chore: avoid runtime array bounds checks

This PR duplicates the verification API for
`List.attach`/`attachWith`/`pmap` over to `Array`.

.github/workflows/pr-body.yml

@@ -1,6 +1,7 @@
 name: Check PR body for changelog convention
 
 on:
+  merge_group:
   pull_request:
     types: [opened, synchronize, reopened, edited, labeled, converted_to_draft, ready_for_review]
 
@@ -9,6 +10,7 @@ jobs:
     runs-on: ubuntu-latest
     steps:
       - name: Check PR body
+        if: github.event_name == 'pull_request'
         uses: actions/github-script@v7
         with:
           script: |

nix/bootstrap.nix

@@ -170,7 +170,7 @@ lib.warn "The Nix-based build is deprecated" rec {
           ln -sf ${lean-all}/* .
         '';
         buildPhase = ''
-          ctest --output-junit test-results.xml --output-on-failure -E 'leancomptest_(doc_example|foreign)|leanlaketest_reverse-ffi' -j$NIX_BUILD_CORES
+         ctest --output-junit test-results.xml --output-on-failure -E 'leancomptest_(doc_example|foreign)|leanlaketest_reverse-ffi|leanruntest_timeIO' -j$NIX_BUILD_CORES
         '';
         installPhase = ''
           mkdir $out

src/Init/Core.lean

@@ -1922,12 +1922,12 @@ represents an element of `Squash α` the same as `α` itself
 `Squash.lift` will extract a value in any subsingleton `β` from a function on `α`,
 while `Nonempty.rec` can only do the same when `β` is a proposition.
 -/
-def Squash (α : Type u) := Quot (fun (_ _ : α) => True)
+def Squash (α : Sort u) := Quot (fun (_ _ : α) => True)
 
 /-- The canonical quotient map into `Squash α`. -/
-def Squash.mk {α : Type u} (x : α) : Squash α := Quot.mk _ x
+def Squash.mk {α : Sort u} (x : α) : Squash α := Quot.mk _ x
 
-theorem Squash.ind {α : Type u} {motive : Squash α → Prop} (h : ∀ (a : α), motive (Squash.mk a)) : ∀ (q : Squash α), motive q :=
+theorem Squash.ind {α : Sort u} {motive : Squash α → Prop} (h : ∀ (a : α), motive (Squash.mk a)) : ∀ (q : Squash α), motive q :=
   Quot.ind h
 
 /-- If `β` is a subsingleton, then a function `α → β` lifts to `Squash α → β`. -/

src/Init/Data.lean

@@ -42,3 +42,4 @@ import Init.Data.PLift
 import Init.Data.Zero
 import Init.Data.NeZero
 import Init.Data.Function
+import Init.Data.RArray

src/Init/Data/Array.lean

@@ -18,3 +18,4 @@ import Init.Data.Array.Bootstrap
 import Init.Data.Array.GetLit
 import Init.Data.Array.MapIdx
 import Init.Data.Array.Set
+import Init.Data.Array.Monadic

src/Init/Data/Array/Attach.lean

@@ -10,6 +10,17 @@ import Init.Data.List.Attach
 
 namespace Array
 
+/--
+`O(n)`. Partial map. If `f : Π a, P a → β` is a partial function defined on
+`a : α` satisfying `P`, then `pmap f l h` is essentially the same as `map f l`
+but is defined only when all members of `l` satisfy `P`, using the proof
+to apply `f`.
+
+We replace this at runtime with a more efficient version via the `csimp` lemma `pmap_eq_pmapImpl`.
+-/
+def pmap {P : α → Prop} (f : ∀ a, P a → β) (l : Array α) (H : ∀ a ∈ l, P a) : Array β :=
+  (l.toList.pmap f (fun a m => H a (mem_def.mpr m))).toArray
+
 /--
 Unsafe implementation of `attachWith`, taking advantage of the fact that the representation of
 `Array {x // P x}` is the same as the input `Array α`.
@@ -35,6 +46,10 @@ Unsafe implementation of `attachWith`, taking advantage of the fact that the rep
     l.toArray.attach = (l.attachWith (· ∈ l.toArray) (by simp)).toArray := by
   simp [attach]
 
+@[simp] theorem _root_.List.pmap_toArray {l : List α} {P : α → Prop} {f : ∀ a, P a → β} {H : ∀ a ∈ l.toArray, P a} :
+    l.toArray.pmap f H = (l.pmap f (by simpa using H)).toArray := by
+  simp [pmap]
+
 @[simp] theorem toList_attachWith {l : Array α} {P : α → Prop} {H : ∀ x ∈ l, P x} :
    (l.attachWith P H).toList = l.toList.attachWith P (by simpa [mem_toList] using H) := by
   simp [attachWith]
@@ -43,6 +58,387 @@ Unsafe implementation of `attachWith`, taking advantage of the fact that the rep
     l.attach.toList = l.toList.attachWith (· ∈ l) (by simp [mem_toList]) := by
   simp [attach]
 
+@[simp] theorem toList_pmap {l : Array α} {P : α → Prop} {f : ∀ a, P a → β} {H : ∀ a ∈ l, P a} :
+    (l.pmap f H).toList = l.toList.pmap f (fun a m => H a (mem_def.mpr m)) := by
+  simp [pmap]
+
+/-- Implementation of `pmap` using the zero-copy version of `attach`. -/
+@[inline] private def pmapImpl {P : α → Prop} (f : ∀ a, P a → β) (l : Array α) (H : ∀ a ∈ l, P a) :
+    Array β := (l.attachWith _ H).map fun ⟨x, h'⟩ => f x h'
+
+@[csimp] private theorem pmap_eq_pmapImpl : @pmap = @pmapImpl := by
+  funext α β p f L h'
+  cases L
+  simp only [pmap, pmapImpl, List.attachWith_toArray, List.map_toArray, mk.injEq, List.map_attachWith]
+  apply List.pmap_congr_left
+  intro a m h₁ h₂
+  congr
+
+@[simp] theorem pmap_empty {P : α → Prop} (f : ∀ a, P a → β) : pmap f #[] (by simp) = #[] := rfl
+
+@[simp] theorem pmap_push {P : α → Prop} (f : ∀ a, P a → β) (a : α) (l : Array α) (h : ∀ b ∈ l.push a, P b) :
+    pmap f (l.push a) h =
+      (pmap f l (fun a m => by simp at h; exact h a (.inl m))).push (f a (h a (by simp))) := by
+  simp [pmap]
+
+@[simp] theorem attach_empty : (#[] : Array α).attach = #[] := rfl
+
+@[simp] theorem attachWith_empty {P : α → Prop} (H : ∀ x ∈ #[], P x) : (#[] : Array α).attachWith P H = #[] := rfl
+
+@[simp] theorem _root_.List.attachWith_mem_toArray {l : List α} :
+    l.attachWith (fun x => x ∈ l.toArray) (fun x h => by simpa using h) =
+      l.attach.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
+  simp only [List.attachWith, List.attach, List.map_pmap]
+  apply List.pmap_congr_left
+  simp
+
+@[simp]
+theorem pmap_eq_map (p : α → Prop) (f : α → β) (l : Array α) (H) :
+    @pmap _ _ p (fun a _ => f a) l H = map f l := by
+  cases l; simp
+
+theorem pmap_congr_left {p q : α → Prop} {f : ∀ a, p a → β} {g : ∀ a, q a → β} (l : Array α) {H₁ H₂}
+    (h : ∀ a ∈ l, ∀ (h₁ h₂), f a h₁ = g a h₂) : pmap f l H₁ = pmap g l H₂ := by
+  cases l
+  simp only [mem_toArray] at h
+  simp only [List.pmap_toArray, mk.injEq]
+  rw [List.pmap_congr_left _ h]
+
+theorem map_pmap {p : α → Prop} (g : β → γ) (f : ∀ a, p a → β) (l H) :
+    map g (pmap f l H) = pmap (fun a h => g (f a h)) l H := by
+  cases l
+  simp [List.map_pmap]
+
+theorem pmap_map {p : β → Prop} (g : ∀ b, p b → γ) (f : α → β) (l H) :
+    pmap g (map f l) H = pmap (fun a h => g (f a) h) l fun _ h => H _ (mem_map_of_mem _ h) := by
+  cases l
+  simp [List.pmap_map]
+
+theorem attach_congr {l₁ l₂ : Array α} (h : l₁ = l₂) :
+    l₁.attach = l₂.attach.map (fun x => ⟨x.1, h ▸ x.2⟩) := by
+  subst h
+  simp
+
+theorem attachWith_congr {l₁ l₂ : Array α} (w : l₁ = l₂) {P : α → Prop} {H : ∀ x ∈ l₁, P x} :
+    l₁.attachWith P H = l₂.attachWith P fun _ h => H _ (w ▸ h) := by
+  subst w
+  simp
+
+@[simp] theorem attach_push {a : α} {l : Array α} :
+    (l.push a).attach =
+      (l.attach.map (fun ⟨x, h⟩ => ⟨x, mem_push_of_mem a h⟩)).push ⟨a, by simp⟩ := by
+  cases l
+  rw [attach_congr (List.push_toArray _ _)]
+  simp [Function.comp_def]
+
+@[simp] theorem attachWith_push {a : α} {l : Array α} {P : α → Prop} {H : ∀ x ∈ l.push a, P x} :
+    (l.push a).attachWith P H =
+      (l.attachWith P (fun x h => by simp at H; exact H x (.inl h))).push ⟨a, H a (by simp)⟩ := by
+  cases l
+  simp [attachWith_congr (List.push_toArray _ _)]
+
+theorem pmap_eq_map_attach {p : α → Prop} (f : ∀ a, p a → β) (l H) :
+    pmap f l H = l.attach.map fun x => f x.1 (H _ x.2) := by
+  cases l
+  simp [List.pmap_eq_map_attach]
+
+theorem attach_map_coe (l : Array α) (f : α → β) :
+    (l.attach.map fun (i : {i // i ∈ l}) => f i) = l.map f := by
+  cases l
+  simp [List.attach_map_coe]
+
+theorem attach_map_val (l : Array α) (f : α → β) : (l.attach.map fun i => f i.val) = l.map f :=
+  attach_map_coe _ _
+
+@[simp]
+theorem attach_map_subtype_val (l : Array α) : l.attach.map Subtype.val = l := by
+  cases l; simp
+
+theorem attachWith_map_coe {p : α → Prop} (f : α → β) (l : Array α) (H : ∀ a ∈ l, p a) :
+    ((l.attachWith p H).map fun (i : { i // p i}) => f i) = l.map f := by
+  cases l; simp
+
+theorem attachWith_map_val {p : α → Prop} (f : α → β) (l : Array α) (H : ∀ a ∈ l, p a) :
+    ((l.attachWith p H).map fun i => f i.val) = l.map f :=
+  attachWith_map_coe _ _ _
+
+@[simp]
+theorem attachWith_map_subtype_val {p : α → Prop} (l : Array α) (H : ∀ a ∈ l, p a) :
+    (l.attachWith p H).map Subtype.val = l := by
+  cases l; simp
+
+@[simp]
+theorem mem_attach (l : Array α) : ∀ x, x ∈ l.attach
+  | ⟨a, h⟩ => by
+    have := mem_map.1 (by rw [attach_map_subtype_val] <;> exact h)
+    rcases this with ⟨⟨_, _⟩, m, rfl⟩
+    exact m
+
+@[simp]
+theorem mem_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H b} :
+    b ∈ pmap f l H ↔ ∃ (a : _) (h : a ∈ l), f a (H a h) = b := by
+  simp only [pmap_eq_map_attach, mem_map, mem_attach, true_and, Subtype.exists, eq_comm]
+
+theorem mem_pmap_of_mem {p : α → Prop} {f : ∀ a, p a → β} {l H} {a} (h : a ∈ l) :
+    f a (H a h) ∈ pmap f l H := by
+  rw [mem_pmap]
+  exact ⟨a, h, rfl⟩
+
+@[simp]
+theorem size_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H} : (pmap f l H).size = l.size := by
+  cases l; simp
+
+@[simp]
+theorem size_attach {L : Array α} : L.attach.size = L.size := by
+  cases L; simp
+
+@[simp]
+theorem size_attachWith {p : α → Prop} {l : Array α} {H} : (l.attachWith p H).size = l.size := by
+  cases l; simp
+
+@[simp]
+theorem pmap_eq_empty_iff {p : α → Prop} {f : ∀ a, p a → β} {l H} : pmap f l H = #[] ↔ l = #[] := by
+  cases l; simp
+
+theorem pmap_ne_empty_iff {P : α → Prop} (f : (a : α) → P a → β) {xs : Array α}
+    (H : ∀ (a : α), a ∈ xs → P a) : xs.pmap f H ≠ #[] ↔ xs ≠ #[] := by
+  cases xs; simp
+
+theorem pmap_eq_self {l : Array α} {p : α → Prop} (hp : ∀ (a : α), a ∈ l → p a)
+    (f : (a : α) → p a → α) : l.pmap f hp = l ↔ ∀ a (h : a ∈ l), f a (hp a h) = a := by
+  cases l; simp [List.pmap_eq_self]
+
+@[simp]
+theorem attach_eq_empty_iff {l : Array α} : l.attach = #[] ↔ l = #[] := by
+  cases l; simp
+
+theorem attach_ne_empty_iff {l : Array α} : l.attach ≠ #[] ↔ l ≠ #[] := by
+  cases l; simp
+
+@[simp]
+theorem attachWith_eq_empty_iff {l : Array α} {P : α → Prop} {H : ∀ a ∈ l, P a} :
+    l.attachWith P H = #[] ↔ l = #[] := by
+  cases l; simp
+
+theorem attachWith_ne_empty_iff {l : Array α} {P : α → Prop} {H : ∀ a ∈ l, P a} :
+    l.attachWith P H ≠ #[] ↔ l ≠ #[] := by
+  cases l; simp
+
+@[simp]
+theorem getElem?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : Array α} (h : ∀ a ∈ l, p a) (n : Nat) :
+    (pmap f l h)[n]? = Option.pmap f l[n]? fun x H => h x (mem_of_getElem? H) := by
+  cases l; simp
+
+@[simp]
+theorem getElem_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : Array α} (h : ∀ a ∈ l, p a) {n : Nat}
+    (hn : n < (pmap f l h).size) :
+    (pmap f l h)[n] =
+      f (l[n]'(@size_pmap _ _ p f l h ▸ hn))
+        (h _ (getElem_mem (@size_pmap _ _ p f l h ▸ hn))) := by
+  cases l; simp
+
+@[simp]
+theorem getElem?_attachWith {xs : Array α} {i : Nat} {P : α → Prop} {H : ∀ a ∈ xs, P a} :
+    (xs.attachWith P H)[i]? = xs[i]?.pmap Subtype.mk (fun _ a => H _ (mem_of_getElem? a)) :=
+  getElem?_pmap ..
+
+@[simp]
+theorem getElem?_attach {xs : Array α} {i : Nat} :
+    xs.attach[i]? = xs[i]?.pmap Subtype.mk (fun _ a => mem_of_getElem? a) :=
+  getElem?_attachWith
+
+@[simp]
+theorem getElem_attachWith {xs : Array α} {P : α → Prop} {H : ∀ a ∈ xs, P a}
+    {i : Nat} (h : i < (xs.attachWith P H).size) :
+    (xs.attachWith P H)[i] = ⟨xs[i]'(by simpa using h), H _ (getElem_mem (by simpa using h))⟩ :=
+  getElem_pmap ..
+
+@[simp]
+theorem getElem_attach {xs : Array α} {i : Nat} (h : i < xs.attach.size) :
+    xs.attach[i] = ⟨xs[i]'(by simpa using h), getElem_mem (by simpa using h)⟩ :=
+  getElem_attachWith h
+
+theorem foldl_pmap (l : Array α) {P : α → Prop} (f : (a : α) → P a → β)
+  (H : ∀ (a : α), a ∈ l → P a) (g : γ → β → γ) (x : γ) :
+    (l.pmap f H).foldl g x = l.attach.foldl (fun acc a => g acc (f a.1 (H _ a.2))) x := by
+  rw [pmap_eq_map_attach, foldl_map]
+
+theorem foldr_pmap (l : Array α) {P : α → Prop} (f : (a : α) → P a → β)
+  (H : ∀ (a : α), a ∈ l → P a) (g : β → γ → γ) (x : γ) :
+    (l.pmap f H).foldr g x = l.attach.foldr (fun a acc => g (f a.1 (H _ a.2)) acc) x := by
+  rw [pmap_eq_map_attach, foldr_map]
+
+/--
+If we fold over `l.attach` with a function that ignores the membership predicate,
+we get the same results as folding over `l` directly.
+
+This is useful when we need to use `attach` to show termination.
+
+Unfortunately this can't be applied by `simp` because of the higher order unification problem,
+and even when rewriting we need to specify the function explicitly.
+See however `foldl_subtype` below.
+-/
+theorem foldl_attach (l : Array α) (f : β → α → β) (b : β) :
+    l.attach.foldl (fun acc t => f acc t.1) b = l.foldl f b := by
+  rcases l with ⟨l⟩
+  simp only [List.attach_toArray, List.attachWith_mem_toArray, List.map_attach, size_toArray,
+    List.length_pmap, List.foldl_toArray', mem_toArray, List.foldl_subtype]
+  congr
+  ext
+  simpa using fun a => List.mem_of_getElem? a
+
+/--
+If we fold over `l.attach` with a function that ignores the membership predicate,
+we get the same results as folding over `l` directly.
+
+This is useful when we need to use `attach` to show termination.
+
+Unfortunately this can't be applied by `simp` because of the higher order unification problem,
+and even when rewriting we need to specify the function explicitly.
+See however `foldr_subtype` below.
+-/
+theorem foldr_attach (l : Array α) (f : α → β → β) (b : β) :
+    l.attach.foldr (fun t acc => f t.1 acc) b = l.foldr f b := by
+  rcases l with ⟨l⟩
+  simp only [List.attach_toArray, List.attachWith_mem_toArray, List.map_attach, size_toArray,
+    List.length_pmap, List.foldr_toArray', mem_toArray, List.foldr_subtype]
+  congr
+  ext
+  simpa using fun a => List.mem_of_getElem? a
+
+theorem attach_map {l : Array α} (f : α → β) :
+    (l.map f).attach = l.attach.map (fun ⟨x, h⟩ => ⟨f x, mem_map_of_mem f h⟩) := by
+  cases l
+  ext <;> simp
+
+theorem attachWith_map {l : Array α} (f : α → β) {P : β → Prop} {H : ∀ (b : β), b ∈ l.map f → P b} :
+    (l.map f).attachWith P H = (l.attachWith (P ∘ f) (fun _ h => H _ (mem_map_of_mem f h))).map
+      fun ⟨x, h⟩ => ⟨f x, h⟩ := by
+  cases l
+  ext
+  · simp
+  · simp only [List.map_toArray, List.attachWith_toArray, List.getElem_toArray,
+      List.getElem_attachWith, List.getElem_map, Function.comp_apply]
+    erw [List.getElem_attachWith] -- Why is `erw` needed here?
+
+theorem map_attachWith {l : Array α} {P : α → Prop} {H : ∀ (a : α), a ∈ l → P a}
+    (f : { x // P x } → β) :
+    (l.attachWith P H).map f =
+      l.pmap (fun a (h : a ∈ l ∧ P a) => f ⟨a, H _ h.1⟩) (fun a h => ⟨h, H a h⟩) := by
+  cases l
+  ext <;> simp
+
+/-- See also `pmap_eq_map_attach` for writing `pmap` in terms of `map` and `attach`. -/
+theorem map_attach {l : Array α} (f : { x // x ∈ l } → β) :
+    l.attach.map f = l.pmap (fun a h => f ⟨a, h⟩) (fun _ => id) := by
+  cases l
+  ext <;> simp
+
+theorem attach_filterMap {l : Array α} {f : α → Option β} :
+    (l.filterMap f).attach = l.attach.filterMap
+      fun ⟨x, h⟩ => (f x).pbind (fun b m => some ⟨b, mem_filterMap.mpr ⟨x, h, m⟩⟩) := by
+  cases l
+  rw [attach_congr (List.filterMap_toArray f _)]
+  simp [List.attach_filterMap, List.map_filterMap, Function.comp_def]
+
+theorem attach_filter {l : Array α} (p : α → Bool) :
+    (l.filter p).attach = l.attach.filterMap
+      fun x => if w : p x.1 then some ⟨x.1, mem_filter.mpr ⟨x.2, w⟩⟩ else none := by
+  cases l
+  rw [attach_congr (List.filter_toArray p _)]
+  simp [List.attach_filter, List.map_filterMap, Function.comp_def]
+
+-- We are still missing here `attachWith_filterMap` and `attachWith_filter`.
+-- Also missing are `filterMap_attach`, `filter_attach`, `filterMap_attachWith` and `filter_attachWith`.
+
+theorem pmap_pmap {p : α → Prop} {q : β → Prop} (g : ∀ a, p a → β) (f : ∀ b, q b → γ) (l H₁ H₂) :
+    pmap f (pmap g l H₁) H₂ =
+      pmap (α := { x // x ∈ l }) (fun a h => f (g a h) (H₂ (g a h) (mem_pmap_of_mem a.2))) l.attach
+        (fun a _ => H₁ a a.2) := by
+  cases l
+  simp [List.pmap_pmap, List.pmap_map]
+
+@[simp] theorem pmap_append {p : ι → Prop} (f : ∀ a : ι, p a → α) (l₁ l₂ : Array ι)
+    (h : ∀ a ∈ l₁ ++ l₂, p a) :
+    (l₁ ++ l₂).pmap f h =
+      (l₁.pmap f fun a ha => h a (mem_append_left l₂ ha)) ++
+        l₂.pmap f fun a ha => h a (mem_append_right l₁ ha) := by
+  cases l₁
+  cases l₂
+  simp
+
+theorem pmap_append' {p : α → Prop} (f : ∀ a : α, p a → β) (l₁ l₂ : Array α)
+    (h₁ : ∀ a ∈ l₁, p a) (h₂ : ∀ a ∈ l₂, p a) :
+    ((l₁ ++ l₂).pmap f fun a ha => (mem_append.1 ha).elim (h₁ a) (h₂ a)) =
+      l₁.pmap f h₁ ++ l₂.pmap f h₂ :=
+  pmap_append f l₁ l₂ _
+
+@[simp] theorem attach_append (xs ys : Array α) :
+    (xs ++ ys).attach = xs.attach.map (fun ⟨x, h⟩ => ⟨x, mem_append_left ys h⟩) ++
+      ys.attach.map fun ⟨x, h⟩ => ⟨x, mem_append_right xs h⟩ := by
+  cases xs
+  cases ys
+  rw [attach_congr (List.append_toArray _ _)]
+  simp [List.attach_append, Function.comp_def]
+
+@[simp] theorem attachWith_append {P : α → Prop} {xs ys : Array α}
+    {H : ∀ (a : α), a ∈ xs ++ ys → P a} :
+    (xs ++ ys).attachWith P H = xs.attachWith P (fun a h => H a (mem_append_left ys h)) ++
+      ys.attachWith P (fun a h => H a (mem_append_right xs h)) := by
+  simp [attachWith, attach_append, map_pmap, pmap_append]
+
+@[simp] theorem pmap_reverse {P : α → Prop} (f : (a : α) → P a → β) (xs : Array α)
+    (H : ∀ (a : α), a ∈ xs.reverse → P a) :
+    xs.reverse.pmap f H = (xs.pmap f (fun a h => H a (by simpa using h))).reverse := by
+  induction xs <;> simp_all
+
+theorem reverse_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : Array α)
+    (H : ∀ (a : α), a ∈ xs → P a) :
+    (xs.pmap f H).reverse = xs.reverse.pmap f (fun a h => H a (by simpa using h)) := by
+  rw [pmap_reverse]
+
+@[simp] theorem attachWith_reverse {P : α → Prop} {xs : Array α}
+    {H : ∀ (a : α), a ∈ xs.reverse → P a} :
+    xs.reverse.attachWith P H =
+      (xs.attachWith P (fun a h => H a (by simpa using h))).reverse := by
+  cases xs
+  simp
+
+theorem reverse_attachWith {P : α → Prop} {xs : Array α}
+    {H : ∀ (a : α), a ∈ xs → P a} :
+    (xs.attachWith P H).reverse = (xs.reverse.attachWith P (fun a h => H a (by simpa using h))) := by
+  cases xs
+  simp
+
+@[simp] theorem attach_reverse (xs : Array α) :
+    xs.reverse.attach = xs.attach.reverse.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
+  cases xs
+  rw [attach_congr (List.reverse_toArray _)]
+  simp
+
+theorem reverse_attach (xs : Array α) :
+    xs.attach.reverse = xs.reverse.attach.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
+  cases xs
+  simp
+
+@[simp] theorem back?_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : Array α)
+    (H : ∀ (a : α), a ∈ xs → P a) :
+    (xs.pmap f H).back? = xs.attach.back?.map fun ⟨a, m⟩ => f a (H a m) := by
+  cases xs
+  simp
+
+@[simp] theorem back?_attachWith {P : α → Prop} {xs : Array α}
+    {H : ∀ (a : α), a ∈ xs → P a} :
+    (xs.attachWith P H).back? = xs.back?.pbind (fun a h => some ⟨a, H _ (mem_of_back?_eq_some h)⟩) := by
+  cases xs
+  simp
+
+@[simp]
+theorem back?_attach {xs : Array α} :
+    xs.attach.back? = xs.back?.pbind fun a h => some ⟨a, mem_of_back?_eq_some h⟩ := by
+  cases xs
+  simp
+
 /-! ## unattach
 
