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2 Commits

Author SHA1 Message Date
Kim Morrison
357e6d9259 fix test 2025-05-28 21:05:47 +10:00
Kim Morrison
ca55c56a50 fix: make Array.size not reducible 2025-05-28 20:31:01 +10:00
17 changed files with 46 additions and 37 deletions

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@@ -91,7 +91,8 @@ theorem ext' {xs ys : Array α} (h : xs.toList = ys.toList) : xs = ys := by
@[simp, grind =] theorem getElem_toList {xs : Array α} {i : Nat} (h : i < xs.size) : xs.toList[i] = xs[i] := rfl
@[simp, grind =] theorem getElem?_toList {xs : Array α} {i : Nat} : xs.toList[i]? = xs[i]? := by
simp [getElem?_def]
simp only [getElem?_def, getElem_toList]
simp only [Array.size]
/-- `a ∈ as` is a predicate which asserts that `a` is in the array `as`. -/
-- NB: This is defined as a structure rather than a plain def so that a lemma

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@@ -78,7 +78,8 @@ theorem foldrM_eq_reverse_foldlM_toList [Monad m] {f : α → β → m β} {init
have : xs = #[] 0 < xs.size :=
match xs with | [] => .inl rfl | a::l => .inr (Nat.zero_lt_succ _)
match xs, this with | _, .inl rfl => simp [foldrM] | xs, .inr h => ?_
simp [foldrM, h, foldrM_eq_reverse_foldlM_toList.aux, List.take_length]
simp only [foldrM, h, foldrM_eq_reverse_foldlM_toList.aux]
simp [Array.size]
@[simp, grind =] theorem foldrM_toList [Monad m]
{f : α β m β} {init : β} {xs : Array α} :

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@@ -105,6 +105,7 @@ theorem boole_getElem_le_countP {xs : Array α} {i : Nat} (h : i < xs.size) :
theorem countP_set {xs : Array α} {i : Nat} {a : α} (h : i < xs.size) :
(xs.set i a).countP p = xs.countP p - (if p xs[i] then 1 else 0) + (if p a then 1 else 0) := by
rcases xs with xs
simp at h
simp [List.countP_set, h]
theorem countP_filter {xs : Array α} :

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@@ -69,7 +69,7 @@ theorem isEqv_eq_decide (xs ys : Array α) (r) :
simpa [isEqv_iff_rel] using h'
@[simp, grind =] theorem isEqv_toList [BEq α] (xs ys : Array α) : (xs.toList.isEqv ys.toList r) = (xs.isEqv ys r) := by
simp [isEqv_eq_decide, List.isEqv_eq_decide]
simp [isEqv_eq_decide, List.isEqv_eq_decide, Array.size]
theorem eq_of_isEqv [DecidableEq α] (xs ys : Array α) (h : Array.isEqv xs ys (fun x y => x = y)) : xs = ys := by
have h, h' := rel_of_isEqv h
@@ -100,7 +100,7 @@ theorem beq_eq_decide [BEq α] (xs ys : Array α) :
simp [BEq.beq, isEqv_eq_decide]
@[simp, grind =] theorem beq_toList [BEq α] (xs ys : Array α) : (xs.toList == ys.toList) = (xs == ys) := by
simp [beq_eq_decide, List.beq_eq_decide]
simp [beq_eq_decide, List.beq_eq_decide, Array.size]
end Array

