fix test

This PR adds theorems `BitVec.(getMsbD, msb)_(rotateLeft, rotateRight)`.

We follow the same strategy taken for `getLsbD`, constructing the
necessary auxilliary theorems first (relying on different hypotheses)
and then generalizing.

---------

Co-authored-by: Siddharth <siddu.druid@gmail.com>
Co-authored-by: Tobias Grosser <tobias@grosser.es>

src/Init/Data/Array/Basic.lean

@@ -613,8 +613,15 @@ def findIdx? {α : Type u} (p : α → Bool) (as : Array α) : Option Nat :=
     decreasing_by simp_wf; decreasing_trivial_pre_omega
   loop 0
 
-def getIdx? [BEq α] (a : Array α) (v : α) : Option Nat :=
-  a.findIdx? fun a => a == v
+@[inline]
+def findFinIdx? {α : Type u} (p : α → Bool) (as : Array α) : Option (Fin as.size) :=
+  let rec @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
+  loop (j : Nat) :=
+    if h : j < as.size then
+      if p as[j] then some ⟨j, h⟩ else loop (j + 1)
+    else none
+    decreasing_by simp_wf; decreasing_trivial_pre_omega
+  loop 0
 
 @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
 def indexOfAux [BEq α] (a : Array α) (v : α) (i : Nat) : Option (Fin a.size) :=
@@ -627,6 +634,10 @@ decreasing_by simp_wf; decreasing_trivial_pre_omega
 def indexOf? [BEq α] (a : Array α) (v : α) : Option (Fin a.size) :=
   indexOfAux a v 0
 
+@[deprecated indexOf? (since := "2024-11-20")]
+def getIdx? [BEq α] (a : Array α) (v : α) : Option Nat :=
+  a.findIdx? fun a => a == v
+
 @[inline]
 def any (as : Array α) (p : α → Bool) (start := 0) (stop := as.size) : Bool :=
   Id.run <| as.anyM p start stop
@@ -766,48 +777,62 @@ def takeWhile (p : α → Bool) (as : Array α) : Array α :=
     decreasing_by simp_wf; decreasing_trivial_pre_omega
   go 0 #[]
 
-/-- Remove the element at a given index from an array without bounds checks, using a `Fin` index.
+/--
+Remove the element at a given index from an array without a runtime bounds checks,
+using a `Nat` index and a tactic-provided bound.
 
-  This function takes worst case O(n) time because
-  it has to backshift all elements at positions greater than `i`.-/
+This function takes worst case O(n) time because
+it has to backshift all elements at positions greater than `i`.-/
 @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
-def feraseIdx (a : Array α) (i : Fin a.size) : Array α :=
-  if h : i.val + 1 < a.size then
-    let a' := a.swap ⟨i.val + 1, h⟩ i
-    let i' : Fin a'.size := ⟨i.val + 1, by simp [a', h]⟩
-    a'.feraseIdx i'
+def eraseIdx (a : Array α) (i : Nat) (h : i < a.size := by get_elem_tactic) : Array α :=
+  if h' : i + 1 < a.size then
+    let a' := a.swap ⟨i + 1, h'⟩ ⟨i, h⟩
+    a'.eraseIdx (i + 1) (by simp [a', h'])
   else
     a.pop
-termination_by a.size - i.val
-decreasing_by simp_wf; exact Nat.sub_succ_lt_self _ _ i.isLt
+termination_by a.size - i
+decreasing_by simp_wf; exact Nat.sub_succ_lt_self _ _ h
 
 -- This is required in `Lean.Data.PersistentHashMap`.
-@[simp] theorem size_feraseIdx (a : Array α) (i : Fin a.size) : (a.feraseIdx i).size = a.size - 1 := by
-  induction a, i using Array.feraseIdx.induct with
-  | @case1 a i h a' _ ih =>
-    unfold feraseIdx
-    simp [h, a', ih]
-  | case2 a i h =>
-    unfold feraseIdx
-    simp [h]
+@[simp] theorem size_eraseIdx (a : Array α) (i : Nat) (h) : (a.eraseIdx i h).size = a.size - 1 := by
+  induction a, i, h using Array.eraseIdx.induct with
+  | @case1 a i h h' a' ih =>
+    unfold eraseIdx
+    simp [h', a', ih]
+  | case2 a i h h' =>
+    unfold eraseIdx
+    simp [h']
 
 /-- Remove the element at a given index from an array, or do nothing if the index is out of bounds.
 
   This function takes worst case O(n) time because
   it has to backshift all elements at positions greater than `i`.-/
-def eraseIdx (a : Array α) (i : Nat) : Array α :=
-  if h : i < a.size then a.feraseIdx ⟨i, h⟩ else a
+def eraseIdxIfInBounds (a : Array α) (i : Nat) : Array α :=
+  if h : i < a.size then a.eraseIdx i h else a
+
+/-- Remove the element at a given index from an array, or panic if the index is out of bounds.
+
+This function takes worst case O(n) time because
+it has to backshift all elements at positions greater than `i`. -/
+def eraseIdx! (a : Array α) (i : Nat) : Array α :=
+  if h : i < a.size then a.eraseIdx i h else panic! "invalid index"
 
 def erase [BEq α] (as : Array α) (a : α) : Array α :=
   match as.indexOf? a with
   | none   => as
-  | some i => as.feraseIdx i
+  | some i => as.eraseIdx i
+
+/-- Erase the first element that satisfies the predicate `p`. -/
+def eraseP (as : Array α) (p : α → Bool) : Array α :=
+  match as.findIdx? p with
+  | none   => as
+  | some i => as.eraseIdxIfInBounds i
 
 /-- Insert element `a` at position `i`. -/
-@[inline] def insertAt (as : Array α) (i : Fin (as.size + 1)) (a : α) : Array α :=
+@[inline] def insertIdx (as : Array α) (i : Nat) (a : α) (_ : i ≤ as.size := by get_elem_tactic) : Array α :=
   let rec @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
   loop (as : Array α) (j : Fin as.size) :=
-    if i.1 < j then
+    if i < j then
       let j' := ⟨j-1, Nat.lt_of_le_of_lt (Nat.pred_le _) j.2⟩
       let as := as.swap j' j
       loop as ⟨j', by rw [size_swap]; exact j'.2⟩
@@ -818,12 +843,23 @@ def erase [BEq α] (as : Array α) (a : α) : Array α :=
   let as := as.push a
   loop as ⟨j, size_push .. ▸ j.lt_succ_self⟩
 
+@[deprecated insertIdx (since := "2024-11-20")] abbrev insertAt := @insertIdx
+
 /-- Insert element `a` at position `i`. Panics if `i` is not `i ≤ as.size`. -/
-def insertAt! (as : Array α) (i : Nat) (a : α) : Array α :=
+def insertIdx! (as : Array α) (i : Nat) (a : α) : Array α :=
   if h : i ≤ as.size then
-    insertAt as ⟨i, Nat.lt_succ_of_le h⟩ a
+    insertIdx as i a
   else panic! "invalid index"
 
+@[deprecated insertIdx! (since := "2024-11-20")] abbrev insertAt! := @insertIdx!
+
+/-- Insert element `a` at position `i`, or do nothing if `as.size < i`. -/
+def insertIdxIfInBounds (as : Array α) (i : Nat) (a : α) : Array α :=
+  if h : i ≤ as.size then
+    insertIdx as i a
+  else
+    as
+
 @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
 def isPrefixOfAux [BEq α] (as bs : Array α) (hle : as.size ≤ bs.size) (i : Nat) : Bool :=
   if h : i < as.size then

src/Init/Data/Array/BinSearch.lean

@@ -52,7 +52,7 @@ namespace Array
     let mid    := (lo + hi)/2
     let midVal := as.get! mid
     if lt midVal k then
-      if mid == lo then do let v ← add (); pure <| as.insertAt! (lo+1) v
+      if mid == lo then do let v ← add (); pure <| as.insertIdx! (lo+1) v
       else binInsertAux lt merge add as k mid hi
     else if lt k midVal then
       binInsertAux lt merge add as k lo mid
@@ -67,7 +67,7 @@ namespace Array
     (k : α) : m (Array α) :=
   let _ := Inhabited.mk k
   if as.isEmpty then do let v ← add (); pure <| as.push v
-  else if lt k (as.get! 0) then do let v ← add (); pure <| as.insertAt! 0 v
+  else if lt k (as.get! 0) then do let v ← add (); pure <| as.insertIdx! 0 v
   else if !lt (as.get! 0) k then as.modifyM 0 <| merge
   else if lt as.back! k then do let v ← add (); pure <| as.push v
   else if !lt k as.back! then as.modifyM (as.size - 1) <| merge

src/Init/Data/Array/Find.lean

@@ -0,0 +1,275 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Kim Morrison
+-/
+prelude
+import Init.Data.List.Find
+import Init.Data.Array.Lemmas
+import Init.Data.Array.Attach
+
+/-!
+# Lemmas about `Array.findSome?`, `Array.find?`.
+-/
+
+namespace Array
+
+open Nat
+
+/-! ### findSome? -/
+
+@[simp] theorem findSomeRev?_push_of_isSome (l : Array α) (h : (f a).isSome) : (l.push a).findSomeRev? f = f a := by
+  cases l; simp_all
+
+@[simp] theorem findSomeRev?_push_of_isNone (l : Array α) (h : (f a).isNone) : (l.push a).findSomeRev? f = l.findSomeRev? f := by
+  cases l; simp_all
+
+theorem exists_of_findSome?_eq_some {f : α → Option β} {l : Array α} (w : l.findSome? f = some b) :
+    ∃ a, a ∈ l ∧ f a = b := by
+  cases l; simp_all [List.exists_of_findSome?_eq_some]
+
+@[simp] theorem findSome?_eq_none_iff : findSome? p l = none ↔ ∀ x ∈ l, p x = none := by
+  cases l; simp
+
+@[simp] theorem findSome?_isSome_iff {f : α → Option β} {l : Array α} :
+    (l.findSome? f).isSome ↔ ∃ x, x ∈ l ∧ (f x).isSome := by
+  cases l; simp
+
+theorem findSome?_eq_some_iff {f : α → Option β} {l : Array α} {b : β} :
+    l.findSome? f = some b ↔ ∃ (l₁ : Array α) (a : α) (l₂ : Array α), l = l₁.push a ++ l₂ ∧ f a = some b ∧ ∀ x ∈ l₁, f x = none := by
+  cases l
+  simp only [List.findSome?_toArray, List.findSome?_eq_some_iff]
+  constructor
+  · rintro ⟨l₁, a, l₂, rfl, h₁, h₂⟩
+    exact ⟨l₁.toArray, a, l₂.toArray, by simp_all⟩
+  · rintro ⟨l₁, a, l₂, h₀, h₁, h₂⟩
+    exact ⟨l₁.toList, a, l₂.toList, by simpa using congrArg toList h₀, h₁, by simpa⟩
+
+@[simp] theorem findSome?_guard (l : Array α) : findSome? (Option.guard fun x => p x) l = find? p l := by
+  cases l; simp
+
+@[simp] theorem getElem?_zero_filterMap (f : α → Option β) (l : Array α) : (l.filterMap f)[0]? = l.findSome? f := by
+  cases l; simp [← List.head?_eq_getElem?]
+
+@[simp] theorem getElem_zero_filterMap (f : α → Option β) (l : Array α) (h) :
+    (l.filterMap f)[0] = (l.findSome? f).get (by cases l; simpa [List.length_filterMap_eq_countP] using h) := by
+  cases l; simp [← List.head_eq_getElem, ← getElem?_zero_filterMap]
+
+@[simp] theorem back?_filterMap (f : α → Option β) (l : Array α) : (l.filterMap f).back? = l.findSomeRev? f := by
+  cases l; simp
+
+@[simp] theorem back!_filterMap [Inhabited β] (f : α → Option β) (l : Array α) :
+    (l.filterMap f).back! = (l.findSomeRev? f).getD default := by
+  cases l; simp
+
+@[simp] theorem map_findSome? (f : α → Option β) (g : β → γ) (l : Array α) :
+    (l.findSome? f).map g = l.findSome? (Option.map g ∘ f) := by
+  cases l; simp
+
+theorem findSome?_map (f : β → γ) (l : Array β) : findSome? p (l.map f) = l.findSome? (p ∘ f) := by
+  cases l; simp [List.findSome?_map]
+
+theorem findSome?_append {l₁ l₂ : Array α} : (l₁ ++ l₂).findSome? f = (l₁.findSome? f).or (l₂.findSome? f) := by
+  cases l₁; cases l₂; simp [List.findSome?_append]
+
+theorem getElem?_zero_flatten (L : Array (Array α)) :
+    (flatten L)[0]? = L.findSome? fun l => l[0]? := by
+  cases L using array_array_induction
+  simp [← List.head?_eq_getElem?, List.head?_flatten, List.findSome?_map, Function.comp_def]
+
+theorem getElem_zero_flatten.proof {L : Array (Array α)} (h : 0 < L.flatten.size) :
+    (L.findSome? fun l => l[0]?).isSome := by
+  cases L using array_array_induction
+  simp only [List.findSome?_toArray, List.findSome?_map, Function.comp_def, List.getElem?_toArray,
+    List.findSome?_isSome_iff, List.isSome_getElem?]
+  simp only [flatten_toArray_map_toArray, size_toArray, List.length_flatten,
+    Nat.sum_pos_iff_exists_pos, List.mem_map] at h
+  obtain ⟨_, ⟨xs, m, rfl⟩, h⟩ := h
+  exact ⟨xs, m, by simpa using h⟩
+
+theorem getElem_zero_flatten {L : Array (Array α)} (h) :
+    (flatten L)[0] = (L.findSome? fun l => l[0]?).get (getElem_zero_flatten.proof h) := by
+  have t := getElem?_zero_flatten L
+  simp [getElem?_eq_getElem, h] at t
+  simp [← t]
+
+theorem back?_flatten {L : Array (Array α)} :
+    (flatten L).back? = (L.findSomeRev? fun l => l.back?) := by
+  cases L using array_array_induction
+  simp [List.getLast?_flatten, ← List.map_reverse, List.findSome?_map, Function.comp_def]
+
+theorem findSome?_mkArray : findSome? f (mkArray n a) = if n = 0 then none else f a := by
+  simp [mkArray_eq_toArray_replicate, List.findSome?_replicate]
+
+@[simp] theorem findSome?_mkArray_of_pos (h : 0 < n) : findSome? f (mkArray n a) = f a := by
+  simp [findSome?_mkArray, Nat.ne_of_gt h]
+
+-- Argument is unused, but used to decide whether `simp` should unfold.
+@[simp] theorem findSome?_mkArray_of_isSome (_ : (f a).isSome) :
+   findSome? f (mkArray n a) = if n = 0 then none else f a := by
+  simp [findSome?_mkArray]
+
+@[simp] theorem findSome?_mkArray_of_isNone (h : (f a).isNone) :
+    findSome? f (mkArray n a) = none := by
+  rw [Option.isNone_iff_eq_none] at h
+  simp [findSome?_mkArray, h]
+
+/-! ### find? -/
+
+@[simp] theorem find?_singleton (a : α) (p : α → Bool) :
+    #[a].find? p = if p a then some a else none := by
+  simp [singleton_eq_toArray_singleton]
+
+@[simp] theorem findRev?_push_of_pos (l : Array α) (h : p a) :
+    findRev? p (l.push a) = some a := by
+  cases l; simp [h]
+
+@[simp] theorem findRev?_cons_of_neg (l : Array α) (h : ¬p a) :
+    findRev? p (l.push a) = findRev? p l := by
+  cases l; simp [h]
+
+@[simp] theorem find?_eq_none : find? p l = none ↔ ∀ x ∈ l, ¬ p x := by
+  cases l; simp
+
+theorem find?_eq_some_iff_append {xs : Array α} :
+    xs.find? p = some b ↔ p b ∧ ∃ (as bs : Array α), xs = as.push b ++ bs ∧ ∀ a ∈ as, !p a := by
+  rcases xs with ⟨xs⟩
+  simp only [List.find?_toArray, List.find?_eq_some_iff_append, Bool.not_eq_eq_eq_not,
+    Bool.not_true, exists_and_right, and_congr_right_iff]
+  intro w
+  constructor
+  · rintro ⟨as, ⟨⟨x, rfl⟩, h⟩⟩
+    exact ⟨as.toArray, ⟨x.toArray, by simp⟩ , by simpa using h⟩
+  · rintro ⟨as, ⟨⟨x, h'⟩, h⟩⟩
+    exact ⟨as.toList, ⟨x.toList, by simpa using congrArg Array.toList h'⟩,
+      by simpa using h⟩
+
+@[simp]
+theorem find?_push_eq_some {xs : Array α} :
+    (xs.push a).find? p = some b ↔ xs.find? p = some b ∨ (xs.find? p = none ∧ (p a ∧ a = b)) := by
+  cases xs; simp
+
+@[simp] theorem find?_isSome {xs : Array α} {p : α → Bool} : (xs.find? p).isSome ↔ ∃ x, x ∈ xs ∧ p x := by
+  cases xs; simp
+
+theorem find?_some {xs : Array α} (h : find? p xs = some a) : p a := by
+  cases xs
+  simp at h
+  exact List.find?_some h
+
+theorem mem_of_find?_eq_some {xs : Array α} (h : find? p xs = some a) : a ∈ xs := by
+  cases xs
+  simp at h
+  simpa using List.mem_of_find?_eq_some h
+
+theorem get_find?_mem {xs : Array α} (h) : (xs.find? p).get h ∈ xs := by
+  cases xs
+  simp [List.get_find?_mem]
+
+@[simp] theorem find?_filter {xs : Array α} (p q : α → Bool) :
+    (xs.filter p).find? q = xs.find? (fun a => p a ∧ q a) := by
+  cases xs; simp
+
+@[simp] theorem getElem?_zero_filter (p : α → Bool) (l : Array α) :
+    (l.filter p)[0]? = l.find? p := by
+  cases l; simp [← List.head?_eq_getElem?]
+
+@[simp] theorem getElem_zero_filter (p : α → Bool) (l : Array α) (h) :
+    (l.filter p)[0] =
+      (l.find? p).get (by cases l; simpa [← List.countP_eq_length_filter] using h) := by
+  cases l
+  simp [List.getElem_zero_eq_head]
+
+@[simp] theorem back?_filter (p : α → Bool) (l : Array α) : (l.filter p).back? = l.findRev? p := by
+  cases l; simp
+
+@[simp] theorem back!_filter [Inhabited α] (p : α → Bool) (l : Array α) :
+    (l.filter p).back! = (l.findRev? p).get! := by
+  cases l; simp [Option.get!_eq_getD]
+
+@[simp] theorem find?_filterMap (xs : Array α) (f : α → Option β) (p : β → Bool) :
+    (xs.filterMap f).find? p = (xs.find? (fun a => (f a).any p)).bind f := by
+  cases xs; simp
+
+@[simp] theorem find?_map (f : β → α) (xs : Array β) :
+    find? p (xs.map f) = (xs.find? (p ∘ f)).map f := by
+  cases xs; simp
+
+@[simp] theorem find?_append {l₁ l₂ : Array α} :
+    (l₁ ++ l₂).find? p = (l₁.find? p).or (l₂.find? p) := by
+  cases l₁
+  cases l₂
+  simp
+
+@[simp] theorem find?_flatten (xs : Array (Array α)) (p : α → Bool) :
+    xs.flatten.find? p = xs.findSome? (·.find? p) := by
+  cases xs using array_array_induction
+  simp [List.findSome?_map, Function.comp_def]
+
+theorem find?_flatten_eq_none {xs : Array (Array α)} {p : α → Bool} :
+    xs.flatten.find? p = none ↔ ∀ ys ∈ xs, ∀ x ∈ ys, !p x := by
+  simp
+
+/--
+If `find? p` returns `some a` from `xs.flatten`, then `p a` holds, and
+some array in `xs` contains `a`, and no earlier element of that array satisfies `p`.
+Moreover, no earlier array in `xs` has an element satisfying `p`.
+-/
+theorem find?_flatten_eq_some {xs : Array (Array α)} {p : α → Bool} {a : α} :
+    xs.flatten.find? p = some a ↔
+      p a ∧ ∃ (as : Array (Array α)) (ys zs : Array α) (bs : Array (Array α)),
+        xs = as.push (ys.push a ++ zs) ++ bs ∧
+        (∀ a ∈ as, ∀ x ∈ a, !p x) ∧ (∀ x ∈ ys, !p x) := by
+  cases xs using array_array_induction
+  simp only [flatten_toArray_map_toArray, List.find?_toArray, List.find?_flatten_eq_some]
+  simp only [Bool.not_eq_eq_eq_not, Bool.not_true, exists_and_right, and_congr_right_iff]
+  intro w
+  constructor
+  · rintro ⟨as, ys, ⟨⟨zs, bs, rfl⟩, h₁, h₂⟩⟩
+    exact ⟨as.toArray.map List.toArray, ys.toArray,
+      ⟨zs.toArray, bs.toArray.map List.toArray, by simp⟩, by simpa using h₁, by simpa using h₂⟩
+  · rintro ⟨as, ys, ⟨⟨zs, bs, h⟩, h₁, h₂⟩⟩
+    replace h := congrArg (·.map Array.toList) (congrArg Array.toList h)
+    simp [Function.comp_def] at h
+    exact ⟨as.toList.map Array.toList, ys.toList,
+      ⟨zs.toList, bs.toList.map Array.toList, by simpa using h⟩,
+        by simpa using h₁, by simpa using h₂⟩
+
+@[simp] theorem find?_flatMap (xs : Array α) (f : α → Array β) (p : β → Bool) :
+    (xs.flatMap f).find? p = xs.findSome? (fun x => (f x).find? p) := by
+  cases xs
+  simp [List.find?_flatMap, Array.flatMap_toArray]
+
+theorem find?_flatMap_eq_none {xs : Array α} {f : α → Array β} {p : β → Bool} :
+    (xs.flatMap f).find? p = none ↔ ∀ x ∈ xs, ∀ y ∈ f x, !p y := by
+  simp
+
+theorem find?_mkArray :
+    find? p (mkArray n a) = if n = 0 then none else if p a then some a else none := by
+  simp [mkArray_eq_toArray_replicate, List.find?_replicate]
+
+@[simp] theorem find?_mkArray_of_length_pos (h : 0 < n) :
+    find? p (mkArray n a) = if p a then some a else none := by
+  simp [find?_mkArray, Nat.ne_of_gt h]
+
+@[simp] theorem find?_mkArray_of_pos (h : p a) :
+    find? p (mkArray n a) = if n = 0 then none else some a := by
+  simp [find?_mkArray, h]
+
+@[simp] theorem find?_mkArray_of_neg (h : ¬ p a) : find? p (mkArray n a) = none := by
+  simp [find?_mkArray, h]
+
+-- This isn't a `@[simp]` lemma since there is already a lemma for `l.find? p = none` for any `l`.
+theorem find?_mkArray_eq_none {n : Nat} {a : α} {p : α → Bool} :
+    (mkArray n a).find? p = none ↔ n = 0 ∨ !p a := by
+  simp [mkArray_eq_toArray_replicate, List.find?_replicate_eq_none, Classical.or_iff_not_imp_left]
+
+@[simp] theorem find?_mkArray_eq_some {n : Nat} {a b : α} {p : α → Bool} :
+    (mkArray n a).find? p = some b ↔ n ≠ 0 ∧ p a ∧ a = b := by
+  simp [mkArray_eq_toArray_replicate]
+
+@[simp] theorem get_find?_mkArray (n : Nat) (a : α) (p : α → Bool) (h) :
+    ((mkArray n a).find? p).get h = a := by
+  simp [mkArray_eq_toArray_replicate]
+
+end Array

src/Init/Data/Array/Lemmas.lean

@@ -601,7 +601,7 @@ theorem getElem?_mkArray (n : Nat) (v : α) (i : Nat) :
 
 /-- # mem -/
 
-theorem mem_toList {a : α} {l : Array α} : a ∈ l.toList ↔ a ∈ l := mem_def.symm
+@[simp] theorem mem_toList {a : α} {l : Array α} : a ∈ l.toList ↔ a ∈ l := mem_def.symm
 
 theorem not_mem_nil (a : α) : ¬ a ∈ #[] := nofun
 
@@ -620,19 +620,19 @@ theorem getElem?_of_mem {a : α} {as : Array α} :
 
 @[simp] theorem mem_dite_empty_left {x : α} [Decidable p] {l : ¬ p → Array α} :
     (x ∈ if h : p then #[] else l h) ↔ ∃ h : ¬ p, x ∈ l h := by
-  split <;> simp_all [mem_def]
+  split <;> simp_all
 
 @[simp] theorem mem_dite_empty_right {x : α} [Decidable p] {l : p → Array α} :
     (x ∈ if h : p then l h else #[]) ↔ ∃ h : p, x ∈ l h := by
-  split <;> simp_all [mem_def]
+  split <;> simp_all
 
 @[simp] theorem mem_ite_empty_left {x : α} [Decidable p] {l : Array α} :
     (x ∈ if p then #[] else l) ↔ ¬ p ∧ x ∈ l := by
-  split <;> simp_all [mem_def]
+  split <;> simp_all
 
 @[simp] theorem mem_ite_empty_right {x : α} [Decidable p] {l : Array α} :
     (x ∈ if p then l else #[]) ↔ p ∧ x ∈ l := by
-  split <;> simp_all [mem_def]
+  split <;> simp_all
 
 /-- # get lemmas -/
 
@@ -1218,6 +1218,14 @@ theorem push_eq_append_singleton (as : Array α) (x) : as.push x = as ++ #[x] :=
 @[simp] theorem size_append (as bs : Array α) : (as ++ bs).size = as.size + bs.size := by
   simp only [size, toList_append, List.length_append]
 
+@[simp] theorem empty_append (as : Array α) : #[] ++ as = as := by
+  cases as
+  simp
+
+@[simp] theorem append_empty (as : Array α) : as ++ #[] = as := by
+  cases as
+  simp
+
 theorem getElem_append {as bs : Array α} (h : i < (as ++ bs).size) :
     (as ++ bs)[i] = if h' : i < as.size then as[i] else bs[i - as.size]'(by simp at h; omega) := by
   cases as; cases bs
@@ -1594,9 +1602,9 @@ theorem swap_comm (a : Array α) {i j : Fin a.size} : a.swap i j = a.swap j i :=
 
 /-! ### eraseIdx -/
 
-theorem feraseIdx_eq_eraseIdx {a : Array α} {i : Fin a.size} :
-    a.feraseIdx i = a.eraseIdx i.1 := by
-  simp [eraseIdx]
+theorem eraseIdx_eq_eraseIdxIfInBounds {a : Array α} {i : Nat} (h : i < a.size) :
+    a.eraseIdx i h = a.eraseIdxIfInBounds i := by
+  simp [eraseIdxIfInBounds, h]
 
 /-! ### isPrefixOf -/
 
@@ -1826,16 +1834,15 @@ theorem takeWhile_go_toArray (p : α → Bool) (l : List α) (i : Nat) :
     l.toArray.takeWhile p = (l.takeWhile p).toArray := by
   simp [Array.takeWhile, takeWhile_go_toArray]
 
-@[simp] theorem feraseIdx_toArray (l : List α) (i : Fin l.toArray.size) :
-    l.toArray.feraseIdx i = (l.eraseIdx i).toArray := by
-  rw [feraseIdx]
-  split <;> rename_i h
-  · rw [feraseIdx_toArray]
+@[simp] theorem eraseIdx_toArray (l : List α) (i : Nat) (h : i < l.toArray.size) :
+    l.toArray.eraseIdx i h = (l.eraseIdx i).toArray := by
+  rw [Array.eraseIdx]
+  split <;> rename_i h'
+  · rw [eraseIdx_toArray]
     simp only [swap_toArray, Fin.getElem_fin, toList_toArray, mk.injEq]
     rw [eraseIdx_set_gt (by simp), eraseIdx_set_eq]
     simp
-  · rcases i with ⟨i, w⟩
-    simp at h w
+  · simp at h h'
     have t : i = l.length - 1 := by omega
     simp [t]
 termination_by l.length - i
@@ -1845,9 +1852,9 @@ decreasing_by
   simp
   omega
 
-@[simp] theorem eraseIdx_toArray (l : List α) (i : Nat) :
-    l.toArray.eraseIdx i = (l.eraseIdx i).toArray := by
-  rw [Array.eraseIdx]
+@[simp] theorem eraseIdxIfInBounds_toArray (l : List α) (i : Nat) :
+    l.toArray.eraseIdxIfInBounds i = (l.eraseIdx i).toArray := by
+  rw [Array.eraseIdxIfInBounds]
   split
   · simp
   · simp_all [eraseIdx_eq_self.2]
@@ -1866,16 +1873,60 @@ namespace Array
     (as.takeWhile p).toList = as.toList.takeWhile p := by
   induction as; simp
 
-@[simp] theorem toList_feraseIdx (as : Array α) (i : Fin as.size) :
-    (as.feraseIdx i).toList = as.toList.eraseIdx i.1 := by
+@[simp] theorem toList_eraseIdx (as : Array α) (i : Nat) (h : i < as.size) :
+    (as.eraseIdx i h).toList = as.toList.eraseIdx i := by
   induction as
   simp
 
-@[simp] theorem toList_eraseIdx (as : Array α) (i : Nat) :
-    (as.eraseIdx i).toList = as.toList.eraseIdx i := by
+@[simp] theorem toList_eraseIdxIfInBounds (as : Array α) (i : Nat) :
+    (as.eraseIdxIfInBounds i).toList = as.toList.eraseIdx i := by
   induction as
   simp
 
+/-! ### map -/
+
+@[simp] theorem map_map {f : α → β} {g : β → γ} {as : Array α} :
+    (as.map f).map g = as.map (g ∘ f) := by
+  cases as; simp
+
+@[simp] theorem map_id_fun : map (id : α → α) = id := by
+  funext l
+  induction l <;> simp_all
+
+/-- `map_id_fun'` differs from `map_id_fun` by representing the identity function as a lambda, rather than `id`. -/
+@[simp] theorem map_id_fun' : map (fun (a : α) => a) = id := map_id_fun
+
+-- This is not a `@[simp]` lemma because `map_id_fun` will apply.
+theorem map_id (as : Array α) : map (id : α → α) as = as := by
+  cases as <;> simp_all
+
+/-- `map_id'` differs from `map_id` by representing the identity function as a lambda, rather than `id`. -/
+-- This is not a `@[simp]` lemma because `map_id_fun'` will apply.
+theorem map_id' (as : Array α) : map (fun (a : α) => a) as = as := map_id as
+
+/-- Variant of `map_id`, with a side condition that the function is pointwise the identity. -/
+theorem map_id'' {f : α → α} (h : ∀ x, f x = x) (as : Array α) : map f as = as := by
+  simp [show f = id from funext h]
+
+theorem array_array_induction (P : Array (Array α) → Prop) (h : ∀ (xss : List (List α)), P (xss.map List.toArray).toArray)
+    (ass : Array (Array α)) : P ass := by
+  specialize h (ass.toList.map toList)
+  simpa [← toList_map, Function.comp_def, map_id] using h
+
+/-! ### flatten -/
+
+@[simp] theorem flatten_empty : flatten (#[] : Array (Array α)) = #[] := rfl
+
+@[simp] theorem flatten_toArray_map_toArray (xss : List (List α)) :
+    (xss.map List.toArray).toArray.flatten = xss.flatten.toArray := by
+  simp [flatten]
+  suffices ∀ as, List.foldl (fun r a => r ++ a) as (List.map List.toArray xss) = as ++ xss.flatten.toArray by
+    simpa using this #[]
+  intro as
+  induction xss generalizing as with
+  | nil => simp
+  | cons xs xss ih => simp [ih]
+
 /-! ### findSomeRevM?, findRevM?, findSomeRev?, findRev? -/
 
 @[simp] theorem findSomeRevM?_eq_findSomeM?_reverse
@@ -1940,6 +1991,27 @@ namespace Array
   cases as
   simp
 
+@[simp] theorem flatMap_empty {β} (f : α → Array β) : (#[] : Array α).flatMap f = #[] := rfl
+
+@[simp] theorem flatMap_toArray_cons {β} (f : α → Array β) (a : α) (as : List α) :
+    (a :: as).toArray.flatMap f = f a ++ as.toArray.flatMap f := by
+  simp [flatMap]
+  suffices ∀ cs, List.foldl (fun bs a => bs ++ f a) (f a ++ cs) as =
+      f a ++ List.foldl (fun bs a => bs ++ f a) cs as by
+    erw [empty_append] -- Why doesn't this work via `simp`?
+    simpa using this #[]
+  intro cs
+  induction as generalizing cs <;> simp_all
+
+@[simp] theorem flatMap_toArray {β} (f : α → Array β) (as : List α) :
+    as.toArray.flatMap f = (as.flatMap (fun a => (f a).toList)).toArray := by
+  induction as with
+  | nil => simp
+  | cons a as ih =>
+    apply ext'
+    simp [ih]
+
+
 end Array
 
 /-! ### Deprecations -/

src/Init/Data/BitVec/Bitblast.lean

@@ -403,7 +403,7 @@ theorem getLsbD_neg {i : Nat} {x : BitVec w} :
       rw [carry_succ_one _ _ (by omega), ← Bool.xor_not, ← decide_not]
       simp only [add_one_ne_zero, decide_false, getLsbD_not, and_eq_true, decide_eq_true_eq,
         not_eq_eq_eq_not, Bool.not_true, false_bne, not_exists, _root_.not_and, not_eq_true,
-        bne_left_inj, decide_eq_decide]
+        bne_right_inj, decide_eq_decide]
       constructor
       · rintro h j hj; exact And.right <| h j (by omega)
       · rintro h j hj; exact ⟨by omega, h j (by omega)⟩
@@ -419,7 +419,7 @@ theorem getMsbD_neg {i : Nat} {x : BitVec w} :
     simp [hi]; omega
   case pos =>
     have h₁ : w - 1 - i < w := by omega
-    simp only [hi, decide_true, h₁, Bool.true_and, Bool.bne_left_inj, decide_eq_decide]
+    simp only [hi, decide_true, h₁, Bool.true_and, Bool.bne_right_inj, decide_eq_decide]
     constructor
     · rintro ⟨j, hj, h⟩
       refine ⟨w - 1 - j, by omega, by omega, by omega, _root_.cast ?_ h⟩

src/Init/Data/BitVec/Lemmas.lean

@@ -2611,7 +2611,7 @@ theorem getLsbD_rotateLeftAux_of_geq {x : BitVec w} {r : Nat} {i : Nat} (hi : i
   apply getLsbD_ge
   omega
 
-/-- When `r < w`, we give a formula for `(x.rotateRight r).getLsbD i`. -/
+/-- When `r < w`, we give a formula for `(x.rotateLeft r).getLsbD i`. -/
 theorem getLsbD_rotateLeft_of_le {x : BitVec w} {r i : Nat} (hr: r < w) :
     (x.rotateLeft r).getLsbD i =
       cond (i < r)
@@ -2638,6 +2638,56 @@ theorem getElem_rotateLeft {x : BitVec w} {r i : Nat} (h : i < w) :
       if h' : i < r % w then x[(w - (r % w) + i)] else x[i - (r % w)] := by
   simp [← BitVec.getLsbD_eq_getElem, h]
 
+/-- If `w ≤ x < 2 * w`, then `x % w = x - w` -/
+theorem mod_eq_sub_of_le_of_lt {x w : Nat} (x_le : w ≤ x) (x_lt : x < 2 * w) :
+    x % w = x - w := by
+  rw [Nat.mod_eq_sub_mod, Nat.mod_eq_of_lt (by omega)]
+  omega
+
+theorem getMsbD_rotateLeftAux_of_lt {x : BitVec w} {r : Nat} {i : Nat} (hi : i < w - r) :
+    (x.rotateLeftAux r).getMsbD i = x.getMsbD (r + i) := by
+  rw [rotateLeftAux, getMsbD_or]
+  simp [show i < w - r by omega, Nat.add_comm]
+
+theorem getMsbD_rotateLeftAux_of_ge {x : BitVec w} {r : Nat} {i : Nat} (hi : i ≥ w - r) :
+    (x.rotateLeftAux r).getMsbD i = (decide (i < w) && x.getMsbD (i - (w - r))) := by
+  simp [rotateLeftAux, getMsbD_or, show i + r ≥ w by omega, show ¬i < w - r by omega]
+
+/-- When `r < w`, we give a formula for `(x.rotateLeft r).getMsbD i`. -/
+theorem getMsbD_rotateLeft_of_lt {n w : Nat} {x : BitVec w} (hi : r < w):
+    (x.rotateLeft r).getMsbD n = (decide (n < w) && x.getMsbD ((r + n) % w)) := by
+  rcases w with rfl | w
+  · simp
+  · rw [BitVec.rotateLeft_eq_rotateLeftAux_of_lt (by omega)]
+    by_cases h : n < (w + 1) - r
+    · simp [getMsbD_rotateLeftAux_of_lt h, Nat.mod_eq_of_lt, show r + n < (w + 1) by omega, show n < w + 1 by omega]
+    · simp [getMsbD_rotateLeftAux_of_ge <| Nat.ge_of_not_lt h]
+      by_cases h₁ : n < w + 1
+      · simp only [h₁, decide_true, Bool.true_and]
+        have h₂ : (r + n) < 2 * (w + 1) := by omega
+        rw [mod_eq_sub_of_le_of_lt (by omega) (by omega)]
+        congr 1
+        omega
+      · simp [h₁]
+
+theorem getMsbD_rotateLeft {r n w : Nat} {x : BitVec w} :
+    (x.rotateLeft r).getMsbD n = (decide (n < w) && x.getMsbD ((r + n) % w)) := by
+  rcases w with rfl | w
+  · simp
+  · by_cases h : r < w
+    · rw [getMsbD_rotateLeft_of_lt (by omega)]
+    · rw [← rotateLeft_mod_eq_rotateLeft, getMsbD_rotateLeft_of_lt (by apply Nat.mod_lt; simp)]
+      simp
+
+@[simp]
+theorem msb_rotateLeft {m w : Nat} {x : BitVec w} :
+    (x.rotateLeft m).msb = x.getMsbD (m % w) := by
+  simp only [BitVec.msb, getMsbD_rotateLeft]
+  by_cases h : w = 0
+  · simp [h]
+  · simp
+    omega
+
 /-! ## Rotate Right -/
 
 /--
@@ -2699,7 +2749,7 @@ theorem rotateRight_mod_eq_rotateRight {x : BitVec w} {r : Nat} :
   simp only [rotateRight, Nat.mod_mod]
 
 /-- When `r < w`, we give a formula for `(x.rotateRight r).getLsb i`. -/
-theorem getLsbD_rotateRight_of_le {x : BitVec w} {r i : Nat} (hr: r < w) :
+theorem getLsbD_rotateRight_of_lt {x : BitVec w} {r i : Nat} (hr: r < w) :
     (x.rotateRight r).getLsbD i =
       cond (i < w - r)
       (x.getLsbD (r + i))
@@ -2717,7 +2767,7 @@ theorem getLsbD_rotateRight {x : BitVec w} {r i : Nat} :
       (decide (i < w) && x.getLsbD (i - (w - (r % w)))) := by
   rcases w with ⟨rfl, w⟩
   · simp
-  · rw [← rotateRight_mod_eq_rotateRight, getLsbD_rotateRight_of_le (Nat.mod_lt _ (by omega))]
+  · rw [← rotateRight_mod_eq_rotateRight, getLsbD_rotateRight_of_lt (Nat.mod_lt _ (by omega))]
 
 @[simp]
 theorem getElem_rotateRight {x : BitVec w} {r i : Nat} (h : i < w) :
@@ -2725,6 +2775,56 @@ theorem getElem_rotateRight {x : BitVec w} {r i : Nat} (h : i < w) :
   simp only [← BitVec.getLsbD_eq_getElem]
   simp [getLsbD_rotateRight, h]
 