 `Array.unattach` is the (one-sided) inverse of `Array.attach`. It is a synonym for `Array.map Subtype.val`.
@@ -83,7 +479,7 @@ def unattach {α : Type _} {p : α → Prop} (l : Array { x // p x }) := l.map (
 
 @[simp] theorem unattach_attach {l : Array α} : l.attach.unattach = l := by
   cases l
-  simp
+  simp only [List.attach_toArray, List.unattach_toArray, List.unattach_attachWith]
 
 @[simp] theorem unattach_attachWith {p : α → Prop} {l : Array α}
     {H : ∀ a ∈ l, p a} :
@@ -91,6 +487,15 @@ def unattach {α : Type _} {p : α → Prop} (l : Array { x // p x }) := l.map (
   cases l
   simp
 
+@[simp] theorem getElem?_unattach {p : α → Prop} {l : Array { x // p x }} (i : Nat) :
+    l.unattach[i]? = l[i]?.map Subtype.val := by
+  simp [unattach]
+
+@[simp] theorem getElem_unattach
+    {p : α → Prop} {l : Array { x // p x }} (i : Nat) (h : i < l.unattach.size) :
+    l.unattach[i] = (l[i]'(by simpa using h)).1 := by
+  simp [unattach]
+
 /-! ### Recognizing higher order functions using a function that only depends on the value. -/
 
 /--

src/Init/Data/Array/Bootstrap.lean

@@ -15,26 +15,26 @@ This file contains some theorems about `Array` and `List` needed for `Init.Data.
 
 namespace Array
 
-theorem foldlM_eq_foldlM_toList.aux [Monad m]
+theorem foldlM_toList.aux [Monad m]
     (f : β → α → m β) (arr : Array α) (i j) (H : arr.size ≤ i + j) (b) :
     foldlM.loop f arr arr.size (Nat.le_refl _) i j b = (arr.toList.drop j).foldlM f b := by
   unfold foldlM.loop
   split; split
   · cases Nat.not_le_of_gt ‹_› (Nat.zero_add _ ▸ H)
   · rename_i i; rw [Nat.succ_add] at H
-    simp [foldlM_eq_foldlM_toList.aux f arr i (j+1) H]
+    simp [foldlM_toList.aux f arr i (j+1) H]
     rw (occs := .pos [2]) [← List.getElem_cons_drop_succ_eq_drop ‹_›]
     rfl
   · rw [List.drop_of_length_le (Nat.ge_of_not_lt ‹_›)]; rfl
 
-theorem foldlM_eq_foldlM_toList [Monad m]
+@[simp] theorem foldlM_toList [Monad m]
     (f : β → α → m β) (init : β) (arr : Array α) :
-    arr.foldlM f init = arr.toList.foldlM f init := by
-  simp [foldlM, foldlM_eq_foldlM_toList.aux]
+    arr.toList.foldlM f init = arr.foldlM f init := by
+  simp [foldlM, foldlM_toList.aux]
 
-theorem foldl_eq_foldl_toList (f : β → α → β) (init : β) (arr : Array α) :
-    arr.foldl f init = arr.toList.foldl f init :=
-  List.foldl_eq_foldlM .. ▸ foldlM_eq_foldlM_toList ..
+@[simp] theorem foldl_toList (f : β → α → β) (init : β) (arr : Array α) :
+    arr.toList.foldl f init = arr.foldl f init :=
+  List.foldl_eq_foldlM .. ▸ foldlM_toList ..
 
 theorem foldrM_eq_reverse_foldlM_toList.aux [Monad m]
     (f : α → β → m β) (arr : Array α) (init : β) (i h) :
@@ -51,23 +51,23 @@ theorem foldrM_eq_reverse_foldlM_toList [Monad m] (f : α → β → m β) (init
   match arr, this with | _, .inl rfl => rfl | arr, .inr h => ?_
   simp [foldrM, h, ← foldrM_eq_reverse_foldlM_toList.aux, List.take_length]
 
-theorem foldrM_eq_foldrM_toList [Monad m]
+@[simp] theorem foldrM_toList [Monad m]
     (f : α → β → m β) (init : β) (arr : Array α) :
-    arr.foldrM f init = arr.toList.foldrM f init := by
+    arr.toList.foldrM f init = arr.foldrM f init := by
   rw [foldrM_eq_reverse_foldlM_toList, List.foldlM_reverse]
 
-theorem foldr_eq_foldr_toList (f : α → β → β) (init : β) (arr : Array α) :
-    arr.foldr f init = arr.toList.foldr f init :=
-  List.foldr_eq_foldrM .. ▸ foldrM_eq_foldrM_toList ..
+@[simp] theorem foldr_toList (f : α → β → β) (init : β) (arr : Array α) :
+    arr.toList.foldr f init = arr.foldr f init :=
+  List.foldr_eq_foldrM .. ▸ foldrM_toList ..
 
 @[simp] theorem push_toList (arr : Array α) (a : α) : (arr.push a).toList = arr.toList ++ [a] := by
   simp [push, List.concat_eq_append]
 
 @[simp] theorem toListAppend_eq (arr : Array α) (l) : arr.toListAppend l = arr.toList ++ l := by
-  simp [toListAppend, foldr_eq_foldr_toList]
+  simp [toListAppend, ← foldr_toList]
 
 @[simp] theorem toListImpl_eq (arr : Array α) : arr.toListImpl = arr.toList := by
-  simp [toListImpl, foldr_eq_foldr_toList]
+  simp [toListImpl, ← foldr_toList]
 
 @[simp] theorem pop_toList (arr : Array α) : arr.pop.toList = arr.toList.dropLast := rfl
 
@@ -76,7 +76,7 @@ theorem foldr_eq_foldr_toList (f : α → β → β) (init : β) (arr : Array α
 @[simp] theorem toList_append (arr arr' : Array α) :
     (arr ++ arr').toList = arr.toList ++ arr'.toList := by
   rw [← append_eq_append]; unfold Array.append
-  rw [foldl_eq_foldl_toList]
+  rw [← foldl_toList]
   induction arr'.toList generalizing arr <;> simp [*]
 
 @[simp] theorem toList_empty : (#[] : Array α).toList = [] := rfl
@@ -98,20 +98,44 @@ theorem foldr_eq_foldr_toList (f : α → β → β) (init : β) (arr : Array α
   rw [← appendList_eq_append]; unfold Array.appendList
   induction l generalizing arr <;> simp [*]
 
-@[deprecated foldlM_eq_foldlM_toList (since := "2024-09-09")]
-abbrev foldlM_eq_foldlM_data := @foldlM_eq_foldlM_toList
+@[deprecated "Use the reverse direction of `foldrM_toList`." (since := "2024-11-13")]
+theorem foldrM_eq_foldrM_toList [Monad m]
+    (f : α → β → m β) (init : β) (arr : Array α) :
+    arr.foldrM f init = arr.toList.foldrM f init := by
+  simp
 
-@[deprecated foldl_eq_foldl_toList (since := "2024-09-09")]
-abbrev foldl_eq_foldl_data := @foldl_eq_foldl_toList
+@[deprecated "Use the reverse direction of `foldlM_toList`." (since := "2024-11-13")]
+theorem foldlM_eq_foldlM_toList [Monad m]
+    (f : β → α → m β) (init : β) (arr : Array α) :
+    arr.foldlM f init = arr.toList.foldlM f init:= by
+  simp
+
+@[deprecated "Use the reverse direction of `foldr_toList`." (since := "2024-11-13")]
+theorem foldr_eq_foldr_toList
+    (f : α → β → β) (init : β) (arr : Array α) :
+    arr.foldr f init = arr.toList.foldr f init := by
+  simp
+
+@[deprecated "Use the reverse direction of `foldl_toList`." (since := "2024-11-13")]
+theorem foldl_eq_foldl_toList
+    (f : β → α → β) (init : β) (arr : Array α) :
+    arr.foldl f init = arr.toList.foldl f init:= by
+  simp
+
+@[deprecated foldlM_toList (since := "2024-09-09")]
+abbrev foldlM_eq_foldlM_data := @foldlM_toList
+
+@[deprecated foldl_toList (since := "2024-09-09")]
+abbrev foldl_eq_foldl_data := @foldl_toList
 
 @[deprecated foldrM_eq_reverse_foldlM_toList (since := "2024-09-09")]
 abbrev foldrM_eq_reverse_foldlM_data := @foldrM_eq_reverse_foldlM_toList
 
-@[deprecated foldrM_eq_foldrM_toList (since := "2024-09-09")]
-abbrev foldrM_eq_foldrM_data := @foldrM_eq_foldrM_toList
+@[deprecated foldrM_toList (since := "2024-09-09")]
+abbrev foldrM_eq_foldrM_data := @foldrM_toList
 
-@[deprecated foldr_eq_foldr_toList (since := "2024-09-09")]
-abbrev foldr_eq_foldr_data := @foldr_eq_foldr_toList
+@[deprecated foldr_toList (since := "2024-09-09")]
+abbrev foldr_eq_foldr_data := @foldr_toList
 
 @[deprecated push_toList (since := "2024-09-09")]
 abbrev push_data := @push_toList

src/Init/Data/Array/Find.lean

@@ -0,0 +1,281 @@
+/-
+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]
+
+theorem find?_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : Array α)
+    (H : ∀ (a : α), a ∈ xs → P a) (p : β → Bool) :
+    (xs.pmap f H).find? p = (xs.attach.find? (fun ⟨a, m⟩ => p (f a (H a m)))).map fun ⟨a, m⟩ => f a (H a m) := by
+  simp only [pmap_eq_map_attach, find?_map]
+  rfl
+
+end Array

src/Init/Data/Array/Lemmas.lean

@@ -23,6 +23,9 @@ import Init.TacticsExtra
 
 namespace Array
 
+@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l := by
+  simp [mem_def]
+
 @[simp] theorem getElem_mk {xs : List α} {i : Nat} (h : i < xs.length) : (Array.mk xs)[i] = xs[i] := rfl
 
 theorem getElem_eq_getElem_toList {a : Array α} (h : i < a.size) : a[i] = a.toList[i] := rfl
@@ -36,12 +39,21 @@ theorem getElem?_eq_getElem {a : Array α} {i : Nat} (h : i < a.size) : a[i]? =
   · rw [getElem?_neg a i h]
     simp_all
 
+@[simp] theorem none_eq_getElem?_iff {a : Array α} {i : Nat} : none = a[i]? ↔ a.size ≤ i := by
+  simp [eq_comm (a := none)]
+
 theorem getElem?_eq {a : Array α} {i : Nat} :
     a[i]? = if h : i < a.size then some a[i] else none := by
   split
   · simp_all [getElem?_eq_getElem]
   · simp_all
 
+theorem getElem?_eq_some_iff {a : Array α} : a[i]? = some b ↔ ∃ h : i < a.size, a[i] = b := by
+  simp [getElem?_eq]
+
+theorem some_eq_getElem?_iff {a : Array α} : some b = a[i]? ↔ ∃ h : i < a.size, a[i] = b := by
+  rw [eq_comm, getElem?_eq_some_iff]
+
 theorem getElem?_eq_getElem?_toList (a : Array α) (i : Nat) : a[i]? = a.toList[i]? := by
   rw [getElem?_eq]
   split <;> simp_all
@@ -66,6 +78,35 @@ theorem getElem_push (a : Array α) (x : α) (i : Nat) (h : i < (a.push x).size)
 @[deprecated getElem_push_lt (since := "2024-10-21")] abbrev get_push_lt := @getElem_push_lt
 @[deprecated getElem_push_eq (since := "2024-10-21")] abbrev get_push_eq := @getElem_push_eq
 
+@[simp] theorem mem_push {a : Array α} {x y : α} : x ∈ a.push y ↔ x ∈ a ∨ x = y := by
+  simp [mem_def]
+
+theorem mem_push_self {a : Array α} {x : α} : x ∈ a.push x :=
+  mem_push.2 (Or.inr rfl)
+
+theorem mem_push_of_mem {a : Array α} {x : α} (y : α) (h : x ∈ a) : x ∈ a.push y :=
+  mem_push.2 (Or.inl h)
+
+theorem getElem_of_mem {a} {l : Array α} (h : a ∈ l) : ∃ (n : Nat) (h : n < l.size), l[n]'h = a := by
+  cases l
+  simp [List.getElem_of_mem (by simpa using h)]
+
+theorem getElem?_of_mem {a} {l : Array α} (h : a ∈ l) : ∃ n : Nat, l[n]? = some a :=
+  let ⟨n, _, e⟩ := getElem_of_mem h; ⟨n, e ▸ getElem?_eq_getElem _⟩
+
+theorem mem_of_getElem? {l : Array α} {n : Nat} {a : α} (e : l[n]? = some a) : a ∈ l :=
+  let ⟨_, e⟩ := getElem?_eq_some_iff.1 e; e ▸ getElem_mem ..
+
+theorem mem_iff_getElem {a} {l : Array α} : a ∈ l ↔ ∃ (n : Nat) (h : n < l.size), l[n]'h = a :=
+  ⟨getElem_of_mem, fun ⟨_, _, e⟩ => e ▸ getElem_mem ..⟩
+
+theorem mem_iff_getElem? {a} {l : Array α} : a ∈ l ↔ ∃ n : Nat, l[n]? = some a := by
+  simp [getElem?_eq_some_iff, mem_iff_getElem]
+
+theorem forall_getElem {l : Array α} {p : α → Prop} :
+    (∀ (n : Nat) h, p (l[n]'h)) ↔ ∀ a, a ∈ l → p a := by
+  cases l; simp [List.forall_getElem]
+
 @[simp] theorem get!_eq_getElem! [Inhabited α] (a : Array α) (i : Nat) : a.get! i = a[i]! := by
   simp [getElem!_def, get!, getD]
   split <;> rename_i h
@@ -93,9 +134,6 @@ We prefer to pull `List.toArray` outwards.
     (a.toArrayAux b).size = b.size + a.length := by
   simp [size]
 
