chore: improve performance of mpure_intro and mvcgen by avoiding whnfD (#12165)

New measurements:

```
goal_10: 181.910200 ms, kernel: 37.241050 ms
goal_20: 386.540215 ms, kernel: 83.497428 ms
goal_30: 648.282057 ms, kernel: 117.038447 ms
goal_40: 946.733191 ms, kernel: 168.369124 ms
goal_50: 1325.846873 ms, kernel: 223.838786 ms
goal_60: 1734.175705 ms, kernel: 285.594486 ms
goal_70: 2199.522317 ms, kernel: 351.659865 ms
goal_80: 2700.077802 ms, kernel: 428.303337 ms
goal_90: 3260.446641 ms, kernel: 515.976499 ms
goal_100: 3865.503733 ms, kernel: 600.229962 ms
```

Previously, goal_100 took 7.8s.

src/Lean/Elab/Tactic/Do/ProofMode/Pure.lean

@@ -82,13 +82,27 @@ def elabMPureIntro : Tactic
     replaceMainGoal [mv]
   | _ => throwUnsupportedSyntax
 
+private def extractPureProp (e : Expr) : MetaM (Option Expr) := do
+  let e ← instantiateMVarsIfMVarApp e
+  let some (_, e) := e.app2? ``ULift.down | return none
+  let f := e.getAppFn
+  unless f.isConstOf ``SPred.pure do return none
+  let args := e.getAppArgs
+  if args.size < 2 then return none
+  let σs := args[0]!
+  let n ← TypeList.length σs
+  unless n = args.size - 2 do return none
+  let p := args[1]!
+  return p
+
 partial def _root_.Lean.MVarId.applyRflAndAndIntro (mvar : MVarId) : MetaM Unit := do
-  -- The target might look like `(⌜?n = nₛ ∧ ?m = b⌝ s).down`, which we reduce to
-  -- `?n = nₛ ∧ ?m = b` by `whnfD`.
+  -- The target might look like `(⌜nₛ = ?n ∧ ?m = b⌝ s).down`, which we reduce to
+  -- `nₛ = ?n ∧ ?m = b` with `extractPureProp`.
   -- (Recall that `⌜s = 4⌝ s` is `SPred.pure (σs:=[Nat]) (s = 4) s` and `SPred.pure` is
   -- semi-reducible.)
-  let ty ← whnfD (← mvar.getType)
-  trace[Elab.Tactic.Do.spec] "whnf: {ty}"
+  let ty ← mvar.getType >>= instantiateMVarsIfMVarApp
+  let ty ← (·.getD ty) <$> extractPureProp ty
+  trace[Elab.Tactic.Do.spec] "pure Prop: {ty}"
   if ty.isAppOf ``True then
     mvar.assign (mkConst ``True.intro)
   else if let some (lhs, rhs) := ty.app2? ``And then
@@ -127,16 +141,3 @@ def MGoal.pureTrivial (goal : MGoal) : OptionT MetaM Expr := do
       return ((), m)
     return prf
   catch _ => failure
-
-/-
-def MGoal.pureRfl (goal : MGoal) : OptionT MetaM Expr := do
-  let mv ← mkFreshExprMVar goal.toExpr
-  let ([], _) ← try runTactic mv.mvarId! (← `(tactic| apply $(mkIdent ``Std.Do.SPred.Tactic.Pure.intro); rfl)) catch _ => failure
-    | failure
-  return mv
-def MGoal.pureRfl (goal : MGoal) : OptionT MetaM Expr := do
-  let mv ← mkFreshExprMVar goal.toExpr
-  let ([], _) ← try runTactic mv.mvarId! (← `(tactic| apply $(mkIdent ``Std.Do.SPred.Tactic.Pure.intro); rfl)) catch _ => failure
-    | failure
-  return mv
--/

tests/bench/mvcgen/add_sub_cancel_StateM.lean

@@ -62,26 +62,26 @@ def solveUsingMeta (n : Nat) (check := true) : MetaM Unit := do
     let ([], _) ← runTactic mvarId (← `(tactic| solve)).raw {} {} | throwError "FAILED!"
 
 def runBenchUsingMeta (sizes : List Nat) : MetaM Unit := do
-  IO.println "=== Symbolic Simulation Tests ==="
+  IO.println "=== VCGen tests ==="
   IO.println ""
   for n in sizes do
     solveUsingMeta n
 
 set_option maxRecDepth 10000
 set_option maxHeartbeats 10000000
-/-
-info: === Symbolic Simulation Tests ===
+/--
+info: === VCGen tests ===
 
-goal_10: 245.576221 ms, kernel: 134.134182 ms
-goal_20: 613.945320 ms, kernel: 115.453811 ms
-goal_30: 1074.053596 ms, kernel: 179.076070 ms
-goal_40: 1680.678302 ms, kernel: 252.066677 ms
-goal_50: 2457.209584 ms, kernel: 293.974096 ms
-goal_60: 3271.773330 ms, kernel: 368.394386 ms
-goal_70: 3981.247921 ms, kernel: 434.297822 ms
-goal_80: 5077.300540 ms, kernel: 507.047772 ms
-goal_90: 6486.990060 ms, kernel: 556.952095 ms
-goal_100: 7791.399986 ms, kernel: 623.605163 ms
+goal_10: 181.910200 ms, kernel: 37.241050 ms
+goal_20: 386.540215 ms, kernel: 83.497428 ms
+goal_30: 648.282057 ms, kernel: 117.038447 ms
+goal_40: 946.733191 ms, kernel: 168.369124 ms
+goal_50: 1325.846873 ms, kernel: 223.838786 ms
+goal_60: 1734.175705 ms, kernel: 285.594486 ms
+goal_70: 2199.522317 ms, kernel: 351.659865 ms
+goal_80: 2700.077802 ms, kernel: 428.303337 ms
+goal_90: 3260.446641 ms, kernel: 515.976499 ms
+goal_100: 3865.503733 ms, kernel: 600.229962 ms
 -/
 #guard_msgs in
 #eval runBenchUsingMeta [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]

tests/lean/run/mvcgenTutorial.lean

@@ -128,6 +128,8 @@ theorem mkFresh_spec [Monad m] [WPMonad m ps] (c : Nat) :
 
 @[spec]
 theorem mkFreshN_spec (n : Nat) : ⦃⌜True⌝⦄ mkFreshN n ⦃⇓ r => ⌜r.Nodup⌝⦄ := by
+  -- This is a great test case for `applyRflAndAndIntro` because it requires
+  -- reducing `(⌜s₁.counter = ?c⌝ s).down` to `s₁ = ?c`.
   mvcgen [mkFreshN, liftCounterM]
   case inv1 => exact ⇓⟨xs, acc⟩ _ state => ⌜(∀ n ∈ acc, n < state.counter) ∧ acc.toList.Nodup⌝
   all_goals mleave; grind