+theorem getMsbD_rotateRightAux_of_lt {x : BitVec w} {r : Nat} {i : Nat} (hi : i < r) :
+    (x.rotateRightAux r).getMsbD i = x.getMsbD (i + (w - r)) := by
+  rw [rotateRightAux, getMsbD_or, getMsbD_ushiftRight]
+  simp [show i < r by omega]
+
+theorem getMsbD_rotateRightAux_of_ge {x : BitVec w} {r : Nat} {i : Nat} (hi : i ≥ r) :
+    (x.rotateRightAux r).getMsbD i = (decide (i < w) && x.getMsbD (i - r)) := by
+  simp [rotateRightAux, show ¬ i < r by omega, show i + (w - r) ≥ w by omega]
+
+/-- When `m < w`, we give a formula for `(x.rotateLeft m).getMsbD i`. -/
+@[simp]
+theorem getMsbD_rotateRight_of_lt {w n m : Nat} {x : BitVec w} (hr : m < w):
+    (x.rotateRight m).getMsbD n = (decide (n < w) && (if (n < m % w)
+    then x.getMsbD ((w + n - m % w) % w) else x.getMsbD (n - m % w))):= by
+  rcases w with rfl | w
+  · simp
+  · rw [rotateRight_eq_rotateRightAux_of_lt (by omega)]
+    by_cases h : n < m
+    · simp only [getMsbD_rotateRightAux_of_lt h, show n < w + 1 by omega, decide_true,
+        show m % (w + 1) = m by rw [Nat.mod_eq_of_lt hr], h, ↓reduceIte,
+        show (w + 1 + n - m) < (w + 1) by omega, Nat.mod_eq_of_lt, Bool.true_and]
+      congr 1
+      omega
+    · simp [h, getMsbD_rotateRightAux_of_ge <| Nat.ge_of_not_lt h]
+      by_cases h₁ : n < w + 1
+      · simp [h, h₁, decide_true, Bool.true_and, Nat.mod_eq_of_lt hr]
+      · simp [h₁]
+
+@[simp]
+theorem getMsbD_rotateRight {w n m : Nat} {x : BitVec w} :
+    (x.rotateRight m).getMsbD n = (decide (n < w) && (if (n < m % w)
+    then x.getMsbD ((w + n - m % w) % w) else x.getMsbD (n - m % w))):= by
+  rcases w with rfl | w
+  · simp
+  · by_cases h₀ : m < w
+    · rw [getMsbD_rotateRight_of_lt (by omega)]
+    · rw [← rotateRight_mod_eq_rotateRight, getMsbD_rotateRight_of_lt (by apply Nat.mod_lt; simp)]
+      simp
+
+@[simp]
+theorem msb_rotateRight {r w : Nat} {x : BitVec w} :
+    (x.rotateRight r).msb = x.getMsbD ((w - r % w) % w) := by
+  simp only [BitVec.msb, getMsbD_rotateRight]
+  by_cases h₀ : 0 < w
+  · simp only [h₀, decide_true, Nat.add_zero, Nat.zero_le, Nat.sub_eq_zero_of_le, Bool.true_and,
+    ite_eq_left_iff, Nat.not_lt, Nat.le_zero_eq]
+    intro h₁
+    simp [h₁]
+  · simp [show w = 0 by omega]
+
 /- ## twoPow -/
 
 theorem twoPow_eq (w : Nat) (i : Nat) : twoPow w i = 1#w <<< i := by

src/Init/Data/Bool.lean

@@ -238,8 +238,8 @@ theorem not_bne_not : ∀ (x y : Bool), ((!x) != (!y)) = (x != y) := by simp
 @[simp] theorem bne_assoc : ∀ (x y z : Bool), ((x != y) != z) = (x != (y != z)) := by decide
 instance : Std.Associative (· != ·) := ⟨bne_assoc⟩
 
-@[simp] theorem bne_left_inj  : ∀ {x y z : Bool}, (x != y) = (x != z) ↔ y = z := by decide
-@[simp] theorem bne_right_inj : ∀ {x y z : Bool}, (x != z) = (y != z) ↔ x = y := by decide
+@[simp] theorem bne_right_inj  : ∀ {x y z : Bool}, (x != y) = (x != z) ↔ y = z := by decide
+@[simp] theorem bne_left_inj : ∀ {x y z : Bool}, (x != z) = (y != z) ↔ x = y := by decide
 
 theorem eq_not_of_ne : ∀ {x y : Bool}, x ≠ y → x = !y := by decide
 
@@ -295,9 +295,9 @@ theorem xor_right_comm : ∀ (x y z : Bool), ((x ^^ y) ^^ z) = ((x ^^ z) ^^ y) :
 
 theorem xor_assoc : ∀ (x y z : Bool), ((x ^^ y) ^^ z) = (x ^^ (y ^^ z)) := bne_assoc
 
-theorem xor_left_inj : ∀ {x y z : Bool}, (x ^^ y) = (x ^^ z) ↔ y = z := bne_left_inj
+theorem xor_right_inj : ∀ {x y z : Bool}, (x ^^ y) = (x ^^ z) ↔ y = z := bne_right_inj
 
-theorem xor_right_inj : ∀ {x y z : Bool}, (x ^^ z) = (y ^^ z) ↔ x = y := bne_right_inj
+theorem xor_left_inj : ∀ {x y z : Bool}, (x ^^ z) = (y ^^ z) ↔ x = y := bne_left_inj
 
 /-! ### le/lt -/
 

src/Init/Data/Float.lean

@@ -47,6 +47,25 @@ def Float.lt : Float → Float → Prop := fun a b =>
 def Float.le : Float → Float → Prop := fun a b =>
   floatSpec.le a.val b.val
 
+/--
+Raw transmutation from `UInt64`.
+
+Floats and UInts have the same endianness on all supported platforms.
+IEEE 754 very precisely specifies the bit layout of floats.
+-/
+@[extern "lean_float_of_bits"] opaque Float.ofBits : UInt64 → Float
+
+/--
+Raw transmutation to `UInt64`.
+
+Floats and UInts have the same endianness on all supported platforms.
+IEEE 754 very precisely specifies the bit layout of floats.
+
+Note that this function is distinct from `Float.toUInt64`, which attempts
+to preserve the numeric value, and not the bitwise value.
+-/
+@[extern "lean_float_to_bits"] opaque Float.toBits : Float → UInt64
+
 instance : Add Float := ⟨Float.add⟩
 instance : Sub Float := ⟨Float.sub⟩
 instance : Mul Float := ⟨Float.mul⟩

src/Init/Data/Int/Lemmas.lean

@@ -329,22 +329,22 @@ theorem toNat_sub (m n : Nat) : toNat (m - n) = m - n := by
 /- ## add/sub injectivity -/
 
 @[simp]
-protected theorem add_right_inj {i j : Int} (k : Int) : (i + k = j + k) ↔ i = j := by
+protected theorem add_left_inj {i j : Int} (k : Int) : (i + k = j + k) ↔ i = j := by
   apply Iff.intro
   · intro p
     rw [←Int.add_sub_cancel i k, ←Int.add_sub_cancel j k, p]
   · exact congrArg (· + k)
 
 @[simp]
-protected theorem add_left_inj {i j : Int} (k : Int) : (k + i = k + j) ↔ i = j := by
+protected theorem add_right_inj {i j : Int} (k : Int) : (k + i = k + j) ↔ i = j := by
   simp [Int.add_comm k]
 
 @[simp]
-protected theorem sub_left_inj {i j : Int} (k : Int) : (k - i = k - j) ↔ i = j := by
+protected theorem sub_right_inj {i j : Int} (k : Int) : (k - i = k - j) ↔ i = j := by
   simp [Int.sub_eq_add_neg, Int.neg_inj]
 
 @[simp]
-protected theorem sub_right_inj {i j : Int} (k : Int) : (i - k = j - k) ↔ i = j := by
+protected theorem sub_left_inj {i j : Int} (k : Int) : (i - k = j - k) ↔ i = j := by
   simp [Int.sub_eq_add_neg]
 
 /- ## Ring properties -/

src/Init/Data/List/Attach.lean

@@ -238,7 +238,7 @@ theorem get_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h :
     (hn : n < (pmap f l h).length) :
     get (pmap f l h) ⟨n, hn⟩ =
       f (get l ⟨n, @length_pmap _ _ p f l h ▸ hn⟩)
-        (h _ (get_mem l n (@length_pmap _ _ p f l h ▸ hn))) := by
+        (h _ (get_mem l ⟨n, @length_pmap _ _ p f l h ▸ hn⟩)) := by
   simp only [get_eq_getElem]
   simp [getElem_pmap]
 

src/Init/Data/List/Lemmas.lean

@@ -372,6 +372,17 @@ theorem getElem?_concat_length (l : List α) (a : α) : (l ++ [a])[l.length]? =
 @[deprecated getElem?_concat_length (since := "2024-06-12")]
 theorem get?_concat_length (l : List α) (a : α) : (l ++ [a]).get? l.length = some a := by simp
 
+@[simp] theorem isSome_getElem? {l : List α} {n : Nat} : l[n]?.isSome ↔ n < l.length := by
+  by_cases h : n < l.length
+  · simp_all
+  · simp [h]
+    simp_all
+
+@[simp] theorem isNone_getElem? {l : List α} {n : Nat} : l[n]?.isNone ↔ l.length ≤ n := by
+  by_cases h : n < l.length
+  · simp_all
+  · simp [h]
+
 /-! ### mem -/
 
 @[simp] theorem not_mem_nil (a : α) : ¬ a ∈ [] := nofun
@@ -492,9 +503,9 @@ theorem getElem?_of_mem {a} {l : List α} (h : a ∈ l) : ∃ n : Nat, l[n]? = s
 theorem get?_of_mem {a} {l : List α} (h : a ∈ l) : ∃ n, l.get? n = some a :=
   let ⟨⟨n, _⟩, e⟩ := get_of_mem h; ⟨n, e ▸ get?_eq_get _⟩
 
-theorem get_mem : ∀ (l : List α) n h, get l ⟨n, h⟩ ∈ l
-  | _ :: _, 0, _ => .head ..
-  | _ :: l, _+1, _ => .tail _ (get_mem l ..)
+theorem get_mem : ∀ (l : List α) n, get l n ∈ l
+  | _ :: _, ⟨0, _⟩ => .head ..
+  | _ :: l, ⟨_+1, _⟩ => .tail _ (get_mem l ..)
 
 theorem getElem?_mem {l : List α} {n : Nat} {a : α} (e : l[n]? = some a) : a ∈ l :=
   let ⟨_, e⟩ := getElem?_eq_some_iff.1 e; e ▸ getElem_mem ..
@@ -1025,6 +1036,10 @@ theorem getLast_eq_getElem : ∀ (l : List α) (h : l ≠ []),
   | _ :: _ :: _, _ => by
     simp [getLast, get, Nat.succ_sub_succ, getLast_eq_getElem]
 
+theorem getElem_length_sub_one_eq_getLast (l : List α) (h) :
+    l[l.length - 1] = getLast l (by cases l; simp at h; simp) := by
+  rw [← getLast_eq_getElem]
+
 @[deprecated getLast_eq_getElem (since := "2024-07-15")]
 theorem getLast_eq_get (l : List α) (h : l ≠ []) :
     getLast l h = l.get ⟨l.length - 1, by
@@ -1149,6 +1164,11 @@ theorem head_eq_getElem (l : List α) (h : l ≠ []) : head l h = l[0]'(length_p
   | nil => simp at h
   | cons _ _ => simp
 
+theorem getElem_zero_eq_head (l : List α) (h) : l[0] = head l (by simpa [length_pos] using h) := by
+  cases l with
+  | nil => simp at h
+  | cons _ _ => simp
+
 theorem head_eq_iff_head?_eq_some {xs : List α} (h) : xs.head h = a ↔ xs.head? = some a := by
   cases xs with
   | nil => simp at h
@@ -2395,7 +2415,7 @@ theorem forall_mem_replicate {p : α → Prop} {a : α} {n} :
 
 @[simp] theorem getElem_replicate (a : α) {n : Nat} {m} (h : m < (replicate n a).length) :
     (replicate n a)[m] = a :=
-  eq_of_mem_replicate (get_mem _ _ _)
+  eq_of_mem_replicate (getElem_mem _)
 
 @[deprecated getElem_replicate (since := "2024-06-12")]
 theorem get_replicate (a : α) {n : Nat} (m : Fin _) : (replicate n a).get m = a := by

src/Init/Data/Nat/Lemmas.lean

@@ -1029,3 +1029,12 @@ instance decidableExistsLT [h : DecidablePred p] : DecidablePred fun n => ∃ m
 instance decidableExistsLE [DecidablePred p] : DecidablePred fun n => ∃ m : Nat, m ≤ n ∧ p m :=
   fun n => decidable_of_iff (∃ m, m < n + 1 ∧ p m)
     (exists_congr fun _ => and_congr_left' Nat.lt_succ_iff)
+
+/-! ### Results about `List.sum` specialized to `Nat` -/
+
+protected theorem sum_pos_iff_exists_pos {l : List Nat} : 0 < l.sum ↔ ∃ x ∈ l, 0 < x := by
+  induction l with
+  | nil => simp
+  | cons x xs ih =>
+    simp [← ih]
+    omega

src/Init/Data/Option/Lemmas.lean

@@ -55,7 +55,9 @@ theorem get_eq_getD {fallback : α} : (o : Option α) → {h : o.isSome} → o.g
 theorem some_get! [Inhabited α] : (o : Option α) → o.isSome → some (o.get!) = o
   | some _, _ => rfl
 
-theorem get!_eq_getD_default [Inhabited α] (o : Option α) : o.get! = o.getD default := rfl
+theorem get!_eq_getD [Inhabited α] (o : Option α) : o.get! = o.getD default := rfl
+
+@[deprecated get!_eq_getD (since := "2024-11-18")] abbrev get!_eq_getD_default := @get!_eq_getD
 
 theorem mem_unique {o : Option α} {a b : α} (ha : a ∈ o) (hb : b ∈ o) : a = b :=
   some.inj <| ha ▸ hb

src/Init/Data/Random.lean

@@ -113,10 +113,10 @@ initialize IO.stdGenRef : IO.Ref StdGen ←
   let seed := UInt64.toNat (ByteArray.toUInt64LE! (← IO.getRandomBytes 8))
   IO.mkRef (mkStdGen seed)
 
-def IO.setRandSeed (n : Nat) : IO Unit :=
+def IO.setRandSeed (n : Nat) : BaseIO Unit :=
   IO.stdGenRef.set (mkStdGen n)
 
-def IO.rand (lo hi : Nat) : IO Nat := do
+def IO.rand (lo hi : Nat) : BaseIO Nat := do
   let gen ← IO.stdGenRef.get
   let (r, gen) := randNat gen lo hi
   IO.stdGenRef.set gen

src/Init/Meta.lean

@@ -374,6 +374,9 @@ partial def structEq : Syntax → Syntax → Bool
 instance : BEq Lean.Syntax := ⟨structEq⟩
 instance : BEq (Lean.TSyntax k) := ⟨(·.raw == ·.raw)⟩
 
+/--
+Finds the first `SourceInfo` from the back of `stx` or `none` if no `SourceInfo` can be found.
+-/
 partial def getTailInfo? : Syntax → Option SourceInfo
   | atom info _   => info
   | ident info .. => info
@@ -382,14 +385,39 @@ partial def getTailInfo? : Syntax → Option SourceInfo
   | node info _ _    => info
   | _             => none
 
+/--
+Finds the first `SourceInfo` from the back of `stx` or `SourceInfo.none`
+if no `SourceInfo` can be found.
+-/
 def getTailInfo (stx : Syntax) : SourceInfo :=
   stx.getTailInfo?.getD SourceInfo.none
 
+/--
+Finds the trailing size of the first `SourceInfo` from the back of `stx`.
+If no `SourceInfo` can be found or the first `SourceInfo` from the back of `stx` contains no
+trailing whitespace, the result is `0`.
+-/
 def getTrailingSize (stx : Syntax) : Nat :=
   match stx.getTailInfo? with
   | some (SourceInfo.original (trailing := trailing) ..) => trailing.bsize
   | _ => 0
 
+/--
+Finds the trailing whitespace substring of the first `SourceInfo` from the back of `stx`.
+If no `SourceInfo` can be found or the first `SourceInfo` from the back of `stx` contains
+no trailing whitespace, the result is `none`.
+-/
+def getTrailing? (stx : Syntax) : Option Substring :=
+  stx.getTailInfo.getTrailing?
+
+/--
+Finds the tail position of the trailing whitespace of the first `SourceInfo` from the back of `stx`.
+If no `SourceInfo` can be found or the first `SourceInfo` from the back of `stx` contains
+no trailing whitespace and lacks a tail position, the result is `none`.
+-/
+def getTrailingTailPos? (stx : Syntax) (canonicalOnly := false) : Option String.Pos :=
+  stx.getTailInfo.getTrailingTailPos? canonicalOnly
+
 /--
   Return substring of original input covering `stx`.
   Result is meaningful only if all involved `SourceInfo.original`s refer to the same string (as is the case after parsing). -/

src/Init/Prelude.lean

@@ -3654,7 +3654,8 @@ namespace SourceInfo
 
 /--
 Gets the position information from a `SourceInfo`, if available.
-If `originalOnly` is true, then `.synthetic` syntax will also return `none`.
+If `canonicalOnly` is true, then `.synthetic` syntax with `canonical := false`
+will also return `none`.
 -/
 def getPos? (info : SourceInfo) (canonicalOnly := false) : Option String.Pos :=
   match info, canonicalOnly with
@@ -3665,7 +3666,8 @@ def getPos? (info : SourceInfo) (canonicalOnly := false) : Option String.Pos :=
 
 /--
 Gets the end position information from a `SourceInfo`, if available.
-If `originalOnly` is true, then `.synthetic` syntax will also return `none`.
+If `canonicalOnly` is true, then `.synthetic` syntax with `canonical := false`
+will also return `none`.
 -/
 def getTailPos? (info : SourceInfo) (canonicalOnly := false) : Option String.Pos :=
   match info, canonicalOnly with
@@ -3674,6 +3676,24 @@ def getTailPos? (info : SourceInfo) (canonicalOnly := false) : Option String.Pos
   | synthetic (endPos := endPos) .., false => some endPos
   | _,                               _     => none
 
+/--
+Gets the substring representing the trailing whitespace of a `SourceInfo`, if available.
+-/
+def getTrailing? (info : SourceInfo) : Option Substring :=
+  match info with
+  | original (trailing := trailing) .. => some trailing
+  | _                                  => none
+
+/--
+Gets the end position information of the trailing whitespace of a `SourceInfo`, if available.
+If `canonicalOnly` is true, then `.synthetic` syntax with `canonical := false`
+will also return `none`.
+-/
+def getTrailingTailPos? (info : SourceInfo) (canonicalOnly := false) : Option String.Pos :=
+  match info.getTrailing? with
+  | some trailing => some trailing.stopPos
+  | none          => info.getTailPos? canonicalOnly
+
 end SourceInfo
 
 /--
@@ -3972,7 +3992,6 @@ position information.
 def getPos? (stx : Syntax) (canonicalOnly := false) : Option String.Pos :=
   stx.getHeadInfo.getPos? canonicalOnly
 
-
 /--
 Get the ending position of the syntax, if possible.
 If `canonicalOnly` is true, non-canonical `synthetic` nodes are treated as not carrying

src/Init/System/IO.lean

@@ -802,6 +802,9 @@ def run (args : SpawnArgs) : IO String := do
 
 end Process
 
+/-- Returns the thread ID of the calling thread. -/
+@[extern "lean_io_get_tid"] opaque getTID : BaseIO UInt64
+
 structure AccessRight where
   read : Bool := false
   write : Bool := false

src/Init/Tactics.lean

@@ -1155,7 +1155,7 @@ Configuration for the `decide` tactic family.
 structure DecideConfig where
   /-- If true (default: false), then use only kernel reduction when reducing the `Decidable` instance.
   This is more efficient, since the default mode reduces twice (once in the elaborator and again in the kernel),
-  however kernel reduction ignores transparency settings. The `decide!` tactic is a synonym for `decide +kernel`. -/
+  however kernel reduction ignores transparency settings. -/
   kernel : Bool := false
   /-- If true (default: false), then uses the native code compiler to evaluate the `Decidable` instance,
   admitting the result via the axiom `Lean.ofReduceBool`.  This can be significantly more efficient,
@@ -1165,7 +1165,9 @@ structure DecideConfig where
   native : Bool := false
   /-- If true (default: true), then when preprocessing the goal, do zeta reduction to attempt to eliminate free variables. -/
   zetaReduce : Bool := true
-  /-- If true (default: false), then when preprocessing reverts free variables. -/
+  /-- If true (default: false), then when preprocessing, removes irrelevant variables and reverts the local context.
+  A variable is *relevant* if it appears in the target, if it appears in a relevant variable,
+  or if it is a proposition that refers to a relevant variable. -/
   revert : Bool := false
 
 /--
@@ -1240,17 +1242,6 @@ example : 1 + 1 = 2 := by rfl
 -/
 syntax (name := decide) "decide" optConfig : tactic
 
-/--
-`decide!` is a variant of the `decide` tactic that uses kernel reduction to prove the goal.
-It has the following properties:
-- Since it uses kernel reduction instead of elaborator reduction, it ignores transparency and can unfold everything.
-- While `decide` needs to reduce the `Decidable` instance twice (once during elaboration to verify whether the tactic succeeds,
-  and once during kernel type checking), the `decide!` tactic reduces it exactly once.
-
-The `decide!` syntax is short for `decide +kernel`.
--/
-syntax (name := decideBang) "decide!" optConfig : tactic
-
 /--
 `native_decide` is a synonym for `decide +native`.
 It will attempt to prove a goal of type `p` by synthesizing an instance

src/Lean/Compiler/LCNF/Basic.lean

@@ -366,10 +366,10 @@ to be updated.
 @[implemented_by updateFunDeclCoreImp] opaque FunDeclCore.updateCore (decl: FunDecl) (type : Expr) (params : Array Param) (value : Code) : FunDecl
 
 def CasesCore.extractAlt! (cases : Cases) (ctorName : Name) : Alt × Cases :=
-  let found (i : Nat) := (cases.alts[i]!, { cases with alts := cases.alts.eraseIdx i })
-  if let some i := cases.alts.findIdx? fun | .alt ctorName' .. => ctorName == ctorName' | _ => false then
+  let found i := (cases.alts[i], { cases with alts := cases.alts.eraseIdx i })
+  if let some i := cases.alts.findFinIdx? fun | .alt ctorName' .. => ctorName == ctorName' | _ => false then
     found i
-  else if let some i := cases.alts.findIdx? fun | .default _ => true | _ => false then
+  else if let some i := cases.alts.findFinIdx? fun | .default _ => true | _ => false then
     found i
   else
     unreachable!

src/Lean/Compiler/LCNF/PassManager.lean

@@ -134,9 +134,9 @@ def withEachOccurrence (targetName : Name) (f : Nat → PassInstaller) : PassIns
 
 def installAfter (targetName : Name) (p : Pass → Pass) (occurrence : Nat := 0) : PassInstaller where
   install passes :=
-    if let some idx := passes.findIdx? (fun p => p.name == targetName && p.occurrence == occurrence) then
-      let passUnderTest := passes[idx]!
-      return passes.insertAt! (idx + 1) (p passUnderTest)
+    if let some idx := passes.findFinIdx? (fun p => p.name == targetName && p.occurrence == occurrence) then
+      let passUnderTest := passes[idx]
+      return passes.insertIdx (idx + 1) (p passUnderTest)
     else
       throwError s!"Tried to insert pass after {targetName}, occurrence {occurrence} but {targetName} is not in the pass list"
 
@@ -145,9 +145,9 @@ def installAfterEach (targetName : Name) (p : Pass → Pass) : PassInstaller :=
 
 def installBefore (targetName : Name) (p : Pass → Pass) (occurrence : Nat := 0): PassInstaller where
   install passes :=
-    if let some idx := passes.findIdx? (fun p => p.name == targetName && p.occurrence == occurrence) then
-      let passUnderTest := passes[idx]!
-      return passes.insertAt! idx (p passUnderTest)
+    if let some idx := passes.findFinIdx? (fun p => p.name == targetName && p.occurrence == occurrence) then
+      let passUnderTest := passes[idx]
+      return passes.insertIdx idx (p passUnderTest)
     else
       throwError s!"Tried to insert pass after {targetName}, occurrence {occurrence} but {targetName} is not in the pass list"
 

src/Lean/Compiler/Specialize.lean

@@ -32,7 +32,7 @@ private def elabSpecArgs (declName : Name) (args : Array Syntax) : MetaM (Array
         result := result.push idx
       else
         let argName := arg.getId
-        if let some idx := argNames.getIdx? argName then
+        if let some idx := argNames.indexOf? argName then
           if result.contains idx then throwErrorAt arg "invalid specialization argument name `{argName}`, it has already been specified as a specialization candidate"
           result := result.push idx
         else

src/Lean/Data/Lsp/Basic.lean

@@ -365,6 +365,7 @@ structure TextDocumentRegistrationOptions where
 
 inductive MarkupKind where
   | plaintext | markdown
+  deriving DecidableEq, Hashable
 
 instance : FromJson MarkupKind := ⟨fun
   | str "plaintext" => Except.ok MarkupKind.plaintext
@@ -378,7 +379,7 @@ instance : ToJson MarkupKind := ⟨fun
 structure MarkupContent where
   kind  : MarkupKind
   value : String
-  deriving ToJson, FromJson
+  deriving ToJson, FromJson, DecidableEq, Hashable
 
 /-- Reference to the progress of some in-flight piece of work.
 

src/Lean/Data/Lsp/LanguageFeatures.lean

@@ -25,7 +25,7 @@ inductive CompletionItemKind where
   | unit | value | enum | keyword | snippet
   | color | file | reference | folder | enumMember
   | constant | struct | event | operator | typeParameter
-  deriving Inhabited, DecidableEq, Repr
+  deriving Inhabited, DecidableEq, Repr, Hashable
 
 instance : ToJson CompletionItemKind where
   toJson a := toJson (a.toCtorIdx + 1)
@@ -39,11 +39,11 @@ structure InsertReplaceEdit where
   newText : String
   insert  : Range
   replace : Range
-  deriving FromJson, ToJson
+  deriving FromJson, ToJson, BEq, Hashable
 
 inductive CompletionItemTag where
   | deprecated
-  deriving Inhabited, DecidableEq, Repr
+  deriving Inhabited, DecidableEq, Repr, Hashable
 
 instance : ToJson CompletionItemTag where
   toJson t := toJson (t.toCtorIdx + 1)
@@ -73,7 +73,7 @@ structure CompletionItem where
   commitCharacters? : string[]
   command? : Command
   -/
-  deriving FromJson, ToJson, Inhabited
+  deriving FromJson, ToJson, Inhabited, BEq, Hashable
 
 structure CompletionList where
   isIncomplete : Bool

src/Lean/Data/PersistentHashMap.lean

@@ -233,10 +233,10 @@ partial def eraseAux [BEq α] : Node α β → USize → α → Node α β
   | n@(Node.collision keys vals heq), _, k =>
     match keys.indexOf? k with
     | some idx =>
-      let keys' := keys.feraseIdx idx
-      have keq := keys.size_feraseIdx idx
-      let vals' := vals.feraseIdx (Eq.ndrec idx heq)
-      have veq := vals.size_feraseIdx (Eq.ndrec idx heq)
+      let keys' := keys.eraseIdx idx
+      have keq := keys.size_eraseIdx idx _
+      let vals' := vals.eraseIdx (Eq.ndrec idx heq)
+      have veq := vals.size_eraseIdx (Eq.ndrec idx heq) _
       have : keys.size - 1 = vals.size - 1 := by rw [heq]
       Node.collision keys' vals' (keq.trans (this.trans veq.symm))
     | none     => n

src/Lean/Elab/App.lean

@@ -1347,7 +1347,7 @@ where
     let mut unusableNamedArgs := unusableNamedArgs
     for x in xs, bInfo in bInfos do
       let xDecl ← x.mvarId!.getDecl
-      if let some idx := remainingNamedArgs.findIdx? (·.name == xDecl.userName) then
+      if let some idx := remainingNamedArgs.findFinIdx? (·.name == xDecl.userName) then
         /- If there is named argument with name `xDecl.userName`, then it is accounted for and we can't make use of it. -/
         remainingNamedArgs := remainingNamedArgs.eraseIdx idx
       else
@@ -1355,9 +1355,9 @@ where
           /- We found a type of the form (baseName ...).
              First, we check if the current argument is an explicit one,
              and if the current explicit position "fits" at `args` (i.e., it must be ≤ arg.size) -/
-          if argIdx ≤ args.size && bInfo.isExplicit then
+          if h : argIdx ≤ args.size ∧ bInfo.isExplicit then
             /- We can insert `e` as an explicit argument -/
-            return (args.insertAt! argIdx (Arg.expr e), namedArgs)
+            return (args.insertIdx argIdx (Arg.expr e), namedArgs)
           else
             /- If we can't add `e` to `args`, we try to add it using a named argument, but this is only possible
                if there isn't an argument with the same name occurring before it. -/
@@ -1399,8 +1399,8 @@ private def elabAppLValsAux (namedArgs : Array NamedArg) (args : Array Arg) (exp
   let rec loop : Expr → List LVal → TermElabM Expr
   | f, []          => elabAppArgs f namedArgs args expectedType? explicit ellipsis
   | f, lval::lvals => do
-    if let LVal.fieldName (fullRef := fullRef) .. := lval then
-      addDotCompletionInfo fullRef f expectedType?
+    if let LVal.fieldName (ref := ref) .. := lval then
+      addDotCompletionInfo ref f expectedType?
     let hasArgs := !namedArgs.isEmpty || !args.isEmpty
     let (f, lvalRes) ← resolveLVal f lval hasArgs
     match lvalRes with
@@ -1650,6 +1650,14 @@ private def getSuccesses (candidates : Array (TermElabResult Expr)) : TermElabM
 -/
 private def mergeFailures (failures : Array (TermElabResult Expr)) : TermElabM α := do
   let exs := failures.map fun | .error ex _ => ex | _ => unreachable!
+  let trees := failures.map (fun | .error _ s => s.meta.core.infoState.trees | _ => unreachable!)
+    |>.filterMap (·[0]?)
+  -- Retain partial `InfoTree` subtrees in an `.ofChoiceInfo` node in case of multiple failures.
+  -- This ensures that the language server still has `Info` to work with when multiple overloaded
+  -- elaborators fail.
+  withInfoContext (mkInfo := pure <| .ofChoiceInfo { elaborator := .anonymous, stx := ← getRef }) do
+    for tree in trees do
+      pushInfoTree tree
   throwErrorWithNestedErrors "overloaded" exs
 
 private def elabAppAux (f : Syntax) (namedArgs : Array NamedArg) (args : Array Arg) (ellipsis : Bool) (expectedType? : Option Expr) : TermElabM Expr := do

src/Lean/Elab/BuiltinCommand.lean

@@ -211,7 +211,7 @@ private def replaceBinderAnnotation (binder : TSyntax ``Parser.Term.bracketedBin
         else
           `(bracketedBinderF| {$id $[: $ty?]?})
       for id in ids.reverse do
-        if let some idx := binderIds.findIdx? fun binderId => binderId.raw.isIdent && binderId.raw.getId == id.raw.getId then
+        if let some idx := binderIds.findFinIdx? fun binderId => binderId.raw.isIdent && binderId.raw.getId == id.raw.getId then
           binderIds := binderIds.eraseIdx idx
           modifiedVarDecls := true
           varDeclsNew := varDeclsNew.push (← mkBinder id explicit)

src/Lean/Elab/BuiltinTerm.lean

@@ -42,16 +42,15 @@ private def elabOptLevel (stx : Syntax) : TermElabM Level :=
 @[builtin_term_elab «completion»] def elabCompletion : TermElab := fun stx expectedType? => do
   /- `ident.` is ambiguous in Lean, we may try to be completing a declaration name or access a "field". -/
   if stx[0].isIdent then
-    /- If we can elaborate the identifier successfully, we assume it is a dot-completion. Otherwise, we treat it as
-       identifier completion with a dangling `.`.
-       Recall that the server falls back to identifier completion when dot-completion fails. -/
+    -- Add both an `id` and a `dot` `CompletionInfo` and have the language server figure out which
+    -- one to use.
+    addCompletionInfo <| CompletionInfo.id stx stx[0].getId (danglingDot := true) (← getLCtx) expectedType?
     let s ← saveState
     try
       let e ← elabTerm stx[0] none
       addDotCompletionInfo stx e expectedType?
     catch _ =>
       s.restore
-      addCompletionInfo <| CompletionInfo.id stx stx[0].getId (danglingDot := true) (← getLCtx) expectedType?
     throwErrorAt stx[1] "invalid field notation, identifier or numeral expected"
   else
     elabPipeCompletion stx expectedType?
@@ -328,7 +327,7 @@ private def mkSilentAnnotationIfHole (e : Expr) : TermElabM Expr := do
 @[builtin_term_elab withAnnotateTerm] def elabWithAnnotateTerm : TermElab := fun stx expectedType? => do
   match stx with
   | `(with_annotate_term $stx $e) =>
-    withInfoContext' stx (elabTerm e expectedType?) (mkTermInfo .anonymous (expectedType? := expectedType?) stx)
+    withTermInfoContext' .anonymous stx (expectedType? := expectedType?) (elabTerm e expectedType?)
   | _ => throwUnsupportedSyntax
 
 private unsafe def evalFilePathUnsafe (stx : Syntax) : TermElabM System.FilePath :=

src/Lean/Elab/Command.lean

@@ -555,7 +555,11 @@ private def getVarDecls (s : State) : Array Syntax :=
 instance {α} : Inhabited (CommandElabM α) where
   default := throw default
 
-private def mkMetaContext : Meta.Context := {
+/--
+The environment linter framework needs to be able to run linters with the same context
+as `liftTermElabM`, so we expose that context as a public function here.
+-/
+def mkMetaContext : Meta.Context := {
   config := { foApprox := true, ctxApprox := true, quasiPatternApprox := true }
 }
 

src/Lean/Elab/Do.lean

@@ -1518,7 +1518,7 @@ mutual
   -/
   partial def doForToCode (doFor : Syntax) (doElems : List Syntax) : M CodeBlock := do
     let doForDecls := doFor[1].getSepArgs
-    if doForDecls.size > 1 then
+    if h : doForDecls.size > 1 then
       /-
         Expand
         ```

src/Lean/Elab/Extra.lean

@@ -327,15 +327,18 @@ private def toExprCore (t : Tree) : TermElabM Expr := do
   | .term _ trees e =>
     modifyInfoState (fun s => { s with trees := s.trees ++ trees }); return e
   | .binop ref kind f lhs rhs =>
-    withRef ref <| withInfoContext' ref (mkInfo := mkTermInfo .anonymous ref) do
-      mkBinOp (kind == .lazy) f (← toExprCore lhs) (← toExprCore rhs)
+    withRef ref <|
+      withTermInfoContext' .anonymous ref do
+        mkBinOp (kind == .lazy) f (← toExprCore lhs) (← toExprCore rhs)
   | .unop ref f arg =>
-    withRef ref <| withInfoContext' ref (mkInfo := mkTermInfo .anonymous ref) do
-      mkUnOp f (← toExprCore arg)
+    withRef ref <|
+      withTermInfoContext' .anonymous ref do
+        mkUnOp f (← toExprCore arg)
   | .macroExpansion macroName stx stx' nested =>
-    withRef stx <| withInfoContext' stx (mkInfo := mkTermInfo macroName stx) do
-      withMacroExpansion stx stx' do
-        toExprCore nested
+    withRef stx <|
+      withTermInfoContext' macroName stx <|
+        withMacroExpansion stx stx' <|
+          toExprCore nested
 
 /--
   Auxiliary function to decide whether we should coerce `f`'s argument to `maxType` or not.

src/Lean/Elab/InfoTree/Main.lean

@@ -139,12 +139,16 @@ def TermInfo.runMetaM (info : TermInfo) (ctx : ContextInfo) (x : MetaM α) : IO
 
 def TermInfo.format (ctx : ContextInfo) (info : TermInfo) : IO Format := do
   info.runMetaM ctx do
-    let ty : Format ← try
-      Meta.ppExpr (← Meta.inferType info.expr)
-    catch _ =>
-      pure "<failed-to-infer-type>"
+    let ty : Format ←
+      try
+        Meta.ppExpr (← Meta.inferType info.expr)
+      catch _ =>
+        pure "<failed-to-infer-type>"
     return f!"{← Meta.ppExpr info.expr} {if info.isBinder then "(isBinder := true) " else ""}: {ty} @ {formatElabInfo ctx info.toElabInfo}"
 
+def PartialTermInfo.format (ctx : ContextInfo) (info : PartialTermInfo) : Format :=
+  f!"Partial term @ {formatElabInfo ctx info.toElabInfo}"
+
 def CompletionInfo.format (ctx : ContextInfo) (info : CompletionInfo) : IO Format :=
   match info with
   | .dot i (expectedType? := expectedType?) .. => return f!"[.] {← i.format ctx} : {expectedType?}"
@@ -191,9 +195,13 @@ def FieldRedeclInfo.format (ctx : ContextInfo) (info : FieldRedeclInfo) : Format
 def OmissionInfo.format (ctx : ContextInfo) (info : OmissionInfo) : IO Format := do
   return f!"Omission @ {← TermInfo.format ctx info.toTermInfo}\nReason: {info.reason}"
 
+def ChoiceInfo.format (ctx : ContextInfo) (info : ChoiceInfo) : Format :=
+  f!"Choice @ {formatElabInfo ctx info.toElabInfo}"
+
 def Info.format (ctx : ContextInfo) : Info → IO Format
   | ofTacticInfo i         => i.format ctx
   | ofTermInfo i           => i.format ctx
+  | ofPartialTermInfo i    => pure <| i.format ctx
   | ofCommandInfo i        => i.format ctx
   | ofMacroExpansionInfo i => i.format ctx
   | ofOptionInfo i         => i.format ctx
@@ -204,10 +212,12 @@ def Info.format (ctx : ContextInfo) : Info → IO Format
   | ofFVarAliasInfo i      => pure <| i.format
   | ofFieldRedeclInfo i    => pure <| i.format ctx
   | ofOmissionInfo i       => i.format ctx
+  | ofChoiceInfo i         => pure <| i.format ctx
 
 def Info.toElabInfo? : Info → Option ElabInfo
   | ofTacticInfo i         => some i.toElabInfo
   | ofTermInfo i           => some i.toElabInfo
+  | ofPartialTermInfo i    => some i.toElabInfo
   | ofCommandInfo i        => some i.toElabInfo
   | ofMacroExpansionInfo _ => none
   | ofOptionInfo _         => none
@@ -218,6 +228,7 @@ def Info.toElabInfo? : Info → Option ElabInfo
   | ofFVarAliasInfo _      => none
   | ofFieldRedeclInfo _    => none
   | ofOmissionInfo i       => some i.toElabInfo
+  | ofChoiceInfo i         => some i.toElabInfo
 
 /--
   Helper function for propagating the tactic metavariable context to its children nodes.
@@ -311,24 +322,36 @@ def realizeGlobalNameWithInfos (ref : Syntax) (id : Name) : CoreM (List (Name ×
       addConstInfo ref n
   return ns
 
-/-- Use this to descend a node on the infotree that is being built.
+/--
+Adds a node containing the `InfoTree`s generated by `x` to the `InfoTree`s in `m`.
 