-@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l := by
-  simp [mem_def]
-
 @[simp] theorem push_toArray (l : List α) (a : α) : l.toArray.push a = (l ++ [a]).toArray := by
   apply ext'
   simp
@@ -151,15 +189,15 @@ theorem foldrM_toArray [Monad m] (f : α → β → m β) (init : β) (l : List
 
 theorem foldlM_toArray [Monad m] (f : β → α → m β) (init : β) (l : List α) :
     l.toArray.foldlM f init = l.foldlM f init := by
-  rw [foldlM_eq_foldlM_toList]
+  rw [foldlM_toList]
 
 theorem foldr_toArray (f : α → β → β) (init : β) (l : List α) :
     l.toArray.foldr f init = l.foldr f init := by
-  rw [foldr_eq_foldr_toList]
+  rw [foldr_toList]
 
 theorem foldl_toArray (f : β → α → β) (init : β) (l : List α) :
     l.toArray.foldl f init = l.foldl f init := by
-  rw [foldl_eq_foldl_toList]
+  rw [foldl_toList]
 
 /-- Variant of `foldrM_toArray` with a side condition for the `start` argument. -/
 @[simp] theorem foldrM_toArray' [Monad m] (f : α → β → m β) (init : β) (l : List α)
@@ -174,21 +212,21 @@ theorem foldl_toArray (f : β → α → β) (init : β) (l : List α) :
     (h : stop = l.toArray.size) :
     l.toArray.foldlM f init 0 stop = l.foldlM f init := by
   subst h
-  rw [foldlM_eq_foldlM_toList]
+  rw [foldlM_toList]
 
 /-- Variant of `foldr_toArray` with a side condition for the `start` argument. -/
 @[simp] theorem foldr_toArray' (f : α → β → β) (init : β) (l : List α)
     (h : start = l.toArray.size) :
     l.toArray.foldr f init start 0 = l.foldr f init := by
   subst h
-  rw [foldr_eq_foldr_toList]
+  rw [foldr_toList]
 
 /-- Variant of `foldl_toArray` with a side condition for the `stop` argument. -/
 @[simp] theorem foldl_toArray' (f : β → α → β) (init : β) (l : List α)
     (h : stop = l.toArray.size) :
     l.toArray.foldl f init 0 stop = l.foldl f init := by
   subst h
-  rw [foldl_eq_foldl_toList]
+  rw [foldl_toList]
 
 @[simp] theorem append_toArray (l₁ l₂ : List α) :
     l₁.toArray ++ l₂.toArray = (l₁ ++ l₂).toArray := by
@@ -202,6 +240,9 @@ theorem foldl_toArray (f : β → α → β) (init : β) (l : List α) :
 @[simp] theorem foldl_push {l : List α} {as : Array α} : l.foldl Array.push as = as ++ l.toArray := by
   induction l generalizing as <;> simp [*]
 
+@[simp] theorem foldr_push {l : List α} {as : Array α} : l.foldr (fun a b => push b a) as = as ++ l.reverse.toArray := by
+  rw [foldr_eq_foldl_reverse, foldl_push]
+
 @[simp] theorem findSomeM?_toArray [Monad m] [LawfulMonad m] (f : α → m (Option β)) (l : List α) :
     l.toArray.findSomeM? f = l.findSomeM? f := by
   rw [Array.findSomeM?]
@@ -362,7 +403,8 @@ namespace Array
 
 theorem foldrM_push [Monad m] (f : α → β → m β) (init : β) (arr : Array α) (a : α) :
     (arr.push a).foldrM f init = f a init >>= arr.foldrM f := by
-  simp [foldrM_eq_reverse_foldlM_toList, -size_push]
+  simp only [foldrM_eq_reverse_foldlM_toList, push_toList, List.reverse_append, List.reverse_cons,
+    List.reverse_nil, List.nil_append, List.singleton_append, List.foldlM_cons, List.foldlM_reverse]
 
 /--
 Variant of `foldrM_push` with `h : start = arr.size + 1`
@@ -388,11 +430,11 @@ rather than `(arr.push a).size` as the argument.
 @[inline] def toListRev (arr : Array α) : List α := arr.foldl (fun l t => t :: l) []
 
 @[simp] theorem toListRev_eq (arr : Array α) : arr.toListRev = arr.toList.reverse := by
-  rw [toListRev, foldl_eq_foldl_toList, ← List.foldr_reverse, List.foldr_cons_nil]
+  rw [toListRev, ← foldl_toList, ← List.foldr_reverse, List.foldr_cons_nil]
 
 theorem mapM_eq_foldlM [Monad m] [LawfulMonad m] (f : α → m β) (arr : Array α) :
     arr.mapM f = arr.foldlM (fun bs a => bs.push <$> f a) #[] := by
-  rw [mapM, aux, foldlM_eq_foldlM_toList]; rfl
+  rw [mapM, aux, ← foldlM_toList]; rfl
 where
   aux (i r) :
       mapM.map f arr i r = (arr.toList.drop i).foldlM (fun bs a => bs.push <$> f a) r := by
@@ -407,7 +449,7 @@ where
 
 @[simp] theorem toList_map (f : α → β) (arr : Array α) : (arr.map f).toList = arr.toList.map f := by
   rw [map, mapM_eq_foldlM]
-  apply congrArg toList (foldl_eq_foldl_toList (fun bs a => push bs (f a)) #[] arr) |>.trans
+  apply congrArg toList (foldl_toList (fun bs a => push bs (f a)) #[] arr).symm |>.trans
   have H (l arr) : List.foldl (fun bs a => push bs (f a)) arr l = ⟨arr.toList ++ l.map f⟩ := by
     induction l generalizing arr <;> simp [*]
   simp [H]
@@ -597,38 +639,25 @@ 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
 
-theorem getElem_of_mem {a : α} {as : Array α} :
-    a ∈ as → (∃ (n : Nat) (h : n < as.size), as[n]'h = a) := by
-  intro ha
-  rcases List.getElem_of_mem ha.val with ⟨i, hbound, hi⟩
-  exists i
-  exists hbound
-
-theorem getElem?_of_mem {a : α} {as : Array α} :
-    a ∈ as → ∃ (n : Nat), as[n]? = some a := by
-  intro ha
-  rcases List.getElem?_of_mem ha.val with ⟨i, hi⟩
-  exists i
-
 @[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 -/
 
@@ -655,10 +684,6 @@ theorem get?_eq_get?_toList (a : Array α) (i : Nat) : a.get? i = a.toList.get?
 theorem get!_eq_get? [Inhabited α] (a : Array α) : a.get! n = (a.get? n).getD default := by
   simp only [get!_eq_getElem?, get?_eq_getElem?]
 
-theorem getElem?_eq_some_iff {as : Array α} : as[n]? = some a ↔ ∃ h : n < as.size, as[n] = a := by
-  cases as
-  simp [List.getElem?_eq_some_iff]
-
 theorem back!_eq_back? [Inhabited α] (a : Array α) : a.back! = a.back?.getD default := by
   simp only [back!, get!_eq_getElem?, get?_eq_getElem?, back?]
 
@@ -668,6 +693,10 @@ theorem back!_eq_back? [Inhabited α] (a : Array α) : a.back! = a.back?.getD de
 @[simp] theorem back!_push [Inhabited α] (a : Array α) : (a.push x).back! = x := by
   simp [back!_eq_back?]
 
+theorem mem_of_back?_eq_some {xs : Array α} {a : α} (h : xs.back? = some a) : a ∈ xs := by
+  cases xs
+  simpa using List.mem_of_getLast?_eq_some (by simpa using h)
+
 theorem getElem?_push_lt (a : Array α) (x : α) (i : Nat) (h : i < a.size) :
     (a.push x)[i]? = some a[i] := by
   rw [getElem?_pos, getElem_push_lt]
@@ -1021,9 +1050,13 @@ theorem foldr_congr {as bs : Array α} (h₀ : as = bs) {f g : α → β → β}
 @[simp] theorem mem_map {f : α → β} {l : Array α} : b ∈ l.map f ↔ ∃ a, a ∈ l ∧ f a = b := by
   simp only [mem_def, toList_map, List.mem_map]
 
+theorem exists_of_mem_map (h : b ∈ map f l) : ∃ a, a ∈ l ∧ f a = b := mem_map.1 h
+
+theorem mem_map_of_mem (f : α → β) (h : a ∈ l) : f a ∈ map f l := mem_map.2 ⟨_, h, rfl⟩
+
 theorem mapM_eq_mapM_toList [Monad m] [LawfulMonad m] (f : α → m β) (arr : Array α) :
     arr.mapM f = List.toArray <$> (arr.toList.mapM f) := by
-  rw [mapM_eq_foldlM, foldlM_eq_foldlM_toList, ← List.foldrM_reverse]
+  rw [mapM_eq_foldlM, ← foldlM_toList, ← List.foldrM_reverse]
   conv => rhs; rw [← List.reverse_reverse arr.toList]
   induction arr.toList.reverse with
   | nil => simp
@@ -1148,7 +1181,7 @@ theorem getElem?_modify {as : Array α} {i : Nat} {f : α → α} {j : Nat} :
 @[simp] theorem toList_filter (p : α → Bool) (l : Array α) :
     (l.filter p).toList = l.toList.filter p := by
   dsimp only [filter]
-  rw [foldl_eq_foldl_toList]
+  rw [← foldl_toList]
   generalize l.toList = l
   suffices ∀ a, (List.foldl (fun r a => if p a = true then push r a else r) a l).toList =
       a.toList ++ List.filter p l by
@@ -1179,7 +1212,7 @@ theorem filter_congr {as bs : Array α} (h : as = bs)
 @[simp] theorem toList_filterMap (f : α → Option β) (l : Array α) :
     (l.filterMap f).toList = l.toList.filterMap f := by
   dsimp only [filterMap, filterMapM]
-  rw [foldlM_eq_foldlM_toList]
+  rw [← foldlM_toList]
   generalize l.toList = l
   have this : ∀ a : Array β, (Id.run (List.foldlM (m := Id) ?_ a l)).toList =
     a.toList ++ List.filterMap f l := ?_
@@ -1211,9 +1244,23 @@ theorem push_eq_append_singleton (as : Array α) (x) : as.push x = as ++ #[x] :=
 @[simp] theorem mem_append {a : α} {s t : Array α} : a ∈ s ++ t ↔ a ∈ s ∨ a ∈ t := by
   simp only [mem_def, toList_append, List.mem_append]
 
+theorem mem_append_left {a : α} {l₁ : Array α} (l₂ : Array α) (h : a ∈ l₁) : a ∈ l₁ ++ l₂ :=
+  mem_append.2 (Or.inl h)
+
+theorem mem_append_right {a : α} (l₁ : Array α) {l₂ : Array α} (h : a ∈ l₂) : a ∈ l₁ ++ l₂ :=
+  mem_append.2 (Or.inr h)
+
 @[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
@@ -1258,7 +1305,7 @@ theorem getElem?_append {as bs : Array α} {n : Nat} :
 @[simp] theorem toList_flatten {l : Array (Array α)} :
     l.flatten.toList = (l.toList.map toList).flatten := by
   dsimp [flatten]
-  simp only [foldl_eq_foldl_toList]
+  simp only [← foldl_toList]
   generalize l.toList = l
   have : ∀ a : Array α, (List.foldl ?_ a l).toList = a.toList ++ ?_ := ?_
   exact this #[]
@@ -1872,6 +1919,76 @@ namespace Array
   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
+
+theorem foldl_map (f : β₁ → β₂) (g : α → β₂ → α) (l : Array β₁) (init : α) :
+    (l.map f).foldl g init = l.foldl (fun x y => g x (f y)) init := by
+  cases l; simp [List.foldl_map]
+
+theorem foldr_map (f : α₁ → α₂) (g : α₂ → β → β) (l : Array α₁) (init : β) :
+    (l.map f).foldr g init = l.foldr (fun x y => g (f x) y) init := by
+  cases l; simp [List.foldr_map]
+
+theorem foldl_filterMap (f : α → Option β) (g : γ → β → γ) (l : Array α) (init : γ) :
+    (l.filterMap f).foldl g init = l.foldl (fun x y => match f y with | some b => g x b | none => x) init := by
+  cases l
+  simp [List.foldl_filterMap]
+  rfl
+
+theorem foldr_filterMap (f : α → Option β) (g : β → γ → γ) (l : Array α) (init : γ) :
+    (l.filterMap f).foldr g init = l.foldr (fun x y => match f x with | some b => g b y | none => y) init := by
+  cases l
+  simp [List.foldr_filterMap]
+  rfl
+
+/-! ### 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]
+
+/-! ### reverse -/
+
+@[simp] theorem mem_reverse {x : α} {as : Array α} : x ∈ as.reverse ↔ x ∈ as := by
+  cases as
+  simp
+
 /-! ### findSomeRevM?, findRevM?, findSomeRev?, findRev? -/
 
 @[simp] theorem findSomeRevM?_eq_findSomeM?_reverse
@@ -1936,6 +2053,27 @@ 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/Array/Monadic.lean

@@ -0,0 +1,159 @@
+/-
+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.Array.Lemmas
+import Init.Data.Array.Attach
+import Init.Data.List.Monadic
+
+/-!
+# Lemmas about `Array.forIn'` and `Array.forIn`.
+-/
+
+namespace Array
+
+open Nat
+
+/-! ## Monadic operations -/
+
+/-! ### mapM -/
+
+theorem mapM_eq_foldlM_push [Monad m] [LawfulMonad m] (f : α → m β) (l : Array α) :
+    mapM f l = l.foldlM (fun acc a => return (acc.push (← f a))) #[] := by
+  rcases l with ⟨l⟩
+  simp only [List.mapM_toArray, bind_pure_comp, size_toArray, List.foldlM_toArray']
+  rw [List.mapM_eq_reverse_foldlM_cons]
+  simp only [bind_pure_comp, Functor.map_map]
+  suffices ∀ (k), (fun a => a.reverse.toArray) <$> List.foldlM (fun acc a => (fun a => a :: acc) <$> f a) k l =
+      List.foldlM (fun acc a => acc.push <$> f a) k.reverse.toArray l by
+    exact this []
+  intro k
+  induction l generalizing k with
+  | nil => simp
+  | cons a as ih =>
+    simp [ih, List.foldlM_cons]
+
+/-! ### foldlM and foldrM -/
+
+theorem foldlM_map [Monad m] (f : β₁ → β₂) (g : α → β₂ → m α) (l : Array β₁) (init : α) :
+    (l.map f).foldlM g init = l.foldlM (fun x y => g x (f y)) init := by
+  cases l
+  rw [List.map_toArray] -- Why doesn't this fire via `simp`?
+  simp [List.foldlM_map]
+
+theorem foldrM_map [Monad m] [LawfulMonad m] (f : β₁ → β₂) (g : β₂ → α → m α) (l : Array β₁)
+    (init : α) : (l.map f).foldrM g init = l.foldrM (fun x y => g (f x) y) init := by
+  cases l
+  rw [List.map_toArray] -- Why doesn't this fire via `simp`?
+  simp [List.foldrM_map]
+
+theorem foldlM_filterMap [Monad m] [LawfulMonad m] (f : α → Option β) (g : γ → β → m γ) (l : Array α) (init : γ) :
+    (l.filterMap f).foldlM g init =
+      l.foldlM (fun x y => match f y with | some b => g x b | none => pure x) init := by
+  cases l
+  rw [List.filterMap_toArray] -- Why doesn't this fire via `simp`?
+  simp [List.foldlM_filterMap]
+  rfl
+
+theorem foldrM_filterMap [Monad m] [LawfulMonad m] (f : α → Option β) (g : β → γ → m γ) (l : Array α) (init : γ) :
+    (l.filterMap f).foldrM g init =
+      l.foldrM (fun x y => match f x with | some b => g b y | none => pure y) init := by
+  cases l
+  rw [List.filterMap_toArray] -- Why doesn't this fire via `simp`?
+  simp [List.foldrM_filterMap]
+  rfl
+
+theorem foldlM_filter [Monad m] [LawfulMonad m] (p : α → Bool) (g : β → α → m β) (l : Array α) (init : β) :
+    (l.filter p).foldlM g init =
+      l.foldlM (fun x y => if p y then g x y else pure x) init := by
+  cases l
+  rw [List.filter_toArray] -- Why doesn't this fire via `simp`?
+  simp [List.foldlM_filter]
+
+theorem foldrM_filter [Monad m] [LawfulMonad m] (p : α → Bool) (g : α → β → m β) (l : Array α) (init : β) :
+    (l.filter p).foldrM g init =
+      l.foldrM (fun x y => if p x then g x y else pure y) init := by
+  cases l
+  rw [List.filter_toArray] -- Why doesn't this fire via `simp`?
+  simp [List.foldrM_filter]
+
+/-! ### forIn' -/
+
+/--
+We can express a for loop over an array as a fold,
+in which whenever we reach `.done b` we keep that value through the rest of the fold.
+-/
+theorem forIn'_eq_foldlM [Monad m] [LawfulMonad m]
+    (l : Array α) (f : (a : α) → a ∈ l → β → m (ForInStep β)) (init : β) :
+    forIn' l init f = ForInStep.value <$>
+      l.attach.foldlM (fun b ⟨a, m⟩ => match b with
+        | .yield b => f a m b
+        | .done b => pure (.done b)) (ForInStep.yield init) := by
+  cases l
+  rw [List.attach_toArray] -- Why doesn't this fire via `simp`?
+  simp only [List.forIn'_toArray, List.forIn'_eq_foldlM, List.attachWith_mem_toArray, size_toArray,
+    List.length_map, List.length_attach, List.foldlM_toArray', List.foldlM_map]
+  congr
+
+/-- We can express a for loop over an array which always yields as a fold. -/
+@[simp] theorem forIn'_yield_eq_foldlM [Monad m] [LawfulMonad m]
+    (l : Array α) (f : (a : α) → a ∈ l → β → m γ) (g : (a : α) → a ∈ l → β → γ → β) (init : β) :
+    forIn' l init (fun a m b => (fun c => .yield (g a m b c)) <$> f a m b) =
+      l.attach.foldlM (fun b ⟨a, m⟩ => g a m b <$> f a m b) init := by
+  cases l
+  rw [List.attach_toArray] -- Why doesn't this fire via `simp`?
+  simp [List.foldlM_map]
+
+theorem forIn'_pure_yield_eq_foldl [Monad m] [LawfulMonad m]
+    (l : Array α) (f : (a : α) → a ∈ l → β → β) (init : β) :
+    forIn' l init (fun a m b => pure (.yield (f a m b))) =
+      pure (f := m) (l.attach.foldl (fun b ⟨a, h⟩ => f a h b) init) := by
+  cases l
+  simp [List.forIn'_pure_yield_eq_foldl, List.foldl_map]
+
+@[simp] theorem forIn'_yield_eq_foldl
+    (l : Array α) (f : (a : α) → a ∈ l → β → β) (init : β) :
+    forIn' (m := Id) l init (fun a m b => .yield (f a m b)) =
+      l.attach.foldl (fun b ⟨a, h⟩ => f a h b) init := by
+  cases l
+  simp [List.foldl_map]
+
+/--
+We can express a for loop over an array as a fold,
+in which whenever we reach `.done b` we keep that value through the rest of the fold.
+-/
+theorem forIn_eq_foldlM [Monad m] [LawfulMonad m]
+    (f : α → β → m (ForInStep β)) (init : β) (l : Array α) :
+    forIn l init f = ForInStep.value <$>
+      l.foldlM (fun b a => match b with
+        | .yield b => f a b
+        | .done b => pure (.done b)) (ForInStep.yield init) := by
+  cases l
+  simp only [List.forIn_toArray, List.forIn_eq_foldlM, size_toArray, List.foldlM_toArray']
+  congr
+
+/-- We can express a for loop over an array which always yields as a fold. -/
+@[simp] theorem forIn_yield_eq_foldlM [Monad m] [LawfulMonad m]
+    (l : Array α) (f : α → β → m γ) (g : α → β → γ → β) (init : β) :
+    forIn l init (fun a b => (fun c => .yield (g a b c)) <$> f a b) =
+      l.foldlM (fun b a => g a b <$> f a b) init := by
+  cases l
+  simp [List.foldlM_map]
+
+theorem forIn_pure_yield_eq_foldl [Monad m] [LawfulMonad m]
+    (l : Array α) (f : α → β → β) (init : β) :
+    forIn l init (fun a b => pure (.yield (f a b))) =
+      pure (f := m) (l.foldl (fun b a => f a b) init) := by
+  cases l
+  simp [List.forIn_pure_yield_eq_foldl, List.foldl_map]
+
+@[simp] theorem forIn_yield_eq_foldl
+    (l : Array α) (f : α → β → β) (init : β) :
+    forIn (m := Id) l init (fun a b => .yield (f a b)) =
+      l.foldl (fun b a => f a b) init := by
+  cases l
+  simp [List.foldl_map]
+
+end Array

