feat: improve performance of instantiateBetaRevRange (#13758)

This PR improves `Expr.instantiateBetaRevRange` to be more efficient in
the common case where lambda functions are not being instantiated, and
it increases expression sharing in applications.

The motivation is that we would like to use this function more
pervasively in elaboration, so that users do not need to write `dsimp
only` as frequently in applications that involve higher-order functions,
plus `inferType` uses it so there is a UX inconsistency when the
elaborator is not using it.

src/Lean/Meta/InferType.lean

@@ -19,6 +19,9 @@ Auxiliary function for instantiating the loose bound variables in `e` with `args
 This function is similar to `instantiateRevRange`, but it applies beta-reduction when
 we instantiate a bound variable with a lambda expression.
 
+If `args` contains no lambda expressions, it is equivalent to `instantiateRevRange`, and in fact
+it will call `instantiateRevRange` for efficiency.
+
 Example: Given the term `#0 a`, and `start := 0, stop := 1, args := #[fun x => x]` the result is
 `a` instead of `(fun x => x) a`.
 This reduction is useful when we are inferring the type of eliminator-like applications.
@@ -32,10 +35,38 @@ We use this to implement `inferAppType`.
 partial def Expr.instantiateBetaRevRange (e : Expr) (start : Nat) (stop : Nat) (args : Array Expr) : Expr :=
   if e.hasLooseBVars && stop > start then
     assert! stop ≤ args.size
-    visit e 0 |>.run
+    if args.any (·.consumeMData.isLambda) start stop then
+      visit e 0 |>.run
+    else
+      -- If there are no lambdas, then `instantiateRevRange` suffices.
+      instantiateRevRange e start stop args
   else
     e
 where
+  /--
+  Visit a bvar `e := .bvar vidx`, assuming `offset < e.looseBVarRange`.
+  -/
+  visitBVar (vidx : Nat) (offset : Nat) : Expr :=
+    -- Recall that `looseBVarRange` for `Expr.bvar` is `vidx+1`.
+    -- So, we must have `offset ≤ vidx`, since `offset < e.looseBVarRange`
+    let n := stop - start
+    if vidx < offset + n then
+      args[stop - (vidx - offset) - 1]!.liftLooseBVars 0 offset
+    else
+      Expr.bvar (vidx - n)
+  visitWithoutBeta (e : Expr) (offset : Nat) : MonadStateCacheT (ExprStructEq × Nat) Expr Id Expr := do
+    if offset >= e.looseBVarRange then
+      -- `e` doesn't have free variables
+      return e
+    else
+      match e with
+      | .app f a =>
+        -- Check the cache only here, since in the other alternative `visit` will check the cache.
+        checkCache ({ val := e : ExprStructEq }, offset) fun _ => visitApp e f a offset
+      | e => visit e offset
+  /-- Visit an application without beta reducing the head -/
+  visitApp (e f a : Expr) (offset : Nat) : MonadStateCacheT (ExprStructEq × Nat) Expr Id Expr :=
+    return e.updateApp! (← visitWithoutBeta f offset) (← visit a offset)
   visit (e : Expr) (offset : Nat) : MonadStateCacheT (ExprStructEq × Nat) Expr Id Expr :=
     if offset >= e.looseBVarRange then
       -- `e` doesn't have free variables
@@ -47,23 +78,17 @@ where
       | .letE _ t v b _  => return e.updateLetE! (← visit t offset) (← visit v offset) (← visit b (offset+1))
       | .mdata _ b       => return e.updateMData! (← visit b offset)
       | .proj _ _ b      => return e.updateProj! (← visit b offset)
-      | .app .. =>
-        e.withAppRev fun f revArgs => do
-        let fNew    ← visit f offset
-        let revArgs ← revArgs.mapM (visit · offset)
-        if f.isBVar then
-          -- try to beta reduce if `f` was a bound variable
-          return fNew.betaRev revArgs
+      | .bvar vidx       => return visitBVar vidx offset
+      | .app f a =>
+        let head := e.getAppFn
+        -- try to beta reduce if the head is a bound variable
+        if head.isBVar then
+          -- using `visit` instead of `visitBVar` for the `offset >= vidx` check and for caching `liftLooseBVars`
+          let head ← visit head offset
+          let revArgs ← e.getAppRevArgs.mapM (visit · offset)
+          return head.betaRev revArgs
         else
-          return mkAppRev fNew revArgs
-      | Expr.bvar vidx         =>
-        -- Recall that looseBVarRange for `Expr.bvar` is `vidx+1`.
-        -- So, we must have offset ≤ vidx, since we are in the "else" branch of  `if offset >= e.looseBVarRange`
-        let n := stop - start
-        if vidx < offset + n then
-          return args[stop - (vidx - offset) - 1]!.liftLooseBVars 0 offset
-        else
-          return mkBVar (vidx - n)
+          visitApp e f a offset
       -- The following cases are unreachable because they never contain loose bound variables
       | .const .. => unreachable!
       | .fvar ..  => unreachable!
@@ -79,8 +104,6 @@ def throwFunctionExpected {α} (f : Expr) : MetaM α :=
 private def inferAppType (f : Expr) (args : Array Expr) : MetaM Expr := do
   let mut fType ← inferType f
   let mut j := 0
-  /- TODO: check whether `instantiateBetaRevRange` is too expensive, and
-     use it only when `args` contains a lambda expression. -/
   for i in *...args.size do
     match fType with
     | Expr.forallE _ _ b _ => fType := b