-It saves the current list of trees `t₀` and resets it and then runs `x >>= mkInfo`, producing either an `i : Info` or a hole id.
-Running `x >>= mkInfo` will modify the trees state and produce a new list of trees `t₁`.
-In the `i : Info` case, `t₁` become the children of a node `node i t₁` that is appended to `t₀`.
- -/
-def withInfoContext' [MonadFinally m] (x : m α) (mkInfo : α → m (Sum Info MVarId)) : m α := do
+If `x` succeeds and `mkInfo` yields an `Info`, the `InfoTree`s of `x` become subtrees of a node
+containing the `Info` produced by `mkInfo`, which is then added to the `InfoTree`s in `m`.
+If `x` succeeds and `mkInfo` yields an `MVarId`, the `InfoTree`s of `x` are discarded and a `hole`
+node is added to the `InfoTree`s in `m`.
+If `x` fails, the `InfoTree`s of `x` become subtrees of a node containing the `Info` produced by
+`mkInfoOnError`, which is then added to the `InfoTree`s in `m`.
+
+The `InfoTree`s in `m` are reset before `x` is executed and restored with the addition of a new tree
+after `x` is executed.
+-/
+def withInfoContext'
+    [MonadFinally m]
+    (x : m α)
+    (mkInfo : α → m (Sum Info MVarId))
+    (mkInfoOnError : m Info) :
+    m α := do
   if (← getInfoState).enabled then
     let treesSaved ← getResetInfoTrees
     Prod.fst <$> MonadFinally.tryFinally' x fun a? => do
-      match a? with
-      | none   => modifyInfoTrees fun _ => treesSaved
-      | some a =>
-        let info ← mkInfo a
-        modifyInfoTrees fun trees =>
-          match info with
-          | Sum.inl info   => treesSaved.push <| InfoTree.node info trees
-          | Sum.inr mvarId => treesSaved.push <| InfoTree.hole mvarId
+      let info ← do
+        match a? with
+        | none => pure <| .inl <| ← mkInfoOnError
+        | some a => mkInfo a
+      modifyInfoTrees fun trees =>
+        match info with
+        | Sum.inl info   => treesSaved.push <| InfoTree.node info trees
+        | Sum.inr mvarId => treesSaved.push <| InfoTree.hole mvarId
   else
     x
 

src/Lean/Elab/InfoTree/Types.lean

@@ -70,6 +70,18 @@ structure TermInfo extends ElabInfo where
   isBinder : Bool := false
   deriving Inhabited
 
+/--
+Used instead of `TermInfo` when a term couldn't successfully be elaborated,
+and so there is no complete expression available.
+
+The main purpose of `PartialTermInfo` is to ensure that the sub-`InfoTree`s of a failed elaborator
+are retained so that they can still be used in the language server.
+-/
+structure PartialTermInfo extends ElabInfo where
+  lctx : LocalContext -- The local context when the term was elaborated.
+  expectedType? : Option Expr
+  deriving Inhabited
+
 structure CommandInfo extends ElabInfo where
   deriving Inhabited
 
@@ -79,7 +91,7 @@ inductive CompletionInfo where
   | dot (termInfo : TermInfo) (expectedType? : Option Expr)
   | id (stx : Syntax) (id : Name) (danglingDot : Bool) (lctx : LocalContext) (expectedType? : Option Expr)
   | dotId (stx : Syntax) (id : Name) (lctx : LocalContext) (expectedType? : Option Expr)
-  | fieldId (stx : Syntax) (id : Name) (lctx : LocalContext) (structName : Name)
+  | fieldId (stx : Syntax) (id : Option Name) (lctx : LocalContext) (structName : Name)
   | namespaceId (stx : Syntax)
   | option (stx : Syntax)
   | endSection (stx : Syntax) (scopeNames : List String)
@@ -165,10 +177,18 @@ regular delaboration settings.
 structure OmissionInfo extends TermInfo where
   reason : String
 
+/--
+Indicates that all overloaded elaborators failed. The subtrees of a `ChoiceInfo` node are the
+partial `InfoTree`s of those failed elaborators. Retaining these partial `InfoTree`s helps
+the language server provide interactivity even when all overloaded elaborators failed.
+-/
+structure ChoiceInfo extends ElabInfo where
+
 /-- Header information for a node in `InfoTree`. -/
 inductive Info where
   | ofTacticInfo (i : TacticInfo)
   | ofTermInfo (i : TermInfo)
+  | ofPartialTermInfo (i : PartialTermInfo)
   | ofCommandInfo (i : CommandInfo)
   | ofMacroExpansionInfo (i : MacroExpansionInfo)
   | ofOptionInfo (i : OptionInfo)
@@ -179,6 +199,7 @@ inductive Info where
   | ofFVarAliasInfo (i : FVarAliasInfo)
   | ofFieldRedeclInfo (i : FieldRedeclInfo)
   | ofOmissionInfo (i : OmissionInfo)
+  | ofChoiceInfo (i : ChoiceInfo)
   deriving Inhabited
 
 /-- The InfoTree is a structure that is generated during elaboration and used

src/Lean/Elab/LetRec.lean

@@ -90,9 +90,12 @@ private def elabLetRecDeclValues (view : LetRecView) : TermElabM (Array Expr) :=
       for i in [0:view.binderIds.size] do
         addLocalVarInfo view.binderIds[i]! xs[i]!
       withDeclName view.declName do
-        withInfoContext' view.valStx (mkInfo := (pure <| .inl <| mkBodyInfo view.valStx ·)) do
-          let value ← elabTermEnsuringType view.valStx type
-          mkLambdaFVars xs value
+        withInfoContext' view.valStx
+          (mkInfo := (pure <| .inl <| mkBodyInfo view.valStx ·))
+          (mkInfoOnError := (pure <| mkBodyInfo view.valStx none))
+          do
+             let value ← elabTermEnsuringType view.valStx type
+             mkLambdaFVars xs value
 
 private def registerLetRecsToLift (views : Array LetRecDeclView) (fvars : Array Expr) (values : Array Expr) : TermElabM Unit := do
   let letRecsToLiftCurr := (← get).letRecsToLift

src/Lean/Elab/Match.lean

@@ -644,7 +644,7 @@ where
       if inaccessible? p |>.isSome then
         return mkMData k (← withReader (fun _ => true) (go b))
       else if let some (stx, p) := patternWithRef? p then
-        Elab.withInfoContext' (go p) fun p => do
+        Elab.withInfoContext' (go p) (mkInfoOnError := mkPartialTermInfo .anonymous stx) fun p => do
           /- If `p` is a free variable and we are not inside of an "inaccessible" pattern, this `p` is a binder. -/
           mkTermInfo Name.anonymous stx p (isBinder := p.isFVar && !(← read))
       else

src/Lean/Elab/MutualDef.lean

@@ -283,7 +283,7 @@ private partial def withFunLocalDecls {α} (headers : Array DefViewElabHeader) (
   loop 0 #[]
 
 private def expandWhereStructInst : Macro
-  | `(Parser.Command.whereStructInst|where $[$decls:letDecl];* $[$whereDecls?:whereDecls]?) => do
+  | whereStx@`(Parser.Command.whereStructInst|where%$whereTk $[$decls:letDecl];* $[$whereDecls?:whereDecls]?) => do
     let letIdDecls ← decls.mapM fun stx => match stx with
       | `(letDecl|$_decl:letPatDecl) => Macro.throwErrorAt stx "patterns are not allowed here"
       | `(letDecl|$decl:letEqnsDecl) => expandLetEqnsDecl decl (useExplicit := false)
@@ -300,7 +300,30 @@ private def expandWhereStructInst : Macro
         `(structInstField|$id:ident := $val)
       | stx@`(letIdDecl|_ $_* $[: $_]? := $_) => Macro.throwErrorAt stx "'_' is not allowed here"
       | _ => Macro.throwUnsupported
+
+    let startOfStructureTkInfo : SourceInfo :=
+      match whereTk.getPos? with
+      | some pos => .synthetic pos ⟨pos.byteIdx + 1⟩ true
+      | none => .none
+    -- Position the closing `}` at the end of the trailing whitespace of `where $[$_:letDecl];*`.
+    -- We need an accurate range of the generated structure instance in the generated `TermInfo`
+    -- so that we can determine the expected type in structure field completion.
+    let structureStxTailInfo :=
+      whereStx[1].getTailInfo?
+      <|> whereStx[0].getTailInfo?
+    let endOfStructureTkInfo : SourceInfo :=
+      match structureStxTailInfo with
+      | some (SourceInfo.original _ _ trailing _) =>
+        let tokenPos := trailing.str.prev trailing.stopPos
+        let tokenEndPos := trailing.stopPos
+        .synthetic tokenPos tokenEndPos true
+      | _ => .none
+
     let body ← `(structInst| { $structInstFields,* })
+    let body := body.raw.setInfo <|
+      match startOfStructureTkInfo.getPos?, endOfStructureTkInfo.getTailPos? with
+      | some startPos, some endPos => .synthetic startPos endPos true
+      | _, _ => .none
     match whereDecls? with
     | some whereDecls => expandWhereDecls whereDecls body
     | none => return body
@@ -417,12 +440,15 @@ private def elabFunValues (headers : Array DefViewElabHeader) (vars : Array Expr
           -- Store instantiated body in info tree for the benefit of the unused variables linter
           -- and other metaprograms that may want to inspect it without paying for the instantiation
           -- again
-          withInfoContext' valStx (mkInfo := (pure <| .inl <| mkBodyInfo valStx ·)) do
-            -- synthesize mvars here to force the top-level tactic block (if any) to run
-            let val ← elabTermEnsuringType valStx type <* synthesizeSyntheticMVarsNoPostponing
-            -- NOTE: without this `instantiatedMVars`, `mkLambdaFVars` may leave around a redex that
-            -- leads to more section variables being included than necessary
-            instantiateMVarsProfiling val
+          withInfoContext' valStx
+            (mkInfo := (pure <| .inl <| mkBodyInfo valStx ·))
+            (mkInfoOnError := (pure <| mkBodyInfo valStx none))
+            do
+              -- synthesize mvars here to force the top-level tactic block (if any) to run
+              let val ← elabTermEnsuringType valStx type <* synthesizeSyntheticMVarsNoPostponing
+              -- NOTE: without this `instantiatedMVars`, `mkLambdaFVars` may leave around a redex that
+              -- leads to more section variables being included than necessary
+              instantiateMVarsProfiling val
         let val ← mkLambdaFVars xs val
         if linter.unusedSectionVars.get (← getOptions) && !header.type.hasSorry && !val.hasSorry then
           let unusedVars ← vars.filterMapM fun var => do

src/Lean/Elab/PatternVar.lean

@@ -332,9 +332,9 @@ where
     else
       let accessible := isNextArgAccessible ctx
       let (d, ctx)   := getNextParam ctx
-      match ctx.namedArgs.findIdx? fun namedArg => namedArg.name == d.1 with
+      match ctx.namedArgs.findFinIdx? fun namedArg => namedArg.name == d.1 with
       | some idx =>
-        let arg := ctx.namedArgs[idx]!
+        let arg := ctx.namedArgs[idx]
         let ctx := { ctx with namedArgs := ctx.namedArgs.eraseIdx idx }
         let ctx ← pushNewArg accessible ctx arg.val
         processCtorAppContext ctx

src/Lean/Elab/PreDefinition/Structural/BRecOn.lean

@@ -292,9 +292,9 @@ def mkBrecOnApp (positions : Positions) (fnIdx : Nat) (brecOnConst : Nat → Exp
     let packedFTypes ← inferArgumentTypesN positions.size brecOn
     let packedFArgs ← positions.mapMwith PProdN.mkLambdas packedFTypes FArgs
     let brecOn := mkAppN brecOn packedFArgs
-    let some poss := positions.find? (·.contains fnIdx)
+    let some (size, idx) := positions.findSome? fun pos => (pos.size, ·) <$> pos.indexOf? fnIdx
       | throwError "mkBrecOnApp: Could not find {fnIdx} in {positions}"
-    let brecOn ← PProdN.proj poss.size (poss.getIdx? fnIdx).get! brecOn
+    let brecOn ← PProdN.proj size idx brecOn
     mkLambdaFVars ys (mkAppN brecOn otherArgs)
 
 end Lean.Elab.Structural

src/Lean/Elab/PreDefinition/Structural/FindRecArg.lean

@@ -243,7 +243,7 @@ def tryAllArgs (fnNames : Array Name) (xs : Array Expr) (values : Array Expr)
     recArgInfoss := recArgInfoss.push recArgInfos
   -- Put non-indices first
   recArgInfoss := recArgInfoss.map nonIndicesFirst
-  trace[Elab.definition.structural] "recArgInfoss: {recArgInfoss.map (·.map (·.recArgPos))}"
+  trace[Elab.definition.structural] "recArgInfos:{indentD (.joinSep (recArgInfoss.flatten.toList.map (repr ·)) Format.line)}"
   -- Inductive groups to consider
   let groups ← inductiveGroups recArgInfoss.flatten
   trace[Elab.definition.structural] "inductive groups: {groups}"

src/Lean/Elab/PreDefinition/Structural/IndGroupInfo.lean

@@ -27,7 +27,7 @@ constituents.
 structure IndGroupInfo where
   all       : Array Name
   numNested : Nat
-deriving BEq, Inhabited
+deriving BEq, Inhabited, Repr
 
 def IndGroupInfo.ofInductiveVal (indInfo : InductiveVal) : IndGroupInfo where
   all       := indInfo.all.toArray
@@ -56,7 +56,7 @@ mutual structural recursion on such incompatible types.
 structure IndGroupInst extends IndGroupInfo where
   levels    : List Level
   params    : Array Expr
-deriving Inhabited
+deriving Inhabited, Repr
 
 def IndGroupInst.toMessageData (igi : IndGroupInst) : MessageData :=
   mkAppN (.const igi.all[0]! igi.levels) igi.params

src/Lean/Elab/PreDefinition/Structural/RecArgInfo.lean

@@ -23,9 +23,9 @@ structure RecArgInfo where
   fnName       : Name
   /-- the fixed prefix of arguments of the function we are trying to justify termination using structural recursion. -/
   numFixed     : Nat
-  /-- position of the argument (counted including fixed prefix) we are recursing on -/
+  /-- position (counted including fixed prefix) of the argument we are recursing on -/
   recArgPos    : Nat
-  /-- position of the indices (counted including fixed prefix) of the inductive datatype indices we are recursing on -/
+  /-- position (counted including fixed prefix) of the indices of the inductive datatype we are recursing on -/
   indicesPos   : Array Nat
   /-- The inductive group (with parameters) of the argument's type -/
   indGroupInst : IndGroupInst
@@ -34,20 +34,23 @@ structure RecArgInfo where
   If `< indAll.all`, a normal data type, else an auxiliary data type due to nested recursion
   -/
   indIdx       : Nat
-deriving Inhabited
+deriving Inhabited, Repr
 
 /--
 If `xs` are the parameters of the functions (excluding fixed prefix), partitions them
 into indices and major arguments, and other parameters.
 -/
 def RecArgInfo.pickIndicesMajor (info : RecArgInfo) (xs : Array Expr) : (Array Expr × Array Expr) := Id.run do
+  -- First indices and major arg, using the order they appear in `info.indicesPos`
   let mut indexMajorArgs := #[]
+  let indexMajorPos := info.indicesPos.push info.recArgPos
+  for j in indexMajorPos do
+    assert! info.numFixed ≤ j && j - info.numFixed < xs.size
+    indexMajorArgs := indexMajorArgs.push xs[j - info.numFixed]!
+  -- Then the other arguments, in the order they appear in `xs`
   let mut otherArgs := #[]
   for h : i in [:xs.size] do
-    let j := i + info.numFixed
-    if j = info.recArgPos || info.indicesPos.contains j then
-      indexMajorArgs := indexMajorArgs.push xs[i]
-    else
+    unless indexMajorPos.contains (i + info.numFixed) do
       otherArgs := otherArgs.push xs[i]
   return (indexMajorArgs, otherArgs)
 

src/Lean/Elab/PreDefinition/WF/PackMutual.lean

@@ -40,7 +40,7 @@ private partial def post (fixedPrefix : Nat) (argsPacker : ArgsPacker) (funNames
     return TransformStep.done e
   let declName := f.constName!
   let us       := f.constLevels!
-  if let some fidx := funNames.getIdx? declName then
+  if let some fidx := funNames.indexOf? declName then
     let arity := fixedPrefix + argsPacker.varNamess[fidx]!.size
     let e' ← withAppN arity e fun args => do
       let fixedArgs := args[:fixedPrefix]

src/Lean/Elab/Print.lean

@@ -22,7 +22,7 @@ private def levelParamsToMessageData (levelParams : List Name) : MessageData :=
       m := m ++ ", " ++ toMessageData u
     return m ++ "}"
 
-private def mkHeader (kind : String) (id : Name) (levelParams : List Name) (type : Expr) (safety : DefinitionSafety) : CommandElabM MessageData := do
+private def mkHeader (kind : String) (id : Name) (levelParams : List Name) (type : Expr) (safety : DefinitionSafety) (sig : Bool := true) : CommandElabM MessageData := do
   let m : MessageData :=
     match (← getReducibilityStatus id) with
     | ReducibilityStatus.irreducible => "@[irreducible] "
@@ -38,11 +38,13 @@ private def mkHeader (kind : String) (id : Name) (levelParams : List Name) (type
   let (m, id) := match privateToUserName? id with
     | some id => (m ++ "private ", id)
     | none    => (m, id)
-  let m := m ++ kind ++ " " ++ id ++ levelParamsToMessageData levelParams ++ " : " ++ type
-  pure m
+  if sig then
+    return m!"{m}{kind} {id}{levelParamsToMessageData levelParams} : {type}"
+  else
+    return m!"{m}{kind}"
 
-private def mkHeader' (kind : String) (id : Name) (levelParams : List Name) (type : Expr) (isUnsafe : Bool) : CommandElabM MessageData :=
-  mkHeader kind id levelParams type (if isUnsafe then DefinitionSafety.unsafe else DefinitionSafety.safe)
+private def mkHeader' (kind : String) (id : Name) (levelParams : List Name) (type : Expr) (isUnsafe : Bool) (sig : Bool := true) : CommandElabM MessageData :=
+  mkHeader kind id levelParams type (if isUnsafe then DefinitionSafety.unsafe else DefinitionSafety.safe) (sig := sig)
 
 private def printDefLike (kind : String) (id : Name) (levelParams : List Name) (type : Expr) (value : Expr) (safety := DefinitionSafety.safe) : CommandElabM Unit := do
   let m ← mkHeader kind id levelParams type safety
@@ -65,32 +67,63 @@ private def printInduct (id : Name) (levelParams : List Name) (numParams : Nat)
     m := m ++ Format.line ++ ctor ++ " : " ++ cinfo.type
   logInfo m
 
+/--
+Computes the origin of a field. Returns its projection function at the origin.
+Multiple parents could be the origin of a field, but we say the first parent that provides it is the one that determines the origin.
+-/
+private partial def getFieldOrigin (structName field : Name) : MetaM Name := do
+  let env ← getEnv
+  for parent in getStructureParentInfo env structName do
+    if (findField? env parent.structName field).isSome then
+      return ← getFieldOrigin parent.structName field
+  let some fi := getFieldInfo? env structName field
+    | throwError "no such field {field} in {structName}"
+  return fi.projFn
+
 open Meta in
 private def printStructure (id : Name) (levelParams : List Name) (numParams : Nat) (type : Expr)
-    (ctor : Name) (fields : Array Name) (isUnsafe : Bool) (isClass : Bool) : CommandElabM Unit := do
-  let kind := if isClass then "class" else "structure"
-  let mut m ← mkHeader' kind id levelParams type isUnsafe
-  m := m ++ Format.line ++ "number of parameters: " ++ toString numParams
-  m := m ++ Format.line ++ "constructor:"
-  let cinfo ← getConstInfo ctor
-  m := m ++ Format.line ++ ctor ++ " : " ++ cinfo.type
-  m := m ++ Format.line ++ "fields:" ++ (← doFields)
-  logInfo m
-where
-  doFields := liftTermElabM do
-    forallTelescope (← getConstInfo id).type fun params _ =>
-      withLocalDeclD `self (mkAppN (Expr.const id (levelParams.map .param)) params) fun self => do
-        let params := params.push self
-        let mut m : MessageData := ""
+    (isUnsafe : Bool) : CommandElabM Unit := do
+  let env ← getEnv
+  let kind := if isClass env id then "class" else "structure"
+  let header ← mkHeader' kind id levelParams type isUnsafe (sig := false)
+  liftTermElabM <| forallTelescope (← getConstInfo id).type fun params _ =>
+    let s := Expr.const id (levelParams.map .param)
+    withLocalDeclD `self (mkAppN s params) fun self => do
+      let mut m : MessageData := header
+      -- Signature
+      m := m ++ " " ++ .ofFormatWithInfosM do
+        let (stx, infos) ← PrettyPrinter.delabCore s (delab := PrettyPrinter.Delaborator.delabConstWithSignature)
+        pure ⟨← PrettyPrinter.ppTerm ⟨stx⟩, infos⟩
+      m := m ++ Format.line ++ m!"number of parameters: {numParams}"
+      -- Parents
+      let parents := getStructureParentInfo env id
+      unless parents.isEmpty do
+        m := m ++ Format.line ++ "parents:"
+        for parent in parents do
+          let ptype ← inferType (mkApp (mkAppN (.const parent.projFn (levelParams.map .param)) params) self)
+          m := m ++ indentD m!"{.ofConstName parent.projFn (fullNames := true)} : {ptype}"
+      -- Fields
+      let fields := getStructureFieldsFlattened env id (includeSubobjectFields := false)
+      if fields.isEmpty then
+        m := m ++ Format.line ++ "fields: (none)"
+      else
+        m := m ++ Format.line ++ "fields:"
         for field in fields do
-          match getProjFnForField? (← getEnv) id field with
-          | some proj =>
-            let field : Format := if isPrivateName proj then "private " ++ toString field else toString field
-            let cinfo ← getConstInfo proj
-            let ftype ← instantiateForall cinfo.type params
-            m := m ++ Format.line ++ field ++ " : " ++ ftype
-          | none => panic! "missing structure field info"
-        addMessageContext m
+          let some source := findField? env id field | panic! "missing structure field info"
+          let proj ← getFieldOrigin source field
+          let modifier := if isPrivateName proj then "private " else ""
+          let ftype ← inferType (← mkProjection self field)
+          m := m ++ indentD (m!"{modifier}{.ofConstName proj (fullNames := true)} : {ftype}")
+      -- Constructor
+      let cinfo := getStructureCtor (← getEnv) id
+      let ctorModifier := if isPrivateName cinfo.name then "private " else ""
+      m := m ++ Format.line ++ "constructor:" ++ indentD (ctorModifier ++ .signature cinfo.name)
+      -- Resolution order
+      let resOrder ← getStructureResolutionOrder id
+      if resOrder.size > 1 then
+        m := m ++ Format.line ++ "resolution order:"
+          ++ indentD (MessageData.joinSep (resOrder.map (.ofConstName · (fullNames := true))).toList ", ")
+      logInfo m
 
 private def printIdCore (id : Name) : CommandElabM Unit := do
   let env ← getEnv
@@ -103,11 +136,10 @@ private def printIdCore (id : Name) : CommandElabM Unit := do
   | ConstantInfo.ctorInfo { levelParams := us, type := t, isUnsafe := u, .. } => printAxiomLike "constructor" id us t u
   | ConstantInfo.recInfo { levelParams := us, type := t, isUnsafe := u, .. } => printAxiomLike "recursor" id us t u
   | ConstantInfo.inductInfo { levelParams := us, numParams, type := t, ctors, isUnsafe := u, .. } =>
-    match getStructureInfo? env id with
-    | some { fieldNames, .. } =>
-      let [ctor] := ctors | panic! "structures have only one constructor"
-      printStructure id us numParams t ctor fieldNames u (isClass env id)
-    | none => printInduct id us numParams t ctors u
+    if isStructure env id then
+      printStructure id us numParams t u
+    else
+      printInduct id us numParams t ctors u
   | none => throwUnknownId id
 
 private def printId (id : Syntax) : CommandElabM Unit := do

src/Lean/Elab/Quotation.lean

@@ -58,7 +58,7 @@ partial def mkTuple : Array Syntax → TermElabM Syntax
   | #[]  => `(Unit.unit)
   | #[e] => return e
   | es   => do
-    let stx ← mkTuple (es.eraseIdx 0)
+    let stx ← mkTuple (es.eraseIdxIfInBounds 0)
     `(Prod.mk $(es[0]!) $stx)
 
 def resolveSectionVariable (sectionVars : NameMap Name) (id : Name) : List (Name × List String) :=

src/Lean/Elab/StructInst.lean

@@ -11,21 +11,40 @@ import Lean.Elab.App
 import Lean.Elab.Binders
 import Lean.PrettyPrinter
 
+/-!
+# Structure instance elaborator
+
+A *structure instance* is notation to construct a term of a `structure`.
+Examples: `{ x := 2, y.z := true }`, `{ s with cache := c' }`, and `{ s with values[2] := v }`.
+Structure instances are the preferred way to invoke a `structure`'s constructor,
+since they hide Lean implementation details such as whether parents are represented as subobjects,
+and also they do correct processing of default values, which are complicated due to the fact that `structure`s can override default values of their parents.
+
+This module elaborates structure instance notation.
+Note that the `where` syntax to define structures (`Lean.Parser.Command.whereStructInst`)
+macro expands into the structure instance notation elaborated by this module.
+-/
+
 namespace Lean.Elab.Term.StructInst
 
 open Meta
 open TSyntax.Compat
 
-/-
-  Structure instances are of the form:
-
-      "{" >> optional (atomic (sepBy1 termParser ", " >> " with "))
-          >> manyIndent (group ((structInstFieldAbbrev <|> structInstField) >> optional ", "))
-          >> optEllipsis
-          >> optional (" : " >> termParser)
-          >> " }"
+/-!
+Recall that structure instances are of the form:
+```
+"{" >> optional (atomic (sepBy1 termParser ", " >> " with "))
+    >> manyIndent (group ((structInstFieldAbbrev <|> structInstField) >> optional ", "))
+    >> optEllipsis
+    >> optional (" : " >> termParser)
+    >> " }"
+```
 -/
 
+/--
+Transforms structure instances such as `{ x := 0 : Foo }` into `({ x := 0 } : Foo)`.
+Structure instance notation makes use of the expected type.
+-/
 @[builtin_macro Lean.Parser.Term.structInst] def expandStructInstExpectedType : Macro := fun stx =>
   let expectedArg := stx[4]
   if expectedArg.isNone then
@@ -35,7 +54,10 @@ open TSyntax.Compat
     let stxNew   := stx.setArg 4 mkNullNode
     `(($stxNew : $expected))
 
-/-- Expand field abbreviations. Example: `{ x, y := 0 }` expands to `{ x := x, y := 0 }` -/
+/--
+Expands field abbreviation notation.
+Example: `{ x, y := 0 }` expands to `{ x := x, y := 0 }`.
+-/
 @[builtin_macro Lean.Parser.Term.structInst] def expandStructInstFieldAbbrev : Macro
   | `({ $[$srcs,* with]? $fields,* $[..%$ell]? $[: $ty]? }) =>
     if fields.getElems.raw.any (·.getKind == ``Lean.Parser.Term.structInstFieldAbbrev) then do
@@ -49,9 +71,12 @@ open TSyntax.Compat
   | _ => Macro.throwUnsupported
 
 /--
-  If `stx` is of the form `{ s₁, ..., sₙ with ... }` and `sᵢ` is not a local variable, expand into `let src := sᵢ; { ..., src, ... with ... }`.
+If `stx` is of the form `{ s₁, ..., sₙ with ... }` and `sᵢ` is not a local variable,
+expands into `let __src := sᵢ; { ..., __src, ... with ... }`.
+The significance of `__src` is that the variable is treated as an implementation-detail local variable,
+which can be unfolded by `simp` when `zetaDelta := false`.
 
-  Note that this one is not a `Macro` because we need to access the local context.
+Note that this one is not a `Macro` because we need to access the local context.
 -/
 private def expandNonAtomicExplicitSources (stx : Syntax) : TermElabM (Option Syntax) := do
   let sourcesOpt := stx[1]
@@ -100,27 +125,44 @@ where
           let r ← go sources (sourcesNew.push sourceNew)
           `(let __src := $source; $r)
 
-structure ExplicitSourceInfo where
+/--
+An *explicit source* is one of the structures `sᵢ` that appear in `{ s₁, …, sₙ with … }`.
+-/
+structure ExplicitSourceView where
+  /-- The syntax of the explicit source. -/
   stx        : Syntax
+  /-- The name of the structure for the type of the explicit source. -/
   structName : Name
   deriving Inhabited
 
-structure Source where
-  explicit : Array ExplicitSourceInfo -- `s₁ ... sₙ with`
-  implicit : Option Syntax -- `..`
+/--
+A view of the sources of fields for the structure instance notation.
+-/
+structure SourcesView where
+  /-- Explicit sources (i.e., one of the structures `sᵢ` that appear in `{ s₁, …, sₙ with … }`). -/
+  explicit : Array ExplicitSourceView
+  /-- The syntax for a trailing `..`. This is "ellipsis mode" for missing fields, similar to ellipsis mode for applications. -/
+  implicit : Option Syntax
   deriving Inhabited
 
-def Source.isNone : Source → Bool
+/-- Returns `true` if the structure instance has no sources (neither explicit sources nor a `..`). -/
+def SourcesView.isNone : SourcesView → Bool
   | { explicit := #[], implicit := none } => true
   | _ => false
 
-/-- `optional (atomic (sepBy1 termParser ", " >> " with ")` -/
+/--
+Given an array of explicit sources, returns syntax of the form
+`optional (atomic (sepBy1 termParser ", " >> " with ")`
+-/
 private def mkSourcesWithSyntax (sources : Array Syntax) : Syntax :=
   let ref := sources[0]!
   let stx := Syntax.mkSep sources (mkAtomFrom ref ", ")
   mkNullNode #[stx, mkAtomFrom ref "with "]
 
-private def getStructSource (structStx : Syntax) : TermElabM Source :=
+/--
+Creates a structure source view from structure instance notation.
+-/
+private def getStructSources (structStx : Syntax) : TermElabM SourcesView :=
   withRef structStx do
     let explicitSource := structStx[1]
     let implicitSource := structStx[3]
@@ -138,13 +180,13 @@ private def getStructSource (structStx : Syntax) : TermElabM Source :=
     return { explicit, implicit }
 
 /--
-  We say a `{ ... }` notation is a `modifyOp` if it contains only one
-  ```
-  def structInstArrayRef := leading_parser "[" >> termParser >>"]"
-  ```
+We say a structure instance notation is a "modifyOp" if it contains only a single array update.
+```lean
+def structInstArrayRef := leading_parser "[" >> termParser >>"]"
+```
 -/
 private def isModifyOp? (stx : Syntax) : TermElabM (Option Syntax) := do
-  let s? ← stx[2].getSepArgs.foldlM (init := none) fun s? arg => do
+  let s? ← stx[2][0].getSepArgs.foldlM (init := none) fun s? arg => do
     /- arg is of the form `structInstFieldAbbrev <|> structInstField` -/
     if arg.getKind == ``Lean.Parser.Term.structInstField then
       /- Remark: the syntax for `structInstField` is
@@ -177,7 +219,11 @@ private def isModifyOp? (stx : Syntax) : TermElabM (Option Syntax) := do
   | none   => return none
   | some s => if s[0][0].getKind == ``Lean.Parser.Term.structInstArrayRef then return s? else return none
 
-private def elabModifyOp (stx modifyOp : Syntax) (sources : Array ExplicitSourceInfo) (expectedType? : Option Expr) : TermElabM Expr := do
+/--
+Given a `stx` that is a structure instance notation that's a modifyOp (according to `isModifyOp?`), elaborates it.
+Only supports structure instances with a single source.
+-/
+private def elabModifyOp (stx modifyOp : Syntax) (sources : Array ExplicitSourceView) (expectedType? : Option Expr) : TermElabM Expr := do
   if sources.size > 1 then
     throwError "invalid \{...} notation, multiple sources and array update is not supported."
   let cont (val : Syntax) : TermElabM Expr := do
@@ -199,17 +245,18 @@ private def elabModifyOp (stx modifyOp : Syntax) (sources : Array ExplicitSource
     let valField  := modifyOp.setArg 0 <| mkNode ``Parser.Term.structInstLVal #[valFirst, valRest]
     let valSource := mkSourcesWithSyntax #[s]
     let val       := stx.setArg 1 valSource
-    let val       := val.setArg 2 <| mkNullNode #[valField]
+    let val       := val.setArg 2 <| mkNode ``Parser.Term.structInstFields #[mkNullNode #[valField]]
     trace[Elab.struct.modifyOp] "{stx}\nval: {val}"
     cont val
 
 /--
-  Get structure name.
-  This method triest to postpone execution if the expected type is not available.
+Gets the structure name for the structure instance from the expected type and the sources.
+This method tries to postpone execution if the expected type is not available.
 
-  If the expected type is available and it is a structure, then we use it.
-  Otherwise, we use the type of the first source. -/
-private def getStructName (expectedType? : Option Expr) (sourceView : Source) : TermElabM Name := do
+If the expected type is available and it is a structure, then we use it.
+Otherwise, we use the type of the first source.
+-/
+private def getStructName (expectedType? : Option Expr) (sourceView : SourcesView) : TermElabM Name := do
   tryPostponeIfNoneOrMVar expectedType?
   let useSource : Unit → TermElabM Name := fun _ => do
     unless sourceView.explicit.isEmpty do
@@ -226,7 +273,7 @@ private def getStructName (expectedType? : Option Expr) (sourceView : Source) :
       unless isStructure (← getEnv) constName do
         throwError "invalid \{...} notation, structure type expected{indentExpr expectedType}"
       return constName
-    | _                        => useSource ()
+    | _ => useSource ()
 where
   throwUnknownExpectedType :=
     throwError "invalid \{...} notation, expected type is not known"
@@ -237,72 +284,92 @@ where
     else
       throwError "invalid \{...} notation, {kind} type is not of the form (C ...){indentExpr type}"
 
+/--
+A component of a left-hand side for a field appearing in structure instance syntax.
+-/
 inductive FieldLHS where
+  /-- A name component for a field left-hand side. For example, `x` and `y` in `{ x.y := v }`. -/
   | fieldName  (ref : Syntax) (name : Name)
+  /-- A numeric index component for a field left-hand side. For example `3` in `{ x.3 := v }`. -/
   | fieldIndex (ref : Syntax) (idx : Nat)
+  /-- An array indexing component for a field left-hand side. For example `[3]` in `{ arr[3] := v }`. -/
   | modifyOp   (ref : Syntax) (index : Syntax)
   deriving Inhabited
 
-instance : ToFormat FieldLHS := ⟨fun lhs =>
-  match lhs with
-  | .fieldName _ n  => format n
-  | .fieldIndex _ i => format i
-  | .modifyOp _ i   => "[" ++ i.prettyPrint ++ "]"⟩
+instance : ToFormat FieldLHS where
+  format
+    | .fieldName _ n  => format n
+    | .fieldIndex _ i => format i
+    | .modifyOp _ i   => "[" ++ i.prettyPrint ++ "]"
 
+/--
+`FieldVal StructInstView` is a representation of a field value in the structure instance.
+-/
 inductive FieldVal (σ : Type) where
-  | term  (stx : Syntax) : FieldVal σ
+  /-- A `term` to use for the value of the field. -/
+  | term (stx : Syntax)  : FieldVal σ
+  /-- A `StructInstView` to use for the value of a subobject field. -/
   | nested (s : σ)       : FieldVal σ
-  | default              : FieldVal σ -- mark that field must be synthesized using default value
+  /-- A field that was not provided and should be synthesized using default values. -/
+  | default              : FieldVal σ
   deriving Inhabited
 
+/--
+`Field StructInstView` is a representation of a field in the structure instance.
+-/
 structure Field (σ : Type) where
+  /-- The whole field syntax. -/
   ref   : Syntax
+  /-- The LHS decomposed into components. -/
   lhs   : List FieldLHS
+  /-- The value of the field. -/
   val   : FieldVal σ
+  /-- The elaborated field value, filled in at `elabStruct`.
+  Missing fields use a metavariable for the elaborated value and are later solved for in `DefaultFields.propagate`. -/
   expr? : Option Expr := none
   deriving Inhabited
 
+/--
+Returns if the field has a single component in its LHS.
+-/
 def Field.isSimple {σ} : Field σ → Bool
   | { lhs := [_], .. } => true
   | _                  => false
 
-inductive Struct where
-  /-- Remark: the field `params` is use for default value propagation. It is initially empty, and then set at `elabStruct`. -/
-  | mk (ref : Syntax) (structName : Name) (params : Array (Name × Expr)) (fields : List (Field Struct)) (source : Source)
+/--
+The view for structure instance notation.
+-/
+structure StructInstView where
+  /-- The syntax for the whole structure instance. -/
+  ref : Syntax
+  /-- The name of the structure for the type of the structure instance. -/
+  structName : Name
+  /-- Used for default values, to propagate structure type parameters. It is initially empty, and then set at `elabStruct`. -/
+  params : Array (Name × Expr)
+  /-- The fields of the structure instance. -/
+  fields : List (Field StructInstView)
+  /-- The additional sources for fields for the structure instance. -/
+  sources : SourcesView
   deriving Inhabited
 
-abbrev Fields := List (Field Struct)
-
-def Struct.ref : Struct → Syntax
-  | ⟨ref, _, _, _, _⟩ => ref
-
-def Struct.structName : Struct → Name
-  | ⟨_, structName, _, _, _⟩ => structName
-
-def Struct.params : Struct → Array (Name × Expr)
-  | ⟨_, _, params, _, _⟩ => params
-
-def Struct.fields : Struct → Fields
-  | ⟨_, _, _, fields, _⟩ => fields
-
-def Struct.source : Struct → Source
-  | ⟨_, _, _, _, s⟩ => s
+/-- Abbreviation for the type of `StructInstView.fields`, namely `List (Field StructInstView)`. -/
+abbrev Fields := List (Field StructInstView)
 
 /-- `true` iff all fields of the given structure are marked as `default` -/
-partial def Struct.allDefault (s : Struct) : Bool :=
+partial def StructInstView.allDefault (s : StructInstView) : Bool :=
   s.fields.all fun { val := val,  .. } => match val with
     | .term _   => false
     | .default  => true
     | .nested s => allDefault s
 
-def formatField (formatStruct : Struct → Format) (field : Field Struct) : Format :=
+def formatField (formatStruct : StructInstView → Format) (field : Field StructInstView) : Format :=
   Format.joinSep field.lhs " . " ++ " := " ++
     match field.val with
     | .term v   => v.prettyPrint
     | .nested s => formatStruct s
     | .default  => "<default>"
 
-partial def formatStruct : Struct → Format
+partial def formatStruct : StructInstView → Format
   | ⟨_, _,          _, fields, source⟩ =>
     let fieldsFmt := Format.joinSep (fields.map (formatField formatStruct)) ", "
     let implicitFmt := if source.implicit.isSome then " .. " else ""
@@ -311,31 +378,39 @@ partial def formatStruct : Struct → Format
     else
       "{" ++ format (source.explicit.map (·.stx)) ++ " with " ++ fieldsFmt ++ implicitFmt ++ "}"
 
-instance : ToFormat Struct     := ⟨formatStruct⟩
-instance : ToString Struct := ⟨toString ∘ format⟩
+instance : ToFormat StructInstView     := ⟨formatStruct⟩
+instance : ToString StructInstView := ⟨toString ∘ format⟩
 
-instance : ToFormat (Field Struct) := ⟨formatField formatStruct⟩
-instance : ToString (Field Struct) := ⟨toString ∘ format⟩
+instance : ToFormat (Field StructInstView) := ⟨formatField formatStruct⟩
+instance : ToString (Field StructInstView) := ⟨toString ∘ format⟩
+
+/--
+Converts a `FieldLHS` back into syntax. This assumes the `ref` fields have the correct structure.
 