src/Init/Data/Array/Subarray.lean

@@ -15,15 +15,6 @@ structure Subarray (α : Type u)  where
   start_le_stop : start ≤ stop
   stop_le_array_size : stop ≤ array.size
 
-@[deprecated Subarray.array (since := "2024-04-13")]
-abbrev Subarray.as (s : Subarray α) : Array α := s.array
-
-@[deprecated Subarray.start_le_stop (since := "2024-04-13")]
-theorem Subarray.h₁ (s : Subarray α) : s.start ≤ s.stop := s.start_le_stop
-
-@[deprecated Subarray.stop_le_array_size (since := "2024-04-13")]
-theorem Subarray.h₂ (s : Subarray α) : s.stop ≤ s.array.size := s.stop_le_array_size
-
 namespace Subarray
 
 def size (s : Subarray α) : Nat :=

src/Init/Data/BitVec/Basic.lean

@@ -29,9 +29,6 @@ section Nat
 
 instance natCastInst : NatCast (BitVec w) := ⟨BitVec.ofNat w⟩
 
-@[deprecated isLt (since := "2024-03-12")]
-theorem toNat_lt (x : BitVec n) : x.toNat < 2^n := x.isLt
-
 /-- Theorem for normalizing the bit vector literal representation. -/
 -- TODO: This needs more usage data to assess which direction the simp should go.
 @[simp, bv_toNat] theorem ofNat_eq_ofNat : @OfNat.ofNat (BitVec n) i _ = .ofNat n i := rfl

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/Fin/Lemmas.lean

@@ -642,7 +642,7 @@ theorem pred_add_one (i : Fin (n + 2)) (h : (i : Nat) < n + 1) :
   ext
   simp
 
-@[simp] theorem subNat_one_succ (i : Fin (n + 1)) (h : 1 ≤ ↑i) : (subNat 1 i h).succ = i := by
+@[simp] theorem subNat_one_succ (i : Fin (n + 1)) (h : 1 ≤ (i : Nat)) : (subNat 1 i h).succ = i := by
   ext
   simp
   omega

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

@@ -13,7 +13,7 @@ namespace List
   `a : α` satisfying `P`, then `pmap f l h` is essentially the same as `map f l`
   but is defined only when all members of `l` satisfy `P`, using the proof
   to apply `f`. -/
-@[simp] def pmap {P : α → Prop} (f : ∀ a, P a → β) : ∀ l : List α, (H : ∀ a ∈ l, P a) → List β
+def pmap {P : α → Prop} (f : ∀ a, P a → β) : ∀ l : List α, (H : ∀ a ∈ l, P a) → List β
   | [], _ => []
   | a :: l, H => f a (forall_mem_cons.1 H).1 :: pmap f l (forall_mem_cons.1 H).2
 
@@ -46,6 +46,11 @@ Unsafe implementation of `attachWith`, taking advantage of the fact that the rep
   | cons _ L', hL' => congrArg _ <| go L' fun _ hx => hL' (.tail _ hx)
   exact go L h'
 
+@[simp] theorem pmap_nil {P : α → Prop} (f : ∀ a, P a → β) : pmap f [] (by simp) = [] := rfl
+
+@[simp] theorem pmap_cons {P : α → Prop} (f : ∀ a, P a → β) (a : α) (l : List α) (h : ∀ b ∈ a :: l, P b) :
+    pmap f (a :: l) h = f a (forall_mem_cons.1 h).1 :: pmap f l (forall_mem_cons.1 h).2 := rfl
+
 @[simp] theorem attach_nil : ([] : List α).attach = [] := rfl
 
 @[simp] theorem attachWith_nil : ([] : List α).attachWith P H = [] := rfl
@@ -148,7 +153,7 @@ theorem mem_pmap_of_mem {p : α → Prop} {f : ∀ a, p a → β} {l H} {a} (h :
   exact ⟨a, h, rfl⟩
 
 @[simp]
-theorem length_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H} : length (pmap f l H) = length l := by
+theorem length_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H} : (pmap f l H).length = l.length := by
   induction l
   · rfl
   · simp only [*, pmap, length]
@@ -199,7 +204,7 @@ theorem attachWith_ne_nil_iff {l : List α} {P : α → Prop} {H : ∀ a ∈ l,
 
 @[simp]
 theorem getElem?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h : ∀ a ∈ l, p a) (n : Nat) :
-    (pmap f l h)[n]? = Option.pmap f l[n]? fun x H => h x (getElem?_mem H) := by
+    (pmap f l h)[n]? = Option.pmap f l[n]? fun x H => h x (mem_of_getElem? H) := by
   induction l generalizing n with
   | nil => simp
   | cons hd tl hl =>
@@ -215,7 +220,7 @@ theorem getElem?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h
       · simp_all
 
 theorem get?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h : ∀ a ∈ l, p a) (n : Nat) :
-    get? (pmap f l h) n = Option.pmap f (get? l n) fun x H => h x (get?_mem H) := by
+    get? (pmap f l h) n = Option.pmap f (get? l n) fun x H => h x (mem_of_get? H) := by
   simp only [get?_eq_getElem?]
   simp [getElem?_pmap, h]
 
@@ -238,18 +243,18 @@ 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 _ (getElem_mem (@length_pmap _ _ p f l h ▸ hn))) := by
   simp only [get_eq_getElem]
   simp [getElem_pmap]
 
 @[simp]
 theorem getElem?_attachWith {xs : List α} {i : Nat} {P : α → Prop} {H : ∀ a ∈ xs, P a} :
-    (xs.attachWith P H)[i]? = xs[i]?.pmap Subtype.mk (fun _ a => H _ (getElem?_mem a)) :=
+    (xs.attachWith P H)[i]? = xs[i]?.pmap Subtype.mk (fun _ a => H _ (mem_of_getElem? a)) :=
   getElem?_pmap ..
 
 @[simp]
 theorem getElem?_attach {xs : List α} {i : Nat} :
-    xs.attach[i]? = xs[i]?.pmap Subtype.mk (fun _ a => getElem?_mem a) :=
+    xs.attach[i]? = xs[i]?.pmap Subtype.mk (fun _ a => mem_of_getElem? a) :=
   getElem?_attachWith
 
 @[simp]
@@ -333,6 +338,7 @@ This is useful when we need to use `attach` to show termination.
 
 Unfortunately this can't be applied by `simp` because of the higher order unification problem,
 and even when rewriting we need to specify the function explicitly.
+See however `foldl_subtype` below.
 -/
 theorem foldl_attach (l : List α) (f : β → α → β) (b : β) :
     l.attach.foldl (fun acc t => f acc t.1) b = l.foldl f b := by
@@ -348,6 +354,7 @@ This is useful when we need to use `attach` to show termination.
 
 Unfortunately this can't be applied by `simp` because of the higher order unification problem,
 and even when rewriting we need to specify the function explicitly.
+See however `foldr_subtype` below.
 -/
 theorem foldr_attach (l : List α) (f : α → β → β) (b : β) :
     l.attach.foldr (fun t acc => f t.1 acc) b = l.foldr f b := by
@@ -452,16 +459,16 @@ theorem pmap_append' {p : α → Prop} (f : ∀ a : α, p a → β) (l₁ l₂ :
   pmap_append f l₁ l₂ _
 
 @[simp] theorem attach_append (xs ys : List α) :
-    (xs ++ ys).attach = xs.attach.map (fun ⟨x, h⟩ => ⟨x, mem_append_of_mem_left ys h⟩) ++
-      ys.attach.map fun ⟨x, h⟩ => ⟨x, mem_append_of_mem_right xs h⟩ := by
+    (xs ++ ys).attach = xs.attach.map (fun ⟨x, h⟩ => ⟨x, mem_append_left ys h⟩) ++
+      ys.attach.map fun ⟨x, h⟩ => ⟨x, mem_append_right xs h⟩ := by
   simp only [attach, attachWith, pmap, map_pmap, pmap_append]
   congr 1 <;>
   exact pmap_congr_left _ fun _ _ _ _ => rfl
 
 @[simp] theorem attachWith_append {P : α → Prop} {xs ys : List α}
     {H : ∀ (a : α), a ∈ xs ++ ys → P a} :
-    (xs ++ ys).attachWith P H = xs.attachWith P (fun a h => H a (mem_append_of_mem_left ys h)) ++
-      ys.attachWith P (fun a h => H a (mem_append_of_mem_right xs h)) := by
+    (xs ++ ys).attachWith P H = xs.attachWith P (fun a h => H a (mem_append_left ys h)) ++
+      ys.attachWith P (fun a h => H a (mem_append_right xs h)) := by
   simp only [attachWith, attach_append, map_pmap, pmap_append]
 
 @[simp] theorem pmap_reverse {P : α → Prop} (f : (a : α) → P a → β) (xs : List α)
@@ -598,6 +605,15 @@ def unattach {α : Type _} {p : α → Prop} (l : List { x // p x }) := l.map (
   | nil => simp
   | cons a l ih => simp [ih, Function.comp_def]
 
+@[simp] theorem getElem?_unattach {p : α → Prop} {l : List { x // p x }} (i : Nat) :
+    l.unattach[i]? = l[i]?.map Subtype.val := by
+  simp [unattach]
+
+@[simp] theorem getElem_unattach
+    {p : α → Prop} {l : List { x // p x }} (i : Nat) (h : i < l.unattach.length) :
+    l.unattach[i] = (l[i]'(by simpa using h)).1 := by
+  simp [unattach]
+
 /-! ### Recognizing higher order functions on subtypes using a function that only depends on the value. -/
 
 /--

src/Init/Data/List/Basic.lean

@@ -551,7 +551,7 @@ theorem reverseAux_eq_append (as bs : List α) : reverseAux as bs = reverseAux a
 /-! ### flatten -/
 
 /--
-`O(|flatten L|)`. `join L` concatenates all the lists in `L` into one list.
+`O(|flatten L|)`. `flatten L` concatenates all the lists in `L` into one list.
 * `flatten [[a], [], [b, c], [d, e, f]] = [a, b, c, d, e, f]`
 -/
 def flatten : List (List α) → List α
@@ -726,13 +726,13 @@ theorem elem_eq_true_of_mem [BEq α] [LawfulBEq α] {a : α} {as : List α} (h :
 instance [BEq α] [LawfulBEq α] (a : α) (as : List α) : Decidable (a ∈ as) :=
   decidable_of_decidable_of_iff (Iff.intro mem_of_elem_eq_true elem_eq_true_of_mem)
 
-theorem mem_append_of_mem_left {a : α} {as : List α} (bs : List α) : a ∈ as → a ∈ as ++ bs := by
+theorem mem_append_left {a : α} {as : List α} (bs : List α) : a ∈ as → a ∈ as ++ bs := by
   intro h
   induction h with
   | head => apply Mem.head
   | tail => apply Mem.tail; assumption
 
-theorem mem_append_of_mem_right {b : α} {bs : List α} (as : List α) : b ∈ bs → b ∈ as ++ bs := by
+theorem mem_append_right {b : α} {bs : List α} (as : List α) : b ∈ bs → b ∈ as ++ bs := by
   intro h
   induction as with
   | nil  => simp [h]

src/Init/Data/List/Control.lean

@@ -256,7 +256,7 @@ theorem findM?_eq_findSomeM? [Monad m] [LawfulMonad m] (p : α → m Bool) (as :
       have : a ∈ as := by
         have ⟨bs, h⟩ := h
         subst h
-        exact mem_append_of_mem_right _ (Mem.head ..)
+        exact mem_append_right _ (Mem.head ..)
       match (← f a this b) with
       | ForInStep.done b  => pure b
       | ForInStep.yield b =>

src/Init/Data/List/Impl.lean

@@ -91,7 +91,7 @@ The following operations are given `@[csimp]` replacements below:
 @[specialize] def foldrTR (f : α → β → β) (init : β) (l : List α) : β := l.toArray.foldr f init
 
 @[csimp] theorem foldr_eq_foldrTR : @foldr = @foldrTR := by
-  funext α β f init l; simp [foldrTR, Array.foldr_eq_foldr_toList, -Array.size_toArray]
+  funext α β f init l; simp [foldrTR, ← Array.foldr_toList, -Array.size_toArray]
 
 /-! ### flatMap  -/
 
@@ -331,7 +331,7 @@ def enumFromTR (n : Nat) (l : List α) : List (Nat × α) :=
     | a::as, n => by
       rw [← show _ + as.length = n + (a::as).length from Nat.succ_add .., foldr, go as]
       simp [enumFrom, f]
-  rw [Array.foldr_eq_foldr_toList]
+  rw [← Array.foldr_toList]
   simp [go]
 
 /-! ## Other list operations -/

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
@@ -383,9 +394,9 @@ theorem get?_concat_length (l : List α) (a : α) : (l ++ [a]).get? l.length = s
 theorem mem_cons_self (a : α) (l : List α) : a ∈ a :: l := .head ..
 
 theorem mem_concat_self (xs : List α) (a : α) : a ∈ xs ++ [a] :=
-  mem_append_of_mem_right xs (mem_cons_self a _)
+  mem_append_right xs (mem_cons_self a _)
 
-theorem mem_append_cons_self : a ∈ xs ++ a :: ys := mem_append_of_mem_right _ (mem_cons_self _ _)
+theorem mem_append_cons_self : a ∈ xs ++ a :: ys := mem_append_right _ (mem_cons_self _ _)
 
 theorem eq_append_cons_of_mem {a : α} {xs : List α} (h : a ∈ xs) :
     ∃ as bs, xs = as ++ a :: bs ∧ a ∉ as := by
@@ -492,16 +503,20 @@ 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 :=
+theorem mem_of_getElem? {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 ..
 
-theorem get?_mem {l : List α} {n a} (e : l.get? n = some a) : a ∈ l :=
+@[deprecated mem_of_getElem? (since := "2024-09-06")] abbrev getElem?_mem := @mem_of_getElem?
+
+theorem mem_of_get? {l : List α} {n a} (e : l.get? n = some a) : a ∈ l :=
   let ⟨_, e⟩ := get?_eq_some.1 e; e ▸ get_mem ..
 
