically do
+      let st ← get
+
+      let consumers ← st.consumers.filterM fun
+        | .normal _ => return true
+        | .select waiter => return !(← waiter.checkFinished)
+
+      set { st with consumers }
+}
+
+end Notify
+end Std

tests/lean/run/sync_notify.lean

@@ -0,0 +1,108 @@
+import Std.Internal.Async
+import Std.Sync
+
+open Std.Internal.IO Async
+
+-- Test basic wait and notifyOne functionality
+def testBasicWaitNotifyOne : Async Unit := do
+  let notify ← Std.Notify.new
+  let waitTask ← notify.wait
+
+  assert! (← waitTask.getState) = .waiting
+  discard <| notify.notifyOne
+  await waitTask
+  assert! (← waitTask.getState) = .finished
+
+#eval testBasicWaitNotifyOne.block
+
+-- Test multiple waiters with notifyOne (only one should be notified)
+def testMultipleWaitersNotifyOne : Async Unit := do
+  let notify ← Std.Notify.new
+  let task1 ← notify.wait
+  let task2 ← notify.wait
+  let task3 ← notify.wait
+
+  assert! (← task1.getState) = .waiting
+  assert! (← task2.getState) = .waiting
+  assert! (← task3.getState) = .waiting
+
+  discard <| notify.notifyOne
+
+  IO.sleep 100
+
+  let states ← [task1, task2, task3].mapM (fun t => t.getState)
+  let finishedCount := states.filter (· == .finished) |>.length
+  let waitingCount := states.filter (· == .waiting) |>.length
+
+  assert! finishedCount == 1
+  assert! waitingCount == 2
+
+  discard <| notify.notifyOne
+
+#eval testMultipleWaitersNotifyOne.block
+
+-- Test multiple waiters with notify (all should be notified)
+def testMultipleWaitersNotifyAll : Async Unit := do
+  let notify ← Std.Notify.new
+  let task1 ← notify.wait
+  let task2 ← notify.wait
+  let task3 ← notify.wait
+
+  assert! (← task1.getState) = .waiting
+  assert! (← task2.getState) = .waiting
+  assert! (← task3.getState) = .waiting
+
+  discard <| notify.notify
+
+  await task1
+  await task2
+  await task3
+
+  assert! (← task1.getState) = .finished
+  assert! (← task2.getState) = .finished
+  assert! (← task3.getState) = .finished
+
+#eval testMultipleWaitersNotifyAll.block
+
+-- Test sequential notification
+def testSequentialNotification : Async Unit := do
+  let notify ← Std.Notify.new
+  let task1 ← notify.wait
+  let task2 ← notify.wait
+  let task3 ← notify.wait
+
+  discard <| notify.notifyOne
+  await task1
+  assert! (← task1.getState) = .finished
+  assert! (← task2.getState) = .waiting
+  assert! (← task3.getState) = .waiting
+
+  discard <| notify.notifyOne
+  await task2
+  assert! (← task2.getState) = .finished
+  assert! (← task3.getState) = .waiting
+
+  discard <| notify.notifyOne
+  await task3
+  assert! (← task3.getState) = .finished
+
+#eval testSequentialNotification.block
+
+def testReuseAfterCompletion : Async Unit := do
+  let notify ← Std.Notify.new
+
+  let task1 ← notify.wait
+  discard <| notify.notifyOne
+  await task1
+  assert! (← task1.getState) = .finished
+
+  let task2 ← notify.wait
+  let task3 ← notify.wait
+  discard <| notify.notify
+  await task2
+  await task3
+
+  assert! (← task2.getState) = .finished
+  assert! (← task3.getState) = .finished
+
+#eval testReuseAfterCompletion.block