-/-
 Recall that `structInstField` elements have the form
-```
-   def structInstField  := leading_parser structInstLVal >> " := " >> termParser
-   def structInstLVal   := leading_parser (ident <|> numLit <|> structInstArrayRef) >> many (("." >> (ident <|> numLit)) <|> structInstArrayRef)
-   def structInstArrayRef := leading_parser "[" >> termParser >>"]"
+```lean
+def structInstField  := leading_parser structInstLVal >> " := " >> termParser
+def structInstLVal   := leading_parser (ident <|> numLit <|> structInstArrayRef) >> many (("." >> (ident <|> numLit)) <|> structInstArrayRef)
+def structInstArrayRef := leading_parser "[" >> termParser >>"]"
 ```
 -/
 -- Remark: this code relies on the fact that `expandStruct` only transforms `fieldLHS.fieldName`
-def FieldLHS.toSyntax (first : Bool) : FieldLHS → Syntax
+private def FieldLHS.toSyntax (first : Bool) : FieldLHS → Syntax
   | .modifyOp   stx _    => stx
   | .fieldName  stx name => if first then mkIdentFrom stx name else mkGroupNode #[mkAtomFrom stx ".", mkIdentFrom stx name]
   | .fieldIndex stx _    => if first then stx else mkGroupNode #[mkAtomFrom stx ".", stx]
 
-def FieldVal.toSyntax : FieldVal Struct → Syntax
+/--
+Converts a `FieldVal StructInstView` back into syntax. Only supports `.term`, and it assumes the `stx` field has the correct structure.
+-/
+private def FieldVal.toSyntax : FieldVal Struct → Syntax
   | .term stx => stx
-  | _                 => unreachable!
+  | _         => unreachable!
 
-def Field.toSyntax : Field Struct → Syntax
+/--
+Converts a `Field StructInstView` back into syntax. Used to construct synthetic structure instance notation for subobjects in `StructInst.expandStruct` processing.
+-/
+private def Field.toSyntax : Field Struct → Syntax
   | field =>
     let stx := field.ref
     let stx := stx.setArg 2 field.val.toSyntax
@@ -343,6 +418,7 @@ def Field.toSyntax : Field Struct → Syntax
     | first::rest => stx.setArg 0 <| mkNullNode #[first.toSyntax true, mkNullNode <| rest.toArray.map (FieldLHS.toSyntax false) ]
     | _ => unreachable!
 
+/-- Creates a view of a field left-hand side. -/
 private def toFieldLHS (stx : Syntax) : MacroM FieldLHS :=
   if stx.getKind == ``Lean.Parser.Term.structInstArrayRef then
     return FieldLHS.modifyOp stx stx[1]
@@ -355,11 +431,16 @@ private def toFieldLHS (stx : Syntax) : MacroM FieldLHS :=
       | some idx => return FieldLHS.fieldIndex stx idx
       | none     => Macro.throwError "unexpected structure syntax"
 
-private def mkStructView (stx : Syntax) (structName : Name) (source : Source) : MacroM Struct := do
+/--
+Creates a structure instance view from structure instance notation
+and the computed structure name (from `Lean.Elab.Term.StructInst.getStructName`)
+and structure source view (from `Lean.Elab.Term.StructInst.getStructSources`).
+-/
+private def mkStructView (stx : Syntax) (structName : Name) (sources : SourcesView) : MacroM StructInstView := do
   /- Recall that `stx` is of the form
      ```
      leading_parser "{" >> optional (atomic (sepBy1 termParser ", " >> " with "))
-                 >> sepByIndent (structInstFieldAbbrev <|> structInstField) ...
+                 >> structInstFields (sepByIndent (structInstFieldAbbrev <|> structInstField) ...)
                  >> optional ".."
                  >> optional (" : " >> termParser)
                  >> " }"
@@ -367,28 +448,22 @@ private def mkStructView (stx : Syntax) (structName : Name) (source : Source) :
 
      This method assumes that `structInstFieldAbbrev` had already been expanded.
   -/
-  let fields ← stx[2].getSepArgs.toList.mapM fun fieldStx => do
+  let fields ← stx[2][0].getSepArgs.toList.mapM fun fieldStx => do
     let val      := fieldStx[2]
     let first    ← toFieldLHS fieldStx[0][0]
     let rest     ← fieldStx[0][1].getArgs.toList.mapM toFieldLHS
-    return { ref := fieldStx, lhs := first :: rest, val := FieldVal.term val : Field Struct }
-  return ⟨stx, structName, #[], fields, source⟩
+    return { ref := fieldStx, lhs := first :: rest, val := FieldVal.term val : Field StructInstView }
+  return { ref := stx, structName, params := #[], fields, sources }
 
-def Struct.modifyFieldsM {m : Type → Type} [Monad m] (s : Struct) (f : Fields → m Fields) : m Struct :=
+def StructInstView.modifyFieldsM {m : Type → Type} [Monad m] (s : StructInstView) (f : Fields → m Fields) : m StructInstView :=
   match s with
-  | ⟨ref, structName, params, fields, source⟩ => return ⟨ref, structName, params, (← f fields), source⟩
+  | { ref, structName, params, fields, sources } => return { ref, structName, params, fields := (← f fields), sources }
 
-def Struct.modifyFields (s : Struct) (f : Fields → Fields) : Struct :=
+def StructInstView.modifyFields (s : StructInstView) (f : Fields → Fields) : StructInstView :=
   Id.run <| s.modifyFieldsM f
 
-def Struct.setFields (s : Struct) (fields : Fields) : Struct :=
-  s.modifyFields fun _ => fields
-
-def Struct.setParams (s : Struct) (ps : Array (Name × Expr)) : Struct :=
-  match s with
-  | ⟨ref, structName, _, fields, source⟩ => ⟨ref, structName, ps, fields, source⟩
-
-private def expandCompositeFields (s : Struct) : Struct :=
+/-- Expands name field LHSs with multi-component names into multi-component LHSs. -/
+private def expandCompositeFields (s : StructInstView) : StructInstView :=
   s.modifyFields fun fields => fields.map fun field => match field with
     | { lhs := .fieldName _ (.str Name.anonymous ..) :: _, .. } => field
     | { lhs := .fieldName ref n@(.str ..) :: rest, .. } =>
@@ -396,7 +471,8 @@ private def expandCompositeFields (s : Struct) : Struct :=
       { field with lhs := newEntries ++ rest }
     | _ => field
 
-private def expandNumLitFields (s : Struct) : TermElabM Struct :=
+/-- Replaces numeric index field LHSs with the corresponding named field, or throws an error if no such field exists. -/
+private def expandNumLitFields (s : StructInstView) : TermElabM StructInstView :=
   s.modifyFieldsM fun fields => do
     let env ← getEnv
     let fieldNames := getStructureFields env s.structName
@@ -407,28 +483,31 @@ private def expandNumLitFields (s : Struct) : TermElabM Struct :=
         else return { field with lhs := .fieldName ref fieldNames[idx - 1]! :: rest }
       | _ => return field
 
-/-- For example, consider the following structures:
-   ```
-   structure A where
-     x : Nat
+/--
+Expands fields that are actually represented as fields of subobject fields.
 
-   structure B extends A where
-     y : Nat
+For example, consider the following structures:
+```
+structure A where
+  x : Nat
 