+@[deprecated mem_of_get? (since := "2024-09-06")] abbrev get?_mem := @mem_of_get?
+
 theorem mem_iff_getElem {a} {l : List α} : a ∈ l ↔ ∃ (n : Nat) (h : n < l.length), l[n]'h = a :=
   ⟨getElem_of_mem, fun ⟨_, _, e⟩ => e ▸ getElem_mem ..⟩
 
@@ -1025,6 +1040,10 @@ 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 +1168,11 @@ 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
@@ -1977,11 +2001,8 @@ theorem not_mem_append {a : α} {s t : List α} (h₁ : a ∉ s) (h₂ : a ∉ t
 theorem mem_append_eq (a : α) (s t : List α) : (a ∈ s ++ t) = (a ∈ s ∨ a ∈ t) :=
   propext mem_append
 
-theorem mem_append_left {a : α} {l₁ : List α} (l₂ : List α) (h : a ∈ l₁) : a ∈ l₁ ++ l₂ :=
-  mem_append.2 (Or.inl h)
-
-theorem mem_append_right {a : α} (l₁ : List α) {l₂ : List α} (h : a ∈ l₂) : a ∈ l₁ ++ l₂ :=
-  mem_append.2 (Or.inr h)
+@[deprecated mem_append_left (since := "2024-11-20")] abbrev mem_append_of_mem_left := @mem_append_left
+@[deprecated mem_append_right (since := "2024-11-20")] abbrev mem_append_of_mem_right := @mem_append_right
 
 theorem mem_iff_append {a : α} {l : List α} : a ∈ l ↔ ∃ s t : List α, l = s ++ a :: t :=
   ⟨append_of_mem, fun ⟨s, t, e⟩ => e ▸ by simp⟩
@@ -2395,7 +2416,7 @@ 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/List/Sublist.lean

@@ -417,7 +417,7 @@ theorem Sublist.of_sublist_append_left (w : ∀ a, a ∈ l → a ∉ l₂) (h :
   obtain ⟨l₁', l₂', rfl, h₁, h₂⟩ := h
   have : l₂' = [] := by
     rw [eq_nil_iff_forall_not_mem]
-    exact fun x m => w x (mem_append_of_mem_right l₁' m) (h₂.mem m)
+    exact fun x m => w x (mem_append_right l₁' m) (h₂.mem m)
   simp_all
 
 theorem Sublist.of_sublist_append_right (w : ∀ a, a ∈ l → a ∉ l₁) (h : l <+ l₁ ++ l₂) : l <+ l₂ := by
@@ -425,7 +425,7 @@ theorem Sublist.of_sublist_append_right (w : ∀ a, a ∈ l → a ∉ l₁) (h :
   obtain ⟨l₁', l₂', rfl, h₁, h₂⟩ := h
   have : l₁' = [] := by
     rw [eq_nil_iff_forall_not_mem]
-    exact fun x m => w x (mem_append_of_mem_left l₂' m) (h₁.mem m)
+    exact fun x m => w x (mem_append_left l₂' m) (h₁.mem m)
   simp_all
 
 theorem Sublist.middle {l : List α} (h : l <+ l₁ ++ l₂) (a : α) : l <+ l₁ ++ a :: l₂ := 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/Nat/Linear.lean

@@ -6,6 +6,7 @@ Authors: Leonardo de Moura
 prelude
 import Init.ByCases
 import Init.Data.Prod
+import Init.Data.RArray
 
 namespace Nat.Linear
 
@@ -15,7 +16,7 @@ namespace Nat.Linear
 
 abbrev Var := Nat
 
-abbrev Context := List Nat
+abbrev Context := Lean.RArray Nat
 
 /--
   When encoding polynomials. We use `fixedVar` for encoding numerals.
@@ -23,12 +24,7 @@ abbrev Context := List Nat
 def fixedVar := 100000000 -- Any big number should work here
 
 def Var.denote (ctx : Context) (v : Var) : Nat :=
-  bif v == fixedVar then 1 else go ctx v
-where
-  go : List Nat → Nat → Nat
-   | [],    _   => 0
-   | a::_,  0   => a
-   | _::as, i+1 => go as i
+  bif v == fixedVar then 1 else ctx.get v
 
 inductive Expr where
   | num  (v : Nat)
@@ -52,25 +48,23 @@ def Poly.denote (ctx : Context) (p : Poly) : Nat :=
   | [] => 0
   | (k, v) :: p => Nat.add (Nat.mul k (v.denote ctx)) (denote ctx p)
 
-def Poly.insertSorted (k : Nat) (v : Var) (p : Poly) : Poly :=
+def Poly.insert (k : Nat) (v : Var) (p : Poly) : Poly :=
   match p with
   | [] => [(k, v)]
-  | (k', v') :: p => bif Nat.blt v v' then (k, v) :: (k', v') :: p else (k', v') :: insertSorted k v p
+  | (k', v') :: p =>
+    bif Nat.blt v v' then
+      (k, v) :: (k', v') :: p
+    else bif Nat.beq v v' then
+      (k + k', v') :: p
+    else
+      (k', v') :: insert k v p
 
-def Poly.sort (p : Poly) : Poly :=
-  let rec go (p : Poly) (r : Poly) : Poly :=
+def Poly.norm (p : Poly) : Poly := go p []
+where
+  go (p : Poly) (r : Poly) : Poly :=
     match p with
     | [] => r
-    | (k, v) :: p => go p (r.insertSorted k v)
-  go p []
-
-def Poly.fuse (p : Poly) : Poly :=
-  match p with
-  | []  => []
-  | (k, v) :: p =>
-    match fuse p with
-    | [] => [(k, v)]
-    | (k', v') :: p' => bif v == v' then (Nat.add k k', v)::p' else (k, v) :: (k', v') :: p'
+    | (k, v) :: p => go p (r.insert k v)
 
 def Poly.mul (k : Nat) (p : Poly) : Poly :=
   bif k == 0 then
@@ -146,15 +140,17 @@ def Poly.combineAux (fuel : Nat) (p₁ p₂ : Poly) : Poly :=
 def Poly.combine (p₁ p₂ : Poly) : Poly :=
   combineAux hugeFuel p₁ p₂
 
-def Expr.toPoly : Expr → Poly
-  | Expr.num k    => bif k == 0 then [] else [ (k, fixedVar) ]
-  | Expr.var i    => [(1, i)]
-  | Expr.add a b  => a.toPoly ++ b.toPoly
-  | Expr.mulL k a => a.toPoly.mul k
-  | Expr.mulR a k => a.toPoly.mul k
-
-def Poly.norm (p : Poly) : Poly :=
-  p.sort.fuse
+def Expr.toPoly (e : Expr) :=
+  go 1 e []
+where
+  -- Implementation note: This assembles the result using difference lists
+  -- to avoid `++` on lists.
+  go (coeff : Nat) : Expr → (Poly → Poly)
+    | Expr.num k    => bif k == 0 then id else ((coeff * k, fixedVar) :: ·)
+    | Expr.var i    => ((coeff, i) :: ·)
+    | Expr.add a b  => go coeff a ∘ go coeff b
+    | Expr.mulL k a
+    | Expr.mulR a k => bif k == 0 then id else go (coeff * k) a
 
 def Expr.toNormPoly (e : Expr) : Poly :=
   e.toPoly.norm
@@ -201,7 +197,7 @@ def PolyCnstr.denote (ctx : Context) (c : PolyCnstr) : Prop :=
     Poly.denote_le ctx (c.lhs, c.rhs)
 
 def PolyCnstr.norm (c : PolyCnstr) : PolyCnstr :=
-  let (lhs, rhs) := Poly.cancel c.lhs.sort.fuse c.rhs.sort.fuse
+  let (lhs, rhs) := Poly.cancel c.lhs.norm c.rhs.norm
   { eq := c.eq, lhs, rhs }
 
 def PolyCnstr.isUnsat (c : PolyCnstr) : Bool :=
@@ -268,24 +264,32 @@ def PolyCnstr.toExpr (c : PolyCnstr) : ExprCnstr :=
   { c with lhs := c.lhs.toExpr, rhs := c.rhs.toExpr }
 
 attribute [local simp] Nat.add_comm Nat.add_assoc Nat.add_left_comm Nat.right_distrib Nat.left_distrib Nat.mul_assoc Nat.mul_comm
-attribute [local simp] Poly.denote Expr.denote Poly.insertSorted Poly.sort Poly.sort.go Poly.fuse Poly.cancelAux
+attribute [local simp] Poly.denote Expr.denote Poly.insert Poly.norm Poly.norm.go Poly.cancelAux
 attribute [local simp] Poly.mul Poly.mul.go
 
-theorem Poly.denote_insertSorted (ctx : Context) (k : Nat) (v : Var) (p : Poly) : (p.insertSorted k v).denote ctx = p.denote ctx + k * v.denote ctx := by
+theorem Poly.denote_insert (ctx : Context) (k : Nat) (v : Var) (p : Poly) :
+    (p.insert k v).denote ctx = p.denote ctx + k * v.denote ctx := by
   match p with
   | [] => simp
-  | (k', v') :: p => by_cases h : Nat.blt v v' <;> simp [h, denote_insertSorted]
+  | (k', v') :: p =>
+    by_cases h₁ : Nat.blt v v'
+    · simp [h₁]
+    · by_cases h₂ : Nat.beq v v'
+      · simp only [insert, h₁, h₂, cond_false, cond_true]
+        simp [Nat.eq_of_beq_eq_true h₂]
+      · simp only [insert, h₁, h₂, cond_false, cond_true]
+        simp [denote_insert]
 
-attribute [local simp] Poly.denote_insertSorted
+attribute [local simp] Poly.denote_insert
 
-theorem Poly.denote_sort_go (ctx : Context) (p : Poly) (r : Poly) : (sort.go p r).denote ctx = p.denote ctx + r.denote ctx := by
+theorem Poly.denote_norm_go (ctx : Context) (p : Poly) (r : Poly) : (norm.go p r).denote ctx = p.denote ctx + r.denote ctx := by
   match p with
   | [] => simp
-  | (k, v):: p => simp [denote_sort_go]
+  | (k, v):: p => simp [denote_norm_go]
 
-attribute [local simp] Poly.denote_sort_go
+attribute [local simp] Poly.denote_norm_go
 
-theorem Poly.denote_sort (ctx : Context) (m : Poly) : m.sort.denote ctx = m.denote ctx := by
+theorem Poly.denote_sort (ctx : Context) (m : Poly) : m.norm.denote ctx = m.denote ctx := by
   simp
 
 attribute [local simp] Poly.denote_sort
@@ -316,18 +320,6 @@ theorem Poly.denote_reverse (ctx : Context) (p : Poly) : denote ctx (List.revers
 
 attribute [local simp] Poly.denote_reverse
 
-theorem Poly.denote_fuse (ctx : Context) (p : Poly) : p.fuse.denote ctx = p.denote ctx := by
-  match p with
-  | [] => rfl
-  | (k, v) :: p =>
-    have ih := denote_fuse ctx p
-    simp
-    split
-    case _ h => simp [← ih, h]
-    case _ k' v' p' h => by_cases he : v == v' <;> simp [he, ← ih, h]; rw [eq_of_beq he]
-
-attribute [local simp] Poly.denote_fuse
-
 theorem Poly.denote_mul (ctx : Context) (k : Nat) (p : Poly) : (p.mul k).denote ctx = k * p.denote ctx := by
   simp
   by_cases h : k == 0 <;> simp [h]; simp [eq_of_beq h]
@@ -516,13 +508,25 @@ theorem Poly.denote_combine (ctx : Context) (p₁ p₂ : Poly) : (p₁.combine p
 
 attribute [local simp] Poly.denote_combine
 
+theorem Expr.denote_toPoly_go (ctx : Context) (e : Expr) :
+  (toPoly.go k e p).denote ctx = k * e.denote ctx + p.denote ctx := by
+  induction k, e using Expr.toPoly.go.induct generalizing p with
+  | case1 k k' =>
+    simp only [toPoly.go]
+    by_cases h : k' == 0
+    · simp [h, eq_of_beq h]
+    · simp [h, Var.denote]
+  | case2 k i => simp [toPoly.go]
+  | case3 k a b iha ihb => simp [toPoly.go, iha, ihb]
+  | case4 k k' a ih
+  | case5 k a k' ih =>
+    simp only [toPoly.go, denote, mul_eq]
+    by_cases h : k' == 0
+    · simp [h, eq_of_beq h]
+    · simp [h, cond_false, ih, Nat.mul_assoc]
+
 theorem Expr.denote_toPoly (ctx : Context) (e : Expr) : e.toPoly.denote ctx = e.denote ctx := by
-  induction e with
-  | num k => by_cases h : k == 0 <;> simp [toPoly, h, Var.denote]; simp [eq_of_beq h]
-  | var i => simp [toPoly]
-  | add a b iha ihb => simp [toPoly, iha, ihb]
-  | mulL k a ih => simp [toPoly, ih, -Poly.mul]
-  | mulR k a ih => simp [toPoly, ih, -Poly.mul]
+  simp [toPoly, Expr.denote_toPoly_go]
 
 attribute [local simp] Expr.denote_toPoly
 
@@ -554,8 +558,8 @@ theorem ExprCnstr.denote_toPoly (ctx : Context) (c : ExprCnstr) : c.toPoly.denot
   cases c; rename_i eq lhs rhs
   simp [ExprCnstr.denote, PolyCnstr.denote, ExprCnstr.toPoly];
   by_cases h : eq = true <;> simp [h]
-  · simp [Poly.denote_eq, Expr.toPoly]
-  · simp [Poly.denote_le, Expr.toPoly]
+  · simp [Poly.denote_eq]
+  · simp [Poly.denote_le]
 
 attribute [local simp] ExprCnstr.denote_toPoly
 

src/Init/Data/Option/Basic.lean

@@ -16,10 +16,6 @@ def getM [Alternative m] : Option α → m α
   | none     => failure
   | some a   => pure a
 
-@[deprecated getM (since := "2024-04-17")]
--- `[Monad m]` is not needed here.
-def toMonad [Monad m] [Alternative m] : Option α → m α := getM
-
 /-- Returns `true` on `some x` and `false` on `none`. -/
 @[inline] def isSome : Option α → Bool
   | some _ => true
@@ -28,8 +24,6 @@ def toMonad [Monad m] [Alternative m] : Option α → m α := getM
 @[simp] theorem isSome_none : @isSome α none = false := rfl
 @[simp] theorem isSome_some : isSome (some a) = true := rfl
 
-@[deprecated isSome (since := "2024-04-17"), inline] def toBool : Option α → Bool := isSome
-
 /-- Returns `true` on `none` and `false` on `some x`. -/
 @[inline] def isNone : Option α → Bool
   | some _ => false

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/RArray.lean

@@ -0,0 +1,69 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Joachim Breitner
+-/
+
+prelude
+import Init.PropLemmas
+
+namespace Lean
+
+/--
+A `RArray` can model `Fin n → α` or `Array α`, but is optimized for a fast kernel-reducible `get`
+operation.
+
+The primary intended use case is the “denote” function of a typical proof by reflection proof, where
+only the `get` operation is necessary. It is not suitable as a general-purpose data structure.
+
+There is no well-formedness invariant attached to this data structure, to keep it concise; it's
+semantics is given through `RArray.get`. In that way one can also view an `RArray` as a decision
+tree implementing `Nat → α`.
+
+See `RArray.ofFn` and `RArray.ofArray` in module `Lean.Data.RArray` for functions that construct an
+`RArray`.
+
+It is not universe-polymorphic. ; smaller proof objects and no complication with the `ToExpr` type
+class.
+-/
+inductive RArray (α : Type) : Type where
+  | leaf : α → RArray α
+  | branch : Nat → RArray α → RArray α → RArray α
+
+variable {α : Type}
+
+/-- The crucial operation, written with very little abstractional overhead -/
+noncomputable def RArray.get (a : RArray α) (n : Nat) : α :=
+  RArray.rec (fun x => x) (fun p _ _ l r => (Nat.ble p n).rec l r) a
+
+private theorem RArray.get_eq_def (a : RArray α) (n : Nat) :
+  a.get n = match a with
+    | .leaf x => x
+    | .branch p l r => (Nat.ble p n).rec (l.get n) (r.get n) := by
+  conv => lhs; unfold RArray.get
+  split <;> rfl
+
+/-- `RArray.get`, implemented conventionally -/
+def RArray.getImpl (a : RArray α) (n : Nat) : α :=
+  match a with
+  | .leaf x => x
+  | .branch p l r => if n < p then l.getImpl n else r.getImpl n
+
+@[csimp]
+theorem RArray.get_eq_getImpl : @RArray.get = @RArray.getImpl := by
+  funext α a n
+  induction a with
+  | leaf _ => rfl
+  | branch p l r ihl ihr =>
+    rw [RArray.getImpl, RArray.get_eq_def]
+    simp only [ihl, ihr, ← Nat.not_le, ← Nat.ble_eq, ite_not]
+    cases hnp : Nat.ble p n <;> rfl
+
+instance : GetElem (RArray α) Nat α (fun _ _ => True) where
+  getElem a n _ := a.get n
+
+def RArray.size : RArray α → Nat
+  | leaf _ => 1
+  | branch _ l r => l.size + r.size
+
+end Lean

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/Data/SInt/Basic.lean

@@ -148,6 +148,9 @@ instance : ShiftLeft Int8   := ⟨Int8.shiftLeft⟩
 instance : ShiftRight Int8  := ⟨Int8.shiftRight⟩
 instance : DecidableEq Int8 := Int8.decEq
 
+@[extern "lean_bool_to_int8"]
+def Bool.toInt8 (b : Bool) : Int8 := if b then 1 else 0
+
 @[extern "lean_int8_dec_lt"]
 def Int8.decLt (a b : Int8) : Decidable (a < b) :=
   inferInstanceAs (Decidable (a.toBitVec.slt b.toBitVec))
@@ -249,6 +252,9 @@ instance : ShiftLeft Int16   := ⟨Int16.shiftLeft⟩
 instance : ShiftRight Int16  := ⟨Int16.shiftRight⟩
 instance : DecidableEq Int16 := Int16.decEq
 
+@[extern "lean_bool_to_int16"]
+def Bool.toInt16 (b : Bool) : Int16 := if b then 1 else 0
+
 @[extern "lean_int16_dec_lt"]
 def Int16.decLt (a b : Int16) : Decidable (a < b) :=
   inferInstanceAs (Decidable (a.toBitVec.slt b.toBitVec))
@@ -354,6 +360,9 @@ instance : ShiftLeft Int32   := ⟨Int32.shiftLeft⟩
 instance : ShiftRight Int32  := ⟨Int32.shiftRight⟩
 instance : DecidableEq Int32 := Int32.decEq
 
+@[extern "lean_bool_to_int32"]
+def Bool.toInt32 (b : Bool) : Int32 := if b then 1 else 0
+
 @[extern "lean_int32_dec_lt"]
 def Int32.decLt (a b : Int32) : Decidable (a < b) :=
   inferInstanceAs (Decidable (a.toBitVec.slt b.toBitVec))
@@ -463,6 +472,9 @@ instance : ShiftLeft Int64   := ⟨Int64.shiftLeft⟩
 instance : ShiftRight Int64  := ⟨Int64.shiftRight⟩
 instance : DecidableEq Int64 := Int64.decEq
 
+@[extern "lean_bool_to_int64"]
+def Bool.toInt64 (b : Bool) : Int64 := if b then 1 else 0
+
 @[extern "lean_int64_dec_lt"]
 def Int64.decLt (a b : Int64) : Decidable (a < b) :=
   inferInstanceAs (Decidable (a.toBitVec.slt b.toBitVec))
@@ -574,6 +586,9 @@ instance : ShiftLeft ISize   := ⟨ISize.shiftLeft⟩
 instance : ShiftRight ISize  := ⟨ISize.shiftRight⟩
 instance : DecidableEq ISize := ISize.decEq
 
+@[extern "lean_bool_to_isize"]
+def Bool.toISize (b : Bool) : ISize := if b then 1 else 0
+
 @[extern "lean_isize_dec_lt"]
 def ISize.decLt (a b : ISize) : Decidable (a < b) :=
   inferInstanceAs (Decidable (a.toBitVec.slt b.toBitVec))

src/Init/Data/String/Basic.lean

@@ -514,9 +514,6 @@ instance : Inhabited String := ⟨""⟩
 
 instance : Append String := ⟨String.append⟩
 
-@[deprecated push (since := "2024-04-06")]
-def str : String → Char → String := push
-
 @[inline] def pushn (s : String) (c : Char) (n : Nat) : String :=
   n.repeat (fun s => s.push c) s
 

src/Init/Data/UInt/Basic.lean

@@ -56,6 +56,9 @@ instance : Xor UInt8       := ⟨UInt8.xor⟩
 instance : ShiftLeft UInt8  := ⟨UInt8.shiftLeft⟩
 instance : ShiftRight UInt8 := ⟨UInt8.shiftRight⟩
 
+@[extern "lean_bool_to_uint8"]
+def Bool.toUInt8 (b : Bool) : UInt8 := if b then 1 else 0
+
 @[extern "lean_uint8_dec_lt"]
 def UInt8.decLt (a b : UInt8) : Decidable (a < b) :=
   inferInstanceAs (Decidable (a.toBitVec < b.toBitVec))
@@ -116,6 +119,9 @@ instance : Xor UInt16       := ⟨UInt16.xor⟩
 instance : ShiftLeft UInt16  := ⟨UInt16.shiftLeft⟩
 instance : ShiftRight UInt16 := ⟨UInt16.shiftRight⟩
 
