fix: add checkSystem calls to long-running elaboration paths

This PR adds `checkSystem` calls to several code paths that can run for
extended periods without checking for cancellation, heartbeat limits, or
stack overflow. This improves responsiveness of the cancellation mechanism
in the language server.

Affected paths:
- `simp` rewrite candidate loops (`Rewrite.lean`)
- `simpAppUsingCongr` argument traversal (`Types.lean`)
- `synthesizeSyntheticMVarsStep` mvar loop (`SyntheticMVars.lean`)
- `abstractNestedProofs` visitor (`AbstractNestedProofs.lean`)
- `transform`/`transformWithCache` visitors (`Transform.lean`)
- LCNF compiler pass runner loop (`Main.lean`)
- LCNF checker recursive traversal (`Check.lean`)
- LCNF simplifier recursive traversal (`Simp/Main.lean`)
- `whnfCore` recursive reduction loop (`WHNF.lean`)

With these changes, at a 50ms monitoring threshold across the full test suite,
the only remaining Lean-side elaborator gaps are:
- bv_decide pure computation wrapped in `IO.lazyPure` (architectural)
- Single deep `whnf` reductions from the `constructorNameAsVariable` linter (~100-180ms)

Remaining C++ gaps (type checker, interpreter module init) are tracked separately.

Found using `LEAN_CHECK_SYSTEM_INTERVAL_MS` monitoring from #13218.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

src/Lean/Compiler/LCNF/Check.lean

@@ -232,6 +232,7 @@ partial def checkCases (c : Cases .pure) : CheckM Unit := do
       withParams params do check k
 
 partial def check (code : Code .pure) : CheckM Unit := do
+  checkSystem "LCNF check"
   match code with
   | .let decl k => checkLetDecl decl; withFVarId decl.fvarId do check k
   | .fun decl k =>

src/Lean/Compiler/LCNF/Main.lean

@@ -188,6 +188,7 @@ where
     profileitM Exception profilerName (← getOptions) do
       let mut state : (pu : Purity) × Array (Decl pu) := ⟨inPhase, decls⟩
       for pass in passes do
+        checkSystem "LCNF compiler"
         state ← withTraceNode `Compiler (fun _ => return m!"compiler phase: {pass.phase}, pass: {pass.name}") do
           let decls ← withPhase pass.phase do
             state.fst.withAssertPurity pass.phase.toPurity fun h => do

src/Lean/CoreM.lean

@@ -453,6 +453,9 @@ Throws an internal interrupt exception if cancellation has been requested. The e
 caught by `try catch` but is intended to be caught by `Command.withLoggingExceptions` at the top
 level of elaboration. In particular, we want to skip producing further incremental snapshots after
 the exception has been thrown.
+
+Like `checkSystem` but without the global heartbeat check, for callers that have their own
+heartbeat tracking (e.g. `SynthInstance`).
  -/
 @[inline] def checkInterrupted : CoreM Unit := do
   if let some tk := (← read).cancelTk? then

src/Lean/Elab/SyntheticMVars.lean

@@ -582,6 +582,7 @@ mutual
     -- We use `filterRevM` instead of `filterM` to make sure we process the synthetic metavariables using the order they were created.
     -- It would not be incorrect to use `filterM`.
     let remainingPendingMVars ← pendingMVars.filterRevM fun mvarId => do
+       checkSystem "synthesize pending MVars"
        -- We use `traceM` because we want to make sure the metavar local context is used to trace the message
        traceM `Elab.postpone (mvarId.withContext do addMessageContext m!"resuming {mkMVar mvarId}")
        let succeeded ← synthesizeSyntheticMVar mvarId postponeOnError runTactics

src/Lean/Meta/AbstractNestedProofs.lean

@@ -70,6 +70,7 @@ structure Context where
 abbrev M := ReaderT Context $ MonadCacheT ExprStructEq Expr MetaM
 
 partial def visit (e : Expr) : M Expr := do
+  checkSystem "abstract nested proofs"
   if e.isAtomic then
     pure e
   else

src/Lean/Meta/Tactic/Simp/Main.lean

@@ -714,7 +714,6 @@ where
 set_option compiler.ignoreBorrowAnnotation true in
 @[export lean_simp]
 def simpImpl (e : Expr) : SimpM Result := withIncRecDepth do
-  checkSystem "simp"
   if (← isProof e) then
     return { expr := e }
   trace[Meta.Tactic.simp.heads] "{repr e.toHeadIndex}"

src/Lean/Meta/Tactic/Simp/Rewrite.lean

@@ -218,6 +218,7 @@ where
     else
       let candidates := candidates.insertionSort fun e₁ e₂ => e₁.1.priority > e₂.1.priority
       for (thm, numExtraArgs) in candidates do
+        checkSystem "simp"
         if inErasedSet thm then continue
         if rflOnly then
           unless thm.rfl do
@@ -245,6 +246,7 @@ where
     else
       let candidates := candidates.insertionSort fun e₁ e₂ => e₁.priority > e₂.priority
       for thm in candidates do
+        checkSystem "simp"
         unless inErasedSet thm || (rflOnly && !thm.rfl) do
           let result? ← withNewMCtxDepth do
             let val  ← thm.getValue

src/Lean/Meta/Tactic/Simp/Types.lean

@@ -722,6 +722,7 @@ def simpAppUsingCongr (e : Expr) : SimpM Result := do
     if i == 0 then
       simp f
     else
+      checkSystem "simp"
       let i := i - 1
       let .app f a := e | unreachable!
       let fr ← visit f i

src/Lean/Meta/Transform.lean

@@ -50,6 +50,7 @@ partial def transform {m} [Monad m] [MonadLiftT CoreM m] [MonadControlT CoreM m]
   let _ : MonadLiftT (ST IO.RealWorld) m := { monadLift := fun x => liftM (m := CoreM) (liftM (m := ST IO.RealWorld) x) }
   let rec visit (e : Expr) : MonadCacheT ExprStructEq Expr m Expr :=
     checkCache { val := e : ExprStructEq } fun _ => Core.withIncRecDepth do
+      Core.checkSystem "transform"
       let rec visitPost (e : Expr) : MonadCacheT ExprStructEq Expr m Expr := do
         match (← post e) with
         | .done e      => pure e
@@ -107,6 +108,7 @@ partial def transformWithCache {m} [Monad m] [MonadLiftT MetaM m] [MonadControlT
   let _ : MonadLiftT (ST IO.RealWorld) m := { monadLift := fun x => liftM (m := MetaM) (liftM (m := ST IO.RealWorld) x) }
   let rec visit (e : Expr) : MonadCacheT ExprStructEq Expr m Expr :=
     checkCache { val := e : ExprStructEq } fun _ => Meta.withIncRecDepth do
+      (Core.checkSystem "transform" : MetaM Unit)
       let rec visitPost (e : Expr) : MonadCacheT ExprStructEq Expr m Expr := do
         match (← post e) with
         | .done e      => pure e

src/Lean/Meta/WHNF.lean

@@ -650,7 +650,7 @@ expand let-expressions, expand assigned meta-variables, unfold aux declarations.
 partial def whnfCore (e : Expr) : MetaM Expr :=
   go e
 where
-  go (e : Expr) : MetaM Expr :=
+  go (e : Expr) : MetaM Expr := do
     whnfEasyCases e fun e => do
       trace[Meta.whnf] e
       match e with