-   structure C extends B where
-     z : Bool
-   ```
-   This method expands parent structure fields using the path to the parent structure.
-   For example,
-   ```
-   { x := 0, y := 0, z := true : C }
-   ```
-   is expanded into
-   ```
-   { toB.toA.x := 0, toB.y := 0, z := true : C }
-   ```
+structure B extends A where
+  y : Nat
+
+structure C extends B where
+  z : Bool
+```
+This method expands parent structure fields using the path to the parent structure.
+For example,
+```
+{ x := 0, y := 0, z := true : C }
+```
+is expanded into
+```
+{ toB.toA.x := 0, toB.y := 0, z := true : C }
+```
 -/
-private def expandParentFields (s : Struct) : TermElabM Struct := do
+private def expandParentFields (s : StructInstView) : TermElabM StructInstView := do
   let env ← getEnv
   s.modifyFieldsM fun fields => fields.mapM fun field => do match field with
     | { lhs := .fieldName ref fieldName :: _,    .. } =>
@@ -448,6 +527,11 @@ private def expandParentFields (s : Struct) : TermElabM Struct := do
 
 private abbrev FieldMap := Std.HashMap Name Fields
 
+/--
+Creates a hash map collecting all fields with the same first name component.
+Throws an error if there are multiple simple fields with the same name.
+Used by `StructInst.expandStruct` processing.
+-/
 private def mkFieldMap (fields : Fields) : TermElabM FieldMap :=
   fields.foldlM (init := {}) fun fieldMap field =>
     match field.lhs with
@@ -461,15 +545,16 @@ private def mkFieldMap (fields : Fields) : TermElabM FieldMap :=
       | _ => return fieldMap.insert fieldName [field]
     | _ => unreachable!
 
-private def isSimpleField? : Fields → Option (Field Struct)
+/--
+Given a value of the hash map created by `mkFieldMap`, returns true if the value corresponds to a simple field.
+-/
+private def isSimpleField? : Fields → Option (Field StructInstView)
   | [field] => if field.isSimple then some field else none
   | _       => none
 
-private def getFieldIdx (structName : Name) (fieldNames : Array Name) (fieldName : Name) : TermElabM Nat := do
-  match fieldNames.findIdx? fun n => n == fieldName with
-  | some idx => return idx
-  | none     => throwError "field '{fieldName}' is not a valid field of '{structName}'"
-
+/--
+Creates projection notation for the given structure field. Used
+-/
 def mkProjStx? (s : Syntax) (structName : Name) (fieldName : Name) : TermElabM (Option Syntax) := do
   if (findField? (← getEnv) structName fieldName).isNone then
     return none
@@ -478,7 +563,10 @@ def mkProjStx? (s : Syntax) (structName : Name) (fieldName : Name) : TermElabM (
       #[mkAtomFrom s "@",
         mkNode ``Parser.Term.proj #[s, mkAtomFrom s ".", mkIdentFrom s fieldName]]
 
-def findField? (fields : Fields) (fieldName : Name) : Option (Field Struct) :=
+/--
+Finds a simple field of the given name.
+-/
+def findField? (fields : Fields) (fieldName : Name) : Option (Field StructInstView) :=
   fields.find? fun field =>
     match field.lhs with
     | [.fieldName _ n] => n == fieldName
@@ -486,7 +574,10 @@ def findField? (fields : Fields) (fieldName : Name) : Option (Field Struct) :=
 
 mutual
 
-  private partial def groupFields (s : Struct) : TermElabM Struct := do
+  /--
+  Groups compound fields according to which subobject they are from.
+  -/
+  private partial def groupFields (s : StructInstView) : TermElabM StructInstView := do
     let env ← getEnv
     withRef s.ref do
     s.modifyFieldsM fun fields => do
@@ -499,26 +590,28 @@ mutual
           let field := fields.head!
           match Lean.isSubobjectField? env s.structName fieldName with
           | some substructName =>
-            let substruct := Struct.mk s.ref substructName #[] substructFields s.source
+            let substruct := { ref := s.ref, structName := substructName, params := #[], fields := substructFields, sources := s.sources }
             let substruct ← expandStruct substruct
             pure { field with lhs := [field.lhs.head!], val := FieldVal.nested substruct }
           | none =>
             let updateSource (structStx : Syntax) : TermElabM Syntax := do
-              let sourcesNew ← s.source.explicit.filterMapM fun source => mkProjStx? source.stx source.structName fieldName
+              let sourcesNew ← s.sources.explicit.filterMapM fun source => mkProjStx? source.stx source.structName fieldName
               let explicitSourceStx := if sourcesNew.isEmpty then mkNullNode else mkSourcesWithSyntax sourcesNew
-              let implicitSourceStx := s.source.implicit.getD mkNullNode
+              let implicitSourceStx := s.sources.implicit.getD mkNullNode
               return (structStx.setArg 1 explicitSourceStx).setArg 3 implicitSourceStx
             let valStx := s.ref -- construct substructure syntax using s.ref as template
             let valStx := valStx.setArg 4 mkNullNode -- erase optional expected type
             let args   := substructFields.toArray.map (·.toSyntax)
-            let valStx := valStx.setArg 2 (mkNullNode <| mkSepArray args (mkAtom ","))
+            let fieldsStx := mkNode ``Parser.Term.structInstFields
+              #[mkNullNode <| mkSepArray args (mkAtom ",")]
+            let valStx := valStx.setArg 2 fieldsStx
             let valStx ← updateSource valStx
             return { field with lhs := [field.lhs.head!], val := FieldVal.term valStx }
   /--
   Adds in the missing fields using the explicit sources.
   Invariant: a missing field always comes from the first source that can provide it.
   -/
-  private partial def addMissingFields (s : Struct) : TermElabM Struct := do
+  private partial def addMissingFields (s : StructInstView) : TermElabM StructInstView := do
     let env ← getEnv
     let fieldNames := getStructureFields env s.structName
     let ref := s.ref.mkSynthetic
@@ -527,7 +620,7 @@ mutual
         match findField? s.fields fieldName with
         | some field => return field::fields
         | none       =>
-          let addField (val : FieldVal Struct) : TermElabM Fields := do
+          let addField (val : FieldVal StructInstView) : TermElabM Fields := do
             return { ref, lhs := [FieldLHS.fieldName ref fieldName], val := val } :: fields
           match Lean.isSubobjectField? env s.structName fieldName with
           | some substructName =>
@@ -535,8 +628,8 @@ mutual
             let downFields := getStructureFieldsFlattened env substructName false
             -- Filter out all explicit sources that do not share a leaf field keeping
             -- structure with no fields
-            let filtered := s.source.explicit.filter fun source =>
-              let sourceFields := getStructureFieldsFlattened env source.structName false
+            let filtered := s.sources.explicit.filter fun sources =>
+              let sourceFields := getStructureFieldsFlattened env sources.structName false
               sourceFields.any (fun name => downFields.contains name) || sourceFields.isEmpty
             -- Take the first such one remaining
             match filtered[0]? with
@@ -550,27 +643,30 @@ mutual
               -- No sources could provide this subobject in the proper order.
               -- Recurse to handle default values for fields.
               else
-                let substruct := Struct.mk ref substructName #[] [] s.source
+                let substruct := { ref, structName := substructName, params := #[], fields := [], sources := s.sources }
                 let substruct ← expandStruct substruct
                 addField (FieldVal.nested substruct)
             -- No sources could provide this subobject.
             -- Recurse to handle default values for fields.
             | none =>
-              let substruct := Struct.mk ref substructName #[] [] s.source
+              let substruct := { ref, structName := substructName, params := #[], fields := [], sources := s.sources }
               let substruct ← expandStruct substruct
               addField (FieldVal.nested substruct)
           -- Since this is not a subobject field, we are free to use the first source that can
             -- provide it.
           | none =>
-            if let some val ← s.source.explicit.findSomeM? fun source => mkProjStx? source.stx source.structName fieldName then
+            if let some val ← s.sources.explicit.findSomeM? fun source => mkProjStx? source.stx source.structName fieldName then
               addField (FieldVal.term val)
-            else if s.source.implicit.isSome then
+            else if s.sources.implicit.isSome then
               addField (FieldVal.term (mkHole ref))
             else
               addField FieldVal.default
-      return s.setFields fields.reverse
+      return { s with fields := fields.reverse }
 
-  private partial def expandStruct (s : Struct) : TermElabM Struct := do
+  /--
+  Expands all fields of the structure instance, consolidates compound fields into subobject fields, and adds missing fields.
+  -/
+  private partial def expandStruct (s : StructInstView) : TermElabM StructInstView := do
     let s := expandCompositeFields s
     let s ← expandNumLitFields s
     let s ← expandParentFields s
@@ -579,10 +675,17 @@ mutual
 
 end
 
+/--
+The constructor to use for the structure instance notation.
+-/
 structure CtorHeaderResult where
+  /-- The constructor function with applied structure parameters. -/
   ctorFn     : Expr
+  /-- The type of `ctorFn` -/
   ctorFnType : Expr
+  /-- Instance metavariables for structure parameters that are instance implicit. -/
   instMVars  : Array MVarId
+  /-- Type parameter names and metavariables for each parameter. Used to seed `StructInstView.params`. -/
   params     : Array (Name × Expr)
 
 private def mkCtorHeaderAux : Nat → Expr → Expr → Array MVarId → Array (Name × Expr) → TermElabM CtorHeaderResult
@@ -604,6 +707,7 @@ private partial def getForallBody : Nat → Expr → Option Expr
   | _+1, _                => none
   | 0,   type             => type
 
+/-- Attempts to use the expected type to solve for structure parameters. -/
 private def propagateExpectedType (type : Expr) (numFields : Nat) (expectedType? : Option Expr) : TermElabM Unit := do
   match expectedType? with
   | none              => return ()
@@ -614,6 +718,7 @@ private def propagateExpectedType (type : Expr) (numFields : Nat) (expectedType?
         unless typeBody.hasLooseBVars do
           discard <| isDefEq expectedType typeBody
 
+/-- Elaborates the structure constructor using the expected type, filling in all structure parameters. -/
 private def mkCtorHeader (ctorVal : ConstructorVal) (expectedType? : Option Expr) : TermElabM CtorHeaderResult := do
   let us ← mkFreshLevelMVars ctorVal.levelParams.length
   let val  := Lean.mkConst ctorVal.name us
@@ -623,32 +728,43 @@ private def mkCtorHeader (ctorVal : ConstructorVal) (expectedType? : Option Expr
   synthesizeAppInstMVars r.instMVars r.ctorFn
   return r
 
+/-- Annotates an expression that it is a value for a missing field. -/
 def markDefaultMissing (e : Expr) : Expr :=
   mkAnnotation `structInstDefault e
 
+/-- If the expression has been annotated by `markDefaultMissing`, returns the unannotated expression. -/
 def defaultMissing? (e : Expr) : Option Expr :=
   annotation? `structInstDefault e
 
+/-- Throws "failed to elaborate field" error. -/
 def throwFailedToElabField {α} (fieldName : Name) (structName : Name) (msgData : MessageData) : TermElabM α :=
   throwError "failed to elaborate field '{fieldName}' of '{structName}, {msgData}"
 
-def trySynthStructInstance? (s : Struct) (expectedType : Expr) : TermElabM (Option Expr) := do
+/-- If the struct has all-missing fields, tries to synthesize the structure using typeclass inference. -/
+def trySynthStructInstance? (s : StructInstView) (expectedType : Expr) : TermElabM (Option Expr) := do
   if !s.allDefault then
     return none
   else
     try synthInstance? expectedType catch _ => return none
 
+/-- The result of elaborating a `StructInstView` structure instance view. -/
 structure ElabStructResult where
+  /-- The elaborated value. -/
   val       : Expr
-  struct    : Struct
+  /-- The modified `StructInstView` view after elaboration. -/
+  struct    : StructInstView
+  /-- Metavariables for instance implicit fields. These will be registered after default value propagation. -/
   instMVars : Array MVarId
 
-private partial def elabStruct (s : Struct) (expectedType? : Option Expr) : TermElabM ElabStructResult := withRef s.ref do
+/--
+Main elaborator for structure instances.
+-/
+private partial def elabStructInstView (s : StructInstView) (expectedType? : Option Expr) : TermElabM ElabStructResult := withRef s.ref do
   let env ← getEnv
   let ctorVal := getStructureCtor env s.structName
   if isPrivateNameFromImportedModule env ctorVal.name then
     throwError "invalid \{...} notation, constructor for `{s.structName}` is marked as private"
-  -- We store the parameters at the resulting `Struct`. We use this information during default value propagation.
+  -- We store the parameters at the resulting `StructInstView`. We use this information during default value propagation.
   let { ctorFn, ctorFnType, params, .. } ← mkCtorHeader ctorVal expectedType?
   let (e, _, fields, instMVars) ← s.fields.foldlM (init := (ctorFn, ctorFnType, [], #[])) fun (e, type, fields, instMVars) field => do
     match field.lhs with
@@ -657,7 +773,7 @@ private partial def elabStruct (s : Struct) (expectedType? : Option Expr) : Term
       trace[Elab.struct] "elabStruct {field}, {type}"
       match type with
       | .forallE _ d b bi =>
-        let cont (val : Expr) (field : Field Struct) (instMVars := instMVars) : TermElabM (Expr × Expr × Fields × Array MVarId) := do
+        let cont (val : Expr) (field : Field StructInstView) (instMVars := instMVars) : TermElabM (Expr × Expr × Fields × Array MVarId) := do
           pushInfoTree <| InfoTree.node (children := {}) <| Info.ofFieldInfo {
             projName := s.structName.append fieldName, fieldName, lctx := (← getLCtx), val, stx := ref }
           let e     := mkApp e val
@@ -671,7 +787,7 @@ private partial def elabStruct (s : Struct) (expectedType? : Option Expr) : Term
           match (← trySynthStructInstance? s d) with
           | some val => cont val { field with val := FieldVal.term (mkHole field.ref) }
           | none     =>
-            let { val, struct := sNew, instMVars := instMVarsNew } ← elabStruct s (some d)
+            let { val, struct := sNew, instMVars := instMVarsNew } ← elabStructInstView s (some d)
             let val ← ensureHasType d val
             cont val { field with val := FieldVal.nested sNew } (instMVars ++ instMVarsNew)
         | .default  =>
@@ -700,17 +816,21 @@ private partial def elabStruct (s : Struct) (expectedType? : Option Expr) : Term
               cont (markDefaultMissing val) field
       | _ => withRef field.ref <| throwFailedToElabField fieldName s.structName m!"unexpected constructor type{indentExpr type}"
     | _ => throwErrorAt field.ref "unexpected unexpanded structure field"
-  return { val := e, struct := s.setFields fields.reverse |>.setParams params, instMVars }
+  return { val := e, struct := { s with fields := fields.reverse, params }, instMVars }
 
 namespace DefaultFields
 
+/--
+Context for default value propagation.
+-/
 structure Context where
-  -- We must search for default values overridden in derived structures
-  structs : Array Struct := #[]
+  /-- The current path through `.nested` subobject structures. We must search for default values overridden in derived structures. -/
+  structs : Array StructInstView := #[]
+  /-- The collection of structures that could provide a default value. -/
   allStructNames : Array Name := #[]
   /--
   Consider the following example:
-  ```
+  ```lean
   structure A where
     x : Nat := 1
 
@@ -736,22 +856,29 @@ structure Context where
   -/
   maxDistance : Nat := 0
 
+/--
+State for default value propagation
+-/
 structure State where
+  /-- Whether progress has been made so far on this round of the propagation loop. -/
   progress : Bool := false
 
-partial def collectStructNames (struct : Struct) (names : Array Name) : Array Name :=
+/-- Collects all structures that may provide default values for fields. -/
+partial def collectStructNames (struct : StructInstView) (names : Array Name) : Array Name :=
   let names := names.push struct.structName
   struct.fields.foldl (init := names) fun names field =>
     match field.val with
     | .nested struct => collectStructNames struct names
     | _ => names
 
-partial def getHierarchyDepth (struct : Struct) : Nat :=
+/-- Gets the maximum nesting depth of subobjects. -/
+partial def getHierarchyDepth (struct : StructInstView) : Nat :=
   struct.fields.foldl (init := 0) fun max field =>
     match field.val with
     | .nested struct => Nat.max max (getHierarchyDepth struct + 1)
     | _ => max
 
+/-- Returns whether the field is still missing. -/
 def isDefaultMissing? [Monad m] [MonadMCtx m] (field : Field Struct) : m Bool := do
   if let some expr := field.expr? then
     if let some (.mvar mvarId) := defaultMissing? expr then
@@ -759,40 +886,51 @@ def isDefaultMissing? [Monad m] [MonadMCtx m] (field : Field Struct) : m Bool :=
         return true
   return false
 
-partial def findDefaultMissing? [Monad m] [MonadMCtx m] (struct : Struct) : m (Option (Field Struct)) :=
+/-- Returns a field that is still missing. -/
+partial def findDefaultMissing? [Monad m] [MonadMCtx m] (struct : StructInstView) : m (Option (Field StructInstView)) :=
   struct.fields.findSomeM? fun field => do
    match field.val with
    | .nested struct => findDefaultMissing? struct
    | _ => return if (← isDefaultMissing? field) then field else none
 
-partial def allDefaultMissing [Monad m] [MonadMCtx m] (struct : Struct) : m (Array (Field Struct)) :=
+/-- Returns all fields that are still missing. -/
+partial def allDefaultMissing [Monad m] [MonadMCtx m] (struct : StructInstView) : m (Array (Field StructInstView)) :=
   go struct *> get |>.run' #[]
 where
-  go (struct : Struct) : StateT (Array (Field Struct)) m Unit :=
+  go (struct : StructInstView) : StateT (Array (Field StructInstView)) m Unit :=
     for field in struct.fields do
       if let .nested struct := field.val then
         go struct
       else if (← isDefaultMissing? field) then
         modify (·.push field)
 
-def getFieldName (field : Field Struct) : Name :=
+/-- Returns the name of the field. Assumes all fields under consideration are simple and named. -/
+def getFieldName (field : Field StructInstView) : Name :=
   match field.lhs with
   | [.fieldName _ fieldName] => fieldName
   | _ => unreachable!
 
 abbrev M := ReaderT Context (StateRefT State TermElabM)
 
+/-- Returns whether we should interrupt the round because we have made progress allowing nonzero depth. -/
 def isRoundDone : M Bool := do
   return (← get).progress && (← read).maxDistance > 0
 
-def getFieldValue? (struct : Struct) (fieldName : Name) : Option Expr :=
+/-- Returns the `expr?` for the given field. -/
+def getFieldValue? (struct : StructInstView) (fieldName : Name) : Option Expr :=
   struct.fields.findSome? fun field =>
     if getFieldName field == fieldName then
       field.expr?
     else
       none
 
-partial def mkDefaultValueAux? (struct : Struct) : Expr → TermElabM (Option Expr)
+/-- Instantiates a default value from the given default value declaration, if applicable. -/
+partial def mkDefaultValue? (struct : StructInstView) (cinfo : ConstantInfo) : TermElabM (Option Expr) :=
+  withRef struct.ref do
+  let us ← mkFreshLevelMVarsFor cinfo
+  process (← instantiateValueLevelParams cinfo us)
+where
+  process : Expr → TermElabM (Option Expr)
   | .lam n d b c => withRef struct.ref do
     if c.isExplicit then
       let fieldName := n
@@ -801,29 +939,26 @@ partial def mkDefaultValueAux? (struct : Struct) : Expr → TermElabM (Option Ex
       | some val =>
         let valType ← inferType val
         if (← isDefEq valType d) then
-          mkDefaultValueAux? struct (b.instantiate1 val)
+          process (b.instantiate1 val)
         else
           return none
     else
       if let some (_, param) := struct.params.find? fun (paramName, _) => paramName == n then
         -- Recall that we did not use to have support for parameter propagation here.
         if (← isDefEq (← inferType param) d) then
-          mkDefaultValueAux? struct (b.instantiate1 param)
+          process (b.instantiate1 param)
         else
           return none
       else
         let arg ← mkFreshExprMVar d
-        mkDefaultValueAux? struct (b.instantiate1 arg)
+        process (b.instantiate1 arg)
   | e =>
     let_expr id _ a := e | return some e
     return some a
 
-def mkDefaultValue? (struct : Struct) (cinfo : ConstantInfo) : TermElabM (Option Expr) :=
-  withRef struct.ref do
-  let us ← mkFreshLevelMVarsFor cinfo
-  mkDefaultValueAux? struct (← instantiateValueLevelParams cinfo us)
-
-/-- Reduce default value. It performs beta reduction and projections of the given structures. -/
+/--
+Reduces a default value. It performs beta reduction and projections of the given structures to reduce them to the provided values for fields.
+-/
 partial def reduce (structNames : Array Name) (e : Expr) : MetaM Expr := do
   match e with
   | .forallE ..   =>
@@ -880,7 +1015,10 @@ where
     else
       k
 
-partial def tryToSynthesizeDefault (structs : Array Struct) (allStructNames : Array Name) (maxDistance : Nat) (fieldName : Name) (mvarId : MVarId) : TermElabM Bool :=
+/--
+Attempts to synthesize a default value for a missing field `fieldName` using default values from each structure in `structs`.
+-/
+def tryToSynthesizeDefault (structs : Array StructInstView) (allStructNames : Array Name) (maxDistance : Nat) (fieldName : Name) (mvarId : MVarId) : TermElabM Bool :=
   let rec loop (i : Nat) (dist : Nat) := do
     if dist > maxDistance then
       return false
@@ -900,14 +1038,25 @@ partial def tryToSynthesizeDefault (structs : Array Struct) (allStructNames : Ar
           | none   =>
             let mvarDecl ← getMVarDecl mvarId
             let val ← ensureHasType mvarDecl.type val
-            mvarId.assign val
-            return true
+            /-
+            We must use `checkedAssign` here to ensure we do not create a cyclic
+            assignment. See #3150.
+            This can happen when there are holes in the the fields the default value
+            depends on.
+            Possible improvement: create a new `_` instead of returning `false` when
+            `checkedAssign` fails. Reason: the field will not be needed after the
+            other `_` are resolved by the user.
+            -/
+            mvarId.checkedAssign val
       | _ => loop (i+1) dist
     else
       return false
   loop 0 0
 
-partial def step (struct : Struct) : M Unit :=
+/--
+Performs one step of default value synthesis.
+-/
+partial def step (struct : StructInstView) : M Unit :=
   unless (← isRoundDone) do
     withReader (fun ctx => { ctx with structs := ctx.structs.push struct }) do
       for field in struct.fields do
@@ -924,7 +1073,10 @@ partial def step (struct : Struct) : M Unit :=
                   modify fun _ => { progress := true }
             | _ => pure ()
 
-partial def propagateLoop (hierarchyDepth : Nat) (d : Nat) (struct : Struct) : M Unit := do
+/--
+Main entry point to default value synthesis in the `M` monad.
+-/
+partial def propagateLoop (hierarchyDepth : Nat) (d : Nat) (struct : StructInstView) : M Unit := do
   match (← findDefaultMissing? struct) with
   | none       => return () -- Done
   | some field =>
@@ -947,16 +1099,22 @@ partial def propagateLoop (hierarchyDepth : Nat) (d : Nat) (struct : Struct) : M
       else
         propagateLoop hierarchyDepth (d+1) struct
 
-def propagate (struct : Struct) : TermElabM Unit :=
+/--
+Synthesizes default values for all missing fields, if possible.
+-/
+def propagate (struct : StructInstView) : TermElabM Unit :=
   let hierarchyDepth := getHierarchyDepth struct
   let structNames := collectStructNames struct #[]
   propagateLoop hierarchyDepth 0 struct { allStructNames := structNames } |>.run' {}
 
 end DefaultFields
 
-private def elabStructInstAux (stx : Syntax) (expectedType? : Option Expr) (source : Source) : TermElabM Expr := do
-  let structName ← getStructName expectedType? source
-  let struct ← liftMacroM <| mkStructView stx structName source
+/--
+Main entry point to elaborator for structure instance notation, unless the structure instance is a modifyOp.
+-/
+private def elabStructInstAux (stx : Syntax) (expectedType? : Option Expr) (sources : SourcesView) : TermElabM Expr := do
+  let structName ← getStructName expectedType? sources
+  let struct ← liftMacroM <| mkStructView stx structName sources
   let struct ← expandStruct struct
   trace[Elab.struct] "{struct}"
   /- We try to synthesize pending problems with `withSynthesize` combinator before trying to use default values.
@@ -974,7 +1132,7 @@ private def elabStructInstAux (stx : Syntax) (expectedType? : Option Expr) (sour
 
      TODO: investigate whether this design decision may have unintended side effects or produce confusing behavior.
   -/
-  let { val := r, struct, instMVars } ← withSynthesize (postpone := .yes) <| elabStruct struct expectedType?
+  let { val := r, struct, instMVars } ← withSynthesize (postpone := .yes) <| elabStructInstView struct expectedType?
   trace[Elab.struct] "before propagate {r}"
   DefaultFields.propagate struct
   synthesizeAppInstMVars instMVars r
@@ -984,13 +1142,13 @@ private def elabStructInstAux (stx : Syntax) (expectedType? : Option Expr) (sour
   match (← expandNonAtomicExplicitSources stx) with
   | some stxNew => withMacroExpansion stx stxNew <| elabTerm stxNew expectedType?
   | none =>
-    let sourceView ← getStructSource stx
+    let sourcesView ← getStructSources stx
     if let some modifyOp ← isModifyOp? stx then
-      if sourceView.explicit.isEmpty then
+      if sourcesView.explicit.isEmpty then
         throwError "invalid \{...} notation, explicit source is required when using '[<index>] := <value>'"
-      elabModifyOp stx modifyOp sourceView.explicit expectedType?
+      elabModifyOp stx modifyOp sourcesView.explicit expectedType?
     else
-      elabStructInstAux stx expectedType? sourceView
+      elabStructInstAux stx expectedType? sourcesView
 
 builtin_initialize
   registerTraceClass `Elab.struct

src/Lean/Elab/Syntax.lean

@@ -142,7 +142,7 @@ where
     let args := stx.getArgs
     if (← checkLeftRec stx[0]) then
       if args.size == 1 then throwErrorAt stx "invalid atomic left recursive syntax"
-      let args := args.eraseIdx 0
+      let args := args.eraseIdxIfInBounds 0
       let args ← args.mapM fun arg => withNestedParser do process arg
       mkParserSeq args
     else
@@ -236,8 +236,9 @@ where
     -- Pretty-printing instructions shouldn't affect validity
     let s := s.trim
     !s.isEmpty &&
-    (s.front != '\'' || s == "''") &&
+    (s.front != '\'' || "''".isPrefixOf s) &&
     s.front != '\"' &&
+    !(isIdBeginEscape s.front) &&
     !(s.front == '`' && (s.endPos == ⟨1⟩ || isIdFirst (s.get ⟨1⟩) || isIdBeginEscape (s.get ⟨1⟩))) &&
     !s.front.isDigit &&
     !(s.any Char.isWhitespace)

src/Lean/Elab/Tactic/Change.lean

@@ -13,6 +13,31 @@ open Meta
 # Implementation of the `change` tactic
 -/
 
+/--
+Elaborates the pattern `p` and ensures that it is defeq to `e`.
+Emulates `(show p from ?m : e)`, returning the type of `?m`, but `e` and `p` do not need to be types.
+Unlike `(show p from ?m : e)`, this can assign synthetic opaque metavariables appearing in `p`.
+-/
+def elabChange (e : Expr) (p : Term) : TacticM Expr := do
+  let p ← runTermElab do
+    let p ← Term.elabTermEnsuringType p (← inferType e)
+    unless ← isDefEq p e do
+      /-
+      Sometimes isDefEq can fail due to postponed elaboration problems.
+      We synthesize pending synthetic mvars while allowing typeclass instances to be postponed,
+      which might enable solving for them with an additional `isDefEq`.
+      -/
+      Term.synthesizeSyntheticMVars (postpone := .partial)
+      discard <| isDefEq p e
+    pure p
+  withAssignableSyntheticOpaque do
+    unless ← isDefEq p e do
+      let (p, tgt) ← addPPExplicitToExposeDiff p e
+      throwError "\
+        'change' tactic failed, pattern{indentExpr p}\n\
+        is not definitionally equal to target{indentExpr tgt}"
+    instantiateMVars p
+
 /-- `change` can be used to replace the main goal or its hypotheses with
 different, yet definitionally equal, goal or hypotheses.
 
@@ -38,15 +63,13 @@ the main goal. -/
   | `(tactic| change $newType:term $[$loc:location]?) => do
     withLocation (expandOptLocation (Lean.mkOptionalNode loc))
       (atLocal := fun h => do
-        let hTy ← h.getType
-        -- This is a hack to get the new type to elaborate in the same sort of way that
-        -- it would for a `show` expression for the goal.
-        let mvar ← mkFreshExprMVar none
-        let (_, mvars) ← elabTermWithHoles
-                          (← `(term | show $newType from $(← Term.exprToSyntax mvar))) hTy `change
+        let (hTy', mvars) ← withCollectingNewGoalsFrom (elabChange (← h.getType) newType) (← getMainTag) `change
         liftMetaTactic fun mvarId => do
-          return (← mvarId.changeLocalDecl h (← inferType mvar)) :: mvars)
-      (atTarget := evalTactic <| ← `(tactic| refine_lift show $newType from ?_))
-      (failed := fun _ => throwError "change tactic failed")
+          return (← mvarId.changeLocalDecl h hTy') :: mvars)
+      (atTarget := do
+        let (tgt', mvars) ← withCollectingNewGoalsFrom (elabChange (← getMainTarget) newType) (← getMainTag) `change
+        liftMetaTactic fun mvarId => do
+          return (← mvarId.replaceTargetDefEq tgt') :: mvars)
+      (failed := fun _ => throwError "'change' tactic failed")
 
 end Lean.Elab.Tactic

src/Lean/Elab/Tactic/Config.lean

@@ -114,6 +114,13 @@ private def elabConfig (recover : Bool) (structName : Name) (items : Array Confi
     let e ← Term.withSynthesize <| Term.elabTermEnsuringType stx (mkConst structName)
     instantiateMVars e
 
+section
+-- We automatically disable the following option for `macro`s but the subsequent `def` both contains
+-- a quotation and is called only by `macro`s, so we disable the option for it manually. Note that
+-- we can't use `in` as it is parsed as a single command and so the option would not influence the
+-- parser.
+set_option internal.parseQuotWithCurrentStage false
+
 private def mkConfigElaborator
     (doc? : Option (TSyntax ``Parser.Command.docComment)) (elabName type monadName : Ident)
     (adapt recover : Term) : MacroM (TSyntax `command) := do
@@ -148,6 +155,8 @@ private def mkConfigElaborator
             throwError msg
       go)
 
+end
+
 /-!
 `declare_config_elab elabName TypeName` declares a function `elabName : Syntax → TacticM TypeName`
 that elaborates a tactic configuration.

src/Lean/Elab/Tactic/Conv/Change.lean

@@ -5,6 +5,7 @@ Authors: Leonardo de Moura
 -/
 prelude
 import Lean.Elab.Tactic.ElabTerm
+import Lean.Elab.Tactic.Change
 import Lean.Elab.Tactic.Conv.Basic
 
 namespace Lean.Elab.Tactic.Conv
@@ -15,11 +16,9 @@ open Meta
   | `(conv| change $e) => withMainContext do
     let lhs ← getLhs
     let mvarCounterSaved := (← getMCtx).mvarCounter
-    let r ← elabTermEnsuringType e (← inferType lhs)
-    logUnassignedAndAbort (← filterOldMVars (← getMVars r) mvarCounterSaved)
-    unless (← isDefEqGuarded r lhs) do
-      throwError "invalid 'change' conv tactic, term{indentExpr r}\nis not definitionally equal to current left-hand-side{indentExpr lhs}"
-    changeLhs r
+    let lhs' ← elabChange lhs e
+    logUnassignedAndAbort (← filterOldMVars (← getMVars lhs') mvarCounterSaved)
+    changeLhs lhs'
   | _ => throwUnsupportedSyntax
 
 end Lean.Elab.Tactic.Conv

src/Lean/Elab/Tactic/DiscrTreeKey.lean

@@ -18,21 +18,22 @@ private def mkKey (e : Expr) (simp : Bool) : MetaM (Array Key) := do
   let (_, _, type) ← withReducible <| forallMetaTelescopeReducing e
   let type ← whnfR type
   if simp then
-    if let some (_, lhs, _) := type.eq? then
-      mkPath lhs simpDtConfig
-    else if let some (lhs, _) := type.iff? then
-      mkPath lhs simpDtConfig
-    else if let some (_, lhs, _) := type.ne? then
-      mkPath lhs simpDtConfig
-    else if let some p := type.not? then
-      match p.eq? with
-      | some (_, lhs, _) =>
-        mkPath lhs simpDtConfig
-      | _ => mkPath p simpDtConfig
-    else
-      mkPath type simpDtConfig
+    withSimpGlobalConfig do
+      if let some (_, lhs, _) := type.eq? then
+        mkPath lhs
+      else if let some (lhs, _) := type.iff? then
+        mkPath lhs
+      else if let some (_, lhs, _) := type.ne? then
+        mkPath lhs
+      else if let some p := type.not? then
+        match p.eq? with
+        | some (_, lhs, _) =>
+          mkPath lhs
+        | _ => mkPath p
+      else
+        mkPath type
   else
-    mkPath type {}
+    mkPath type
 
 private def getType (t : TSyntax `term) : TermElabM Expr := do
   if let `($id:ident) := t then

src/Lean/Elab/Tactic/ElabTerm.lean

@@ -542,11 +542,6 @@ declare_config_elab elabDecideConfig Parser.Tactic.DecideConfig
   let cfg ← elabDecideConfig stx[1]
   evalDecideCore `decide cfg
 
-@[builtin_tactic Lean.Parser.Tactic.decideBang] def evalDecideBang : Tactic := fun stx => do
-  let cfg ← elabDecideConfig stx[1]
-  let cfg := { cfg with kernel := true }
-  evalDecideCore `decide! cfg
-
 @[builtin_tactic Lean.Parser.Tactic.nativeDecide] def evalNativeDecide : Tactic := fun stx => do
   let cfg ← elabDecideConfig stx[1]
   let cfg := { cfg with native := true }

src/Lean/Elab/Tactic/Ext.lean

@@ -195,9 +195,6 @@ structure ExtTheorems where
   erased  : PHashSet Name := {}
   deriving Inhabited
 
-/-- Discrimation tree settings for the `ext` extension. -/
-def extExt.config : WhnfCoreConfig := {}
-
 /-- The environment extension to track `@[ext]` theorems. -/
 builtin_initialize extExtension :
     SimpleScopedEnvExtension ExtTheorem ExtTheorems ←
@@ -211,7 +208,7 @@ builtin_initialize extExtension :
 ordered from high priority to low. -/
 @[inline] def getExtTheorems (ty : Expr) : MetaM (Array ExtTheorem) := do
   let extTheorems := extExtension.getState (← getEnv)
-  let arr ← extTheorems.tree.getMatch ty extExt.config
+  let arr ← extTheorems.tree.getMatch ty
   let erasedArr := arr.filter fun thm => !extTheorems.erased.contains thm.declName
   -- Using insertion sort because it is stable and the list of matches should be mostly sorted.
   -- Most ext theorems have default priority.
@@ -258,7 +255,7 @@ builtin_initialize registerBuiltinAttribute {
       but this theorem proves{indentD declTy}"
     let some (ty, lhs, rhs) := declTy.eq? | failNotEq
     unless lhs.isMVar && rhs.isMVar do failNotEq
-    let keys ← withReducible <| DiscrTree.mkPath ty extExt.config
+    let keys ← withReducible <| DiscrTree.mkPath ty
     let priority ← liftCommandElabM <| Elab.liftMacroM do evalPrio (prio.getD (← `(prio| default)))
     extExtension.add {declName, keys, priority} kind
     -- Realize iff theorem

src/Lean/Elab/Tactic/Induction.lean

@@ -340,9 +340,9 @@ where
     for h : altStxIdx in [0:altStxs.size] do
       let altStx := altStxs[altStxIdx]
       let altName := getAltName altStx
-      if let some i := alts.findIdx? (·.1 == altName) then
+      if let some i := alts.findFinIdx? (·.1 == altName) then
         -- cover named alternative
-        applyAltStx tacSnaps altStxIdx altStx alts[i]!
+        applyAltStx tacSnaps altStxIdx altStx alts[i]
         alts := alts.eraseIdx i
       else if !alts.isEmpty && isWildcard altStx then
         -- cover all alternatives

src/Lean/Elab/Tactic/LibrarySearch.lean

@@ -40,7 +40,7 @@ def exact? (ref : Syntax) (required : Option (Array (TSyntax `term))) (requireCl
     | some suggestions =>
       if requireClose then throwError
         "`exact?` could not close the goal. Try `apply?` to see partial suggestions."
-      reportOutOfHeartbeats `library_search ref
+      reportOutOfHeartbeats `apply? ref
       for (_, suggestionMCtx) in suggestions do
         withMCtx suggestionMCtx do
           addExactSuggestion ref (← instantiateMVars (mkMVar mvar)).headBeta (addSubgoalsMsg := true)

src/Lean/Elab/Tactic/Simp.lean

@@ -91,7 +91,7 @@ def elabSimpConfig (optConfig : Syntax) (kind : SimpKind) : TacticM Meta.Simp.Co
   | .simpAll => return (← elabSimpConfigCtxCore optConfig).toConfig
   | .dsimp   => return { (← elabDSimpConfigCore optConfig) with }
 
-private def addDeclToUnfoldOrTheorem (thms : SimpTheorems) (id : Origin) (e : Expr) (post : Bool) (inv : Bool) (kind : SimpKind) : MetaM SimpTheorems := do
+private def addDeclToUnfoldOrTheorem (config : Meta.ConfigWithKey) (thms : SimpTheorems) (id : Origin) (e : Expr) (post : Bool) (inv : Bool) (kind : SimpKind) : MetaM SimpTheorems := do
   if e.isConst then
     let declName := e.constName!
     let info ← getConstInfo declName
@@ -108,7 +108,7 @@ private def addDeclToUnfoldOrTheorem (thms : SimpTheorems) (id : Origin) (e : Ex
     let fvarId := e.fvarId!
     let decl ← fvarId.getDecl
     if (← isProp decl.type) then
-      thms.add id #[] e (post := post) (inv := inv)
+      thms.add id #[] e (post := post) (inv := inv) (config := config)
     else if !decl.isLet then
       throwError "invalid argument, variable is not a proposition or let-declaration"
     else if inv then
@@ -116,9 +116,9 @@ private def addDeclToUnfoldOrTheorem (thms : SimpTheorems) (id : Origin) (e : Ex
     else
       return thms.addLetDeclToUnfold fvarId
   else
-    thms.add id #[] e (post := post) (inv := inv)
+    thms.add id #[] e (post := post) (inv := inv) (config := config)
 
-private def addSimpTheorem (thms : SimpTheorems) (id : Origin) (stx : Syntax) (post : Bool) (inv : Bool) : TermElabM SimpTheorems := do
+private def addSimpTheorem (config : Meta.ConfigWithKey) (thms : SimpTheorems) (id : Origin) (stx : Syntax) (post : Bool) (inv : Bool) : TermElabM SimpTheorems := do
   let thm? ← Term.withoutModifyingElabMetaStateWithInfo <| withRef stx do
     let e ← Term.elabTerm stx none
     Term.synthesizeSyntheticMVars (postpone := .no) (ignoreStuckTC := true)
@@ -132,7 +132,7 @@ private def addSimpTheorem (thms : SimpTheorems) (id : Origin) (stx : Syntax) (p
     else
       return some (#[], e)
   if let some (levelParams, proof) := thm? then
-    thms.add id levelParams proof (post := post) (inv := inv)
+    thms.add id levelParams proof (post := post) (inv := inv) (config := config)
   else
     return thms
 
@@ -212,7 +212,7 @@ def elabSimpArgs (stx : Syntax) (ctx : Simp.Context) (simprocs : Simp.SimprocsAr
             match (← resolveSimpIdTheorem? term) with
             | .expr e  =>
               let name ← mkFreshId
-              thms ← addDeclToUnfoldOrTheorem thms (.stx name arg) e post inv kind
+              thms ← addDeclToUnfoldOrTheorem ctx.indexConfig thms (.stx name arg) e post inv kind
             | .simproc declName =>
               simprocs ← simprocs.add declName post
             | .ext (some ext₁) (some ext₂) _ =>
@@ -224,7 +224,7 @@ def elabSimpArgs (stx : Syntax) (ctx : Simp.Context) (simprocs : Simp.SimprocsAr
               simprocs  := simprocs.push (← ext₂.getSimprocs)
             | .none    =>
               let name ← mkFreshId
-              thms ← addSimpTheorem thms (.stx name arg) term post inv
+              thms ← addSimpTheorem ctx.indexConfig thms (.stx name arg) term post inv
           else if arg.getKind == ``Lean.Parser.Tactic.simpStar then
             starArg := true
           else
@@ -329,7 +329,7 @@ def mkSimpContext (stx : Syntax) (eraseLocal : Bool) (kind := SimpKind.simp)
     let hs ← getPropHyps
     for h in hs do
       unless simpTheorems.isErased (.fvar h) do
-        simpTheorems ← simpTheorems.addTheorem (.fvar h) (← h.getDecl).toExpr
+        simpTheorems ← simpTheorems.addTheorem (.fvar h) (← h.getDecl).toExpr (config := ctx.indexConfig)
     let ctx := ctx.setSimpTheorems simpTheorems
     return { ctx, simprocs, dischargeWrapper }
 

src/Lean/Elab/Tactic/Simproc.lean

@@ -25,7 +25,7 @@ def elabSimprocPattern (stx : Syntax) : MetaM Expr := do
 
 def elabSimprocKeys (stx : Syntax) : MetaM (Array Meta.SimpTheoremKey) := do
   let pattern ← elabSimprocPattern stx
-  DiscrTree.mkPath pattern simpDtConfig
+  withSimpGlobalConfig <| DiscrTree.mkPath pattern
 
 def checkSimprocType (declName : Name) : CoreM Bool := do
   let decl ← getConstInfo declName

src/Lean/Elab/Term.lean

@@ -1298,13 +1298,20 @@ def isTacticOrPostponedHole? (e : Expr) : TermElabM (Option MVarId) := do
     | _                                  => return none
   | _ => pure none
 
-def mkTermInfo (elaborator : Name) (stx : Syntax) (e : Expr) (expectedType? : Option Expr := none) (lctx? : Option LocalContext := none) (isBinder := false) : TermElabM (Sum Info MVarId) := do
+def mkTermInfo (elaborator : Name) (stx : Syntax) (e : Expr) (expectedType? : Option Expr := none)
+    (lctx? : Option LocalContext := none) (isBinder := false) :
+    TermElabM (Sum Info MVarId) := do
   match (← isTacticOrPostponedHole? e) with
   | some mvarId => return Sum.inr mvarId
   | none =>
     let e := removeSaveInfoAnnotation e
     return Sum.inl <| Info.ofTermInfo { elaborator, lctx := lctx?.getD (← getLCtx), expr := e, stx, expectedType?, isBinder }
 
+def mkPartialTermInfo (elaborator : Name) (stx : Syntax) (expectedType? : Option Expr := none)
+    (lctx? : Option LocalContext := none) :
+    TermElabM Info := do
+  return Info.ofPartialTermInfo { elaborator, lctx := lctx?.getD (← getLCtx), stx, expectedType? }
+
 /--
 Pushes a new leaf node to the info tree associating the expression `e` to the syntax `stx`.
 As a result, when the user hovers over `stx` they will see the type of `e`, and if `e`
@@ -1326,41 +1333,54 @@ def addTermInfo (stx : Syntax) (e : Expr) (expectedType? : Option Expr := none)
   if (← read).inPattern && !force then
     return mkPatternWithRef e stx
   else
-    withInfoContext' (pure ()) (fun _ => mkTermInfo elaborator stx e expectedType? lctx? isBinder) |> discard
+    discard <| withInfoContext'
+      (pure ())
+      (fun _ => mkTermInfo elaborator stx e expectedType? lctx? isBinder)
+      (mkPartialTermInfo elaborator stx expectedType? lctx?)
     return e
 
 def addTermInfo' (stx : Syntax) (e : Expr) (expectedType? : Option Expr := none) (lctx? : Option LocalContext := none) (elaborator := Name.anonymous) (isBinder := false) : TermElabM Unit :=
   discard <| addTermInfo stx e expectedType? lctx? elaborator isBinder
 
-def withInfoContext' (stx : Syntax) (x : TermElabM Expr) (mkInfo : Expr → TermElabM (Sum Info MVarId)) : TermElabM Expr := do
+def withInfoContext' (stx : Syntax) (x : TermElabM Expr)
+    (mkInfo : Expr → TermElabM (Sum Info MVarId)) (mkInfoOnError : TermElabM Info) :
+    TermElabM Expr := do
   if (← read).inPattern then
     let e ← x
     return mkPatternWithRef e stx
   else
-    Elab.withInfoContext' x mkInfo
+    Elab.withInfoContext' x mkInfo mkInfoOnError
 
 /-- Info node capturing `def/let rec` bodies, used by the unused variables linter. -/
 structure BodyInfo where
-  /-- The body as a fully elaborated term. -/
-  value : Expr
+  /-- The body as a fully elaborated term. `none` if the body failed to elaborate. -/
+  value? : Option Expr
 deriving TypeName
 
 /-- Creates an `Info.ofCustomInfo` node backed by a `BodyInfo`. -/
-def mkBodyInfo (stx : Syntax) (value : Expr) : Info :=
-  .ofCustomInfo { stx, value := .mk { value : BodyInfo } }
+def mkBodyInfo (stx : Syntax) (value? : Option Expr) : Info :=
+  .ofCustomInfo { stx, value := .mk { value? : BodyInfo } }
 
 /-- Extracts a `BodyInfo` custom info. -/
 def getBodyInfo? : Info → Option BodyInfo
   | .ofCustomInfo { value, .. } => value.get? BodyInfo
   | _ => none
 
+def withTermInfoContext' (elaborator : Name) (stx : Syntax) (x : TermElabM Expr)
+    (expectedType? : Option Expr := none) (lctx? : Option LocalContext := none)
+    (isBinder : Bool := false) :
+    TermElabM Expr :=
+  withInfoContext' stx x
+    (mkTermInfo elaborator stx (expectedType? := expectedType?) (lctx? := lctx?) (isBinder := isBinder))
+    (mkPartialTermInfo elaborator stx (expectedType? := expectedType?) (lctx? := lctx?))
+
 /--
 Postpone the elaboration of `stx`, return a metavariable that acts as a placeholder, and
 ensures the info tree is updated and a hole id is introduced.
 When `stx` is elaborated, new info nodes are created and attached to the new hole id in the info tree.