+@[extern "lean_bool_to_uint16"]
+def Bool.toUInt16 (b : Bool) : UInt16 := if b then 1 else 0
+
 set_option bootstrap.genMatcherCode false in
 @[extern "lean_uint16_dec_lt"]
 def UInt16.decLt (a b : UInt16) : Decidable (a < b) :=
@@ -174,6 +180,9 @@ instance : Xor UInt32       := ⟨UInt32.xor⟩
 instance : ShiftLeft UInt32  := ⟨UInt32.shiftLeft⟩
 instance : ShiftRight UInt32 := ⟨UInt32.shiftRight⟩
 
+@[extern "lean_bool_to_uint32"]
+def Bool.toUInt32 (b : Bool) : UInt32 := if b then 1 else 0
+
 @[extern "lean_uint64_add"]
 def UInt64.add (a b : UInt64) : UInt64 := ⟨a.toBitVec + b.toBitVec⟩
 @[extern "lean_uint64_sub"]
@@ -278,5 +287,8 @@ instance : Xor USize        := ⟨USize.xor⟩
 instance : ShiftLeft USize  := ⟨USize.shiftLeft⟩
 instance : ShiftRight USize := ⟨USize.shiftRight⟩
 
+@[extern "lean_bool_to_usize"]
+def Bool.toUSize (b : Bool) : USize := if b then 1 else 0
+
 instance : Max USize := maxOfLe
 instance : Min USize := minOfLe

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). -/
@@ -403,21 +431,20 @@ def getSubstring? (stx : Syntax) (withLeading := true) (withTrailing := true) :
     }
   | _, _ => none
 
-@[specialize] private partial def updateLast {α} [Inhabited α] (a : Array α) (f : α → Option α) (i : Nat) : Option (Array α) :=
-  if i == 0 then
-    none
-  else
-    let i := i - 1
-    let v := a[i]!
+@[specialize] private partial def updateLast {α} (a : Array α) (f : α → Option α) (i : Fin (a.size + 1)) : Option (Array α) :=
+  match i with
+  | 0 => none
+  | ⟨i + 1, h⟩ =>
+    let v := a[i]'(Nat.succ_lt_succ_iff.mp h)
     match f v with
-    | some v => some <| a.set! i v
-    | none   => updateLast a f i
+    | some v => some <| a.set i v (Nat.succ_lt_succ_iff.mp h)
+    | none   => updateLast a f ⟨i, Nat.lt_of_succ_lt h⟩
 
 partial def setTailInfoAux (info : SourceInfo) : Syntax → Option Syntax
   | atom _ val             => some <| atom info val
   | ident _ rawVal val pre => some <| ident info rawVal val pre
   | node info' k args      =>
-    match updateLast args (setTailInfoAux info) args.size with
+    match updateLast args (setTailInfoAux info) ⟨args.size, by simp⟩ with
     | some args => some <| node info' k args
     | none      => none
   | _                      => none

src/Init/NotationExtra.lean

@@ -22,28 +22,28 @@ syntax explicitBinders            := (ppSpace bracketedExplicitBinders)+ <|> unb
 
 open TSyntax.Compat in
 def expandExplicitBindersAux (combinator : Syntax) (idents : Array Syntax) (type? : Option Syntax) (body : Syntax) : MacroM Syntax :=
-  let rec loop (i : Nat) (acc : Syntax) := do
+  let rec loop (i : Nat) (h : i ≤ idents.size) (acc : Syntax) := do
     match i with
     | 0   => pure acc
-    | i+1 =>
-      let ident := idents[i]![0]
+    | i + 1 =>
+      let ident := idents[i][0]
       let acc ← match ident.isIdent, type? with
         | true,  none      => `($combinator fun $ident => $acc)
         | true,  some type => `($combinator fun $ident : $type => $acc)
         | false, none      => `($combinator fun _ => $acc)
         | false, some type => `($combinator fun _ : $type => $acc)
-      loop i acc
-  loop idents.size body
+      loop i (Nat.le_of_succ_le h) acc
+  loop idents.size (by simp) body
 
 def expandBrackedBindersAux (combinator : Syntax) (binders : Array Syntax) (body : Syntax) : MacroM Syntax :=
-  let rec loop (i : Nat) (acc : Syntax) := do
+  let rec loop (i : Nat) (h : i ≤ binders.size) (acc : Syntax) := do
     match i with
     | 0   => pure acc
     | i+1 =>
-      let idents := binders[i]![1].getArgs
-      let type   := binders[i]![3]
-      loop i (← expandExplicitBindersAux combinator idents (some type) acc)
-  loop binders.size body
+      let idents := binders[i][1].getArgs
+      let type   := binders[i][3]
+      loop i (Nat.le_of_succ_le h) (← expandExplicitBindersAux combinator idents (some type) acc)
+  loop binders.size (by simp) body
 
 def expandExplicitBinders (combinatorDeclName : Name) (explicitBinders : Syntax) (body : Syntax) : MacroM Syntax := do
   let combinator := mkCIdentFrom (← getRef) combinatorDeclName

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/System/Uri.lean

@@ -29,13 +29,13 @@ def decodeUri (uri : String) : String := Id.run do
   let len := rawBytes.size
   let mut i := 0
   let percent := '%'.toNat.toUInt8
-  while i < len do
-    let c := rawBytes[i]!
-    (decoded, i) := if c == percent && i + 1 < len then
-      let h1 := rawBytes[i + 1]!
+  while h : i < len do
+    let c := rawBytes[i]
+    (decoded, i) := if h₁ : c == percent ∧ i + 1 < len then
+      let h1 := rawBytes[i + 1]
       if let some hd1 := hexDigitToUInt8? h1 then
-        if i + 2 < len then
-          let h2 := rawBytes[i + 2]!
+        if h₂ : i + 2 < len then
+          let h2 := rawBytes[i + 2]
           if let some hd2 := hexDigitToUInt8? h2 then
             -- decode the hex digits into a byte.
             (decoded.push (hd1 * 16 + hd2), i + 3)

src/Init/Tactics.lean

@@ -466,7 +466,7 @@ hypotheses or the goal. It can have one of the forms:
 * `at h₁ h₂ ⊢`: target the hypotheses `h₁` and `h₂`, and the goal
 * `at *`: target all hypotheses and the goal
 -/
-syntax location := withPosition(" at" (locationWildcard <|> locationHyp))
+syntax location := withPosition(ppGroup(" at" (locationWildcard <|> locationHyp)))
 
 /--
 * `change tgt'` will change the goal from `tgt` to `tgt'`,
@@ -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/ConstFolding.lean

@@ -133,8 +133,8 @@ def foldNatBinBoolPred (fn : Nat → Nat → Bool) (a₁ a₂ : Expr) : Option E
     return mkConst ``Bool.false
 
 def foldNatBeq := fun _ : Bool => foldNatBinBoolPred (fun a b => a == b)
-def foldNatBle := fun _ : Bool => foldNatBinBoolPred (fun a b => a < b)
-def foldNatBlt := fun _ : Bool => foldNatBinBoolPred (fun a b => a ≤ b)
+def foldNatBlt := fun _ : Bool => foldNatBinBoolPred (fun a b => a < b)
+def foldNatBle := fun _ : Bool => foldNatBinBoolPred (fun a b => a ≤ b)
 
 def natFoldFns : List (Name × BinFoldFn) :=
   [(``Nat.add, foldNatAdd),

src/Lean/Compiler/IR/EmitC.lean

@@ -271,9 +271,9 @@ def emitTag (x : VarId) (xType : IRType) : M Unit := do
     emit x
 
 def isIf (alts : Array Alt) : Option (Nat × FnBody × FnBody) :=
-  if alts.size != 2 then none
-  else match alts[0]! with
-    | Alt.ctor c b => some (c.cidx, b, alts[1]!.body)
+  if h : alts.size ≠ 2 then none
+  else match alts[0] with
+    | Alt.ctor c b => some (c.cidx, b, alts[1].body)
     | _            => none
 
 def emitInc (x : VarId) (n : Nat) (checkRef : Bool) : M Unit := do

src/Lean/Compiler/IR/EmitLLVM.lean

@@ -1172,8 +1172,8 @@ def emitFnArgs (builder : LLVM.Builder llvmctx)
     (needsPackedArgs? : Bool)  (llvmfn : LLVM.Value llvmctx) (params : Array Param) : M llvmctx Unit := do
   if needsPackedArgs? then do
       let argsp ← LLVM.getParam llvmfn 0 -- lean_object **args
-      for i in List.range params.size do
-          let param := params[i]!
+      for h : i in [:params.size] do
+          let param := params[i]
           -- argsi := (args + i)
           let argsi ← LLVM.buildGEP2 builder (← LLVM.voidPtrType llvmctx) argsp #[← constIntUnsigned i] s!"packed_arg_{i}_slot"
           let llvmty ← toLLVMType param.ty
@@ -1182,15 +1182,16 @@ def emitFnArgs (builder : LLVM.Builder llvmctx)
           -- slot for arg[i] which is always void* ?
           let alloca ← buildPrologueAlloca builder llvmty s!"arg_{i}"
           LLVM.buildStore builder pv alloca
-          addVartoState params[i]!.x alloca llvmty
+          addVartoState param.x alloca llvmty
   else
       let n ← LLVM.countParams llvmfn
-      for i in (List.range n.toNat) do
-        let llvmty ← toLLVMType params[i]!.ty
+      for i in [:n.toNat] do
+        let param := params[i]!
+        let llvmty ← toLLVMType param.ty
         let alloca ← buildPrologueAlloca builder  llvmty s!"arg_{i}"
         let arg ← LLVM.getParam llvmfn (UInt64.ofNat i)
         let _ ← LLVM.buildStore builder arg alloca
-        addVartoState params[i]!.x alloca llvmty
+        addVartoState param.x alloca llvmty
 
 def emitDeclAux (mod : LLVM.Module llvmctx) (builder : LLVM.Builder llvmctx) (d : Decl) : M llvmctx Unit := do
   let env ← getEnv

src/Lean/Compiler/IR/ExpandResetReuse.lean

@@ -54,7 +54,7 @@ abbrev Mask := Array (Option VarId)
 partial def eraseProjIncForAux (y : VarId) (bs : Array FnBody) (mask : Mask) (keep : Array FnBody) : Array FnBody × Mask :=
   let done (_ : Unit)        := (bs ++ keep.reverse, mask)
   let keepInstr (b : FnBody) := eraseProjIncForAux y bs.pop mask (keep.push b)
-  if bs.size < 2 then done ()
+  if h : bs.size < 2 then done ()
   else
     let b := bs.back!
     match b with
@@ -62,7 +62,7 @@ partial def eraseProjIncForAux (y : VarId) (bs : Array FnBody) (mask : Mask) (ke
     | .vdecl _ _ (.uproj _ _) _   => keepInstr b
     | .inc z n c p _ =>
       if n == 0 then done () else
-      let b' := bs[bs.size - 2]!
+      let b' := bs[bs.size - 2]
       match b' with
       | .vdecl w _ (.proj i x) _ =>
         if w == z && y == x then

src/Lean/Compiler/LCNF/SpecInfo.lean

@@ -152,8 +152,8 @@ def saveSpecParamInfo (decls : Array Decl) : CompilerM Unit := do
       let specArgs? := getSpecializationArgs? (← getEnv) decl.name
       let contains (i : Nat) : Bool := specArgs?.getD #[] |>.contains i
       let mut paramsInfo : Array SpecParamInfo := #[]
-      for i in [:decl.params.size] do
-        let param := decl.params[i]!
+      for h :i in [:decl.params.size] do
+        let param := decl.params[i]
         let info ←
           if contains i then
             pure .user
@@ -181,14 +181,14 @@ def saveSpecParamInfo (decls : Array Decl) : CompilerM Unit := do
       declsInfo := declsInfo.push paramsInfo
   if declsInfo.any fun paramsInfo => paramsInfo.any (· matches .user | .fixedInst | .fixedHO) then
     let m := mkFixedParamsMap decls
-    for i in [:decls.size] do
-      let decl := decls[i]!
+    for hi : i in [:decls.size] do
+      let decl := decls[i]
       let mut paramsInfo := declsInfo[i]!
       let some mask := m.find? decl.name | unreachable!
       trace[Compiler.specialize.info] "{decl.name} {mask}"
       paramsInfo := paramsInfo.zipWith mask fun info fixed => if fixed || info matches .user then info else .other
       for j in [:paramsInfo.size] do
-        let mut info  := paramsInfo[j]!
+        let mut info := paramsInfo[j]!
         if info matches .fixedNeutral && !hasFwdDeps decl paramsInfo j then
           paramsInfo := paramsInfo.set! j .other
       if paramsInfo.any fun info => info matches .fixedInst | .fixedHO | .user then

src/Lean/Compiler/LCNF/ToLCNF.lean

@@ -499,8 +499,8 @@ where
       match app with
       | .fvar f =>
         let mut argsNew := #[]
-        for i in [arity : args.size] do
-          argsNew := argsNew.push (← visitAppArg args[i]!)
+        for h :i in [arity : args.size] do
+          argsNew := argsNew.push (← visitAppArg args[i])
         letValueToArg <| .fvar f argsNew
       | .erased | .type .. => return .erased
 

src/Lean/Compiler/Specialize.lean

@@ -26,10 +26,11 @@ private def elabSpecArgs (declName : Name) (args : Array Syntax) : MetaM (Array
       if let some idx := arg.isNatLit? then
         if idx == 0 then throwErrorAt arg "invalid specialization argument index, index must be greater than 0"
         let idx := idx - 1
-        if idx >= argNames.size then
+        if h : idx >= argNames.size then
           throwErrorAt arg "invalid argument index, `{declName}` has #{argNames.size} arguments"
-        if result.contains idx then throwErrorAt arg "invalid specialization argument index, `{argNames[idx]!}` has already been specified as a specialization candidate"
-        result := result.push idx
+        else
+          if result.contains idx then throwErrorAt arg "invalid specialization argument index, `{argNames[idx]}` has already been specified as a specialization candidate"
+          result := result.push idx
       else
         let argName := arg.getId
         if let some idx := argNames.getIdx? argName then

src/Lean/Data.lean

@@ -29,4 +29,4 @@ import Lean.Data.Xml
 import Lean.Data.NameTrie
 import Lean.Data.RBTree
 import Lean.Data.RBMap
-import Lean.Data.Rat
+import Lean.Data.RArray

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/NameMap.lean

@@ -33,6 +33,16 @@ def find? (m : NameMap α) (n : Name) : Option α := RBMap.find? m n
 instance : ForIn m (NameMap α) (Name × α) :=
   inferInstanceAs (ForIn _ (RBMap ..) ..)
 
+/-- `filter f m` returns the `NameMap` consisting of all
+"`key`/`val`"-pairs in `m` where `f key val` returns `true`. -/
+def filter (f : Name → α → Bool) (m : NameMap α) : NameMap α := RBMap.filter f m
+
+/-- `filterMap f m` filters an `NameMap` and simultaneously modifies the filtered values.
+
+It takes a function `f : Name → α → Option β` and applies `f name` to the value with key `name`.
+The resulting entries with non-`none` value are collected to form the output `NameMap`. -/
+def filterMap (f : Name → α → Option β) (m : NameMap α) : NameMap β := RBMap.filterMap f m
+
 end NameMap
 
 def NameSet := RBTree Name Name.quickCmp
@@ -53,6 +63,9 @@ def append (s t : NameSet) : NameSet :=
 instance : Append NameSet where
   append := NameSet.append
 
+/-- `filter f s` returns the `NameSet` consisting of all `x` in `s` where `f x` returns `true`. -/
+def filter (f : Name → Bool) (s : NameSet) : NameSet := RBTree.filter f s
+
 end NameSet
 
 def NameSSet := SSet Name
@@ -73,6 +86,9 @@ instance : EmptyCollection NameHashSet := ⟨empty⟩
 instance : Inhabited NameHashSet := ⟨{}⟩
 def insert (s : NameHashSet) (n : Name) := Std.HashSet.insert s n
 def contains (s : NameHashSet) (n : Name) : Bool := Std.HashSet.contains s n
+
+/-- `filter f s` returns the `NameHashSet` consisting of all `x` in `s` where `f x` returns `true`. -/
+def filter (f : Name → Bool) (s : NameHashSet) : NameHashSet := Std.HashSet.filter f s
 end NameHashSet
 
 def MacroScopesView.isPrefixOf (v₁ v₂ : MacroScopesView) : Bool :=

src/Lean/Data/RArray.lean

@@ -0,0 +1,75 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Joachim Breitner
+-/
+
+prelude
+import Init.Data.RArray
+import Lean.ToExpr
+
+/-!
+Auxillary definitions related to `Lean.RArray` that are typically only used in meta-code, in
+particular the `ToExpr` instance.
+-/
+
+namespace Lean
+
+-- This function could live in Init/Data/RArray.lean, but without omega it's tedious to implement
+def RArray.ofFn {n : Nat} (f : Fin n → α) (h : 0 < n) : RArray α :=
+  go 0 n h (Nat.le_refl _)
+where
+  go (lb ub : Nat) (h1 : lb < ub) (h2 : ub ≤ n) : RArray α :=
+    if h : lb + 1 = ub then
+      .leaf (f ⟨lb, Nat.lt_of_lt_of_le h1 h2⟩)
+    else
+      let mid := (lb + ub)/2
+      .branch mid (go lb mid (by omega) (by omega)) (go mid ub (by omega) h2)
+
+def RArray.ofArray (xs : Array α) (h : 0 < xs.size) : RArray α :=
+  .ofFn (xs[·]) h
+
+/-- The correctness theorem for `ofFn` -/
+theorem RArray.get_ofFn {n : Nat} (f : Fin n → α) (h : 0 < n) (i : Fin n) :
+    (ofFn f h).get i = f i :=
+  go 0 n h (Nat.le_refl _) (Nat.zero_le _) i.2
+where
+  go lb ub h1 h2 (h3 : lb ≤ i.val) (h3 : i.val < ub) : (ofFn.go f lb ub h1 h2).get i = f i := by
+    induction lb, ub, h1, h2 using RArray.ofFn.go.induct (f := f) (n := n)
+    case case1 =>
+      simp [ofFn.go, RArray.get_eq_getImpl, RArray.getImpl]
+      congr
+      omega
+    case case2 ih1 ih2 hiu =>
+      rw [ofFn.go]; simp only [↓reduceDIte, *]
+      simp [RArray.get_eq_getImpl, RArray.getImpl] at *
+      split
+      · rw [ih1] <;> omega
+      · rw [ih2] <;> omega
+
+@[simp]
+theorem RArray.size_ofFn {n : Nat} (f : Fin n → α) (h : 0 < n) :
+    (ofFn f h).size = n :=
+  go 0 n h (Nat.le_refl _)
+where
+  go lb ub h1 h2 : (ofFn.go f lb ub h1 h2).size = ub - lb := by
+    induction lb, ub, h1, h2 using RArray.ofFn.go.induct (f := f) (n := n)
+    case case1 => simp [ofFn.go, size]; omega
+    case case2 ih1 ih2 hiu => rw [ofFn.go]; simp [size, *]; omega
+
+section Meta
+open Lean
+
+def RArray.toExpr (ty : Expr) (f : α → Expr) : RArray α → Expr
+  | .leaf x  =>
+    mkApp2 (mkConst ``RArray.leaf) ty (f x)
+  | .branch p l r =>
+    mkApp4 (mkConst ``RArray.branch) ty (mkRawNatLit p) (l.toExpr ty f) (r.toExpr ty f)
+
+instance [ToExpr α] : ToExpr (RArray α) where
+  toTypeExpr := mkApp (mkConst ``RArray) (toTypeExpr α)
+  toExpr a := a.toExpr (toTypeExpr α) toExpr
+
+end Meta
+
+end Lean

src/Lean/Data/RBMap.lean

@@ -404,6 +404,24 @@ def intersectBy {γ : Type v₁} {δ : Type v₂} (mergeFn : α → β → γ
       | some b₂ => acc.insert a <| mergeFn a b₁ b₂
       | none => acc
 