 -/
 def postponeElabTerm (stx : Syntax) (expectedType? : Option Expr) : TermElabM Expr := do
-  withInfoContext' stx (mkInfo := mkTermInfo .anonymous (expectedType? := expectedType?) stx) do
+  withTermInfoContext' .anonymous stx (expectedType? := expectedType?) do
     postponeElabTermCore stx expectedType?
 
 /--
@@ -1372,7 +1392,7 @@ private def elabUsingElabFnsAux (s : SavedState) (stx : Syntax) (expectedType? :
   | (elabFn::elabFns) =>
     try
       -- record elaborator in info tree, but only when not backtracking to other elaborators (outer `try`)
-      withInfoContext' stx (mkInfo := mkTermInfo elabFn.declName (expectedType? := expectedType?) stx)
+      withTermInfoContext' elabFn.declName stx (expectedType? := expectedType?)
         (try
           elabFn.value stx expectedType?
         catch ex => match ex with
@@ -1755,7 +1775,7 @@ private partial def elabTermAux (expectedType? : Option Expr) (catchExPostpone :
     let result ← match (← liftMacroM (expandMacroImpl? env stx)) with
     | some (decl, stxNew?) =>
       let stxNew ← liftMacroM <| liftExcept stxNew?
-      withInfoContext' stx (mkInfo := mkTermInfo decl (expectedType? := expectedType?) stx) <|
+      withTermInfoContext' decl stx (expectedType? := expectedType?) <|
         withMacroExpansion stx stxNew <|
           withRef stxNew <|
             elabTermAux expectedType? catchExPostpone implicitLambda stxNew

src/Lean/Level.lean

@@ -599,17 +599,20 @@ def geq (u v : Level) : Bool :=
 where
   go (u v : Level) : Bool :=
     u == v ||
+    let k := fun () =>
+      match v with
+      | imax v₁ v₂ => go u v₁ && go u v₂
+      | _          =>
+        let v' := v.getLevelOffset
+        (u.getLevelOffset == v' || v'.isZero)
+        && u.getOffset ≥ v.getOffset
     match u, v with
-    | _,          zero       => true
-    | u,          max v₁ v₂  => go u v₁ && go u v₂
-    | max u₁ u₂,  v          => go u₁ v || go u₂ v
-    | u,          imax v₁ v₂ => go u v₁ && go u v₂
-    | imax _  u₂, v          => go u₂ v
-    | succ u,     succ v     => go u v
-    | _, _ =>
-      let v' := v.getLevelOffset
-      (u.getLevelOffset == v' || v'.isZero)
-      && u.getOffset ≥ v.getOffset
+    | _,          zero      => true
+    | u,          max v₁ v₂ => go u v₁ && go u v₂
+    | max u₁ u₂,  v         => go u₁ v || go u₂ v || k ()
+    | imax _  u₂, v         => go u₂ v
+    | succ u,     succ v    => go u v
+    | _,          _         => k ()
   termination_by (u, v)
 
 end Level

src/Lean/Linter/UnusedVariables.lean

@@ -393,16 +393,17 @@ where
         | .ofCustomInfo ti =>
           if !linter.unusedVariables.analyzeTactics.get ci.options then
             if let some bodyInfo := ti.value.get? Elab.Term.BodyInfo then
-              -- the body is the only `Expr` we will analyze in this case
-              -- NOTE: we include it even if no tactics are present as at least for parameters we want
-              -- to lint only truly unused binders
-              let (e, _) := instantiateMVarsCore ci.mctx bodyInfo.value
-              modify fun s => { s with
-                assignments := s.assignments.push (.insert {} ⟨.anonymous⟩ e) }
-              let tacticsPresent := children.any (·.findInfo? (· matches .ofTacticInfo ..) |>.isSome)
-              withReader (· || tacticsPresent) do
-                go children.toArray ci
-              return false
+              if let some value := bodyInfo.value? then
+                -- the body is the only `Expr` we will analyze in this case
+                -- NOTE: we include it even if no tactics are present as at least for parameters we want
+                -- to lint only truly unused binders
+                let (e, _) := instantiateMVarsCore ci.mctx value
+                modify fun s => { s with
+                  assignments := s.assignments.push (.insert {} ⟨.anonymous⟩ e) }
+                let tacticsPresent := children.any (·.findInfo? (· matches .ofTacticInfo ..) |>.isSome)
+                withReader (· || tacticsPresent) do
+                  go children.toArray ci
+                return false
         | .ofTermInfo ti =>
           if ignored then return true
           match ti.expr with

src/Lean/Meta/ACLt.lean

@@ -32,6 +32,9 @@ inductive ReduceMode where
   | reduceSimpleOnly
   | none
 
+private def config : ConfigWithKey :=
+  { transparency := .reducible, iota := false, proj := .no : Config }.toConfigWithKey
+
 mutual
 
 /--
@@ -61,8 +64,8 @@ where
       -- Drawback: cost.
       return e
     else match mode with
-      | .reduce => DiscrTree.reduce e {}
-      | .reduceSimpleOnly => DiscrTree.reduce e { iota := false, proj := .no }
+      | .reduce => DiscrTree.reduce e
+      | .reduceSimpleOnly => withConfigWithKey config <| DiscrTree.reduce e
       | .none => return e
 
   lt (a b : Expr) : MetaM Bool := do

src/Lean/Meta/ArgsPacker.lean

@@ -196,13 +196,13 @@ where
       let packedArg := Unary.pack packedDomain args
       return e.beta #[packedArg]
   | [n] => do
-    withLocalDecl n .default domain fun x => do
+    withLocalDeclD n domain fun x => do
       let dummy := Expr.const ``Unit []
       mkLambdaFVars #[x] (← go packedDomain dummy (args.push x) [])
   | n :: ns =>
     match_expr domain with
     | PSigma a b =>
-      withLocalDecl n .default a fun x => do
+      withLocalDeclD n a fun x => do
         mkLambdaFVars #[x] (← go packedDomain (b.beta #[x]) (args.push x) ns)
     | _ => throwError "curryPSigma: Expected PSigma type, got {domain}"
 
@@ -319,7 +319,7 @@ def uncurryType (types : Array Expr) : MetaM Expr := do
     unless type.isForall do
       throwError "Mutual.uncurryType: Expected forall type, got {type}"
   let domain ← packType (types.map (·.bindingDomain!))
-  withLocalDeclD `x domain fun x => do
+  withLocalDeclD (← mkFreshUserName `x) domain fun x => do
     let codomain ← Mutual.mkCodomain types x
     mkForallFVars #[x] codomain
 
@@ -485,13 +485,14 @@ projects to the `i`th function of type,
 -/
 def curryProj (argsPacker : ArgsPacker) (e : Expr) (i : Nat) : MetaM Expr := do
   let n := argsPacker.numFuncs
-  let packedDomain := (← inferType e).bindingDomain!
+  let t ← inferType e
+  let packedDomain := t.bindingDomain!
   let unaryTypes ← Mutual.unpackType n packedDomain
   unless i < unaryTypes.length do
     throwError "curryProj: index out of range"
   let unaryType := unaryTypes[i]!
   -- unary : (x : a ⊗ b) → e[inl x]
-  let unary ← withLocalDecl `x .default unaryType fun x => do
+  let unary ← withLocalDeclD t.bindingName! unaryType fun x => do
       let packedArg ← Mutual.pack unaryTypes.length packedDomain i x
       mkLambdaFVars #[x] (e.beta #[packedArg])
   -- nary : (x : a) → (y : b) → e[inl (x,y)]

src/Lean/Meta/Basic.lean

@@ -27,6 +27,51 @@ namespace Lean.Meta
 
 builtin_initialize isDefEqStuckExceptionId : InternalExceptionId ← registerInternalExceptionId `isDefEqStuck
 
+def TransparencyMode.toUInt64 : TransparencyMode → UInt64
+  | .all       => 0
+  | .default   => 1
+  | .reducible => 2
+  | .instances => 3
+
+def EtaStructMode.toUInt64 : EtaStructMode → UInt64
+  | .all        => 0
+  | .notClasses => 1
+  | .none       => 2
+
+/--
+Configuration for projection reduction. See `whnfCore`.
+-/
+inductive ProjReductionKind where
+  /-- Projections `s.i` are not reduced at `whnfCore`. -/
+  | no
+  /--
+  Projections `s.i` are reduced at `whnfCore`, and `whnfCore` is used at `s` during the process.
+  Recall that `whnfCore` does not perform `delta` reduction (i.e., it will not unfold constant declarations).
+  -/
+  | yes
+  /--
+  Projections `s.i` are reduced at `whnfCore`, and `whnf` is used at `s` during the process.
+  Recall that `whnfCore` does not perform `delta` reduction (i.e., it will not unfold constant declarations), but `whnf` does.
+  -/
+  | yesWithDelta
+  /--
+  Projections `s.i` are reduced at `whnfCore`, and `whnfAtMostI` is used at `s` during the process.
+  Recall that `whnfAtMostI` is like `whnf` but uses transparency at most `instances`.
+  This option is stronger than `yes`, but weaker than `yesWithDelta`.
+  We use this option to ensure we reduce projections to prevent expensive defeq checks when unifying TC operations.
+  When unifying e.g. `(@Field.toNeg α inst1).1 =?= (@Field.toNeg α inst2).1`,
+  we only want to unify negation (and not all other field operations as well).
+  Unifying the field instances slowed down unification: https://github.com/leanprover/lean4/issues/1986
+  -/
+  | yesWithDeltaI
+  deriving DecidableEq, Inhabited, Repr
+
+def ProjReductionKind.toUInt64 : ProjReductionKind → UInt64
+  | .no  => 0
+  | .yes => 1
+  | .yesWithDelta => 2
+  | .yesWithDeltaI => 3
+
 /--
 Configuration flags for the `MetaM` monad.
 Many of them are used to control the `isDefEq` function that checks whether two terms are definitionally equal or not.
@@ -118,9 +163,64 @@ structure Config where
   - `max u w =?= mav u ?v` is solved with `?v := w` ignoring the solution `?v := max u w`
   -/
   univApprox : Bool := true
+  /-- If `true`, reduce recursor/matcher applications, e.g., `Nat.rec true (fun _ _ => false) Nat.zero` reduces to `true` -/
+  iota : Bool := true
+  /-- If `true`, reduce terms such as `(fun x => t[x]) a` into `t[a]` -/
+  beta : Bool := true
+  /-- Control projection reduction at `whnfCore`. -/
+  proj : ProjReductionKind := .yesWithDelta
+  /--
+  Zeta reduction: `let x := v; e[x]` reduces to `e[v]`.
+  We say a let-declaration `let x := v; e` is non dependent if it is equivalent to `(fun x => e) v`.
+  Recall that
+  ```
+  fun x : BitVec 5 => let n := 5; fun y : BitVec n => x = y
+  ```
+  is type correct, but
+  ```
+  fun x : BitVec 5 => (fun n => fun y : BitVec n => x = y) 5
+  ```
+  is not.
+  -/
+  zeta : Bool := true
+  /--
+  Zeta-delta reduction: given a local context containing entry `x : t := e`, free variable `x` reduces to `e`.
+  -/
+  zetaDelta : Bool := true
+  deriving Inhabited
+
+/-- Convert `isDefEq` and `WHNF` relevant parts into a key for caching results -/
+private def Config.toKey (c : Config) : UInt64 :=
+  c.transparency.toUInt64 |||
+  (c.foApprox.toUInt64 <<< 2) |||
+  (c.ctxApprox.toUInt64 <<< 3) |||
+  (c.quasiPatternApprox.toUInt64 <<< 4) |||
+  (c.constApprox.toUInt64 <<< 5) |||
+  (c.isDefEqStuckEx.toUInt64 <<< 6) |||
+  (c.unificationHints.toUInt64 <<< 7) |||
+  (c.proofIrrelevance.toUInt64 <<< 8) |||
+  (c.assignSyntheticOpaque.toUInt64 <<< 9) |||
+  (c.offsetCnstrs.toUInt64 <<< 10) |||
+  (c.iota.toUInt64 <<< 11) |||
+  (c.beta.toUInt64 <<< 12) |||
+  (c.zeta.toUInt64 <<< 13) |||
+  (c.zetaDelta.toUInt64 <<< 14) |||
+  (c.univApprox.toUInt64 <<< 15) |||
+  (c.etaStruct.toUInt64 <<< 16) |||
+  (c.proj.toUInt64 <<< 18)
+
+/-- Configuration with key produced by `Config.toKey`. -/
+structure ConfigWithKey where
+  private mk ::
+  config : Config
+  key    : UInt64
+  deriving Inhabited
+
+def Config.toConfigWithKey (c : Config) : ConfigWithKey :=
+  { config := c, key := c.toKey }
 
 /--
-  Function parameter information cache.
+Function parameter information cache.
 -/
 structure ParamInfo where
   /-- The binder annotation for the parameter. -/
@@ -178,7 +278,6 @@ def ParamInfo.isStrictImplicit (p : ParamInfo) : Bool :=
 def ParamInfo.isExplicit (p : ParamInfo) : Bool :=
   p.binderInfo == BinderInfo.default
 
-
 /--
   Function information cache. See `ParamInfo`.
 -/
@@ -192,11 +291,12 @@ structure FunInfo where
   resultDeps : Array Nat       := #[]
 
 /--
-  Key for the function information cache.
+Key for the function information cache.
 -/
 structure InfoCacheKey where
-  /-- The transparency mode used to compute the `FunInfo`. -/
-  transparency : TransparencyMode
+  private mk ::
+  /-- key produced using `Config.toKey`. -/
+  configKey : UInt64
   /-- The function being cached information about. It is quite often an `Expr.const`. -/
   expr         : Expr
   /--
@@ -207,11 +307,10 @@ structure InfoCacheKey where
   nargs?       : Option Nat
   deriving Inhabited, BEq
 
-namespace InfoCacheKey
-instance : Hashable InfoCacheKey :=
-  ⟨fun ⟨transparency, expr, nargs⟩ => mixHash (hash transparency) <| mixHash (hash expr) (hash nargs)⟩
-end InfoCacheKey
+instance : Hashable InfoCacheKey where
+  hash := fun { configKey, expr, nargs? } => mixHash (hash configKey) <| mixHash (hash expr) (hash nargs?)
 
+-- Remark: we don't need to store `Config.toKey` because typeclass resolution uses a fixed configuration.
 structure SynthInstanceCacheKey where
   localInsts        : LocalInstances
   type              : Expr
@@ -231,38 +330,50 @@ structure AbstractMVarsResult where
 
 abbrev SynthInstanceCache := PersistentHashMap SynthInstanceCacheKey (Option AbstractMVarsResult)
 
-abbrev InferTypeCache := PersistentExprStructMap Expr
+-- Key for `InferType` and `WHNF` caches
+structure ExprConfigCacheKey where
+  private mk ::
+  expr      : Expr
+  configKey : UInt64
+  deriving Inhabited
+
+instance : BEq ExprConfigCacheKey where
+  beq a b :=
+    Expr.equal a.expr b.expr &&
+    a.configKey == b.configKey
+
+instance : Hashable ExprConfigCacheKey where
+  hash := fun { expr, configKey } => mixHash (hash expr) (hash configKey)
+
+abbrev InferTypeCache := PersistentHashMap ExprConfigCacheKey Expr
 abbrev FunInfoCache   := PersistentHashMap InfoCacheKey FunInfo
-abbrev WhnfCache      := PersistentExprStructMap Expr
+abbrev WhnfCache      := PersistentHashMap ExprConfigCacheKey Expr
+
+structure DefEqCacheKey where
+  private mk ::
+  lhs       : Expr
+  rhs       : Expr
+  configKey : UInt64
+  deriving Inhabited, BEq
+
+instance : Hashable DefEqCacheKey where
+  hash := fun { lhs, rhs, configKey } => mixHash (hash lhs) <| mixHash (hash rhs) (hash configKey)
 
 /--
-  A mapping `(s, t) ↦ isDefEq s t` per transparency level.
-  TODO: consider more efficient representations (e.g., a proper set) and caching policies (e.g., imperfect cache).
-  We should also investigate the impact on memory consumption. -/
-structure DefEqCache where
-  reducible : PersistentHashMap (Expr × Expr) Bool := {}
-  instances : PersistentHashMap (Expr × Expr) Bool := {}
-  default   : PersistentHashMap (Expr × Expr) Bool := {}
-  all       : PersistentHashMap (Expr × Expr) Bool := {}
-  deriving Inhabited
-
-/--
-  A cache for `inferType` at transparency levels `.default` an `.all`.
+A mapping `(s, t) ↦ isDefEq s t`.
+TODO: consider more efficient representations (e.g., a proper set) and caching policies (e.g., imperfect cache).
+We should also investigate the impact on memory consumption.
 -/
-structure InferTypeCaches where
-  default   : InferTypeCache
-  all       : InferTypeCache
-  deriving Inhabited
+abbrev DefEqCache := PersistentHashMap DefEqCacheKey Bool
 
 /--
-  Cache datastructures for type inference, type class resolution, whnf, and definitional equality.
+Cache datastructures for type inference, type class resolution, whnf, and definitional equality.
 -/
 structure Cache where
-  inferType      : InferTypeCaches := ⟨{}, {}⟩
+  inferType      : InferTypeCache := {}
   funInfo        : FunInfoCache := {}
   synthInstance  : SynthInstanceCache := {}
-  whnfDefault    : WhnfCache := {} -- cache for closed terms and `TransparencyMode.default`
-  whnfAll        : WhnfCache := {} -- cache for closed terms and `TransparencyMode.all`
+  whnf           : WhnfCache := {}
   defEqTrans     : DefEqCache := {} -- transient cache for terms containing mvars or using nonstandard configuration options, it is frequently reset.
   defEqPerm      : DefEqCache := {} -- permanent cache for terms not containing mvars and using standard configuration options
   deriving Inhabited
@@ -333,6 +444,7 @@ register_builtin_option maxSynthPendingDepth : Nat := {
 -/
 structure Context where
   private config    : Config               := {}
+  private configKey : UInt64               := config.toKey
   /-- Local context -/
   lctx              : LocalContext         := {}
   /-- Local instances in `lctx`. -/
@@ -483,17 +595,27 @@ variable [MonadControlT MetaM n] [Monad n]
 @[inline] def modifyCache (f : Cache → Cache) : MetaM Unit :=
   modify fun { mctx, cache, zetaDeltaFVarIds, postponed, diag } => { mctx, cache := f cache, zetaDeltaFVarIds, postponed, diag }
 
-@[inline] def modifyInferTypeCacheDefault (f : InferTypeCache → InferTypeCache) : MetaM Unit :=
-  modifyCache fun ⟨⟨icd, ica⟩, c1, c2, c3, c4, c5, c6⟩ => ⟨⟨f icd, ica⟩, c1, c2, c3, c4, c5, c6⟩
-
-@[inline] def modifyInferTypeCacheAll (f : InferTypeCache → InferTypeCache) : MetaM Unit :=
-  modifyCache fun ⟨⟨icd, ica⟩, c1, c2, c3, c4, c5, c6⟩ => ⟨⟨icd, f ica⟩, c1, c2, c3, c4, c5, c6⟩
+@[inline] def modifyInferTypeCache (f : InferTypeCache → InferTypeCache) : MetaM Unit :=
+  modifyCache fun ⟨ic, c1, c2, c3, c4, c5⟩ => ⟨f ic, c1, c2, c3, c4, c5⟩
 
 @[inline] def modifyDefEqTransientCache (f : DefEqCache → DefEqCache) : MetaM Unit :=
-  modifyCache fun ⟨c1, c2, c3, c4, c5, defeqTrans, c6⟩ => ⟨c1, c2, c3, c4, c5, f defeqTrans, c6⟩
+  modifyCache fun ⟨c1, c2, c3, c4, defeqTrans, c5⟩ => ⟨c1, c2, c3, c4, f defeqTrans, c5⟩
 
 @[inline] def modifyDefEqPermCache (f : DefEqCache → DefEqCache) : MetaM Unit :=
-  modifyCache fun ⟨c1, c2, c3, c4, c5, c6, defeqPerm⟩ => ⟨c1, c2, c3, c4, c5, c6, f defeqPerm⟩
+  modifyCache fun ⟨c1, c2, c3, c4, c5, defeqPerm⟩ => ⟨c1, c2, c3, c4, c5, f defeqPerm⟩
+
+def mkExprConfigCacheKey (expr : Expr) : MetaM ExprConfigCacheKey :=
+  return { expr, configKey := (← read).configKey }
+
+def mkDefEqCacheKey (lhs rhs : Expr) : MetaM DefEqCacheKey := do
+  let configKey := (← read).configKey
+  if Expr.quickLt lhs rhs then
+    return { lhs, rhs, configKey }
+  else
+    return { lhs := rhs, rhs := lhs, configKey }
+
+def mkInfoCacheKey (expr : Expr) (nargs? : Option Nat) : MetaM InfoCacheKey :=
+  return { expr, nargs?, configKey := (← read).configKey }
 
 @[inline] def resetDefEqPermCaches : MetaM Unit :=
   modifyDefEqPermCache fun _ => {}
@@ -538,6 +660,9 @@ def getLocalInstances : MetaM LocalInstances :=
 def getConfig : MetaM Config :=
   return (← read).config
 
+def getConfigWithKey : MetaM ConfigWithKey :=
+  return (← getConfig).toConfigWithKey
+
 def resetZetaDeltaFVarIds : MetaM Unit :=
   modify fun s => { s with zetaDeltaFVarIds := {} }
 
@@ -941,7 +1066,16 @@ def elimMVarDeps (xs : Array Expr) (e : Expr) (preserveOrder : Bool := false) :
 
 /-- `withConfig f x` executes `x` using the updated configuration object obtained by applying `f`. -/
 @[inline] def withConfig (f : Config → Config) : n α → n α :=
-  mapMetaM <| withReader (fun ctx => { ctx with config := f ctx.config })
+  mapMetaM <| withReader fun ctx =>
+    let config := f ctx.config
+    let configKey := config.toKey
+    { ctx with config, configKey }
+
+@[inline] def withConfigWithKey (c : ConfigWithKey) : n α → n α :=
+  mapMetaM <| withReader fun ctx =>
+    let config := c.config
+    let configKey := c.key
+    { ctx with config, configKey }
 
 @[inline] def withCanUnfoldPred (p : Config → ConstantInfo → CoreM Bool) : n α → n α :=
   mapMetaM <| withReader (fun ctx => { ctx with canUnfold? := p })
@@ -961,8 +1095,15 @@ Executes `x` tracking zetaDelta reductions `Config.trackZetaDelta := true`
 @[inline] def withoutProofIrrelevance (x : n α) : n α :=
   withConfig (fun cfg => { cfg with proofIrrelevance := false }) x
 
+@[inline] private def Context.setTransparency (ctx : Context) (transparency : TransparencyMode) : Context :=
+  let config := { ctx.config with transparency }
+  -- Recall that `transparency` is stored in the first 2 bits
+  let configKey : UInt64 := ((ctx.configKey >>> (2 : UInt64)) <<< 2) ||| transparency.toUInt64
+  { ctx with config, configKey }
+
 @[inline] def withTransparency (mode : TransparencyMode) : n α → n α :=
-  withConfig (fun config => { config with transparency := mode })
+  -- We avoid `withConfig` for performance reasons.
+  mapMetaM <| withReader (·.setTransparency mode)
 
 /-- `withDefault x` executes `x` using the default transparency setting. -/
 @[inline] def withDefault (x : n α) : n α :=
@@ -983,13 +1124,10 @@ or type class instances are unfolded.
 Execute `x` ensuring the transparency setting is at least `mode`.
 Recall that `.all > .default > .instances > .reducible`.
 -/
-@[inline] def withAtLeastTransparency (mode : TransparencyMode) (x : n α) : n α :=
-  withConfig
-    (fun config =>
-      let oldMode := config.transparency
-      let mode    := if oldMode.lt mode then mode else oldMode
-      { config with transparency := mode })
-    x
+@[inline] def withAtLeastTransparency (mode : TransparencyMode) : n α → n α :=
+  mapMetaM <| withReader fun ctx =>
+    let modeOld := ctx.config.transparency
+    ctx.setTransparency <| if modeOld.lt mode then mode else modeOld
 
 /-- Execute `x` allowing `isDefEq` to assign synthetic opaque metavariables. -/
 @[inline] def withAssignableSyntheticOpaque (x : n α) : n α :=
@@ -1011,8 +1149,8 @@ def getTheoremInfo (info : ConstantInfo) : MetaM (Option ConstantInfo) := do
 
 private def getDefInfoTemp (info : ConstantInfo) : MetaM (Option ConstantInfo) := do
   match (← getTransparency) with
-  | TransparencyMode.all => return some info
-  | TransparencyMode.default => return some info
+  | .all => return some info
+  | .default => return some info
   | _ =>
     if (← isReducible info.name) then
       return some info

src/Lean/Meta/Canonicalizer.lean

@@ -91,7 +91,15 @@ private partial def mkKey (e : Expr) : CanonM UInt64 := do
           let eNew ← instantiateMVars e
           unless eNew == e do
             return (← mkKey eNew)
-        let info ← getFunInfo f
+        let info ← if f.hasLooseBVars then
+          -- If `f` has loose bound variables, `getFunInfo` will fail.
+          -- This can only happen if `f` contains local variables.
+          -- Instead we use an empty `FunInfo`, which results in the
+          -- `i < info.paramInfo.size` check below failing for all indices,
+          -- and hence mixing in the hash for all arguments.
+          pure {}
+        else
+          getFunInfo f
         let mut k ← mkKey f
         for i in [:e.getAppNumArgs] do
           if h : i < info.paramInfo.size then
@@ -101,10 +109,13 @@ private partial def mkKey (e : Expr) : CanonM UInt64 := do
           else
               k := mixHash k (← mkKey (e.getArg! i))
         return k
-      | .lam _ t b _
-      | .forallE _ t b _ =>
+      | .lam n t b bi
+      | .forallE n t b bi =>
+        -- Note that we do not use `withLocalDecl` here, for performance reasons.
+        -- Instead we have a guard for loose bound variables in the `.app` case above.
         return mixHash (← mkKey t) (← mkKey b)
-      | .letE _ _ v b _ =>
+      | .letE n t v b _ =>
+        -- Similarly, we do not use `withLetDecl` here.
         return mixHash (← mkKey v) (← mkKey b)
       | .proj _ i s =>
         return mixHash i.toUInt64 (← mkKey s)
@@ -124,11 +135,11 @@ def canon (e : Expr) : CanonM Expr := do
         if (← isDefEq e e') then
           return e'
       -- `e` is not definitionally equal to any expression in `es'`. We claim this should be rare.
-      unsafe modify fun { cache, keyToExprs } => { cache, keyToExprs := keyToExprs.insert k (e :: es') }
+      modify fun { cache, keyToExprs } => { cache, keyToExprs := keyToExprs.insert k (e :: es') }
       return e
   else
     -- `e` is the first expression we found with key `k`.
-    unsafe modify fun { cache, keyToExprs } => { cache, keyToExprs := keyToExprs.insert k [e] }
+    modify fun { cache, keyToExprs } => { cache, keyToExprs := keyToExprs.insert k [e] }
     return e
 
 end Canonicalizer

src/Lean/Meta/DiscrTree.lean

@@ -305,16 +305,13 @@ def hasNoindexAnnotation (e : Expr) : Bool :=
 
 /--
 Reduction procedure for the discrimination tree indexing.
-The parameter `config` controls how aggressively the term is reduced.
-The parameter at type `DiscrTree` controls this value.
-See comment at `DiscrTree`.
 -/
-partial def reduce (e : Expr) (config : WhnfCoreConfig) : MetaM Expr := do
-  let e ← whnfCore e config
+partial def reduce (e : Expr) : MetaM Expr := do
+  let e ← whnfCore e
   match (← unfoldDefinition? e) with
-  | some e => reduce e config
+  | some e => reduce e
   | none => match e.etaExpandedStrict? with
-    | some e => reduce e config
+    | some e => reduce e
     | none   => return e
 
 /--
@@ -333,24 +330,24 @@ private def isBadKey (fn : Expr) : Bool :=
   | _           => true
 
 /--
-  Reduce `e` until we get an irreducible term (modulo current reducibility setting) or the resulting term
-  is a bad key (see comment at `isBadKey`).
-  We use this method instead of `reduce` for root terms at `pushArgs`. -/
-private partial def reduceUntilBadKey (e : Expr) (config : WhnfCoreConfig) : MetaM Expr := do
+Reduce `e` until we get an irreducible term (modulo current reducibility setting) or the resulting term
+is a bad key (see comment at `isBadKey`).
+We use this method instead of `reduce` for root terms at `pushArgs`. -/
+private partial def reduceUntilBadKey (e : Expr) : MetaM Expr := do
   let e ← step e
   match e.etaExpandedStrict? with
-  | some e => reduceUntilBadKey e config
+  | some e => reduceUntilBadKey e
   | none   => return e
 where
   step (e : Expr) := do
-    let e ← whnfCore e config
+    let e ← whnfCore e
     match (← unfoldDefinition? e) with
     | some e' => if isBadKey e'.getAppFn then return e else step e'
     | none    => return e
 
 /-- whnf for the discrimination tree module -/
-def reduceDT (e : Expr) (root : Bool) (config : WhnfCoreConfig) : MetaM Expr :=
-  if root then reduceUntilBadKey e config else reduce e config
+def reduceDT (e : Expr) (root : Bool) : MetaM Expr :=
+  if root then reduceUntilBadKey e else reduce e
 
 /- Remark: we use `shouldAddAsStar` only for nested terms, and `root == false` for nested terms -/
 
@@ -372,11 +369,11 @@ In this issue, we have a local hypotheses `(h : ∀ p : α × β, f p p.2 = p.2)
 For example, it was introduced by another tactic. Thus, when populating the discrimination tree explicit arguments provided to `simp` (e.g., `simp [h]`),
 we use `noIndexAtArgs := true`. See comment: https://github.com/leanprover/lean4/issues/2670#issuecomment-1758889365
 -/
-private def pushArgs (root : Bool) (todo : Array Expr) (e : Expr) (config : WhnfCoreConfig) (noIndexAtArgs : Bool) : MetaM (Key × Array Expr) := do
+private def pushArgs (root : Bool) (todo : Array Expr) (e : Expr) (noIndexAtArgs : Bool) : MetaM (Key × Array Expr) := do
   if hasNoindexAnnotation e then
     return (.star, todo)
   else
-    let e ← reduceDT e root config
+    let e ← reduceDT e root
     let fn := e.getAppFn
     let push (k : Key) (nargs : Nat) (todo : Array Expr): MetaM (Key × Array Expr) := do
       let info ← getFunInfoNArgs fn nargs
@@ -422,23 +419,23 @@ private def pushArgs (root : Bool) (todo : Array Expr) (e : Expr) (config : Whnf
     | _ => return (.other, todo)
 
 @[inherit_doc pushArgs]
-partial def mkPathAux (root : Bool) (todo : Array Expr) (keys : Array Key) (config : WhnfCoreConfig) (noIndexAtArgs : Bool) : MetaM (Array Key) := do
+partial def mkPathAux (root : Bool) (todo : Array Expr) (keys : Array Key) (noIndexAtArgs : Bool) : MetaM (Array Key) := do
   if todo.isEmpty then
     return keys
   else
     let e    := todo.back!
     let todo := todo.pop
-    let (k, todo) ← pushArgs root todo e config noIndexAtArgs
-    mkPathAux false todo (keys.push k) config noIndexAtArgs
+    let (k, todo) ← pushArgs root todo e noIndexAtArgs
+    mkPathAux false todo (keys.push k) noIndexAtArgs
 
 private def initCapacity := 8
 
 @[inherit_doc pushArgs]
-def mkPath (e : Expr) (config : WhnfCoreConfig) (noIndexAtArgs := false) : MetaM (Array Key) := do
+def mkPath (e : Expr) (noIndexAtArgs := false) : MetaM (Array Key) := do
   withReducible do
     let todo : Array Expr := .mkEmpty initCapacity
     let keys : Array Key := .mkEmpty initCapacity
-    mkPathAux (root := true) (todo.push e) keys config noIndexAtArgs
+    mkPathAux (root := true) (todo.push e) keys noIndexAtArgs
 
 private partial def createNodes (keys : Array Key) (v : α) (i : Nat) : Trie α :=
   if h : i < keys.size then
@@ -492,23 +489,23 @@ def insertCore [BEq α] (d : DiscrTree α) (keys : Array Key) (v : α) : DiscrTr
       let c := insertAux keys v 1 c
       { root := d.root.insert k c }
 
-def insert [BEq α] (d : DiscrTree α) (e : Expr) (v : α) (config : WhnfCoreConfig) (noIndexAtArgs := false) : MetaM (DiscrTree α) := do
-  let keys ← mkPath e config noIndexAtArgs
+def insert [BEq α] (d : DiscrTree α) (e : Expr) (v : α) (noIndexAtArgs := false) : MetaM (DiscrTree α) := do
+  let keys ← mkPath e noIndexAtArgs
   return d.insertCore keys v
 
 /--
 Inserts a value into a discrimination tree,
 but only if its key is not of the form `#[*]` or `#[=, *, *, *]`.
 -/
-def insertIfSpecific [BEq α] (d : DiscrTree α) (e : Expr) (v : α) (config : WhnfCoreConfig) (noIndexAtArgs := false) : MetaM (DiscrTree α) := do
-  let keys ← mkPath e config noIndexAtArgs
+def insertIfSpecific [BEq α] (d : DiscrTree α) (e : Expr) (v : α) (noIndexAtArgs := false) : MetaM (DiscrTree α) := do
+  let keys ← mkPath e noIndexAtArgs
   return if keys == #[Key.star] || keys == #[Key.const `Eq 3, Key.star, Key.star, Key.star] then
     d
   else
     d.insertCore keys v
 
-private def getKeyArgs (e : Expr) (isMatch root : Bool) (config : WhnfCoreConfig) : MetaM (Key × Array Expr) := do
-  let e ← reduceDT e root config
+private def getKeyArgs (e : Expr) (isMatch root : Bool) : MetaM (Key × Array Expr) := do
+  let e ← reduceDT e root
   unless root do
     -- See pushArgs
     if let some v := toNatLit? e then
@@ -580,11 +577,11 @@ private def getKeyArgs (e : Expr) (isMatch root : Bool) (config : WhnfCoreConfig
   | .forallE _ d _ _ => return (.arrow, #[d])
   | _ => return (.other, #[])
 
-private abbrev getMatchKeyArgs (e : Expr) (root : Bool) (config : WhnfCoreConfig) : MetaM (Key × Array Expr) :=
-  getKeyArgs e (isMatch := true) (root := root) (config := config)
+private abbrev getMatchKeyArgs (e : Expr) (root : Bool) : MetaM (Key × Array Expr) :=
+  getKeyArgs e (isMatch := true) (root := root)
 
-private abbrev getUnifyKeyArgs (e : Expr) (root : Bool) (config : WhnfCoreConfig) : MetaM (Key × Array Expr) :=
-  getKeyArgs e (isMatch := false) (root := root) (config := config)
+private abbrev getUnifyKeyArgs (e : Expr) (root : Bool) : MetaM (Key × Array Expr) :=
+  getKeyArgs e (isMatch := false) (root := root)
 
 private def getStarResult (d : DiscrTree α) : Array α :=
   let result : Array α := .mkEmpty initCapacity
@@ -595,7 +592,7 @@ private def getStarResult (d : DiscrTree α) : Array α :=
 private abbrev findKey (cs : Array (Key × Trie α)) (k : Key) : Option (Key × Trie α) :=
   cs.binSearch (k, default) (fun a b => a.1 < b.1)
 
-private partial def getMatchLoop (todo : Array Expr) (c : Trie α) (result : Array α) (config : WhnfCoreConfig) : MetaM (Array α) := do
+private partial def getMatchLoop (todo : Array Expr) (c : Trie α) (result : Array α) : MetaM (Array α) := do
   match c with
   | .node vs cs =>
     if todo.isEmpty then
@@ -606,48 +603,48 @@ private partial def getMatchLoop (todo : Array Expr) (c : Trie α) (result : Arr
       let e     := todo.back!
       let todo  := todo.pop
       let first := cs[0]! /- Recall that `Key.star` is the minimal key -/
-      let (k, args) ← getMatchKeyArgs e (root := false) config
+      let (k, args) ← getMatchKeyArgs e (root := false)
       /- We must always visit `Key.star` edges since they are wildcards.
          Thus, `todo` is not used linearly when there is `Key.star` edge
          and there is an edge for `k` and `k != Key.star`. -/
       let visitStar (result : Array α) : MetaM (Array α) :=
         if first.1 == .star then
-          getMatchLoop todo first.2 result config
+          getMatchLoop todo first.2 result
         else
           return result
       let visitNonStar (k : Key) (args : Array Expr) (result : Array α) : MetaM (Array α) :=
         match findKey cs k with
         | none   => return result
-        | some c => getMatchLoop (todo ++ args) c.2 result config
+        | some c => getMatchLoop (todo ++ args) c.2 result
       let result ← visitStar result
       match k with
       | .star  => return result
       | _      => visitNonStar k args result
 
-private def getMatchRoot (d : DiscrTree α) (k : Key) (args : Array Expr) (result : Array α) (config : WhnfCoreConfig) : MetaM (Array α) :=
+private def getMatchRoot (d : DiscrTree α) (k : Key) (args : Array Expr) (result : Array α) : MetaM (Array α) :=
   match d.root.find? k with
   | none   => return result
-  | some c => getMatchLoop args c result config
+  | some c => getMatchLoop args c result
 
-private def getMatchCore (d : DiscrTree α) (e : Expr) (config : WhnfCoreConfig) : MetaM (Key × Array α) :=
+private def getMatchCore (d : DiscrTree α) (e : Expr) : MetaM (Key × Array α) :=
   withReducible do
     let result := getStarResult d
-    let (k, args) ← getMatchKeyArgs e (root := true) config
+    let (k, args) ← getMatchKeyArgs e (root := true)
     match k with
     | .star  => return (k, result)
-    | _      => return (k, (← getMatchRoot d k args result config))
+    | _      => return (k, (← getMatchRoot d k args result))
 
 /--
   Find values that match `e` in `d`.
 -/
-def getMatch (d : DiscrTree α) (e : Expr) (config : WhnfCoreConfig) : MetaM (Array α) :=
-  return (← getMatchCore d e config).2
+def getMatch (d : DiscrTree α) (e : Expr) : MetaM (Array α) :=
+  return (← getMatchCore d e).2
 
 /--
   Similar to `getMatch`, but returns solutions that are prefixes of `e`.
   We store the number of ignored arguments in the result.-/
-partial def getMatchWithExtra (d : DiscrTree α) (e : Expr) (config : WhnfCoreConfig) : MetaM (Array (α × Nat)) := do
-  let (k, result) ← getMatchCore d e config
+partial def getMatchWithExtra (d : DiscrTree α) (e : Expr) : MetaM (Array (α × Nat)) := do
+  let (k, result) ← getMatchCore d e
   let result := result.map (·, 0)
   if !e.isApp then
     return result
@@ -669,7 +666,7 @@ where
     | _               => return false
 
   go (e : Expr) (numExtra : Nat) (result : Array (α × Nat)) : MetaM (Array (α × Nat)) := do
-    let result := result ++ (← getMatchCore d e config).2.map (., numExtra)
+    let result := result ++ (← getMatchCore d e).2.map (., numExtra)
     if e.isApp then
       go e.appFn! (numExtra + 1) result
     else
@@ -678,8 +675,8 @@ where
 /--
 Return the root symbol for `e`, and the number of arguments after `reduceDT`.
 -/
-def getMatchKeyRootFor (e : Expr) (config : WhnfCoreConfig) : MetaM (Key × Nat) := do
-  let e ← reduceDT e (root := true) config
+def getMatchKeyRootFor (e : Expr) : MetaM (Key × Nat) := do
+  let e ← reduceDT e (root := true)
   let numArgs := e.getAppNumArgs
   let key := match e.getAppFn with
     | .lit v         => .lit v
@@ -716,17 +713,17 @@ We use this method to simulate Lean 3's indexing.
 
 The natural number in the result is the number of arguments in `e` after `reduceDT`.
 -/
-def getMatchLiberal (d : DiscrTree α) (e : Expr) (config : WhnfCoreConfig) : MetaM (Array α × Nat) := do
+def getMatchLiberal (d : DiscrTree α) (e : Expr) : MetaM (Array α × Nat) := do
   withReducible do
     let result := getStarResult d
-    let (k, numArgs) ← getMatchKeyRootFor e config
+    let (k, numArgs) ← getMatchKeyRootFor e
     match k with
     | .star  => return (result, numArgs)
     | _      => return (getAllValuesForKey d k result, numArgs)
 
-partial def getUnify (d : DiscrTree α) (e : Expr) (config : WhnfCoreConfig) : MetaM (Array α) :=
+partial def getUnify (d : DiscrTree α) (e : Expr) : MetaM (Array α) :=
   withReducible do
-    let (k, args) ← getUnifyKeyArgs e (root := true) config
+    let (k, args) ← getUnifyKeyArgs e (root := true)
     match k with
     | .star => d.root.foldlM (init := #[]) fun result k c => process k.arity #[] c result
     | _ =>
@@ -750,7 +747,7 @@ where
       else
         let e     := todo.back!
         let todo  := todo.pop
-        let (k, args) ← getUnifyKeyArgs e (root := false) config
+        let (k, args) ← getUnifyKeyArgs e (root := false)
         let visitStar (result : Array α) : MetaM (Array α) :=
           let first := cs[0]!
           if first.1 == .star then

src/Lean/Meta/ExprDefEq.lean

@@ -1387,15 +1387,21 @@ private abbrev unfold (e : Expr) (failK : MetaM α) (successK : Expr → MetaM
 /-- Auxiliary method for isDefEqDelta -/
 private def unfoldBothDefEq (fn : Name) (t s : Expr) : MetaM LBool := do
   match t, s with
-  | Expr.const _ ls₁, Expr.const _ ls₂ => isListLevelDefEq ls₁ ls₂
-  | Expr.app _ _,     Expr.app _ _     =>
+  | .const _ ls₁, .const _ ls₂ =>
+    match (← isListLevelDefEq ls₁ ls₂) with
+    | .true => return .true
+    | _ =>
+    unfold t (pure .undef) fun t =>
+    unfold s (pure .undef) fun s =>
+      isDefEqLeftRight fn t s
+  | .app _ _,     .app _ _     =>
     if (← tryHeuristic t s) then
-      pure LBool.true
+      return .true
     else
       unfold t
-       (unfold s (pure LBool.undef) (fun s => isDefEqRight fn t s))
+       (unfold s (pure .undef) fun s => isDefEqRight fn t s)
        (fun t => unfold s (isDefEqLeft fn t s) (fun s => isDefEqLeftRight fn t s))
-  | _, _ => pure LBool.false
+  | _, _ => return .false
 
 private def sameHeadSymbol (t s : Expr) : Bool :=
   match t.getAppFn, s.getAppFn with
@@ -1674,11 +1680,12 @@ private partial def isDefEqQuick (t s : Expr) : MetaM LBool :=
   -- | Expr.mdata _ t _,    s                   => isDefEqQuick t s
   -- | t,                   Expr.mdata _ s _    => isDefEqQuick t s
   | .fvar fvarId₁, .fvar fvarId₂ => do
-    if (← fvarId₁.isLetVar <||> fvarId₂.isLetVar) then
-      return LBool.undef
-    else if fvarId₁ == fvarId₂ then
-      return LBool.true
+    if fvarId₁ == fvarId₂ then
+      return .true
+    else if (← fvarId₁.isLetVar <||> fvarId₂.isLetVar) then
+      return .undef
     else
+      -- If `t` and `s` are not proofs or let-variables, we still return `.undef` and let other rules (e.g., unit-like) kick in.
       isDefEqProofIrrel t s
   | t, s =>
     isDefEqQuickOther t s
@@ -2079,50 +2086,37 @@ Structure for storing defeq cache key information.
 -/
 structure DefEqCacheKeyInfo where
   kind : DefEqCacheKind
-  key  : Expr × Expr
+  key  : DefEqCacheKey
 
 private def mkCacheKey (t s : Expr) : MetaM DefEqCacheKeyInfo := do
   let kind ← getDefEqCacheKind t s
-  let key := if Expr.quickLt t s then (t, s) else (s, t)
+  let key ← mkDefEqCacheKey t s
   return { key, kind }
 
 private def getCachedResult (keyInfo : DefEqCacheKeyInfo) : MetaM LBool := do
   let cache ← match keyInfo.kind with
     | .transient => pure (← get).cache.defEqTrans
     | .permanent => pure (← get).cache.defEqPerm
-  let cache := match (← getTransparency) with
-    | .reducible => cache.reducible
-    | .instances => cache.instances
-    | .default   => cache.default
-    | .all       => cache.all
   match cache.find? keyInfo.key with
   | some val => return val.toLBool
   | none => return .undef
 
-def DefEqCache.update (cache : DefEqCache) (mode : TransparencyMode) (key : Expr × Expr) (result : Bool) : DefEqCache :=
-  match mode with
-  | .reducible => { cache with reducible := cache.reducible.insert key result }
-  | .instances => { cache with instances := cache.instances.insert key result }
-  | .default   => { cache with default   := cache.default.insert key result }
-  | .all       => { cache with all       := cache.all.insert key result }
-
 private def cacheResult (keyInfo : DefEqCacheKeyInfo) (result : Bool) : MetaM Unit := do
-  let mode ← getTransparency
   let key := keyInfo.key
   match keyInfo.kind with
-  | .permanent => modifyDefEqPermCache fun c => c.update mode key result
+  | .permanent => modifyDefEqPermCache fun c => c.insert key result
   | .transient =>
     /-
     We must ensure that all assigned metavariables in the key are replaced by their current assignments.
     Otherwise, the key is invalid after the assignment is "backtracked".
     See issue #1870 for an example.
     -/
-    let key := (← instantiateMVars key.1, ← instantiateMVars key.2)
-    modifyDefEqTransientCache fun c => c.update mode key result
+    let key ← mkDefEqCacheKey (← instantiateMVars key.lhs) (← instantiateMVars key.rhs)
+    modifyDefEqTransientCache fun c => c.insert key result
 
 private def whnfCoreAtDefEq (e : Expr) : MetaM Expr := do
   if backward.isDefEq.lazyWhnfCore.get (← getOptions) then
-    whnfCore e (config := { proj := .yesWithDeltaI })
+    withConfig (fun ctx => { ctx with proj := .yesWithDeltaI }) <| whnfCore e
   else
     whnfCore e
 

src/Lean/Meta/FunInfo.lean

@@ -10,13 +10,13 @@ import Lean.Meta.InferType
 namespace Lean.Meta
 
 @[inline] private def checkFunInfoCache (fn : Expr) (maxArgs? : Option Nat) (k : MetaM FunInfo) : MetaM FunInfo := do
-  let t ← getTransparency
-  match (← get).cache.funInfo.find? ⟨t, fn, maxArgs?⟩ with
-  | some finfo => pure finfo
+  let key ← mkInfoCacheKey fn maxArgs?
+  match (← get).cache.funInfo.find? key with
+  | some finfo => return finfo
   | none       => do
     let finfo ← k
-    modify fun s => { s with cache := { s.cache with funInfo := s.cache.funInfo.insert ⟨t, fn, maxArgs?⟩ finfo } }
-    pure finfo
+    modify fun s => { s with cache := { s.cache with funInfo := s.cache.funInfo.insert key finfo } }
+    return finfo
 
 @[inline] private def whenHasVar {α} (e : Expr) (deps : α) (k : α → α) : α :=
   if e.hasFVar then k deps else deps

src/Lean/Meta/IndPredBelow.lean

@@ -83,7 +83,7 @@ where
       forallTelescopeReducing t fun xs s => do
         let motiveType ← instantiateForall motive xs[:numParams]
         withLocalDecl motiveName BinderInfo.implicit motiveType fun motive => do
-          mkForallFVars (xs.insertAt! numParams motive) s)
+          mkForallFVars (xs.insertIdxIfInBounds numParams motive) s)
 
   motiveType (indVal : InductiveVal) : MetaM Expr :=
     forallTelescopeReducing indVal.type fun xs _ => do

src/Lean/Meta/InferType.lean

@@ -97,8 +97,8 @@ private def inferConstType (c : Name) (us : List Level) : MetaM Expr := do
 private def inferProjType (structName : Name) (idx : Nat) (e : Expr) : MetaM Expr := do
   let structType ← inferType e
   let structType ← whnf structType
-  let failed {α} : Unit → MetaM α := fun _ =>
-    throwError "invalid projection{indentExpr (mkProj structName idx e)} from type {structType}"
+  let failed {α} : Unit → MetaM α := fun _ => do
+    throwError "invalid projection{indentExpr (mkProj structName idx e)}\nfrom type{indentExpr structType}"
   matchConstStructure structType.getAppFn failed fun structVal structLvls ctorVal =>
     let structTypeArgs := structType.getAppArgs
     if structVal.numParams + structVal.numIndices != structTypeArgs.size then
@@ -165,24 +165,27 @@ private def inferFVarType (fvarId : FVarId) : MetaM Expr := do
   | none   => fvarId.throwUnknown
 
 @[inline] private def checkInferTypeCache (e : Expr) (inferType : MetaM Expr) : MetaM Expr := do
-  match (← getTransparency) with
-  | .default =>
-    match (← get).cache.inferType.default.find? e with
+  if e.hasMVar then
+    inferType
+  else
+    let key ← mkExprConfigCacheKey e
+    match (← get).cache.inferType.find? key with
     | some type => return type
     | none =>
       let type ← inferType
-      unless e.hasMVar || type.hasMVar do
-        modifyInferTypeCacheDefault fun c => c.insert e type
+      unless type.hasMVar do
+        modifyInferTypeCache fun c => c.insert key type
       return type
-  | .all =>
-    match (← get).cache.inferType.all.find? e with
-    | some type => return type
-    | none =>
-      let type ← inferType
-      unless e.hasMVar || type.hasMVar do
-        modifyInferTypeCacheAll fun c => c.insert e type
-      return type
-  | _ => panic! "checkInferTypeCache: transparency mode not default or all"
+
+private def defaultConfig : ConfigWithKey :=
+  { : Config }.toConfigWithKey
+
+private def allConfig : ConfigWithKey :=
+  { transparency := .all : Config }.toConfigWithKey
+
+@[inline] def withInferTypeConfig (x : MetaM α) : MetaM α := do
+  let cfg := if (← getTransparency) == .all then allConfig else defaultConfig
+  withConfigWithKey cfg x
 
 @[export lean_infer_type]
 def inferTypeImp (e : Expr) : MetaM Expr :=
@@ -201,7 +204,7 @@ def inferTypeImp (e : Expr) : MetaM Expr :=
     | .forallE ..    => checkInferTypeCache e (inferForallType e)
     | .lam ..        => checkInferTypeCache e (inferLambdaType e)
     | .letE ..       => checkInferTypeCache e (inferLambdaType e)
-  withIncRecDepth <| withAtLeastTransparency TransparencyMode.default (infer e)
+  withIncRecDepth <| withInferTypeConfig (infer e)
 
 /--
   Return `LBool.true` if given level is always equivalent to universe level zero.

src/Lean/Meta/Instances.lean

@@ -72,9 +72,6 @@ structure Instances where
   erased        : PHashSet Name := {}
   deriving Inhabited
 
-/-- Configuration for the discrimination tree module -/
-def tcDtConfig : WhnfCoreConfig := {}
-
 def addInstanceEntry (d : Instances) (e : InstanceEntry) : Instances :=
   match e.globalName? with
   | some n => { d with discrTree := d.discrTree.insertCore e.keys e, instanceNames := d.instanceNames.insert n e, erased := d.erased.erase n }
@@ -98,7 +95,7 @@ private def mkInstanceKey (e : Expr) : MetaM (Array InstanceKey) := do
   let type ← inferType e
   withNewMCtxDepth do
     let (_, _, type) ← forallMetaTelescopeReducing type
-    DiscrTree.mkPath type tcDtConfig
+    DiscrTree.mkPath type
 
 /--
 Compute the order the arguments of `inst` should be synthesized.

src/Lean/Meta/LazyDiscrTree.lean

@@ -184,9 +184,9 @@ private def elimLooseBVarsByBeta (e : Expr) : CoreM Expr :=
       else
         return .continue)
 
-private def getKeyArgs (e : Expr) (isMatch root : Bool) (config : WhnfCoreConfig) :
+private def getKeyArgs (e : Expr) (isMatch root : Bool) :
     MetaM (Key × Array Expr) := do
-  let e ← DiscrTree.reduceDT e root config
+  let e ← DiscrTree.reduceDT e root
   unless root do
     -- See pushArgs
     if let some v := toNatLit? e then
@@ -259,9 +259,9 @@ private def getKeyArgs (e : Expr) (isMatch root : Bool) (config : WhnfCoreConfig
 /-
 Given an expression we are looking for patterns that match, return the key and sub-expressions.
 -/
-private abbrev getMatchKeyArgs (e : Expr) (root : Bool) (config : WhnfCoreConfig) :
+private abbrev getMatchKeyArgs (e : Expr) (root : Bool) :
     MetaM (Key × Array Expr) :=
-  getKeyArgs e (isMatch := true) (root := root) (config := config)
+  getKeyArgs e (isMatch := true) (root := root)
 
 end MatchClone
 
@@ -313,8 +313,6 @@ discriminator key is computed and processing the remaining
 terms is deferred until demanded by a match.
 -/
 structure LazyDiscrTree (α : Type) where
-  /-- Configuration for normalization. -/
-  config : Lean.Meta.WhnfCoreConfig := {}
   /-- Backing array of trie entries.  Should be owned by this trie. -/
   tries : Array (LazyDiscrTree.Trie α) := #[default]
   /-- Map from discriminator trie roots to the index. -/
@@ -332,12 +330,12 @@ open Lean.Meta.DiscrTree (mkNoindexAnnotation hasNoindexAnnotation reduceDT)
 /--
 Specialization of Lean.Meta.DiscrTree.pushArgs
 -/
-private def pushArgs (root : Bool) (todo : Array Expr) (e : Expr) (config : WhnfCoreConfig) :
+private def pushArgs (root : Bool) (todo : Array Expr) (e : Expr) :
     MetaM (Key × Array Expr) := do
   if hasNoindexAnnotation e then
     return (.star, todo)
   else
-    let e ← reduceDT e root config
+    let e ← reduceDT e root
     let fn := e.getAppFn
     let push (k : Key) (nargs : Nat) (todo : Array Expr) : MetaM (Key × Array Expr) := do
       let info ← getFunInfoNArgs fn nargs
@@ -389,8 +387,8 @@ private def initCapacity := 8
 /--
 Get the root key and rest of terms of an expression using the specified config.
 -/
-private def rootKey (cfg: WhnfCoreConfig) (e : Expr) : MetaM (Key × Array Expr) :=
-  pushArgs true (Array.mkEmpty initCapacity) e cfg
+private def rootKey (e : Expr) : MetaM (Key × Array Expr) :=
+  pushArgs true (Array.mkEmpty initCapacity) e
 
 private partial def buildPath (op : Bool → Array Expr → Expr → MetaM (Key × Array Expr)) (root : Bool) (todo : Array Expr) (keys : Array Key) : MetaM (Array Key) := do
   if todo.isEmpty then
@@ -407,9 +405,9 @@ Create a key path from an expression using the function used for patterns.
 This differs from Lean.Meta.DiscrTree.mkPath and targetPath in that the expression
 should uses free variables rather than meta-variables for holes.
 -/
-def patternPath (e : Expr) (config : WhnfCoreConfig) : MetaM (Array Key) := do
+def patternPath (e : Expr) : MetaM (Array Key) := do
   let todo : Array Expr := .mkEmpty initCapacity
-  let op root todo e := pushArgs root todo e config
+  let op root todo e := pushArgs root todo e
   buildPath op (root := true) (todo.push e) (.mkEmpty initCapacity)
 
 /--
@@ -417,21 +415,21 @@ Create a key path from an expression we are matching against.
 
 This should have mvars instantiated where feasible.
 -/
-def targetPath (e : Expr) (config : WhnfCoreConfig) : MetaM (Array Key) := do
+def targetPath (e : Expr) : MetaM (Array Key) := do
   let todo : Array Expr := .mkEmpty initCapacity
   let op root todo e := do
-        let (k, args) ← MatchClone.getMatchKeyArgs e root config
+        let (k, args) ← MatchClone.getMatchKeyArgs e root
         pure (k, todo ++ args)
   buildPath op (root := true) (todo.push e) (.mkEmpty initCapacity)
 
 /- Monad for finding matches while resolving deferred patterns. -/
 @[reducible]
-private def MatchM α := ReaderT WhnfCoreConfig (StateRefT (Array (Trie α)) MetaM)
+private def MatchM α := StateRefT (Array (Trie α)) MetaM
 
 private def runMatch (d : LazyDiscrTree α) (m : MatchM α β)  : MetaM (β × LazyDiscrTree α) := do
-  let { config := c, tries := a, roots := r } := d
-  let (result, a) ← withReducible $ (m.run c).run a
-  pure (result, { config := c, tries := a, roots := r})
+  let { tries := a, roots := r } := d
+  let (result, a) ← withReducible <| m.run a
+  return (result, { tries := a, roots := r})
 
 private def setTrie (i : TrieIndex) (v : Trie α) : MatchM α Unit :=
   modify (·.set! i v)
@@ -444,7 +442,7 @@ private def newTrie [Monad m] [MonadState (Array (Trie α)) m] (e : LazyEntry α
 private def addLazyEntryToTrie (i:TrieIndex) (e : LazyEntry α) : MatchM α Unit :=
   modify (·.modify i (·.pushPending e))
 
-private def evalLazyEntry (config : WhnfCoreConfig)
+private def evalLazyEntry
     (p : Array α × TrieIndex × Std.HashMap Key TrieIndex)
     (entry : LazyEntry α)
     : MatchM α (Array α × TrieIndex × Std.HashMap Key TrieIndex) := do
@@ -456,7 +454,7 @@ private def evalLazyEntry (config : WhnfCoreConfig)
   else
     let e    := todo.back!
     let todo := todo.pop
-    let (k, todo) ← withLCtx lctx.1 lctx.2 $ pushArgs false todo e config
+    let (k, todo) ← withLCtx lctx.1 lctx.2 <| pushArgs false todo e
     if k == .star then
       if starIdx = 0 then
         let starIdx ← newTrie (todo, lctx, v)
@@ -477,26 +475,25 @@ private def evalLazyEntry (config : WhnfCoreConfig)
 This evaluates all lazy entries in a trie and updates `values`, `starIdx`, and `children`
 accordingly.
 -/
-private partial def evalLazyEntries (config : WhnfCoreConfig)
+private partial def evalLazyEntries
     (values : Array α) (starIdx : TrieIndex) (children : Std.HashMap Key TrieIndex)
     (entries : Array (LazyEntry α)) :
     MatchM α (Array α × TrieIndex × Std.HashMap Key TrieIndex) := do
   let mut values := values
   let mut starIdx := starIdx
   let mut children := children
-  entries.foldlM (init := (values, starIdx, children)) (evalLazyEntry config)
+  entries.foldlM (init := (values, starIdx, children)) evalLazyEntry
 
 private def evalNode (c : TrieIndex) :
     MatchM α (Array α × TrieIndex × Std.HashMap Key TrieIndex) := do
   let .node vs star cs pending := (←get).get! c
   if pending.size = 0 then
-    pure (vs, star, cs)
+    return (vs, star, cs)
   else
-    let config ← read
     setTrie c default
-    let (vs, star, cs) ← evalLazyEntries config vs star cs pending
+    let (vs, star, cs) ← evalLazyEntries vs star cs pending
     setTrie c <| .node vs star cs #[]
-    pure (vs, star, cs)
+    return (vs, star, cs)
 
 def dropKeyAux (next : TrieIndex) (rest : List Key) :
     MatchM α Unit :=
@@ -723,11 +720,11 @@ private def push (d : PreDiscrTree α) (k : Key) (e : LazyEntry α) : PreDiscrTr
   d.modifyAt k (·.push e)
 
 /-- Convert a pre-discrimination tree to a lazy discrimination tree. -/
-private def toLazy (d : PreDiscrTree α) (config : WhnfCoreConfig := {}) : LazyDiscrTree α :=
+private def toLazy (d : PreDiscrTree α) : LazyDiscrTree α :=
   let { roots, tries } := d
   -- Adjust trie indices so the first value is reserved (so 0 is never a valid trie index)
   let roots := roots.fold (init := roots) (fun m k n => m.insert k (n+1))
-  { config, roots, tries := #[default] ++ tries.map (.node {} 0 {}) }
+  { roots, tries := #[default] ++ tries.map (.node {} 0 {}) }
 
 /-- Merge two discrimination trees. -/
 protected def append (x y : PreDiscrTree α) : PreDiscrTree α :=
@@ -756,12 +753,12 @@ namespace InitEntry
 /--
 Constructs an initial entry from an expression and value.
 -/
-def fromExpr (expr : Expr) (value : α) (config : WhnfCoreConfig := {}) : MetaM (InitEntry α) := do
+def fromExpr (expr : Expr) (value : α) : MetaM (InitEntry α) := do
   let lctx ← getLCtx
   let linst ← getLocalInstances
   let lctx := (lctx, linst)
-  let (key, todo) ← LazyDiscrTree.rootKey config expr
-  pure <| { key, entry := (todo, lctx, value) }
+  let (key, todo) ← LazyDiscrTree.rootKey expr
+  return { key, entry := (todo, lctx, value) }
 
 /--
 Creates an entry for a subterm of an initial entry.
@@ -769,11 +766,11 @@ Creates an entry for a subterm of an initial entry.
 This is slightly more efficient than using `fromExpr` on subterms since it avoids a redundant call
 to `whnf`.
 -/
-def mkSubEntry (e : InitEntry α) (idx : Nat) (value : α) (config : WhnfCoreConfig := {}) :
+def mkSubEntry (e : InitEntry α) (idx : Nat) (value : α) :
     MetaM (InitEntry α) := do
   let (todo, lctx, _) := e.entry
-  let (key, todo) ← LazyDiscrTree.rootKey config todo[idx]!
-  pure <| { key, entry := (todo, lctx, value) }
+  let (key, todo) ← LazyDiscrTree.rootKey todo[idx]!
+  return { key, entry := (todo, lctx, value) }
 
 end InitEntry
 

src/Lean/Meta/Match/MatchEqs.lean

@@ -129,9 +129,9 @@ where
           let typeNew := b.instantiate1 y
           if let some (_, lhs, rhs) ← matchEq? d then
             if lhs.isFVar && ys.contains lhs && args.contains lhs && isNamedPatternProof typeNew y then
-               let some j  := ys.getIdx? lhs | unreachable!
+               let some j  := ys.indexOf? lhs | unreachable!
                let ys      := ys.eraseIdx j
-               let some k  := args.getIdx? lhs | unreachable!
+               let some k  := args.indexOf? lhs | unreachable!
                let mask    := mask.set! k false
                let args    := args.map fun arg => if arg == lhs then rhs else arg
                let arg     ← mkEqRefl rhs

src/Lean/Meta/RecursorInfo.lean

@@ -107,7 +107,7 @@ private def getMajorPosDepElim (declName : Name) (majorPos? : Option Nat) (xs :
     if motiveArgs.isEmpty then
       throwError "invalid user defined recursor, '{declName}' does not support dependent elimination, and position of the major premise was not specified (solution: set attribute '[recursor <pos>]', where <pos> is the position of the major premise)"
     let major := motiveArgs.back!
-    match xs.getIdx? major with
+    match xs.indexOf? major with
     | some majorPos => pure (major, majorPos, true)
     | none          => throwError "ill-formed recursor '{declName}'"
 

src/Lean/Meta/SynthInstance.lean

@@ -207,7 +207,7 @@ def getInstances (type : Expr) : MetaM (Array Instance) := do
     | none   => throwError "type class instance expected{indentExpr type}"
     | some className =>
       let globalInstances ← getGlobalInstancesIndex
-      let result ← globalInstances.getUnify type tcDtConfig
+      let result ← globalInstances.getUnify type
       -- Using insertion sort because it is stable and the array `result` should be mostly sorted.
       -- Most instances have default priority.
       let result := result.insertionSort fun e₁ e₂ => e₁.priority < e₂.priority

src/Lean/Meta/Tactic/Clear.lean

@@ -27,7 +27,7 @@ def _root_.Lean.MVarId.clear (mvarId : MVarId) (fvarId : FVarId) : MetaM MVarId
       throwTacticEx `clear mvarId m!"target depends on '{mkFVar fvarId}'"
     let lctx := lctx.erase fvarId
     let localInsts ← getLocalInstances
-    let localInsts := match localInsts.findIdx? fun localInst => localInst.fvar.fvarId! == fvarId with
+    let localInsts := match localInsts.findFinIdx? fun localInst => localInst.fvar.fvarId! == fvarId with
       | none => localInsts
       | some idx => localInsts.eraseIdx idx
     let newMVar ← mkFreshExprMVarAt lctx localInsts mvarDecl.type MetavarKind.syntheticOpaque tag

src/Lean/Meta/Tactic/FunInd.lean

@@ -776,7 +776,8 @@ In the type of `value`, reduces
 and then wraps `value` in an appropriate type hint.
 -/
 def cleanPackedArgs (eqnInfo : WF.EqnInfo) (value : Expr) : MetaM Expr := do
-  let t ← Meta.transform (← inferType value) (skipConstInApp := true) (pre := fun e => do
+  let type ← inferType value
+  let cleanType ← Meta.transform type (skipConstInApp := true) (pre := fun e => do
     -- Need to beta-reduce first
     let e' := e.headBeta
     if e' != e then
@@ -819,7 +820,7 @@ def cleanPackedArgs (eqnInfo : WF.EqnInfo) (value : Expr) : MetaM Expr := do
           return .continue e'
 
     return .continue e)
-  mkExpectedTypeHint value t
+  mkExpectedTypeHint value cleanType
 
 /--
 Takes `foo._unary.induct`, where the motive is a `PSigma`/`PSum` type and

src/Lean/Meta/Tactic/Injection.lean

@@ -114,10 +114,11 @@ where
         if lhs.isRawNatLit && rhs.isRawNatLit then cont
         else
           try
-            match (← injection mvarId fvarId newNames) with
-            | .solved  => return .solved
-            | .subgoal mvarId newEqs remainingNames =>
-              mvarId.withContext <| go d (newEqs.toList ++ fvarIds) mvarId remainingNames
+            commitIfNoEx do
+              match (← injection mvarId fvarId newNames) with
+              | .solved  => return .solved
+              | .subgoal mvarId newEqs remainingNames =>
+                mvarId.withContext <| go d (newEqs.toList ++ fvarIds) mvarId remainingNames
           catch _ => cont
       else cont
 

src/Lean/Meta/Tactic/Replace.lean

@@ -33,17 +33,21 @@ def _root_.Lean.MVarId.replaceTargetEq (mvarId : MVarId) (targetNew : Expr) (eqP
     return mvarNew.mvarId!
 
 /--
-  Convert the given goal `Ctx |- target` into `Ctx |- targetNew`. It assumes the goals are definitionally equal.
-  We use the proof term
-  ```
-  @id target mvarNew
-  ```
-  to create a checkpoint. -/
+Converts the given goal `Ctx |- target` into `Ctx |- targetNew`. It assumes the goals are definitionally equal.
+We use the proof term
+```
+@id target mvarNew
+```
+to create a checkpoint.
+
+If `targetNew` is equal to `target`, then returns `mvarId` unchanged.
+Uses `Expr.equal` for the comparison so that it is possible to update binder names, etc., which are user-visible.
+-/
 def _root_.Lean.MVarId.replaceTargetDefEq (mvarId : MVarId) (targetNew : Expr) : MetaM MVarId :=
   mvarId.withContext do
     mvarId.checkNotAssigned `change
     let target  ← mvarId.getType
-    if target == targetNew then
+    if Expr.equal target targetNew then
       return mvarId
     else
       let tag     ← mvarId.getTag
@@ -95,12 +99,15 @@ abbrev _root_.Lean.MVarId.replaceLocalDecl (mvarId : MVarId) (fvarId : FVarId) (
   replaceLocalDeclCore mvarId fvarId typeNew eqProof
 
 /--
-Replace the type of `fvarId` at `mvarId` with `typeNew`.
+Replaces the type of `fvarId` at `mvarId` with `typeNew`.
 Remark: this method assumes that `typeNew` is definitionally equal to the current type of `fvarId`.
+
+If `typeNew` is equal to current type of `fvarId`, then returns `mvarId` unchanged.
+Uses `Expr.equal` for the comparison so that it is possible to update binder names, etc., which are user-visible.
 -/
 def _root_.Lean.MVarId.replaceLocalDeclDefEq (mvarId : MVarId) (fvarId : FVarId) (typeNew : Expr) : MetaM MVarId := do
   mvarId.withContext do
-    if typeNew == (← fvarId.getType) then
+    if Expr.equal typeNew (← fvarId.getType) then
       return mvarId
     else
       let mvarDecl ← mvarId.getDecl

src/Lean/Meta/Tactic/Rfl.lean

@@ -19,9 +19,6 @@ namespace Lean.Meta.Rfl
 
 open Lean Meta
 
-/-- Discrimation tree settings for the `refl` extension. -/
-def reflExt.config : WhnfCoreConfig := {}
-
 /-- Environment extensions for `refl` lemmas -/
 initialize reflExt :
     SimpleScopedEnvExtension (Name × Array DiscrTree.Key) (DiscrTree Name) ←
@@ -42,7 +39,7 @@ initialize registerBuiltinAttribute {
     if let .app (.const ``Eq [_]) _ := rel then
       throwError "@[refl] attribute may not be used on `Eq.refl`."
     unless ← withNewMCtxDepth <| isDefEq lhs rhs do fail
-    let key ← DiscrTree.mkPath rel reflExt.config
+    let key ← DiscrTree.mkPath rel
     reflExt.add (decl, key) kind
 }
 
@@ -91,7 +88,7 @@ def _root_.Lean.MVarId.applyRfl (goal : MVarId) : MetaM Unit := goal.withContext
     goal.setType (.app t.appFn! lhs)
     let s ← saveState
     let mut ex? := none
-    for lem in ← (reflExt.getState (← getEnv)).getMatch rel reflExt.config do
+    for lem in ← (reflExt.getState (← getEnv)).getMatch rel do
       try
         let gs ← goal.apply (← mkConstWithFreshMVarLevels lem)
         if gs.isEmpty then return () else
@@ -123,7 +120,7 @@ def _root_.Lean.MVarId.liftReflToEq (mvarId : MVarId) : MetaM MVarId := do
   if rel.isAppOf `Eq then
     -- No need to lift Eq to Eq
     return mvarId
-  for lem in ← (reflExt.getState (← getEnv)).getMatch rel reflExt.config do
+  for lem in ← (reflExt.getState (← getEnv)).getMatch rel do
     let res ← observing? do
       -- First create an equality relating the LHS and RHS
       -- and reduce the goal to proving that LHS is related to LHS.

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

@@ -239,9 +239,10 @@ def withNewLemmas {α} (xs : Array Expr) (f : SimpM α) : SimpM α := do
     withFreshCache do
       let mut s ← getSimpTheorems
       let mut updated := false
+      let ctx ← getContext
       for x in xs do
         if (← isProof x) then
-          s ← s.addTheorem (.fvar x.fvarId!) x
+          s ← s.addTheorem (.fvar x.fvarId!) x (config := ctx.indexConfig)
           updated := true
       if updated then
         withSimpTheorems s f
@@ -832,7 +833,7 @@ def simpTargetStar (mvarId : MVarId) (ctx : Simp.Context) (simprocs : SimprocsAr
   for h in (← getPropHyps) do
     let localDecl ← h.getDecl
     let proof  := localDecl.toExpr
-    let simpTheorems ← ctx.simpTheorems.addTheorem (.fvar h) proof
+    let simpTheorems ← ctx.simpTheorems.addTheorem (.fvar h) proof (config := ctx.indexConfig)
     ctx := ctx.setSimpTheorems simpTheorems
   match (← simpTarget mvarId ctx simprocs discharge? (stats := stats)) with
   | (none, stats) => return (TacticResultCNM.closed, stats)

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

@@ -203,7 +203,7 @@ def rewrite? (e : Expr) (s : SimpTheoremTree) (erased : PHashSet Origin) (tag :
 where
   /-- For `(← getConfig).index := true`, use discrimination tree structure when collecting `simp` theorem candidates. -/
   rewriteUsingIndex? : SimpM (Option Result) := do
-    let candidates ← s.getMatchWithExtra e (getDtConfig (← getConfig))
+    let candidates ← withSimpIndexConfig <| s.getMatchWithExtra e
     if candidates.isEmpty then
       trace[Debug.Meta.Tactic.simp] "no theorems found for {tag}-rewriting {e}"
       return none
@@ -221,7 +221,7 @@ where
   Only the root symbol is taken into account. Most of the structure of the discrimination tree is ignored.
   -/
   rewriteNoIndex? : SimpM (Option Result) := do
-    let (candidates, numArgs) ← s.getMatchLiberal e (getDtConfig (← getConfig))
+    let (candidates, numArgs) ← withSimpIndexConfig <| s.getMatchLiberal e
     if candidates.isEmpty then
       trace[Debug.Meta.Tactic.simp] "no theorems found for {tag}-rewriting {e}"
       return none
@@ -245,7 +245,7 @@ where
 
   diagnoseWhenNoIndex (thm : SimpTheorem) : SimpM Unit := do
     if (← isDiagnosticsEnabled) then
-      let candidates ← s.getMatchWithExtra e (getDtConfig (← getConfig))
+      let candidates ← withSimpIndexConfig <| s.getMatchWithExtra e
       for (candidate, _) in candidates do
         if unsafe ptrEq thm candidate then
           return ()

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

@@ -42,7 +42,8 @@ private def initEntries : M Unit := do
     unless simpThms.isErased (.fvar h) do
       let localDecl ← h.getDecl
       let proof  := localDecl.toExpr
-      simpThms ← simpThms.addTheorem (.fvar h) proof
+      let ctx := (← get).ctx
+      simpThms ← simpThms.addTheorem (.fvar h) proof (config := ctx.indexConfig)
       modify fun s => { s with ctx := s.ctx.setSimpTheorems simpThms }
       if hsNonDeps.contains h then
         -- We only simplify nondependent hypotheses
@@ -95,7 +96,7 @@ private partial def loop : M Bool := do
         trace[Meta.Tactic.simp.all] "entry.id: {← ppOrigin entry.id}, {entry.type} => {typeNew}"
         let mut simpThmsNew := (← getSimpTheorems).eraseTheorem (.fvar entry.fvarId)
         let idNew ← mkFreshId
-        simpThmsNew ← simpThmsNew.addTheorem (.other idNew) (← mkExpectedTypeHint proofNew typeNew)
+        simpThmsNew ← simpThmsNew.addTheorem (.other idNew) (← mkExpectedTypeHint proofNew typeNew) (config := ctx.indexConfig)
         modify fun s => { s with
           modified         := true
           ctx              := ctx.setSimpTheorems simpThmsNew

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

@@ -204,8 +204,18 @@ structure SimpTheorems where
   toUnfoldThms : PHashMap Name (Array Name) := {}
   deriving Inhabited
 
-/-- Configuration for the discrimination tree. -/
-def simpDtConfig : WhnfCoreConfig := { iota := false, proj := .no, zetaDelta := false }
+/--
+Configuration for `MetaM` used to process global simp theorems
+-/
+def simpGlobalConfig : ConfigWithKey :=
+  { iota         := false
+    proj         := .no
+    zetaDelta    := false
+    transparency := .reducible
+  : Config }.toConfigWithKey
+
+@[inline] def withSimpGlobalConfig : MetaM α → MetaM α :=
+  withConfigWithKey simpGlobalConfig
 
 partial def SimpTheorems.eraseCore (d : SimpTheorems) (thmId : Origin) : SimpTheorems :=
   let d := { d with erased := d.erased.insert thmId, lemmaNames := d.lemmaNames.erase thmId }
@@ -298,7 +308,7 @@ private partial def isPerm : Expr → Expr → MetaM Bool
   | s, t => return s == t
 
 private def checkBadRewrite (lhs rhs : Expr) : MetaM Unit := do
-  let lhs ← DiscrTree.reduceDT lhs (root := true) simpDtConfig
+  let lhs ← withSimpGlobalConfig <| DiscrTree.reduceDT lhs (root := true)
   if lhs == rhs && lhs.isFVar then
     throwError "invalid `simp` theorem, equation is equivalent to{indentExpr (← mkEq lhs rhs)}"
 
@@ -381,11 +391,11 @@ private def mkSimpTheoremCore (origin : Origin) (e : Expr) (levelParams : Array
   assert! origin != .fvar ⟨.anonymous⟩
   let type ← instantiateMVars (← inferType e)
   withNewMCtxDepth do
-    let (_, _, type) ← withReducible <| forallMetaTelescopeReducing type
+    let (_, _, type) ← forallMetaTelescopeReducing type
     let type ← whnfR type
     let (keys, perm) ←
       match type.eq? with
-      | some (_, lhs, rhs) => pure (← DiscrTree.mkPath lhs simpDtConfig noIndexAtArgs, ← isPerm lhs rhs)
+      | some (_, lhs, rhs) => pure (← DiscrTree.mkPath lhs noIndexAtArgs, ← isPerm lhs rhs)
       | none => throwError "unexpected kind of 'simp' theorem{indentExpr type}"
     return { origin, keys, perm, post, levelParams, proof, priority := prio, rfl := (← isRflProof proof) }
 
@@ -394,7 +404,7 @@ private def mkSimpTheoremsFromConst (declName : Name) (post : Bool) (inv : Bool)
   let us := cinfo.levelParams.map mkLevelParam
   let origin := .decl declName post inv
   let val := mkConst declName us
-  withReducible do
+  withSimpGlobalConfig do
     let type ← inferType val
     checkTypeIsProp type
     if inv || (← shouldPreprocess type) then
@@ -464,18 +474,10 @@ private def preprocessProof (val : Expr) (inv : Bool) : MetaM (Array Expr) := do
   return ps.toArray.map fun (val, _) => val
 
 /-- Auxiliary method for creating simp theorems from a proof term `val`. -/
-def mkSimpTheorems (id : Origin) (levelParams : Array Name) (proof : Expr) (post := true) (inv := false) (prio : Nat := eval_prio default) : MetaM (Array SimpTheorem) :=
+private def mkSimpTheorems (id : Origin) (levelParams : Array Name) (proof : Expr) (post := true) (inv := false) (prio : Nat := eval_prio default) : MetaM (Array SimpTheorem) :=
   withReducible do
     (← preprocessProof proof inv).mapM fun val => mkSimpTheoremCore id val levelParams val post prio (noIndexAtArgs := true)
 
-/-- Auxiliary method for adding a local simp theorem to a `SimpTheorems` datastructure. -/
-def SimpTheorems.add (s : SimpTheorems) (id : Origin) (levelParams : Array Name) (proof : Expr) (inv := false) (post := true) (prio : Nat := eval_prio default) : MetaM SimpTheorems := do
-  if proof.isConst then
-    s.addConst proof.constName! post inv prio
-  else
-    let simpThms ← mkSimpTheorems id levelParams proof post inv prio
-    return simpThms.foldl addSimpTheoremEntry s
-
 /--
 Reducible functions and projection functions should always be put in `toUnfold`, instead
 of trying to use equational theorems.
@@ -533,14 +535,25 @@ def SimpTheorems.addDeclToUnfold (d : SimpTheorems) (declName : Name) : MetaM Si
   else
     return d.addDeclToUnfoldCore declName
 
+/-- Auxiliary method for adding a local simp theorem to a `SimpTheorems` datastructure. -/
+def SimpTheorems.add (s : SimpTheorems) (id : Origin) (levelParams : Array Name) (proof : Expr)
+        (inv := false) (post := true) (prio : Nat := eval_prio default)
+        (config : ConfigWithKey := simpGlobalConfig) : MetaM SimpTheorems := do
+  if proof.isConst then
+    -- Recall that we use `simpGlobalConfig` for processing global declarations.
+    s.addConst proof.constName! post inv prio
+  else
+    let simpThms ← withConfigWithKey config <| mkSimpTheorems id levelParams proof post inv prio
+    return simpThms.foldl addSimpTheoremEntry s
+
 abbrev SimpTheoremsArray := Array SimpTheorems
 
-def SimpTheoremsArray.addTheorem (thmsArray : SimpTheoremsArray) (id : Origin) (h : Expr) : MetaM SimpTheoremsArray :=
+def SimpTheoremsArray.addTheorem (thmsArray : SimpTheoremsArray) (id : Origin) (h : Expr) (config : ConfigWithKey := simpGlobalConfig) : MetaM SimpTheoremsArray :=
   if thmsArray.isEmpty then
     let thms : SimpTheorems := {}
-    return #[ (← thms.add id #[] h) ]
+    return #[ (← thms.add id #[] h (config := config)) ]
   else
-    thmsArray.modifyM 0 fun thms => thms.add id #[] h
+    thmsArray.modifyM 0 fun thms => thms.add id #[] h (config := config)
 
 def SimpTheoremsArray.eraseTheorem (thmsArray : SimpTheoremsArray) (thmId : Origin) : SimpTheoremsArray :=
   thmsArray.map fun thms => thms.eraseCore thmId

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

@@ -213,7 +213,7 @@ def SimprocEntry.tryD (s : SimprocEntry) (numExtraArgs : Nat) (e : Expr) : SimpM
   | .inr proc => return (← proc e).addExtraArgs extraArgs
 
 def simprocCore (post : Bool) (s : SimprocTree) (erased : PHashSet Name) (e : Expr) : SimpM Step := do
-  let candidates ← s.getMatchWithExtra e (getDtConfig (← getConfig))
+  let candidates ← withSimpIndexConfig <| s.getMatchWithExtra e
   if candidates.isEmpty then
     let tag := if post then "post" else "pre"
     trace[Debug.Meta.Tactic.simp] "no {tag}-simprocs found for {e}"
@@ -250,7 +250,7 @@ def simprocCore (post : Bool) (s : SimprocTree) (erased : PHashSet Name) (e : Ex
       return .continue
 
 def dsimprocCore (post : Bool) (s : SimprocTree) (erased : PHashSet Name) (e : Expr) : SimpM DStep := do
-  let candidates ← s.getMatchWithExtra e (getDtConfig (← getConfig))
+  let candidates ← withSimpIndexConfig <| s.getMatchWithExtra e
   if candidates.isEmpty then
     let tag := if post then "post" else "pre"
     trace[Debug.Meta.Tactic.simp] "no {tag}-simprocs found for {e}"

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

@@ -53,7 +53,9 @@ abbrev CongrCache := ExprMap (Option CongrTheorem)
 
 structure Context where
   private mk ::
-  config           : Config := {}
+  config            : Config := {}
+  metaConfig        : ConfigWithKey := default
+  indexConfig       : ConfigWithKey := default
   /-- `maxDischargeDepth` from `config` as an `UInt32`. -/
   maxDischargeDepth : UInt32 := UInt32.ofNatTruncate config.maxDischargeDepth
   simpTheorems      : SimpTheoremsArray := {}
@@ -117,9 +119,32 @@ private def updateArith (c : Config) : CoreM Config := do
   else
     return c
 
+/--
+Converts `Simp.Config` into `Meta.ConfigWithKey` used for indexing.
+-/
+private def mkIndexConfig (c : Config) : ConfigWithKey :=
+  { c with
+    proj         := .no
+    transparency := .reducible
+  : Meta.Config }.toConfigWithKey
+
+/--
+Converts `Simp.Config` into `Meta.ConfigWithKey` used for `isDefEq`.
+-/
+-- TODO: use `metaConfig` at `isDefEq`. It is not being used yet because it will break Mathlib.
+private def mkMetaConfig (c : Config) : ConfigWithKey :=
+  { c with
+    proj         := if c.proj then .yesWithDelta else .no
+    transparency := .reducible
+  : Meta.Config }.toConfigWithKey
+
 def mkContext (config : Config := {}) (simpTheorems : SimpTheoremsArray := {}) (congrTheorems : SimpCongrTheorems := {}) : MetaM Context := do
   let config ← updateArith config
-  return { config, simpTheorems, congrTheorems }
+  return {
+    config, simpTheorems, congrTheorems
+    metaConfig := mkMetaConfig config
+    indexConfig := mkIndexConfig config
+  }
 
 def Context.setConfig (context : Context) (config : Config) : Context :=
   { context with config }
@@ -203,6 +228,15 @@ abbrev SimpM := ReaderT MethodsRef $ ReaderT Context $ StateRefT State MetaM
 @[inline] def withInDSimp : SimpM α → SimpM α :=
   withTheReader Context (fun ctx => { ctx with inDSimp := true })
 
+/--
+Executes `x` using a `MetaM` configuration for indexing terms.
+It is inferred from `Simp.Config`.
+For example, if the user has set `simp (config := { zeta := false })`,
+`isDefEq` and `whnf` in `MetaM` should not perform `zeta` reduction.
+-/
+@[inline] def withSimpIndexConfig (x : SimpM α) : SimpM α := do
+  withConfigWithKey (← readThe Simp.Context).indexConfig x
+
 @[extern "lean_simp"]
 opaque simp (e : Expr) : SimpM Result
 
@@ -679,16 +713,6 @@ def tryAutoCongrTheorem? (e : Expr) : SimpM (Option Result) := do
     /- See comment above. This is reachable if `hasCast == true`. The `rhs` is not structurally equal to `mkAppN f argsNew` -/
     return some { expr := rhs }
 
-/--
-Return a WHNF configuration for retrieving `[simp]` from the discrimination tree.
-If user has disabled `zeta` and/or `beta` reduction in the simplifier, or enabled `zetaDelta`,
-we must also disable/enable them when retrieving lemmas from discrimination tree. See issues: #2669 and #2281
--/
-def getDtConfig (cfg : Config) : WhnfCoreConfig :=
-  match cfg.beta, cfg.zeta, cfg.zetaDelta with
-  | true, true, false => simpDtConfig
-  | _,    _,    _     => { simpDtConfig with zeta := cfg.zeta, beta := cfg.beta, zetaDelta := cfg.zetaDelta }
-
 def Result.addExtraArgs (r : Result) (extraArgs : Array Expr) : MetaM Result := do
   match r.proof? with
   | none => return { expr := mkAppN r.expr extraArgs }

src/Lean/Meta/Tactic/Symm.lean

@@ -18,9 +18,6 @@ open Lean Meta
 
 namespace Lean.Meta.Symm
 
-/-- Discrimation tree settings for the `symm` extension. -/
-def symmExt.config : WhnfCoreConfig := {}
-
 /-- Environment extensions for symm lemmas -/
 builtin_initialize symmExt :
     SimpleScopedEnvExtension (Name × Array DiscrTree.Key) (DiscrTree Name) ←
@@ -40,7 +37,7 @@ builtin_initialize registerBuiltinAttribute {
     let some _ := xs.back? | fail
     let targetTy ← reduce targetTy
     let .app (.app rel _) _ := targetTy | fail
-    let key ← withReducible <| DiscrTree.mkPath rel symmExt.config
+    let key ← withReducible <| DiscrTree.mkPath rel
     symmExt.add (decl, key) kind
 }
 
@@ -54,7 +51,7 @@ namespace Lean.Expr
 def getSymmLems (tgt : Expr) : MetaM (Array Name) := do
   let .app (.app rel _) _ := tgt
     | throwError "symmetry lemmas only apply to binary relations, not{indentExpr tgt}"
-  (symmExt.getState (← getEnv)).getMatch rel symmExt.config
+  (symmExt.getState (← getEnv)).getMatch rel
 
 /-- Given a term `e : a ~ b`, construct a term in `b ~ a` using `@[symm]` lemmas. -/
 def applySymm (e : Expr) : MetaM Expr := do

src/Lean/Meta/Tactic/TryThis.lean

@@ -430,11 +430,13 @@ def addSuggestions (ref : Syntax) (suggestions : Array Suggestion)
   logInfoAt ref m!"{header}{msgs}"
   addSuggestionCore ref suggestions header (isInline := false) origSpan? style? codeActionPrefix?
 
-private def addExactSuggestionCore (addSubgoalsMsg : Bool) (e : Expr) : MetaM Suggestion := do
+private def addExactSuggestionCore (addSubgoalsMsg : Bool) (e : Expr) : MetaM Suggestion :=
+  withOptions (pp.mvars.set · false) do
   let stx ← delabToRefinableSyntax e
   let mvars ← getMVars e
   let suggestion ← if mvars.isEmpty then `(tactic| exact $stx) else `(tactic| refine $stx)
-  let messageData? := if mvars.isEmpty then m!"exact {e}" else m!"refine {e}"
+  let pp ← ppExpr e
+  let messageData? := if mvars.isEmpty then m!"exact {pp}" else m!"refine {pp}"
   let postInfo? ← if !addSubgoalsMsg || mvars.isEmpty then pure none else
     let mut str := "\nRemaining subgoals:"
     for g in mvars do

src/Lean/Meta/UnificationHint.lean

@@ -6,6 +6,7 @@ Authors: Leonardo de Moura
 prelude
 import Lean.ScopedEnvExtension
 import Lean.Util.Recognizers
+import Lean.Meta.Basic
 import Lean.Meta.DiscrTree
 import Lean.Meta.SynthInstance
 
@@ -27,7 +28,8 @@ structure UnificationHints where
 instance : ToFormat UnificationHints where
   format h := format h.discrTree
 
-def UnificationHints.config : WhnfCoreConfig := { iota := false, proj := .no }
+private def config : ConfigWithKey :=
+  { iota := false, proj := .no : Config }.toConfigWithKey
 
 def UnificationHints.add (hints : UnificationHints) (e : UnificationHintEntry) : UnificationHints :=
   { hints with discrTree := hints.discrTree.insertCore e.keys e.val }
@@ -81,7 +83,7 @@ def addUnificationHint (declName : Name) (kind : AttributeKind) : MetaM Unit :=
       match decodeUnificationHint body with
       | Except.error msg => throwError msg
       | Except.ok hint =>
-        let keys ← DiscrTree.mkPath hint.pattern.lhs UnificationHints.config
+        let keys ← withConfigWithKey config <| DiscrTree.mkPath hint.pattern.lhs
         validateHint hint
         unificationHintExtension.add { keys := keys, val := declName } kind
 
@@ -101,7 +103,7 @@ def tryUnificationHints (t s : Expr) : MetaM Bool := do
   if t.isMVar then
     return false
   let hints := unificationHintExtension.getState (← getEnv)
-  let candidates ← hints.discrTree.getMatch t UnificationHints.config
+  let candidates ← withConfigWithKey config <| hints.discrTree.getMatch t
   for candidate in candidates do
     if (← tryCandidate candidate) then
       return true

src/Lean/Meta/WHNF.lean

@@ -328,65 +328,8 @@ end
 /-! # Weak Head Normal Form auxiliary combinators -/
 -- ===========================
 
-/--
-Configuration for projection reduction. See `whnfCore`.
--/
-inductive ProjReductionKind where
-  /-- Projections `s.i` are not reduced at `whnfCore`. -/
-  | no
-  /--
-  Projections `s.i` are reduced at `whnfCore`, and `whnfCore` is used at `s` during the process.
-  Recall that `whnfCore` does not perform `delta` reduction (i.e., it will not unfold constant declarations).
-  -/
-  | yes
-  /--
-  Projections `s.i` are reduced at `whnfCore`, and `whnf` is used at `s` during the process.
-  Recall that `whnfCore` does not perform `delta` reduction (i.e., it will not unfold constant declarations), but `whnf` does.
-  -/
-  | yesWithDelta
-  /--
-  Projections `s.i` are reduced at `whnfCore`, and `whnfAtMostI` is used at `s` during the process.
-  Recall that `whnfAtMostI` is like `whnf` but uses transparency at most `instances`.
-  This option is stronger than `yes`, but weaker than `yesWithDelta`.
-  We use this option to ensure we reduce projections to prevent expensive defeq checks when unifying TC operations.
-  When unifying e.g. `(@Field.toNeg α inst1).1 =?= (@Field.toNeg α inst2).1`,
-  we only want to unify negation (and not all other field operations as well).
-  Unifying the field instances slowed down unification: https://github.com/leanprover/lean4/issues/1986
-  -/
-  | yesWithDeltaI
-  deriving DecidableEq, Inhabited, Repr
-
-/--
-Configuration options for `whnfEasyCases` and `whnfCore`.
--/
-structure WhnfCoreConfig where
-  /-- If `true`, reduce recursor/matcher applications, e.g., `Nat.rec true (fun _ _ => false) Nat.zero` reduces to `true` -/
-  iota : Bool := true
-  /-- If `true`, reduce terms such as `(fun x => t[x]) a` into `t[a]` -/
-  beta : Bool := true
-  /-- Control projection reduction at `whnfCore`. -/
-  proj : ProjReductionKind := .yesWithDelta
-  /--
-  Zeta reduction: `let x := v; e[x]` reduces to `e[v]`.
-  We say a let-declaration `let x := v; e` is non dependent if it is equivalent to `(fun x => e) v`.
-  Recall that
-  ```
-  fun x : BitVec 5 => let n := 5; fun y : BitVec n => x = y
-  ```
-  is type correct, but
-  ```
-  fun x : BitVec 5 => (fun n => fun y : BitVec n => x = y) 5
-  ```
-  is not.
-  -/
-  zeta : Bool := true
-  /--
-  Zeta-delta reduction: given a local context containing entry `x : t := e`, free variable `x` reduces to `e`.
-  -/
-  zetaDelta : Bool := true
-
 /-- Auxiliary combinator for handling easy WHNF cases. It takes a function for handling the "hard" cases as an argument -/
-@[specialize] partial def whnfEasyCases (e : Expr) (k : Expr → MetaM Expr) (config : WhnfCoreConfig := {}) : MetaM Expr := do
+@[specialize] partial def whnfEasyCases (e : Expr) (k : Expr → MetaM Expr) : MetaM Expr := do
   match e with
   | .forallE ..    => return e
   | .lam ..        => return e
@@ -397,7 +340,7 @@ structure WhnfCoreConfig where
   | .const ..      => k e
   | .app ..        => k e
   | .proj ..       => k e
-  | .mdata _ e     => whnfEasyCases e k config
+  | .mdata _ e     => whnfEasyCases e k
   | .fvar fvarId   =>
     let decl ← fvarId.getDecl
     match decl with
@@ -405,13 +348,14 @@ structure WhnfCoreConfig where
     | .ldecl (value := v) .. =>
       -- Let-declarations marked as implementation detail should always be unfolded
       -- We initially added this feature for `simp`, and added it here for consistency.
-      unless config.zetaDelta || decl.isImplementationDetail do return e
-      if (← getConfig).trackZetaDelta then
+      let cfg ← getConfig
+      unless cfg.zetaDelta || decl.isImplementationDetail do return e
+      if cfg.trackZetaDelta then
         modify fun s => { s with zetaDeltaFVarIds := s.zetaDeltaFVarIds.insert fvarId }
-      whnfEasyCases v k config
+      whnfEasyCases v k
   | .mvar mvarId   =>
     match (← getExprMVarAssignment? mvarId) with
-    | some v => whnfEasyCases v k config
+    | some v => whnfEasyCases v k
     | none   => return e
 
 @[specialize] private def deltaDefinition (c : ConstantInfo) (lvls : List Level)
@@ -611,30 +555,31 @@ private def whnfDelayedAssigned? (f' : Expr) (e : Expr) : MetaM (Option Expr) :=
 Apply beta-reduction, zeta-reduction (i.e., unfold let local-decls), iota-reduction,
 expand let-expressions, expand assigned meta-variables.
 -/
-partial def whnfCore (e : Expr) (config : WhnfCoreConfig := {}): MetaM Expr :=
+partial def whnfCore (e : Expr) : MetaM Expr :=
   go e
 where
   go (e : Expr) : MetaM Expr :=
-    whnfEasyCases e (config := config) fun e => do
+    whnfEasyCases e fun e => do
       trace[Meta.whnf] e
       match e with
       | .const ..  => pure e
-      | .letE _ _ v b _ => if config.zeta then go <| b.instantiate1 v else return e
+      | .letE _ _ v b _ => if (← getConfig).zeta then go <| b.instantiate1 v else return e
       | .app f ..       =>
-        if config.zeta then
+        let cfg ← getConfig
+        if cfg.zeta then
           if let some (args, _, _, v, b) := e.letFunAppArgs? then
             -- When zeta reducing enabled, always reduce `letFun` no matter the current reducibility level
             return (← go <| mkAppN (b.instantiate1 v) args)
         let f := f.getAppFn
         let f' ← go f
-        if config.beta && f'.isLambda then
+        if cfg.beta && f'.isLambda then
           let revArgs := e.getAppRevArgs
           go <| f'.betaRev revArgs
         else if let some eNew ← whnfDelayedAssigned? f' e then
           go eNew
         else
           let e := if f == f' then e else e.updateFn f'
-          unless config.iota do return e
+          unless cfg.iota do return e
           match (← reduceMatcher? e) with
           | .reduced eNew => go eNew
           | .partialApp   => pure e
@@ -656,7 +601,7 @@ where
           match (← projectCore? c i) with
           | some e => go e
           | none => return e
-        match config.proj with
+        match (← getConfig).proj with
         | .no => return e
         | .yes => k (← go c)
         | .yesWithDelta => k (← whnf c)
@@ -967,26 +912,18 @@ def reduceNat? (e : Expr) : MetaM (Option Expr) :=
   if e.hasFVar || e.hasExprMVar || (← read).canUnfold?.isSome then
     return false
   else
-    match (← getConfig).transparency with
-    | .default => return true
-    | .all     => return true
-    | _        => return false
+    return true
 
 @[inline] private def cached? (useCache : Bool) (e : Expr) : MetaM (Option Expr) := do
   if useCache then
-    match (← getConfig).transparency with
-    | .default => return (← get).cache.whnfDefault.find? e
-    | .all     => return (← get).cache.whnfAll.find? e
-    | _        => unreachable!
+    return (← get).cache.whnf.find? (← mkExprConfigCacheKey e)
   else
     return none
 
 private def cache (useCache : Bool) (e r : Expr) : MetaM Expr := do
   if useCache then
-    match (← getConfig).transparency with
-    | .default => modify fun s => { s with cache.whnfDefault := s.cache.whnfDefault.insert e r }
-    | .all     => modify fun s => { s with cache.whnfAll     := s.cache.whnfAll.insert e r }
-    | _        => unreachable!
+    let key ← mkExprConfigCacheKey e
+    modify fun s => { s with cache.whnf := s.cache.whnf.insert key r }
   return r
 
 @[export lean_whnf]

src/Lean/MetavarContext.lean

@@ -248,9 +248,7 @@ instance : Hashable LocalInstance where
 
 /-- Remove local instance with the given `fvarId`. Do nothing if `localInsts` does not contain any free variable with id `fvarId`. -/
 def LocalInstances.erase (localInsts : LocalInstances) (fvarId : FVarId) : LocalInstances :=
-  match localInsts.findIdx? (fun inst => inst.fvar.fvarId! == fvarId) with
-  | some idx => localInsts.eraseIdx idx
-  | _        => localInsts
+  localInsts.eraseP (fun inst => inst.fvar.fvarId! == fvarId)
 
 /-- A kind for the metavariable that determines its unification behaviour.
 For more information see the large comment at the beginning of this file. -/
@@ -1219,7 +1217,7 @@ private def mkLambda' (x : Name) (bi : BinderInfo) (t : Expr) (b : Expr) (etaRed
   Similar to `LocalContext.mkBinding`, but handles metavariables correctly.
   If `usedOnly == true` then `forall` and `lambda` expressions are created only for used variables.
   If `usedLetOnly == true` then `let` expressions are created only for used (let-) variables. -/
-@[specialize] def mkBinding (isLambda : Bool) (lctx : LocalContext) (xs : Array Expr) (e : Expr) (usedOnly : Bool) (usedLetOnly : Bool) (etaReduce : Bool) : M Expr := do
+def mkBinding (isLambda : Bool) (lctx : LocalContext) (xs : Array Expr) (e : Expr) (usedOnly : Bool) (usedLetOnly : Bool) (etaReduce : Bool) : M Expr := do
   let e ← abstractRange xs xs.size e
   xs.size.foldRevM (init := e) fun i e => do
       let x := xs[i]!

src/Lean/Parser/Command.lean

@@ -137,7 +137,7 @@ def declValEqns      := leading_parser
 def whereStructField := leading_parser
   Term.letDecl
 def whereStructInst  := leading_parser
-  ppIndent ppSpace >> "where" >> sepByIndent (ppGroup whereStructField) "; " (allowTrailingSep := true) >>
+  ppIndent ppSpace >> "where" >> Term.structInstFields (sepByIndent (ppGroup whereStructField) "; " (allowTrailingSep := true)) >>
   optional Term.whereDecls
 /-- `declVal` matches the right-hand side of a declaration, one of:
 * `:= expr` (a "simple declaration")

src/Lean/Parser/Term.lean

@@ -281,6 +281,12 @@ def structInstFieldAbbrev := leading_parser
   atomic (ident >> notFollowedBy ("." <|> ":=" <|> symbol "[") "invalid field abbreviation")
 def optEllipsis      := leading_parser
   optional " .."
+/-
+Tags the structure instance field syntax with a `Lean.Parser.Term.structInstFields` syntax node.