+/--
+`filter f m` returns the `RBMap` consisting of all
+"`key`/`val`"-pairs in `m` where `f key val` returns `true`.
+-/
+def filter (f : α → β → Bool) (m : RBMap α β cmp) : RBMap α β cmp :=
+  m.fold (fun r k v => if f k v then r.insert k v else r) {}
+
+/--
+`filterMap f m` filters an `RBMap` and simultaneously modifies the filtered values.
+
+It takes a function `f : α → β → Option γ` and applies `f k v` to the value with key `k`.
+The resulting entries with non-`none` value are collected to form the output `RBMap`.
+-/
+def filterMap (f : α → β → Option γ) (m : RBMap α β cmp) : RBMap α γ cmp :=
+  m.fold (fun r k v => match f k v with
+    | none => r
+    | some b => r.insert k b) {}
+
 end RBMap
 
 def rbmapOf {α : Type u} {β : Type v} (l : List (α × β)) (cmp : α → α → Ordering) : RBMap α β cmp :=

src/Lean/Data/RBTree.lean

@@ -114,6 +114,13 @@ def union (t₁ t₂ : RBTree α cmp) : RBTree α cmp :=
 def diff (t₁ t₂ : RBTree α cmp) : RBTree α cmp :=
   t₂.fold .erase t₁
 
+/--
+`filter f m` returns the `RBTree` consisting of all
+`x` in `m` where `f x` returns `true`.
+-/
+def filter (f : α → Bool) (m : RBTree α cmp) : RBTree α cmp :=
+  RBMap.filter (fun a _ => f a) m
+
 end RBTree
 
 def rbtreeOf {α : Type u} (l : List α) (cmp : α → α → Ordering) : RBTree α cmp :=

src/Lean/Elab/App.lean

@@ -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/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

@@ -214,7 +214,7 @@ private def addTraceAsMessagesCore (ctx : Context) (log : MessageLog) (traceStat
   let mut log := log
   let traces' := traces.toArray.qsort fun ((a, _), _) ((b, _), _) => a < b
   for ((pos, endPos), traceMsg) in traces' do
-    let data := .tagged `_traceMsg <| .joinSep traceMsg.toList "\n"
+    let data := .tagged `trace <| .joinSep traceMsg.toList "\n"
     log := log.add <| mkMessageCore ctx.fileName ctx.fileMap data .information pos endPos
   return log
 
@@ -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/Deriving/Util.lean

@@ -49,9 +49,9 @@ invoking ``mkInstImplicitBinders `BarClass foo #[`α, `n, `β]`` gives `` `([Bar
 def mkInstImplicitBinders (className : Name) (indVal : InductiveVal) (argNames : Array Name) : TermElabM (Array Syntax) :=
   forallBoundedTelescope indVal.type indVal.numParams fun xs _ => do
     let mut binders := #[]
-    for i in [:xs.size] do
+    for h : i in [:xs.size] do
       try
-        let x := xs[i]!
+        let x := xs[i]
         let c ← mkAppM className #[x]
         if (← isTypeCorrect c) then
           let argName := argNames[i]!
@@ -86,8 +86,8 @@ def mkContext (fnPrefix : String) (typeName : Name) : TermElabM Context := do
 
 def mkLocalInstanceLetDecls (ctx : Context) (className : Name) (argNames : Array Name) : TermElabM (Array (TSyntax ``Parser.Term.letDecl)) := do
   let mut letDecls := #[]
-  for i in [:ctx.typeInfos.size] do
-    let indVal       := ctx.typeInfos[i]!
+  for h : i in [:ctx.typeInfos.size] do
+    let indVal       := ctx.typeInfos[i]
     let auxFunName   := ctx.auxFunNames[i]!
     let currArgNames ← mkInductArgNames indVal
     let numParams    := indVal.numParams

src/Lean/Elab/Do.lean

@@ -796,10 +796,10 @@ Note that we are not restricting the macro power since the
 actions to be in the same universe.
 -/
 private def mkTuple (elems : Array Syntax) : MacroM Syntax := do
-  if elems.size == 0 then
+  if elems.size = 0 then
     mkUnit
-  else if elems.size == 1 then
-    return elems[0]!
+  else if h : elems.size = 1 then
+    return elems[0]
   else
     elems.extract 0 (elems.size - 1) |>.foldrM (init := elems.back!) fun elem tuple =>
       ``(MProd.mk $elem $tuple)
@@ -831,10 +831,10 @@ def isDoExpr? (doElem : Syntax) : Option Syntax :=
   We use this method when expanding the `for-in` notation.
 -/
 private def destructTuple (uvars : Array Var) (x : Syntax) (body : Syntax) : MacroM Syntax := do
-  if uvars.size == 0 then
+  if uvars.size = 0 then
     return body
-  else if uvars.size == 1 then
-    `(let $(uvars[0]!):ident := $x; $body)
+  else if h : uvars.size = 1 then
+    `(let $(uvars[0]):ident := $x; $body)
   else
     destruct uvars.toList x body
 where
@@ -1314,9 +1314,9 @@ private partial def expandLiftMethodAux (inQuot : Bool) (inBinder : Bool) : Synt
     else if liftMethodDelimiter k then
       return stx
     -- For `pure` if-then-else, we only lift `(<- ...)` occurring in the condition.
-    else if args.size >= 2 && (k == ``termDepIfThenElse || k == ``termIfThenElse) then do
+    else if h : args.size >= 2 ∧ (k == ``termDepIfThenElse || k == ``termIfThenElse) then do
       let inAntiquot := stx.isAntiquot && !stx.isEscapedAntiquot
-      let arg1 ← expandLiftMethodAux (inQuot && !inAntiquot || stx.isQuot) inBinder args[1]!
+      let arg1 ← expandLiftMethodAux (inQuot && !inAntiquot || stx.isQuot) inBinder args[1]
       let args := args.set! 1 arg1
       return Syntax.node i k args
     else if k == ``Parser.Term.liftMethod && !inQuot then withFreshMacroScope do

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/Inductive.lean

@@ -173,15 +173,15 @@ private def checkUnsafe (rs : Array ElabHeaderResult) : TermElabM Unit := do
       throwErrorAt r.view.ref "invalid inductive type, cannot mix unsafe and safe declarations in a mutually inductive datatypes"
 
 private def InductiveView.checkLevelNames (views : Array InductiveView) : TermElabM Unit := do
-  if views.size > 1 then
-    let levelNames := views[0]!.levelNames
+  if h : views.size > 1 then
+    let levelNames := views[0].levelNames
     for view in views do
       unless view.levelNames == levelNames do
         throwErrorAt view.ref "invalid inductive type, universe parameters mismatch in mutually inductive datatypes"
 
 private def ElabHeaderResult.checkLevelNames (rs : Array ElabHeaderResult) : TermElabM Unit := do
-  if rs.size > 1 then
-    let levelNames := rs[0]!.levelNames
+  if h : rs.size > 1 then
+    let levelNames := rs[0].levelNames
     for r in rs do
       unless r.levelNames == levelNames do
         throwErrorAt r.view.ref "invalid inductive type, universe parameters mismatch in mutually inductive datatypes"
@@ -433,8 +433,8 @@ where
         let mut args := e.getAppArgs
         unless args.size ≥ params.size do
           throwError "unexpected inductive type occurrence{indentExpr e}"
-        for i in [:params.size] do
-          let param := params[i]!
+        for h : i in [:params.size] do
+          let param := params[i]
           let arg := args[i]!
           unless (← isDefEq param arg) do
             throwError "inductive datatype parameter mismatch{indentExpr arg}\nexpected{indentExpr param}"
@@ -694,8 +694,8 @@ private def collectLevelParamsInInductive (indTypes : List InductiveType) : Arra
 private def mkIndFVar2Const (views : Array InductiveView) (indFVars : Array Expr) (levelNames : List Name) : ExprMap Expr := Id.run do
   let levelParams := levelNames.map mkLevelParam;
   let mut m : ExprMap Expr := {}
-  for i in [:views.size] do
-    let view    := views[i]!
+  for h : i in [:views.size] do
+    let view    := views[i]
     let indFVar := indFVars[i]!
     m := m.insert indFVar (mkConst view.declName levelParams)
   return m
@@ -856,9 +856,9 @@ private def mkInductiveDecl (vars : Array Expr) (views : Array InductiveView) :
     withInductiveLocalDecls rs fun params indFVars => do
       trace[Elab.inductive] "indFVars: {indFVars}"
       let mut indTypesArray := #[]
-      for i in [:views.size] do
+      for h : i in [:views.size] do
         let indFVar := indFVars[i]!
-        Term.addLocalVarInfo views[i]!.declId indFVar
+        Term.addLocalVarInfo views[i].declId indFVar
         let r     := rs[i]!
         /- At this point, because of `withInductiveLocalDecls`, the only fvars that are in context are the ones related to the first inductive type.
            Because of this, we need to replace the fvars present in each inductive type's header of the mutual block with those of the first inductive.

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

@@ -87,12 +87,15 @@ private def elabLetRecDeclValues (view : LetRecView) : TermElabM (Array Expr) :=
   view.decls.mapM fun view => do
     forallBoundedTelescope view.type view.binderIds.size fun xs type => do
       -- Add new info nodes for new fvars. The server will detect all fvars of a binder by the binder's source location.
-      for i in [0:view.binderIds.size] do
-        addLocalVarInfo view.binderIds[i]! xs[i]!
+      for h : 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

@@ -282,8 +282,8 @@ where
         let dArg := dArgs[i]!
         unless (← isDefEq tArg dArg) do
           return i :: (← goType tArg dArg)
-      for i in [info.numParams : tArgs.size] do
-        let tArg := tArgs[i]!
+      for h : i in [info.numParams : tArgs.size] do
+        let tArg := tArgs[i]
         let dArg := dArgs[i]!
         unless (← isDefEq tArg dArg) do
           return i :: (← goIndex tArg dArg)
@@ -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/Open.lean

@@ -49,12 +49,12 @@ private def resolveNameUsingNamespacesCore (nss : List Name) (idStx : Syntax) :
       exs := exs.push ex
   if exs.size == nss.length then
     withRef idStx do
-      if exs.size == 1 then
-        throw exs[0]!
+      if h : exs.size = 1 then
+        throw exs[0]
       else
         throwErrorWithNestedErrors "failed to open" exs
-  if result.size == 1 then
-    return result[0]!
+  if h : result.size = 1 then
+    return result[0]
   else
     withRef idStx do throwError "ambiguous identifier '{idStx.getId}', possible interpretations: {result.map mkConst}"
 

src/Lean/Elab/PreDefinition/Basic.lean

@@ -244,8 +244,8 @@ def checkCodomainsLevel (preDefs : Array PreDefinition) : MetaM Unit := do
     lambdaTelescope preDef.value fun xs _ => return xs.size
   forallBoundedTelescope preDefs[0]!.type arities[0]!  fun _ type₀ => do
     let u₀ ← getLevel type₀
-    for i in [1:preDefs.size] do
-      forallBoundedTelescope preDefs[i]!.type arities[i]! fun _ typeᵢ =>
+    for h : i in [1:preDefs.size] do
+      forallBoundedTelescope preDefs[i].type arities[i]! fun _ typeᵢ =>
       unless ← isLevelDefEq u₀ (← getLevel typeᵢ) do
         withOptions (fun o => pp.sanitizeNames.set o false) do
           throwError m!"invalid mutual definition, result types must be in the same universe " ++

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/TerminationArgument.lean

@@ -53,10 +53,10 @@ def TerminationArgument.elab (funName : Name) (type : Expr) (arity extraParams :
     (hint : TerminationBy) : TermElabM TerminationArgument := withDeclName funName do
   assert! extraParams ≤ arity
 
-  if hint.vars.size > extraParams then
+  if h : hint.vars.size > extraParams then
     let mut msg := m!"{parameters hint.vars.size} bound in `termination_by`, but the body of " ++
       m!"{funName} only binds {parameters extraParams}."
-    if let `($ident:ident) := hint.vars[0]! then
+    if let `($ident:ident) := hint.vars[0] then
       if ident.getId.isSuffixOf funName then
           msg := msg ++ m!" (Since Lean v4.6.0, the `termination_by` clause no longer " ++
             "expects the function name here.)"

src/Lean/Elab/PreDefinition/TerminationHint.lean

@@ -90,10 +90,10 @@ lambda of `value`, and throws appropriate errors.
 -/
 def TerminationBy.checkVars (funName : Name) (extraParams : Nat) (tb : TerminationBy) : MetaM Unit := do
   unless tb.synthetic do
-    if tb.vars.size > extraParams then
+    if h : tb.vars.size > extraParams then
       let mut msg := m!"{parameters tb.vars.size} bound in `termination_by`, but the body of " ++
         m!"{funName} only binds {parameters extraParams}."
-      if let `($ident:ident) := tb.vars[0]! then
+      if let `($ident:ident) := tb.vars[0] then
         if ident.getId.isSuffixOf funName then
             msg := msg ++ m!" (Since Lean v4.6.0, the `termination_by` clause no longer " ++
               "expects the function name here.)"

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

@@ -227,7 +227,7 @@ def mkFix (preDef : PreDefinition) (prefixArgs : Array Expr) (argsPacker : ArgsP
     -- decreasing goals when the function has only one non fixed argument.
     -- This renaming is irrelevant if the function has multiple non fixed arguments. See `process*` functions above.
     let lctx := (← getLCtx).setUserName x.fvarId! varName
-    withTheReader Meta.Context (fun ctx => { ctx with lctx }) do
+    withLCtx' lctx do
       let F   := xs[1]!
       let val := preDef.value.beta (prefixArgs.push x)
       let val ← processSumCasesOn x F val fun x F val => do

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

@@ -166,7 +166,7 @@ def mayOmitSizeOf (is_mutual : Bool) (args : Array Expr) (x : Expr) : MetaM Bool
 def withUserNames {α} (xs : Array Expr) (ns : Array Name) (k : MetaM α) : MetaM α := do
   let mut lctx ←  getLCtx
   for x in xs, n in ns do lctx := lctx.setUserName x.fvarId! n
-  withTheReader Meta.Context (fun ctx => { ctx with lctx }) k
+  withLCtx' lctx k
 
 /-- Create one measure for each (eligible) parameter of the given predefintion.  -/
 def simpleMeasures (preDefs : Array PreDefinition) (fixedPrefixSize : Nat)

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

@@ -21,8 +21,8 @@ open Meta
 private partial def addNonRecPreDefs (fixedPrefixSize : Nat) (argsPacker : ArgsPacker) (preDefs : Array PreDefinition) (preDefNonRec : PreDefinition)  : TermElabM Unit := do
   let us := preDefNonRec.levelParams.map mkLevelParam
   let all := preDefs.toList.map (·.declName)
-  for fidx in [:preDefs.size] do
-    let preDef := preDefs[fidx]!
+  for h : fidx in [:preDefs.size] do
+    let preDef := preDefs[fidx]
     let value ← forallBoundedTelescope preDef.type (some fixedPrefixSize) fun xs _ => do
       let value := mkAppN (mkConst preDefNonRec.declName us) xs
       let value ← argsPacker.curryProj value fidx

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/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

@@ -19,12 +19,12 @@ def expandOptPrecedence (stx : Syntax) : MacroM (Option Nat) :=
     return some (← evalPrec stx[0][1])
 
 private def mkParserSeq (ds : Array (Term × Nat)) : TermElabM (Term × Nat) := do
-  if ds.size == 0 then
+  if h₀ : ds.size = 0 then
     throwUnsupportedSyntax
-  else if ds.size == 1 then
-    pure ds[0]!
+  else if h₁ : ds.size = 1 then
+    pure ds[0]
   else
-    let mut (r, stackSum) := ds[0]!
+    let mut (r, stackSum) := ds[0]
     for (d, stackSz) in ds[1:ds.size] do
       r ← `(ParserDescr.binary `andthen $r $d)
       stackSum := stackSum + stackSz
@@ -233,11 +233,15 @@ where
     return (← `((with_annotate_term $(stx[0]) @ParserDescr.sepBy1) $p $sep $psep $(quote allowTrailingSep)), 1)
 
   isValidAtom (s : String) : Bool :=
+    -- Pretty-printing instructions shouldn't affect validity
+    let s := s.trim
     !s.isEmpty &&
-    s.front != '\'' &&
+    (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.front.isDigit &&
+    !(s.any Char.isWhitespace)
 
   processAtom (stx : Syntax) := do
     match stx[0].isStrLit? with

src/Lean/Elab/SyntheticMVars.lean

@@ -149,8 +149,8 @@ where
         -- Succeeded. Collect new TC problems
         trace[Elab.defaultInstance] "isDefEq worked {mkMVar mvarId} : {← inferType (mkMVar mvarId)} =?= {candidate} : {← inferType candidate}"
         let mut pending := []
-        for i in [:bis.size] do
-          if bis[i]! == BinderInfo.instImplicit then
+        for h : i in [:bis.size] do
+          if bis[i] == BinderInfo.instImplicit then
             pending := mvars[i]!.mvarId! :: pending
         synthesizePending pending
       else

src/Lean/Elab/Tactic/BVDecide/Frontend/Normalize.lean

@@ -216,35 +216,23 @@ Flatten out ands. That is look for hypotheses of the form `h : (x && y) = true`
 with `h.left : x = true` and `h.right : y = true`. This can enable more fine grained substitutions
 in embedded constraint substitution.
 -/
-def andFlatteningPass : Pass where
+partial def andFlatteningPass : Pass where
   name := `andFlattening
   run goal := do
     goal.withContext do
       let hyps ← goal.getNondepPropHyps
       let mut newHyps := #[]
       let mut oldHyps := #[]
-      for hyp in hyps do
-        let typ ← hyp.getType
-        let_expr Eq α eqLhs eqRhs := typ | continue
-        let_expr Bool.and lhs rhs := eqLhs | continue
-        let_expr Bool := α | continue
-        let_expr Bool.true := eqRhs | continue
-        let mkEqTrue (lhs : Expr) : Expr :=
-          mkApp3 (mkConst ``Eq [1]) (mkConst ``Bool) lhs (mkConst ``Bool.true)
-        let hypExpr := (← hyp.getDecl).toExpr
-        let leftHyp : Hypothesis := {
-          userName := (← hyp.getUserName) ++ `left,
-          type := mkEqTrue lhs,
-          value := mkApp3 (mkConst ``Std.Tactic.BVDecide.Normalize.Bool.and_left) lhs rhs hypExpr
+      for fvar in hyps do
+        let hyp : Hypothesis := {
+          userName := (← fvar.getDecl).userName
+          type := ← fvar.getType
+          value := mkFVar fvar
         }
-        let rightHyp : Hypothesis := {
-          userName := (← hyp.getUserName) ++ `right,
-          type := mkEqTrue rhs,
-          value := mkApp3 (mkConst ``Std.Tactic.BVDecide.Normalize.Bool.and_right) lhs rhs hypExpr
-        }
-        newHyps := newHyps.push leftHyp
-        newHyps := newHyps.push rightHyp
-        oldHyps := oldHyps.push hyp
+        let sizeBefore := newHyps.size
+        newHyps ← splitAnds hyp newHyps
+        if newHyps.size > sizeBefore then
+          oldHyps := oldHyps.push fvar
       if newHyps.size == 0 then
         return goal
       else
@@ -252,6 +240,38 @@ def andFlatteningPass : Pass where
         -- Given that we collected the hypotheses in the correct order above the invariant is given
         let goal ← goal.tryClearMany oldHyps
         return goal
+where
+  splitAnds (hyp : Hypothesis) (hyps : Array Hypothesis) (first : Bool := true) :
+      MetaM (Array Hypothesis) := do
+    match ← trySplit hyp with
+    | some (left, right) =>
+      let hyps ← splitAnds left hyps false
+      splitAnds right hyps false
+    | none =>
+      if first then
+        return hyps
+      else
+        return hyps.push hyp
+
+  trySplit (hyp : Hypothesis) : MetaM (Option (Hypothesis × Hypothesis)) := do
+    let typ := hyp.type
+    let_expr Eq α eqLhs eqRhs := typ | return none
+    let_expr Bool.and lhs rhs := eqLhs | return none
+    let_expr Bool.true := eqRhs | return none
+    let_expr Bool := α | return none
+    let mkEqTrue (lhs : Expr) : Expr :=
+      mkApp3 (mkConst ``Eq [1]) (mkConst ``Bool) lhs (mkConst ``Bool.true)
+    let leftHyp : Hypothesis := {
+      userName := hyp.userName,
+      type := mkEqTrue lhs,
+      value := mkApp3 (mkConst ``Std.Tactic.BVDecide.Normalize.Bool.and_left) lhs rhs hyp.value
+    }
+    let rightHyp : Hypothesis := {
+      userName := hyp.userName,
+      type := mkEqTrue rhs,
+      value := mkApp3 (mkConst ``Std.Tactic.BVDecide.Normalize.Bool.and_right) lhs rhs hyp.value
+    }
+    return some (leftHyp, rightHyp)
 