+This node is used to enable structure instance field completion in the whitespace
+of a structure instance notation.
+-/
+def structInstFields (p : Parser) : Parser := node `Lean.Parser.Term.structInstFields p
 /--
 Structure instance. `{ x := e, ... }` assigns `e` to field `x`, which may be
 inherited. If `e` is itself a variable called `x`, it can be elided:
@@ -292,7 +298,7 @@ The structure type can be specified if not inferable:
 -/
 @[builtin_term_parser] def structInst := leading_parser
   "{ " >> withoutPosition (optional (atomic (sepBy1 termParser ", " >> " with "))
-    >> sepByIndent (structInstFieldAbbrev <|> structInstField) ", " (allowTrailingSep := true)
+    >> structInstFields (sepByIndent (structInstFieldAbbrev <|> structInstField) ", " (allowTrailingSep := true))
     >> optEllipsis
     >> optional (" : " >> termParser)) >> " }"
 def typeSpec := leading_parser " : " >> termParser
@@ -984,6 +990,7 @@ builtin_initialize
   register_parser_alias bracketedBinder
   register_parser_alias attrKind
   register_parser_alias optSemicolon
+  register_parser_alias structInstFields
 
 end Parser
 end Lean

src/Lean/PrettyPrinter/Delaborator/Builtins.lean

@@ -91,21 +91,32 @@ Rather, it is called through the `app` delaborator.
 -/
 def delabConst : Delab := do
   let Expr.const c₀ ls ← getExpr | unreachable!
-  let c₀ := if (← getPPOption getPPPrivateNames) then c₀ else (privateToUserName? c₀).getD c₀
-
-  let mut c ← unresolveNameGlobal c₀ (fullNames := ← getPPOption getPPFullNames)
-  let stx ← if ls.isEmpty || !(← getPPOption getPPUniverses) then
-    if (← getLCtx).usesUserName c then
-      -- `c` is also a local declaration
-      if c == c₀ && !(← read).inPattern then
-        -- `c` is the fully qualified named. So, we append the `_root_` prefix
-        c := `_root_ ++ c
+  let mut c₀ := c₀
+  let mut c  := c₀
+  if let some n := privateToUserName? c₀ then
+    unless (← getPPOption getPPPrivateNames) do
+      if c₀ == mkPrivateName (← getEnv) n then
+        -- The name is defined in this module, so use `n` as the name and unresolve like any other name.
+        c₀ := n
+        c ← unresolveNameGlobal n (fullNames := ← getPPOption getPPFullNames)
       else
-        c := c₀
-    pure <| mkIdent c
+        -- The name is not defined in this module, so make inaccessible. Unresolving does not make sense to do.
+        c ← withFreshMacroScope <| MonadQuotation.addMacroScope n
   else
-    let mvars ← getPPOption getPPMVarsLevels
-    `($(mkIdent c).{$[$(ls.toArray.map (Level.quote · (prec := 0) (mvars := mvars)))],*})
+    c ← unresolveNameGlobal c (fullNames := ← getPPOption getPPFullNames)
+  let stx ←
+    if ls.isEmpty || !(← getPPOption getPPUniverses) then
+      if (← getLCtx).usesUserName c then
+        -- `c` is also a local declaration
+        if c == c₀ && !(← read).inPattern then
+          -- `c` is the fully qualified named. So, we append the `_root_` prefix
+          c := `_root_ ++ c
+        else
+          c := c₀
+      pure <| mkIdent c
+    else
+      let mvars ← getPPOption getPPMVarsLevels
+      `($(mkIdent c).{$[$(ls.toArray.map (Level.quote · (prec := 0) (mvars := mvars)))],*})
 
   let stx ← maybeAddBlockImplicit stx
   if (← getPPOption getPPTagAppFns) then
@@ -338,7 +349,7 @@ def delabAppExplicitCore (fieldNotation : Bool) (numArgs : Nat) (delabHead : (in
     if idx == 0 then
       -- If it's the first argument, then we can tag `obj.field` with the first app.
       head ← withBoundedAppFn (numArgs - 1) <| annotateTermInfo head
-    return Syntax.mkApp head (argStxs.eraseIdx idx)
+    return Syntax.mkApp head (argStxs.eraseIdxIfInBounds idx)
   else
     return Syntax.mkApp fnStx argStxs
 
@@ -865,7 +876,7 @@ def delabLam : Delab :=
           -- "default" binder group is the only one that expects binder names
           -- as a term, i.e. a single `Syntax.ident` or an application thereof
           let stxCurNames ←
-            if curNames.size > 1 then
+            if h : curNames.size > 1 then
               `($(curNames.get! 0) $(curNames.eraseIdx 0)*)
             else
               pure $ curNames.get! 0;

src/Lean/PrettyPrinter/Delaborator/Options.lean

@@ -24,6 +24,11 @@ register_builtin_option pp.notation : Bool := {
   group    := "pp"
   descr    := "(pretty printer) disable/enable notation (infix, mixfix, postfix operators and unicode characters)"
 }
+register_builtin_option pp.parens : Bool := {
+  defValue := false
+  group    := "pp"
+  descr    := "(pretty printer) if set to true, notation is wrapped in parentheses regardless of precedence"
+}
 register_builtin_option pp.unicode.fun : Bool := {
   defValue := false
   group    := "pp"
@@ -248,6 +253,7 @@ def getPPNatLit (o : Options) : Bool := o.get pp.natLit.name (getPPNumericTypes
 def getPPCoercions (o : Options) : Bool := o.get pp.coercions.name (!getPPAll o)
 def getPPExplicit (o : Options) : Bool := o.get pp.explicit.name (getPPAll o)
 def getPPNotation (o : Options) : Bool := o.get pp.notation.name (!getPPAll o)
+def getPPParens (o : Options) : Bool := o.get pp.parens.name pp.parens.defValue
 def getPPUnicodeFun (o : Options) : Bool := o.get pp.unicode.fun.name false
 def getPPMatch (o : Options) : Bool := o.get pp.match.name (!getPPAll o)
 def getPPFieldNotation (o : Options) : Bool := o.get pp.fieldNotation.name (!getPPAll o)

src/Lean/PrettyPrinter/Parenthesizer.lean

@@ -8,6 +8,7 @@ import Lean.Parser.Extension
 import Lean.Parser.StrInterpolation
 import Lean.ParserCompiler.Attribute
 import Lean.PrettyPrinter.Basic
+import Lean.PrettyPrinter.Delaborator.Options
 
 
 /-!
@@ -82,8 +83,10 @@ namespace PrettyPrinter
 namespace Parenthesizer
 
 structure Context where
-  -- We need to store this `categoryParser` argument to deal with the implicit Pratt parser call in `trailingNode.parenthesizer`.
+  /-- We need to store this `categoryParser` argument to deal with the implicit Pratt parser call in `trailingNode.parenthesizer`. -/
   cat : Name := Name.anonymous
+  /-- Whether to add parentheses regardless of any other conditions. This is cached from the `pp.parens` option. -/
+  forceParens : Bool := false
 
 structure State where
   stxTrav : Syntax.Traverser
@@ -217,8 +220,13 @@ def maybeParenthesize (cat : Name) (canJuxtapose : Bool) (mkParen : Syntax → S
   let { minPrec := some minPrec, trailPrec := trailPrec, trailCat := trailCat, .. } ← get
     | trace[PrettyPrinter.parenthesize] "visited a syntax tree without precedences?!{line ++ format stx}"
   trace[PrettyPrinter.parenthesize] (m!"...precedences are {prec} >? {minPrec}" ++ if canJuxtapose then m!", {(trailPrec, trailCat)} <=? {(st.contPrec, st.contCat)}" else "")
-  -- Should we parenthesize?
-  if (prec > minPrec || canJuxtapose && match trailPrec, st.contPrec with | some trailPrec, some contPrec => trailCat == st.contCat && trailPrec <= contPrec | _, _ => false) then
+  /- Should we parenthesize?
+     * Note about forceParens mode: we don't insert outermost parentheses (we use the syntax traverser parents to detect this),
+       and we don't insert parentheses when we are at `maxPrec` (since this is effectively infinity).
+  -/
+  if (((← read).forceParens && !st.stxTrav.parents.isEmpty && minPrec < Parser.maxPrec)
+      || prec > minPrec
+      || canJuxtapose && match trailPrec, st.contPrec with | some trailPrec, some contPrec => trailCat == st.contCat && trailPrec <= contPrec | _, _ => false) then
       -- The recursive `visit` call, by the invariant, has moved to the preceding node. In order to parenthesize
       -- the original node, we must first move to the right, except if we already were at the left-most child in the first
       -- place.
@@ -540,16 +548,23 @@ instance : Coe (Parenthesizer → Parenthesizer → Parenthesizer) Parenthesizer
 end Parenthesizer
 open Parenthesizer
 
-/-- Add necessary parentheses in `stx` parsed by `parser`. -/
+/--
+Adds necessary parentheses in `stx` parsed by `parser`.
+-/
 def parenthesize (parenthesizer : Parenthesizer) (stx : Syntax) : CoreM Syntax := do
   trace[PrettyPrinter.parenthesize.input] "{format stx}"
+  let opts ← getOptions
   catchInternalId backtrackExceptionId
     (do
-      let (_, st) ← (parenthesizer {}).run { stxTrav := Syntax.Traverser.fromSyntax stx }
+      let (_, st) ← (parenthesizer { forceParens := getPPParens opts }).run { stxTrav := Syntax.Traverser.fromSyntax stx }
       pure st.stxTrav.cur)
     (fun _ => throwError "parenthesize: uncaught backtrack exception")
 
-def parenthesizeCategory (cat : Name) := parenthesize <| categoryParser.parenthesizer cat 0
+/--
+Adds necessary parentheses to the syntax in the given category (for example, `term`, `tactic`, or `command`).
+-/
+def parenthesizeCategory (cat : Name) (stx : Syntax) :=
+  parenthesize (categoryParser.parenthesizer cat 0) stx
 
 def parenthesizeTerm := parenthesizeCategory `term
 def parenthesizeTactic := parenthesizeCategory `tactic

src/Lean/Server/Completion/CompletionCollectors.lean

@@ -0,0 +1,610 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura, Marc Huisinga
+-/
+prelude
+import Lean.Data.FuzzyMatching
+import Lean.Elab.Tactic.Doc
+import Lean.Server.Completion.CompletionResolution
+import Lean.Server.Completion.EligibleHeaderDecls
+
+namespace Lean.Server.Completion
+open Elab
+open Lean.Lsp
+open Meta
+open FuzzyMatching
+
+section Infrastructure
+
+  structure ScoredCompletionItem where
+    item  : CompletionItem
+    score : Float
+    deriving Inhabited
+
+  private structure Context where
+    params            : CompletionParams
+    completionInfoPos : Nat
+
+
+  /-- Intermediate state while completions are being computed. -/
+  private structure State where
+    /-- All completion items and their fuzzy match scores so far. -/
+    items  : Array ScoredCompletionItem := #[]
+
+  /--
+  Monad used for completion computation that allows modifying a completion `State` and reading
+  `CompletionParams`.
+  -/
+  private abbrev M := ReaderT Context $ StateRefT State MetaM
+
+  /-- Adds a new completion item to the state in `M`. -/
+  private def addItem
+      (item  : CompletionItem)
+      (score : Float)
+      (id?   : Option CompletionIdentifier := none)
+      : M Unit := do
+    let ctx ← read
+    let data := {
+      params := ctx.params,
+      cPos := ctx.completionInfoPos,
+      id?
+      : ResolvableCompletionItemData
+    }
+    let item := { item with data? := toJson data }
+    modify fun s => { s with items := s.items.push ⟨item, score⟩ }
+
+  /--
+  Adds a new completion item with the given `label`, `id`, `kind` and `score` to the state in `M`.
+  Computes the doc string from the environment if available.
+  -/
+  private def addUnresolvedCompletionItem
+      (label         : Name)
+      (id            : CompletionIdentifier)
+      (kind          : CompletionItemKind)
+      (score         : Float)
+      : M Unit := do
+    let env ← getEnv
+    let (docStringPrefix?, tags?) := Id.run do
+      let .const declName := id
+        | (none, none)
+      let some param := Linter.deprecatedAttr.getParam? env declName
+        | (none, none)
+      let docstringPrefix :=
+        if let some text := param.text? then
+          text
+        else if let some newName := param.newName? then
+          s!"`{declName}` has been deprecated, use `{newName}` instead."
+        else
+          s!"`{declName}` has been deprecated."
+      (some docstringPrefix, some #[CompletionItemTag.deprecated])
+    let docString? ← do
+      let .const declName := id
+        | pure none
+      findDocString? env declName
+    let doc? := do
+      let docValue ←
+        match docStringPrefix?, docString? with
+        | none,                 none           => none
+        | some docStringPrefix, none           => docStringPrefix
+        | none,                 docString      => docString
+        | some docStringPrefix, some docString => s!"{docStringPrefix}\n\n{docString}"
+      pure { value := docValue , kind := MarkupKind.markdown : MarkupContent }
+    let item := { label := label.toString, kind? := kind, documentation? := doc?, tags?}
+    addItem item score id
+
+  private def getCompletionKindForDecl (constInfo : ConstantInfo) : M CompletionItemKind := do
+    let env ← getEnv
+    if constInfo.isCtor then
+      return CompletionItemKind.constructor
+    else if constInfo.isInductive then
+      if isClass env constInfo.name then
+        return CompletionItemKind.class
+      else if (← isEnumType constInfo.name) then
+        return CompletionItemKind.enum
+      else
+        return CompletionItemKind.struct
+    else if constInfo.isTheorem then
+      return CompletionItemKind.event
+    else if (← isProjectionFn constInfo.name) then
+      return CompletionItemKind.field
+    else
+      let isFunction : Bool ← withTheReader Core.Context ({ · with maxHeartbeats := 0 }) do
+        return (← whnf constInfo.type).isForall
+      if isFunction then
+        return CompletionItemKind.function
+      else
+        return CompletionItemKind.constant
+
+  private def addUnresolvedCompletionItemForDecl (label : Name) (declName : Name) (score : Float) : M Unit := do
+    if let some c := (← getEnv).find? declName then
+      addUnresolvedCompletionItem label (.const declName) (← getCompletionKindForDecl c) score
+
+  private def addKeywordCompletionItem (keyword : String) (score : Float) : M Unit := do
+    let item := { label := keyword, detail? := "keyword", documentation? := none, kind? := CompletionItemKind.keyword }
+    addItem item score
+
+  private def addNamespaceCompletionItem (ns : Name) (score : Float) : M Unit := do
+    let item := { label := ns.toString, detail? := "namespace", documentation? := none, kind? := CompletionItemKind.module }
+    addItem item score
+
+  private def runM
+      (params            : CompletionParams)
+      (completionInfoPos : Nat)
+      (ctx               : ContextInfo)
+      (lctx              : LocalContext)
+      (x                 : M Unit)
+      : IO (Array ScoredCompletionItem) :=
+    ctx.runMetaM lctx do
+      let (_, s) ← x.run ⟨params, completionInfoPos⟩ |>.run {}
+      return s.items
+
+end Infrastructure
+
+section Utils
+
+  private def normPrivateName? (declName : Name) : MetaM (Option Name) := do
+    match privateToUserName? declName with
+    | none => return declName
+    | some userName =>
+      if mkPrivateName (← getEnv) userName == declName then
+        return userName
+      else
+        return none
+
+  /--
+    Return the auto-completion label if `id` can be auto completed using `declName` assuming namespace `ns` is open.
+    This function only succeeds with atomic labels. BTW, it seems most clients only use the last part.
+
+    Remark: `danglingDot == true` when the completion point is an identifier followed by `.`.
+  -/
+  private def matchDecl? (ns : Name) (id : Name) (danglingDot : Bool) (declName : Name) : MetaM (Option (Name × Float)) := do
+    let some declName ← normPrivateName? declName
+      | return none
+    if !ns.isPrefixOf declName then
+      return none
+    let declName := declName.replacePrefix ns Name.anonymous
+    if danglingDot then
+      -- If the input is `id.` and `declName` is of the form `id.atomic`, complete with `atomicName`
+      if id.isPrefixOf declName then
+        let declName := declName.replacePrefix id Name.anonymous
+        if declName.isAtomic && !declName.isAnonymous then
+          return some (declName, 1)
+    else if let (.str p₁ s₁, .str p₂ s₂) := (id, declName) then
+      if p₁ == p₂ then
+        -- If the namespaces agree, fuzzy-match on the trailing part
+        return fuzzyMatchScoreWithThreshold? s₁ s₂ |>.map (.mkSimple s₂, ·)
+      else if p₁.isAnonymous then
+        -- If `id` is namespace-less, also fuzzy-match declaration names in arbitrary namespaces
+        -- (but don't match the namespace itself).
+        -- Penalize score by component length of added namespace.
+        return fuzzyMatchScoreWithThreshold? s₁ s₂ |>.map (declName, · / (p₂.getNumParts + 1).toFloat)
+    return none
+
+end Utils
+
+section IdCompletionUtils
+
+  private def matchAtomic (id : Name) (declName : Name) (danglingDot : Bool) : Option Float := do
+    if danglingDot then
+      none
+    match id, declName with
+    | .str .anonymous s₁, .str .anonymous s₂ => fuzzyMatchScoreWithThreshold? s₁ s₂
+    | _, _ => none
+
+  /--
+  Truncate the given identifier and make sure it has length `≤ newLength`.
+  This function assumes `id` does not contain `Name.num` constructors.
+  -/
+  private partial def truncate (id : Name) (newLen : Nat) : Name :=
+    let rec go (id : Name) : Name × Nat :=
+      match id with
+      | Name.anonymous => (id, 0)
+      | Name.num ..    => unreachable!
+      | .str p s =>
+        let (p', len) := go p
+        if len + 1 >= newLen then
+          (p', len)
+        else
+          let optDot := if p.isAnonymous then 0 else 1
+          let len'   := len + optDot + s.length
+          if len' ≤ newLen then
+            (id, len')
+          else
+            (Name.mkStr p (s.extract 0 ⟨newLen - optDot - len⟩), newLen)
+    (go id).1
+
+  def matchNamespace (ns : Name) (nsFragment : Name) (danglingDot : Bool) : Option Float :=
+    if danglingDot then
+      if nsFragment != ns && nsFragment.isPrefixOf ns then
+        some 1
+      else
+        none
+    else
+      match ns, nsFragment with
+      | .str p₁ s₁, .str p₂ s₂ =>
+        if p₁ == p₂ then fuzzyMatchScoreWithThreshold? s₂ s₁ else none
+      | _, _ => none
+
+  def completeNamespaces (ctx : ContextInfo) (id : Name) (danglingDot : Bool) : M Unit := do
+    let env ← getEnv
+    let add (ns : Name) (ns' : Name) (score : Float) : M Unit :=
+      if danglingDot then
+        addNamespaceCompletionItem (ns.replacePrefix (ns' ++ id) Name.anonymous) score
+      else
+        addNamespaceCompletionItem (ns.replacePrefix ns' Name.anonymous) score
+    env.getNamespaceSet |>.forM fun ns => do
+      unless ns.isInternal || env.contains ns do -- Ignore internal and namespaces that are also declaration names
+        for openDecl in ctx.openDecls do
+          match openDecl with
+          | OpenDecl.simple ns' _      =>
+            if let some score := matchNamespace ns (ns' ++ id) danglingDot then
+              add ns ns' score
+              return ()
+          | _ => pure ()
+        -- use current namespace
+        let rec visitNamespaces (ns' : Name) : M Unit := do
+          if let some score := matchNamespace ns (ns' ++ id) danglingDot then
+            add ns ns' score
+          else
+            match ns' with
+            | Name.str p .. => visitNamespaces p
+            | _ => return ()
+        visitNamespaces ctx.currNamespace
+
+end IdCompletionUtils
+
+section DotCompletionUtils
+
+  private def unfoldeDefinitionGuarded? (e : Expr) : MetaM (Option Expr) :=
+    try unfoldDefinition? e catch _ => pure none
+
+  /-- Return `true` if `e` is a `declName`-application, or can be unfolded (delta-reduced) to one. -/
+  private partial def isDefEqToAppOf (e : Expr) (declName : Name) : MetaM Bool := do
+    let isConstOf := match e.getAppFn with
+      | .const name .. => (privateToUserName? name).getD name == declName
+      | _ => false
+    if isConstOf then
+      return true
+    let some e ← unfoldeDefinitionGuarded? e | return false
+    isDefEqToAppOf e declName
+
+  private def isDotCompletionMethod (typeName : Name) (info : ConstantInfo) : MetaM Bool :=
+    forallTelescopeReducing info.type fun xs _ => do
+      for x in xs do
+        let localDecl ← x.fvarId!.getDecl
+        let type := localDecl.type.consumeMData
+        if (← isDefEqToAppOf type typeName) then
+          return true
+      return false
+
+  /--
+  Checks whether the expected type of `info.type` can be reduced to an application of `typeName`.
+  -/
+  private def isDotIdCompletionMethod (typeName : Name) (info : ConstantInfo) : MetaM Bool := do
+    forallTelescopeReducing info.type fun _ type =>
+      isDefEqToAppOf type.consumeMData typeName
+
+  /--
+  Converts `n` to `Name.anonymous` if `n` is a private prefix (see `Lean.isPrivatePrefix`).
+  -/
+  private def stripPrivatePrefix (n : Name) : Name :=
+    match n with
+    | .num _ 0 => if isPrivatePrefix n then .anonymous else n
+    | _ => n
+
+  /--
+  Compares `n₁` and `n₂` modulo private prefixes. Similar to `Name.cmp` but ignores all
+  private prefixes in both names.
+  Necessary because the namespaces of private names do not contain private prefixes.
+  -/
+  private partial def cmpModPrivate (n₁ n₂ : Name) : Ordering :=
+    let n₁ := stripPrivatePrefix n₁
+    let n₂ := stripPrivatePrefix n₂
+    match n₁, n₂ with
+    | .anonymous, .anonymous => Ordering.eq
+    | .anonymous, _          => Ordering.lt
+    | _,          .anonymous => Ordering.gt
+    | .num p₁ i₁, .num p₂ i₂ =>
+      match compare i₁ i₂ with
+      | Ordering.eq => cmpModPrivate p₁ p₂
+      | ord         => ord
+    | .num _ _,   .str _ _   => Ordering.lt
+    | .str _ _,   .num _ _   => Ordering.gt
+    | .str p₁ n₁, .str p₂ n₂ =>
+      match compare n₁ n₂ with
+      | Ordering.eq => cmpModPrivate p₁ p₂
+      | ord         => ord
+
+  /--
+  `NameSet` where names are compared according to `cmpModPrivate`.
+  Helps speed up dot completion because it allows us to look up names without first having to
+  strip the private prefix from deep in the name, letting us reject most names without
+  having to scan the full name first.
+  -/
+  private def NameSetModPrivate := RBTree Name cmpModPrivate
+
+  /--
+    Given a type, try to extract relevant type names for dot notation field completion.
+    We extract the type name, parent struct names, and unfold the type.
+    The process mimics the dot notation elaboration procedure at `App.lean` -/
+  private partial def getDotCompletionTypeNames (type : Expr) : MetaM NameSetModPrivate :=
+    return (← visit type |>.run RBTree.empty).2
+  where
+    visit (type : Expr) : StateRefT NameSetModPrivate MetaM Unit := do
+      let .const typeName _ := type.getAppFn | return ()
+      modify fun s => s.insert typeName
+      if isStructure (← getEnv) typeName then
+        for parentName in (← getAllParentStructures typeName) do
+          modify fun s => s.insert parentName
+      let some type ← unfoldeDefinitionGuarded? type | return ()
+      visit type
+
+end DotCompletionUtils
+
+private def idCompletionCore
+    (ctx         : ContextInfo)
+    (stx         : Syntax)
+    (id          : Name)
+    (hoverInfo   : HoverInfo)
+    (danglingDot : Bool)
+    : M Unit := do
+  let mut id := id
+  if id.hasMacroScopes then
+    if stx.getHeadInfo matches .original .. then
+      id := id.eraseMacroScopes
+    else
+      -- Identifier is synthetic and has macro scopes => no completions
+      -- Erasing the macro scopes does not make sense in this case because the identifier name
+      -- is some random synthetic string.
+      return
+  let mut danglingDot := danglingDot
+  if let HoverInfo.inside delta := hoverInfo then
+    id := truncate id delta
+    danglingDot := false
+  if id.isAtomic then
+    -- search for matches in the local context
+    for localDecl in (← getLCtx) do
+      if let some score := matchAtomic id localDecl.userName danglingDot then
+        addUnresolvedCompletionItem localDecl.userName (.fvar localDecl.fvarId) (kind := CompletionItemKind.variable) score
+  -- search for matches in the environment
+  let env ← getEnv
+  forEligibleDeclsM fun declName c => do
+    let bestMatch? ← (·.2) <$> StateT.run (s := none) do
+      let matchUsingNamespace (ns : Name) : StateT (Option (Name × Float)) M Unit := do
+        let some (label, score) ← matchDecl? ns id danglingDot declName
+          | return
+        modify fun
+          | none =>
+            some (label, score)
+          | some (bestLabel, bestScore) =>
+            -- for open namespaces `A` and `A.B` and a decl `A.B.c`, pick the decl `c` over `B.c`
+            if label.isSuffixOf bestLabel then
+              some (label, score)
+            else
+              some (bestLabel, bestScore)
+      let rec visitNamespaces (ns : Name) : StateT (Option (Name × Float)) M Unit := do
+        let Name.str p .. := ns
+          | return ()
+        matchUsingNamespace ns
+        visitNamespaces p
+      -- use current namespace
+      visitNamespaces ctx.currNamespace
+      -- use open decls
+      for openDecl in ctx.openDecls do
+        let OpenDecl.simple ns exs := openDecl
+          | pure ()
+        if exs.contains declName then
+          continue
+        matchUsingNamespace ns
+      matchUsingNamespace Name.anonymous
+    if let some (bestLabel, bestScore) := bestMatch? then
+      addUnresolvedCompletionItem bestLabel (.const declName) (← getCompletionKindForDecl c) bestScore
+  let matchAlias (ns : Name) (alias : Name) : Option Float :=
+    -- Recall that aliases may not be atomic and include the namespace where they were created.
+    if ns.isPrefixOf alias then
+      let alias := alias.replacePrefix ns Name.anonymous
+      matchAtomic id alias danglingDot
+    else
+      none
+  let eligibleHeaderDecls ← getEligibleHeaderDecls env
+  -- Auxiliary function for `alias`
+  let addAlias (alias : Name) (declNames : List Name) (score : Float) : M Unit := do
+    declNames.forM fun declName => do
+      if allowCompletion eligibleHeaderDecls env declName then
+        addUnresolvedCompletionItemForDecl (.mkSimple alias.getString!) declName score
+  -- search explicitly open `ids`
+  for openDecl in ctx.openDecls do
+    match openDecl with
+    | OpenDecl.explicit openedId resolvedId =>
+      if allowCompletion eligibleHeaderDecls env resolvedId then
+        if let some score := matchAtomic id openedId danglingDot then
+          addUnresolvedCompletionItemForDecl (.mkSimple openedId.getString!) resolvedId score
+    | OpenDecl.simple ns _      =>
+      getAliasState env |>.forM fun alias declNames => do
+        if let some score := matchAlias ns alias then
+          addAlias alias declNames score
+  -- search for aliases
+  getAliasState env |>.forM fun alias declNames => do
+    -- use current namespace
+    let rec searchAlias (ns : Name) : M Unit := do
+      if let some score := matchAlias ns alias then
+        addAlias alias declNames score
+      else
+        match ns with
+        | Name.str p ..  => searchAlias p
+        | _ => return ()
+    searchAlias ctx.currNamespace
+  -- Search keywords
+  if !danglingDot then
+    if let .str .anonymous s := id then
+      let keywords := Parser.getTokenTable env
+      for keyword in keywords.findPrefix s do
+        if let some score := fuzzyMatchScoreWithThreshold? s keyword then
+          addKeywordCompletionItem keyword score
+  -- Search namespaces
+  completeNamespaces ctx id danglingDot
+
+def idCompletion
+    (params            : CompletionParams)
+    (completionInfoPos : Nat)
+    (ctx               : ContextInfo)
+    (lctx              : LocalContext)
+    (stx               : Syntax)
+    (id                : Name)
+    (hoverInfo         : HoverInfo)
+    (danglingDot       : Bool)
+    : IO (Array ScoredCompletionItem) :=
+  runM params completionInfoPos ctx lctx do
+    idCompletionCore ctx stx id hoverInfo danglingDot
+
+def dotCompletion
+    (params            : CompletionParams)
+    (completionInfoPos : Nat)
+    (ctx               : ContextInfo)
+    (info              : TermInfo)
+    : IO (Array ScoredCompletionItem) :=
+  runM params completionInfoPos ctx info.lctx do
+    let nameSet ← try
+      getDotCompletionTypeNames (← instantiateMVars (← inferType info.expr))
+    catch _ =>
+      pure RBTree.empty
+    if nameSet.isEmpty then
+      return
+
+    forEligibleDeclsM fun declName c => do
+      let unnormedTypeName := declName.getPrefix
+      if ! nameSet.contains unnormedTypeName then
+        return
+      let some declName ← normPrivateName? declName
+        | return
+      let typeName := declName.getPrefix
+      if ! (← isDotCompletionMethod typeName c) then
+        return
+      let completionKind ← getCompletionKindForDecl c
+      addUnresolvedCompletionItem (.mkSimple c.name.getString!) (.const c.name) (kind := completionKind) 1
+
+def dotIdCompletion
+    (params            : CompletionParams)
+    (completionInfoPos : Nat)
+    (ctx               : ContextInfo)
+    (lctx              : LocalContext)
+    (id                : Name)
+    (expectedType?     : Option Expr)
+    : IO (Array ScoredCompletionItem) :=
+  runM params completionInfoPos ctx lctx do
+    let some expectedType := expectedType?
+      | return ()
+
+    let resultTypeFn := (← instantiateMVars expectedType).cleanupAnnotations.getAppFn.cleanupAnnotations
+    let .const .. := resultTypeFn
+      | return ()
+
+    let nameSet ← try
+      getDotCompletionTypeNames resultTypeFn
+    catch _ =>
+      pure RBTree.empty
+
+    forEligibleDeclsM fun declName c => do
+      let unnormedTypeName := declName.getPrefix
+      if ! nameSet.contains unnormedTypeName then
+        return
+
+      let some declName ← normPrivateName? declName
+        | return
+
+      let typeName := declName.getPrefix
+      if ! (← isDotIdCompletionMethod typeName c) then
+        return
+
+      let completionKind ← getCompletionKindForDecl c
+      if id.isAnonymous then
+        -- We're completing a lone dot => offer all decls of the type
+        addUnresolvedCompletionItem (.mkSimple c.name.getString!) (.const c.name) completionKind 1
+        return
+
+      let some (label, score) ← matchDecl? typeName id (danglingDot := false) declName | pure ()
+      addUnresolvedCompletionItem label (.const c.name) completionKind score
+
+def fieldIdCompletion
+    (params            : CompletionParams)
+    (completionInfoPos : Nat)
+    (ctx               : ContextInfo)
+    (lctx              : LocalContext)
+    (id                : Option Name)
+    (structName        : Name)
+    : IO (Array ScoredCompletionItem) :=
+  runM params completionInfoPos ctx lctx do
+    let idStr := id.map (·.toString) |>.getD ""
+    let fieldNames := getStructureFieldsFlattened (← getEnv) structName (includeSubobjectFields := false)
+    for fieldName in fieldNames do
+      let .str _ fieldName := fieldName | continue
+      let some score := fuzzyMatchScoreWithThreshold? idStr fieldName | continue
+      let item := { label := fieldName, detail? := "field", documentation? := none, kind? := CompletionItemKind.field }
+      addItem item score
+
+def optionCompletion
+    (params            : CompletionParams)
+    (completionInfoPos : Nat)
+    (ctx               : ContextInfo)
+    (stx               : Syntax)
+    (caps              : ClientCapabilities)
+    : IO (Array ScoredCompletionItem) :=
+  ctx.runMetaM {} do
+    let (partialName, trailingDot) :=
+      -- `stx` is from `"set_option" >> ident`
+      match stx[1].getSubstring? (withLeading := false) (withTrailing := false) with
+      | none => ("", false)  -- the `ident` is `missing`, list all options
+      | some ss =>
+        if !ss.str.atEnd ss.stopPos && ss.str.get ss.stopPos == '.' then
+          -- include trailing dot, which is not parsed by `ident`
+          (ss.toString ++ ".", true)
+        else
+          (ss.toString, false)
+    -- HACK(WN): unfold the type so ForIn works
+    let (decls : RBMap _ _ _) ← getOptionDecls
+    let opts ← getOptions
+    let mut items := #[]
+    for ⟨name, decl⟩ in decls do
+      if let some score := fuzzyMatchScoreWithThreshold? partialName name.toString then
+        let textEdit :=
+          if !caps.textDocument?.any (·.completion?.any (·.completionItem?.any (·.insertReplaceSupport?.any (·)))) then
+            none -- InsertReplaceEdit not supported by client
+          else if let some ⟨start, stop⟩ := stx[1].getRange? then
+            let stop := if trailingDot then stop + ' ' else stop
+            let range := ⟨ctx.fileMap.utf8PosToLspPos start, ctx.fileMap.utf8PosToLspPos stop⟩
+            some { newText := name.toString, insert := range, replace := range : InsertReplaceEdit }
+          else
+            none
+        items := items.push ⟨{
+            label := name.toString
+            detail? := s!"({opts.get name decl.defValue}), {decl.descr}"
+            documentation? := none,
+            kind? := CompletionItemKind.property -- TODO: investigate whether this is the best kind for options.
+            textEdit? := textEdit
+            data? := toJson {
+              params,
+              cPos := completionInfoPos,
+              id? := none : ResolvableCompletionItemData
+            }
+          }, score⟩
+    return items
+
+def tacticCompletion
+    (params            : CompletionParams)
+    (completionInfoPos : Nat)
+    (ctx               : ContextInfo)
+    : IO (Array ScoredCompletionItem) := ctx.runMetaM .empty do
+  let allTacticDocs ← Tactic.Doc.allTacticDocs
+  let items : Array ScoredCompletionItem := allTacticDocs.map fun tacticDoc =>
+    ⟨{
+      label          := tacticDoc.userName
+      detail?        := none
+      documentation? := tacticDoc.docString.map fun docString =>
+        { value := docString, kind := MarkupKind.markdown : MarkupContent }
+      kind?          := CompletionItemKind.keyword
+      data?          := toJson { params, cPos := completionInfoPos, id? := none : ResolvableCompletionItemData }
+    }, 1⟩
+  return items
+
+end Lean.Server.Completion

src/Lean/Server/Completion/CompletionInfoSelection.lean

@@ -0,0 +1,131 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura, Marc Huisinga
+-/
+prelude
+import Lean.Server.Completion.SyntheticCompletion
+
+namespace Lean.Server.Completion
+open Elab
+
+private def filterDuplicateCompletionInfos
+    (infos : Array ContextualizedCompletionInfo)
+    : Array ContextualizedCompletionInfo := Id.run do
+  -- We don't expect there to be too many duplicate completion infos,
+  -- so it's fine if this is quadratic (we don't need to implement `Hashable` / `LT` this way).
+  let mut deduplicatedInfos : Array ContextualizedCompletionInfo := #[]
+  for i in infos do
+    if deduplicatedInfos.any (fun di => eq di.info i.info) then
+      continue
+    deduplicatedInfos := deduplicatedInfos.push i
+  deduplicatedInfos
+where
+  eq : CompletionInfo → CompletionInfo → Bool
+    | .dot ti₁ .., .dot ti₂ .. =>
+      ti₁.stx.eqWithInfo ti₂.stx && ti₁.expr == ti₂.expr
+    | .id stx₁ id₁ .., .id stx₂ id₂ .. =>
+      stx₁.eqWithInfo stx₂ && id₁ == id₂
+    | .dotId stx₁ id₁ .., .id stx₂ id₂ .. =>
+      stx₁.eqWithInfo stx₂ && id₁ == id₂
+    | .fieldId stx₁ id₁? _ structName₁, .fieldId stx₂ id₂? _ structName₂ =>
+      stx₁.eqWithInfo stx₂ && id₁? == id₂? && structName₁ == structName₂
+    | .namespaceId stx₁, .namespaceId stx₂ =>
+      stx₁.eqWithInfo stx₂
+    | .option stx₁, .option stx₂ =>
+      stx₁.eqWithInfo stx₂
+    | .endSection stx₁ scopeNames₁, .endSection stx₂ scopeNames₂ =>
+      stx₁.eqWithInfo stx₂ && scopeNames₁ == scopeNames₂
+    | .tactic stx₁, .tactic stx₂ =>
+      stx₁.eqWithInfo stx₂
+    | _, _ =>
+      false
+
+def findCompletionInfosAt
+    (fileMap  : FileMap)
+    (hoverPos : String.Pos)
+    (cmdStx   : Syntax)
+    (infoTree : InfoTree)
+    : Array ContextualizedCompletionInfo := Id.run do
+  let ⟨hoverLine, _⟩ := fileMap.toPosition hoverPos
+  let mut completionInfoCandidates := infoTree.foldInfo (init := #[]) (go hoverLine)
+  if completionInfoCandidates.isEmpty then
+    completionInfoCandidates := findSyntheticCompletions fileMap hoverPos cmdStx infoTree
+  return filterDuplicateCompletionInfos completionInfoCandidates
+where
+  go
+      (hoverLine : Nat)
+      (ctx       : ContextInfo)
+      (info      : Info)
+      (best     : Array ContextualizedCompletionInfo)
+      : Array ContextualizedCompletionInfo := Id.run do
+    let .ofCompletionInfo completionInfo := info
+      | return best
+    if ! info.occursInOrOnBoundary hoverPos then
+      return best
+    let headPos := info.pos?.get!
+    let tailPos := info.tailPos?.get!
+    let hoverInfo :=
+      if hoverPos < tailPos then
+        HoverInfo.inside (hoverPos - headPos).byteIdx
+      else
+        HoverInfo.after
+    let ⟨headPosLine, _⟩ := fileMap.toPosition headPos
+    let ⟨tailPosLine, _⟩ := fileMap.toPosition info.tailPos?.get!
+    if headPosLine != hoverLine || headPosLine != tailPosLine then
+      return best
+    return best.push { hoverInfo, ctx, info := completionInfo }
+
+private def computePrioritizedCompletionPartitions
+    (items : Array (ContextualizedCompletionInfo × Nat))
+    : Array (Array (ContextualizedCompletionInfo × Nat)) :=
+  let partitions := items.groupByKey fun (i, _) =>
+    let isId := i.info matches .id ..
+    let size? := Info.ofCompletionInfo i.info |>.size?
+    (isId, size?)
+  -- Sort partitions so that non-id completions infos come before id completion infos and
+  -- within those two groups, smaller sizes come before larger sizes.
+  let partitionsByPriority := partitions.toArray.qsort
+    fun ((isId₁, size₁?), _) ((isId₂, size₂?), _) =>
+      match size₁?, size₂? with
+      | some _, none   => true
+      | none,   some _ => false
+      | _, _ =>
+        match isId₁, isId₂ with
+        | false, true  => true
+        | true,  false => false
+        | _,     _     => Id.run do
+          let some size₁ := size₁?
+            | return false
+          let some size₂ := size₂?
+            | return false
+          return size₁ < size₂
+  partitionsByPriority.map (·.2)
+
+/--
+Finds all `CompletionInfo`s (both from the `InfoTree` and synthetic ones), prioritizes them,
+arranges them in partitions of `CompletionInfo`s with the same priority and sorts these partitions
+so that `CompletionInfo`s with the highest priority come first.
+The returned `CompletionInfo`s are also tagged with their index in `findCompletionInfosAt` so that
+when resolving a `CompletionItem`, we can reconstruct which `CompletionInfo` it was created from.
+
+In general, the `InfoTree` may contain multiple different `CompletionInfo`s covering `hoverPos`,
+and so we need to decide which of these `CompletionInfo`s we want to use to show completions to the
+user. We choose priorities by the following rules:
+- Synthetic completions have the lowest priority since they are only intended as a backup.
+- Non-identifier completions have the highest priority since they tend to be much more helpful than
+  identifier completions when available since there are typically way too many of the latter.
+- Within the three groups [non-id completions, id completions, synthetic completions],
+  `CompletionInfo`s with a smaller range are considered to be better.
+-/
+def findPrioritizedCompletionPartitionsAt
+    (fileMap  : FileMap)
+    (hoverPos : String.Pos)
+    (cmdStx   : Syntax)
+    (infoTree : InfoTree)
+    : Array (Array (ContextualizedCompletionInfo × Nat)) :=
+  findCompletionInfosAt fileMap hoverPos cmdStx infoTree
+    |>.zipWithIndex
+    |> computePrioritizedCompletionPartitions
+
+end Lean.Server.Completion

src/Lean/Server/Completion/CompletionResolution.lean

@@ -0,0 +1,91 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura, Marc Huisinga
+-/
+prelude
+import Lean.Server.Completion.CompletionItemData
+import Lean.Server.Completion.CompletionInfoSelection
+
+namespace Lean.Lsp
+
+/--
+Identifier that is sent from the server to the client as part of the `CompletionItem.data?` field.
+Needed to resolve the `CompletionItem` when the client sends a `completionItem/resolve` request
+for that item, again containing the `data?` field provided by the server.
+-/
+inductive CompletionIdentifier where
+  | const (declName : Name)
+  | fvar  (id       : FVarId)
+  deriving FromJson, ToJson
+
+/--
+`CompletionItemData` that contains additional information to identify the item
+in order to resolve it.
+-/
+structure ResolvableCompletionItemData extends CompletionItemData where
+  /-- Position of the completion info that this completion item was created from. -/
+  cPos : Nat
+  id?  : Option CompletionIdentifier
+  deriving FromJson, ToJson
+
+private partial def consumeImplicitPrefix (e : Expr) (k : Expr → MetaM α) : MetaM α := do
+  match e with
+  | Expr.forallE n d b c =>
+    -- We do not consume instance implicit arguments because the user probably wants be aware of this dependency
+    if c == .implicit then
+      Meta.withLocalDecl n c d fun arg =>
+        consumeImplicitPrefix (b.instantiate1 arg) k
+    else
+      k e
+  | _ => k e
+
+/--
+Fills the `CompletionItem.detail?` field of `item` using the pretty-printed type identified by `id`.
+-/
+def CompletionItem.resolve
+    (item : CompletionItem)
+    (id   : CompletionIdentifier)
+    : MetaM CompletionItem := do
+  let env ← getEnv
+  let lctx ← getLCtx
+  let mut item := item
+
+  if item.detail?.isNone then
+    let type? := match id with
+      | .const declName =>
+        env.find? declName |>.map ConstantInfo.type
+      | .fvar id =>
+        lctx.find? id |>.map LocalDecl.type
+    let detail? ← type?.mapM fun type =>
+      consumeImplicitPrefix type fun typeWithoutImplicits =>
+        return toString (← Meta.ppExpr typeWithoutImplicits)
+    item := { item with detail? := detail? }
+
+  return item
+
+end Lean.Lsp
+
+namespace Lean.Server.Completion
+open Lean.Lsp
+open Elab
+
+/--
+Fills the `CompletionItem.detail?` field of `item` using the pretty-printed type identified by `id`
+in the context found at `hoverPos` in `infoTree`.
+-/
+def resolveCompletionItem?
+    (fileMap           : FileMap)
+    (hoverPos          : String.Pos)
+    (cmdStx            : Syntax)
+    (infoTree          : InfoTree)
+    (item              : CompletionItem)
+    (id                : CompletionIdentifier)
+    (completionInfoPos : Nat)
+    : IO CompletionItem := do
+  let completionInfos := findCompletionInfosAt fileMap hoverPos cmdStx infoTree
+  let some i := completionInfos.get? completionInfoPos
+    | return item
+  i.ctx.runMetaM i.info.lctx (item.resolve id)
+
+end Lean.Server.Completion

src/Lean/Server/Completion/CompletionUtils.lean

@@ -0,0 +1,22 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura, Marc Huisinga
+-/
+prelude
+import Init.Prelude
+import Lean.Elab.InfoTree.Types
+
+namespace Lean.Server.Completion
+open Elab
+
+inductive HoverInfo : Type where
+  | after
+  | inside (delta : Nat)
+
+structure ContextualizedCompletionInfo where
+  hoverInfo : HoverInfo
+  ctx       : ContextInfo
+  info      : CompletionInfo
+
+end Lean.Server.Completion

src/Lean/Server/Completion/EligibleHeaderDecls.lean

@@ -0,0 +1,53 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Marc Huisinga
+-/
+prelude
+import Lean.Meta.CompletionName
+
+namespace Lean.Server.Completion
+open Meta
+
+abbrev EligibleHeaderDecls := Std.HashMap Name ConstantInfo
+
+/-- Cached header declarations for which `allowCompletion headerEnv decl` is true. -/
+builtin_initialize eligibleHeaderDeclsRef : IO.Ref (Option EligibleHeaderDecls) ←
+  IO.mkRef none
+
+/--
+Returns the declarations in the header for which `allowCompletion env decl` is true, caching them
+if not already cached.
+-/
+def getEligibleHeaderDecls (env : Environment) : IO EligibleHeaderDecls := do
+  eligibleHeaderDeclsRef.modifyGet fun
+    | some eligibleHeaderDecls => (eligibleHeaderDecls, some eligibleHeaderDecls)
+    | none =>
+      let (_, eligibleHeaderDecls) :=
+        StateT.run (m := Id) (s := {}) do
+          -- `map₁` are the header decls
+          env.constants.map₁.forM fun declName c => do
+            modify fun eligibleHeaderDecls =>
+              if allowCompletion env declName then
+                eligibleHeaderDecls.insert declName c
+              else
+                eligibleHeaderDecls
+      (eligibleHeaderDecls, some eligibleHeaderDecls)
+
+/-- Iterate over all declarations that are allowed in completion results. -/
+def forEligibleDeclsM [Monad m] [MonadEnv m] [MonadLiftT (ST IO.RealWorld) m]
+    [MonadLiftT IO m] (f : Name → ConstantInfo → m PUnit) : m PUnit := do
+  let env ← getEnv
+  (← getEligibleHeaderDecls env).forM f
+  -- map₂ are exactly the local decls
+  env.constants.map₂.forM fun name c => do
+    if allowCompletion env name then
+      f name c
+
+/-- Checks whether this declaration can appear in completion results. -/
+def allowCompletion (eligibleHeaderDecls : EligibleHeaderDecls) (env : Environment)
+    (declName : Name) : Bool :=
+  eligibleHeaderDecls.contains declName ||
+    env.constants.map₂.contains declName && Lean.Meta.allowCompletion env declName
+
+end Lean.Server.Completion