 /--
 Substitute embedded constraints. That is look for hypotheses of the form `h : x = true` and use
@@ -308,22 +328,18 @@ def acNormalizePass : Pass where
 
     return newGoal
 
-/--
-The normalization passes used by `bv_normalize` and thus `bv_decide`.
--/
-def defaultPipeline (cfg : BVDecideConfig ): List Pass :=
-  [
-    rewriteRulesPass cfg.maxSteps,
-    andFlatteningPass,
-    embeddedConstraintPass cfg.maxSteps
-  ]
-
 def passPipeline (cfg : BVDecideConfig) : List Pass := Id.run do
-  let mut passPipeline := defaultPipeline cfg
+  let mut passPipeline := [rewriteRulesPass cfg.maxSteps]
 
   if cfg.acNf then
     passPipeline := passPipeline ++ [acNormalizePass]
 
+  if cfg.andFlattening then
+    passPipeline := passPipeline ++ [andFlatteningPass]
+
+  if cfg.embeddedConstraintSubst then
+    passPipeline := passPipeline ++ [embeddedConstraintPass cfg.maxSteps]
+
   return passPipeline
 
 end Pass

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/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/Omega/Frontend.lean

@@ -6,7 +6,6 @@ Authors: Kim Morrison
 prelude
 import Lean.Elab.Tactic.Omega.Core
 import Lean.Elab.Tactic.FalseOrByContra
-import Lean.Meta.Tactic.Cases
 import Lean.Elab.Tactic.Config
 
 /-!
@@ -520,23 +519,6 @@ partial def processFacts (p : MetaProblem) : OmegaM (MetaProblem × Nat) := do
 
 end MetaProblem
 
-/--
-Given `p : P ∨ Q` (or any inductive type with two one-argument constructors),
-split the goal into two subgoals:
-one containing the hypothesis `h : P` and another containing `h : Q`.
--/
-def cases₂ (mvarId : MVarId) (p : Expr) (hName : Name := `h) :
-    MetaM ((MVarId × FVarId) × (MVarId × FVarId)) := do
-  let mvarId ← mvarId.assert `hByCases (← inferType p) p
-  let (fvarId, mvarId) ← mvarId.intro1
-  let #[s₁, s₂] ← mvarId.cases fvarId #[{ varNames := [hName] }, { varNames := [hName] }] |
-    throwError "'cases' tactic failed, unexpected number of subgoals"
-  let #[Expr.fvar f₁ ..] ← pure s₁.fields
-    | throwError "'cases' tactic failed, unexpected new hypothesis"
-  let #[Expr.fvar f₂ ..] ← pure s₂.fields
-    | throwError "'cases' tactic failed, unexpected new hypothesis"
-  return ((s₁.mvarId, f₁), (s₂.mvarId, f₂))
-
 /--
 Helpful error message when omega cannot find a solution
 -/
@@ -628,33 +610,36 @@ mutual
 Split a disjunction in a `MetaProblem`, and if we find a new usable fact
 call `omegaImpl` in both branches.
 -/
-partial def splitDisjunction (m : MetaProblem) (g : MVarId) : OmegaM Unit := g.withContext do
+partial def splitDisjunction (m : MetaProblem) : OmegaM Expr := do
   match m.disjunctions with
     | [] => throwError "omega could not prove the goal:\n{← formatErrorMessage m.problem}"
-    | h :: t =>
-      trace[omega] "Case splitting on {← inferType h}"
-      let ctx ← getMCtx
-      let (⟨g₁, h₁⟩, ⟨g₂, h₂⟩) ← cases₂ g h
-      trace[omega] "Adding facts:\n{← g₁.withContext <| inferType (.fvar h₁)}"
-      let m₁ := { m with facts := [.fvar h₁], disjunctions := t }
-      let r ← withoutModifyingState do
-        let (m₁, n) ← g₁.withContext m₁.processFacts
+    | h :: t => do
+      let hType ← whnfD (← inferType h)
+      trace[omega] "Case splitting on {hType}"
+      let_expr Or hType₁ hType₂ := hType | throwError "Unexpected disjunction {hType}"
+      let p?₁ ← withoutModifyingState do withLocalDeclD `h₁ hType₁ fun h₁ => do
+        withTraceNode `omega (msg := fun _ => do pure m!"Assuming fact:{indentExpr hType₁}") do
+        let m₁ := { m with facts := [h₁], disjunctions := t }
+        let (m₁, n) ← m₁.processFacts
         if 0 < n then
-          omegaImpl m₁ g₁
-          pure true
+          let p₁ ← omegaImpl m₁
+          let p₁ ← mkLambdaFVars #[h₁] p₁
+          return some p₁
         else
-          pure false
-      if r then
-        trace[omega] "Adding facts:\n{← g₂.withContext <| inferType (.fvar h₂)}"
-        let m₂ := { m with facts := [.fvar h₂], disjunctions := t }
-        omegaImpl m₂ g₂
+          return none
+      if let some p₁ := p?₁ then
+         withLocalDeclD `h₂ hType₂ fun h₂ => do
+          withTraceNode `omega (msg := fun _ => do pure m!"Assuming fact:{indentExpr hType₂}") do
+          let m₂ := { m with facts := [h₂], disjunctions := t }
+          let p₂ ← omegaImpl m₂
+          let p₂ ← mkLambdaFVars #[h₂] p₂
+          return mkApp6 (mkConst ``Or.elim) hType₁ hType₂ (mkConst ``False) h p₁ p₂
       else
         trace[omega] "No new facts found."
-        setMCtx ctx
-        splitDisjunction { m with disjunctions := t } g
+        splitDisjunction { m with disjunctions := t }
 
 /-- Implementation of the `omega` algorithm, and handling disjunctions. -/
-partial def omegaImpl (m : MetaProblem) (g : MVarId) : OmegaM Unit := g.withContext do
+partial def omegaImpl (m : MetaProblem) : OmegaM Expr := do
   let (m, _) ← m.processFacts
   guard m.facts.isEmpty
   let p := m.problem
@@ -663,12 +648,12 @@ partial def omegaImpl (m : MetaProblem) (g : MVarId) : OmegaM Unit := g.withCont
   trace[omega] "After elimination:\nAtoms: {← atomsList}\n{p'}"
   match p'.possible, p'.proveFalse?, p'.proveFalse?_spec with
   | true, _, _ =>
-    splitDisjunction m g
+    splitDisjunction m
   | false, .some prf, _ =>
     trace[omega] "Justification:\n{p'.explanation?.get}"
     let prf ← instantiateMVars (← prf)
     trace[omega] "omega found a contradiction, proving {← inferType prf}"
-    g.assign prf
+    return prf
 
 end
 
@@ -677,7 +662,9 @@ Given a collection of facts, try prove `False` using the omega algorithm,
 and close the goal using that.
 -/
 def omega (facts : List Expr) (g : MVarId) (cfg : OmegaConfig := {}) : MetaM Unit :=
-  OmegaM.run (omegaImpl { facts } g) cfg
+  g.withContext do
+    let prf ← OmegaM.run (omegaImpl { facts }) cfg
+    g.assign prf
 
 open Lean Elab Tactic Parser.Tactic
 

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/Environment.lean

@@ -317,8 +317,8 @@ partial def ensureExtensionsArraySize (exts : Array EnvExtensionState) : IO (Arr
 where
   loop (i : Nat) (exts : Array EnvExtensionState) : IO (Array EnvExtensionState) := do
     let envExtensions ← envExtensionsRef.get
-    if i < envExtensions.size then
-      let s ← envExtensions[i]!.mkInitial
+    if h : i < envExtensions.size then
+      let s ← envExtensions[i].mkInitial
       let exts := exts.push s
       loop (i + 1) exts
     else
@@ -726,7 +726,6 @@ def mkExtNameMap (startingAt : Nat) : IO (Std.HashMap Name Nat) := do
   let descrs ← persistentEnvExtensionsRef.get
   let mut result := {}
   for h : i in [startingAt : descrs.size] do
-    have : i < descrs.size := h.upper
     let descr := descrs[i]
     result := result.insert descr.name i
   return result
@@ -740,7 +739,6 @@ private def setImportedEntries (env : Environment) (mods : Array ModuleData) (st
   /- For each module `mod`, and `mod.entries`, if the extension name is one of the extensions after `startingAt`, set `entries` -/
   let extNameIdx ← mkExtNameMap startingAt
   for h : modIdx in [:mods.size] do
-    have : modIdx < mods.size := h.upper
     let mod := mods[modIdx]
     for (extName, entries) in mod.entries do
       if let some entryIdx := extNameIdx[extName]? then
@@ -860,7 +858,7 @@ def finalizeImport (s : ImportState) (imports : Array Import) (opts : Options) (
   let mut const2ModIdx : Std.HashMap Name ModuleIdx := Std.HashMap.empty (capacity := numConsts)
   let mut constantMap : Std.HashMap Name ConstantInfo := Std.HashMap.empty (capacity := numConsts)
   for h : modIdx in [0:s.moduleData.size] do
-    let mod := s.moduleData[modIdx]'h.upper
+    let mod := s.moduleData[modIdx]
     for cname in mod.constNames, cinfo in mod.constants do
       match constantMap.getThenInsertIfNew? cname cinfo with
       | (cinfoPrev?, constantMap') =>

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/Message.lean

@@ -116,7 +116,7 @@ variable (p : Name → Bool) in
 /-- Returns true when the message contains a `MessageData.tagged tag ..` constructor where `p tag`
 is true.
 
-This does not descend into lazily generated subtress (`.ofLazy`); message tags
+This does not descend into lazily generated subtrees (`.ofLazy`); message tags
 of interest (like those added by `logLinter`) are expected to be near the root
 of the `MessageData`, and not hidden inside `.ofLazy`.
 -/
@@ -130,6 +130,19 @@ partial def hasTag : MessageData → Bool
   | trace data msg msgs     => p data.cls || hasTag msg || msgs.any hasTag
   | _                       => false
 
+/--
+Returns the top-level tag of the message.
+If none, returns `Name.anonymous`.
+
+This does not descend into message subtrees (e.g., `.compose`, `.ofLazy`).
+The message kind is expected to describe the whole message.
+-/
+def kind : MessageData → Name
+  | withContext _ msg       => kind msg
+  | withNamingContext _ msg => kind msg
+  | tagged n _              => n
+  | _                       => .anonymous
+
 /-- An empty message. -/
 def nil : MessageData :=
   ofFormat Format.nil
@@ -315,7 +328,7 @@ structure BaseMessage (α : Type u) where
   endPos        : Option Position := none
   /-- If `true`, report range as given; see `msgToInteractiveDiagnostic`. -/
   keepFullRange : Bool := false
-  severity      : MessageSeverity := MessageSeverity.error
+  severity      : MessageSeverity := .error
   caption       : String          := ""
   /-- The content of the message. -/
   data          : α
@@ -328,7 +341,10 @@ abbrev Message := BaseMessage MessageData
 /-- A `SerialMessage` is a `Message` whose `MessageData` has been eagerly
 serialized and is thus appropriate for use in pure contexts where the effectful
 `MessageData.toString` cannot be used. -/
-abbrev SerialMessage := BaseMessage String
+structure SerialMessage extends BaseMessage String where
+  /-- The message kind (i.e., the top-level tag). -/
+  kind          : Name
+  deriving ToJson, FromJson
 
 namespace SerialMessage
 
@@ -354,8 +370,12 @@ end SerialMessage
 
 namespace Message
 
+@[inherit_doc MessageData.kind] abbrev kind (msg : Message) :=
+  msg.data.kind
+
+/-- Serializes the message, converting its data into a string and saving its kind. -/
 @[inline] def serialize (msg : Message) : IO SerialMessage := do
-  return {msg with data := ← msg.data.toString}
+  return {msg with kind := msg.kind, data := ← msg.data.toString}
 
 protected def toString (msg : Message) (includeEndPos := false) : IO String := do
   -- Remark: The inline here avoids a new message allocation when `msg` is shared

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
@@ -332,7 +443,8 @@ register_builtin_option maxSynthPendingDepth : Nat := {
   Contextual information for the `MetaM` monad.
 -/
 structure Context where
-  config            : Config               := {}
+  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 +1066,25 @@ 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 })
+
+@[inline] def withIncSynthPending : n α → n α :=
+  mapMetaM <| withReader (fun ctx => { ctx with synthPendingDepth := ctx.synthPendingDepth + 1 })
+
+@[inline] def withInTypeClassResolution : n α → n α :=
+  mapMetaM <| withReader (fun ctx => { ctx with inTypeClassResolution := true })
 
 /--
 Executes `x` tracking zetaDelta reductions `Config.trackZetaDelta := true`
@@ -952,8 +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 :=
@@ -974,13 +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 :=
@@ -1002,8 +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
@@ -1422,6 +1569,14 @@ def withLocalDecl (name : Name) (bi : BinderInfo) (type : Expr) (k : Expr → n
 def withLocalDeclD (name : Name) (type : Expr) (k : Expr → n α) : n α :=
   withLocalDecl name BinderInfo.default type k
 
+/--
+Similar to `withLocalDecl`, but it does **not** check whether the new variable is a local instance or not.
+-/
+def withLocalDeclNoLocalInstanceUpdate (name : Name) (bi : BinderInfo) (type : Expr) (x : Expr → MetaM α) : MetaM α := do
+  let fvarId ← mkFreshFVarId
+  withReader (fun ctx => { ctx with lctx := ctx.lctx.mkLocalDecl fvarId name type bi }) do
+    x (mkFVar fvarId)
+
 /-- Append an array of free variables `xs` to the local context and execute `k xs`.
 `declInfos` takes the form of an array consisting of:
 - the name of the variable
@@ -1538,11 +1693,11 @@ def withReplaceFVarId {α} (fvarId : FVarId) (e : Expr) : MetaM α → MetaM α
     localInstances := ctx.localInstances.erase fvarId }
 
 /--
-  `withNewMCtxDepth k` executes `k` with a higher metavariable context depth,
-  where metavariables created outside the `withNewMCtxDepth` (with a lower depth) cannot be assigned.
-  If `allowLevelAssignments` is set to true, then the level metavariable depth
-  is not increased, and level metavariables from the outer scope can be
-  assigned.  (This is used by TC synthesis.)
+`withNewMCtxDepth k` executes `k` with a higher metavariable context depth,
+where metavariables created outside the `withNewMCtxDepth` (with a lower depth) cannot be assigned.
+If `allowLevelAssignments` is set to true, then the level metavariable depth
+is not increased, and level metavariables from the outer scope can be
+assigned.  (This is used by TC synthesis.)
 -/
 def withNewMCtxDepth (k : n α) (allowLevelAssignments := false) : n α :=
   mapMetaM (withNewMCtxDepthImp allowLevelAssignments) k
@@ -1552,13 +1707,20 @@ private def withLocalContextImp (lctx : LocalContext) (localInsts : LocalInstanc
     x
 
 /--
-  `withLCtx lctx localInsts k` replaces the local context and local instances, and then executes `k`.
-  The local context and instances are restored after executing `k`.
-  This method assumes that the local instances in `localInsts` are in the local context `lctx`.
+`withLCtx lctx localInsts k` replaces the local context and local instances, and then executes `k`.
+The local context and instances are restored after executing `k`.
+This method assumes that the local instances in `localInsts` are in the local context `lctx`.
 -/
 def withLCtx (lctx : LocalContext) (localInsts : LocalInstances) : n α → n α :=
   mapMetaM <| withLocalContextImp lctx localInsts
 
+/--
+Simpler version of `withLCtx` which just updates the local context. It is the resposability of the
+caller ensure the local instances are also properly updated.
+-/
+def withLCtx' (lctx : LocalContext) : n α → n α :=
+  mapMetaM <| withReader (fun ctx => { ctx with lctx })
+
 /--
 Runs `k` in a local environment with the `fvarIds` erased.
 -/

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/Coe.lean

@@ -157,9 +157,11 @@ def coerceMonadLift? (e expectedType : Expr) : MetaM (Option Expr) := do
   let eType ← instantiateMVars (← inferType e)
   let some (n, β) ← isTypeApp? expectedType | return none
   let some (m, α) ← isTypeApp? eType | return none
+  -- Need to save and restore the state in case `m` and `n` are defeq but not monads to prevent this procedure from having side effects.
+  let saved ← saveState
   if (← isDefEq m n) then
-    let some monadInst ← isMonad? n | return none
-    try expandCoe (← mkAppOptM ``Lean.Internal.coeM #[m, α, β, none, monadInst, e]) catch _ => return none
+    let some monadInst ← isMonad? n | restoreState saved; return none
+    try expandCoe (← mkAppOptM ``Lean.Internal.coeM #[m, α, β, none, monadInst, e]) catch _ => restoreState saved; return none
   else if autoLift.get (← getOptions) then
     try
       -- Construct lift from `m` to `n`