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@@ -655,13 +655,13 @@ theorem findFinIdx?_append {xs ys : Array α} {p : α → Bool} :
theorem isSome_findFinIdx? {xs : Array α} {p : α Bool} :
(xs.findFinIdx? p).isSome = xs.any p := by
rcases xs with xs
simp
simp [Array.size]
@[simp]
theorem isNone_findFinIdx? {xs : Array α} {p : α Bool} :
(xs.findFinIdx? p).isNone = xs.all (fun x => ¬ p x) := by
rcases xs with xs
simp
simp [Array.size]
@[simp] theorem findFinIdx?_subtype {p : α Prop} {xs : Array { x // p x }}
{f : { x // p x } Bool} {g : α Bool} (hf : x h, f x, h = g x) :
@@ -669,7 +669,8 @@ theorem isNone_findFinIdx? {xs : Array α} {p : α → Bool} :
cases xs
simp only [List.findFinIdx?_toArray, hf, List.findFinIdx?_subtype]
rw [findFinIdx?_congr List.unattach_toArray]
simp [Function.comp_def]
simp only [Option.map_map, Function.comp_def, Fin.cast_trans]
simp [Array.size]
/-! ### idxOf
@@ -733,18 +734,19 @@ theorem finIdxOf?_empty [BEq α] : (#[] : Array α).finIdxOf? a = none := by sim
@[simp] theorem finIdxOf?_eq_none_iff [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
xs.finIdxOf? a = none a xs := by
rcases xs with xs
simp [List.finIdxOf?_eq_none_iff]
simp [List.finIdxOf?_eq_none_iff, Array.size]
@[simp] theorem finIdxOf?_eq_some_iff [BEq α] [LawfulBEq α] {xs : Array α} {a : α} {i : Fin xs.size} :
xs.finIdxOf? a = some i xs[i] = a j (_ : j < i), ¬xs[j] = a := by
rcases xs with xs
unfold Array.size at i
simp [List.finIdxOf?_eq_some_iff]
@[simp]
theorem isSome_finIdxOf? [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
(xs.finIdxOf? a).isSome a xs := by
rcases xs with xs
simp
simp [Array.size]
theorem isNone_finIdxOf? [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
(xs.finIdxOf? a).isNone = ¬ a xs := by

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@@ -44,6 +44,7 @@ theorem insertIdx_zero {xs : Array α} {x : α} : xs.insertIdx 0 x = #[x] ++ xs
@[simp] theorem size_insertIdx {xs : Array α} (h : i xs.size) : (xs.insertIdx i a).size = xs.size + 1 := by
rcases xs with xs
simp at h
simp [List.length_insertIdx, h]
theorem eraseIdx_insertIdx {i : Nat} {xs : Array α} (h : i xs.size) :

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@@ -75,7 +75,7 @@ theorem ne_empty_of_size_pos (h : 0 < xs.size) : xs ≠ #[] := by
cases xs
simpa using List.ne_nil_of_length_pos h
theorem size_eq_zero_iff : xs.size = 0 xs = #[] :=
@[simp] theorem size_eq_zero_iff : xs.size = 0 xs = #[] :=
eq_empty_of_size_eq_zero, fun h => h rfl
@[deprecated size_eq_zero_iff (since := "2025-02-24")]
@@ -169,6 +169,7 @@ theorem getD_getElem? {xs : Array α} {i : Nat} {d : α} :
theorem getElem_push_lt {xs : Array α} {x : α} {i : Nat} (h : i < xs.size) :
have : i < (xs.push x).size := by simp [*, Nat.lt_succ_of_le, Nat.le_of_lt]
(xs.push x)[i] = xs[i] := by
rw [Array.size] at h
simp only [push, getElem_toList, List.concat_eq_append, List.getElem_append_left, h]
@[simp] theorem getElem_push_eq {xs : Array α} {x : α} : (xs.push x)[xs.size] = x := by
@@ -1858,7 +1859,7 @@ theorem getElem_append_right {xs ys : Array α} {h : i < (xs ++ ys).size} (hle :
(xs ++ ys)[i] = ys[i - xs.size]'(Nat.sub_lt_left_of_lt_add hle (size_append .. h)) := by
simp only [ getElem_toList]
have h' : i < (xs.toList ++ ys.toList).length := by rwa [ length_toList, toList_append] at h
conv => rhs; rw [ List.getElem_append_right (h₁ := hle) (h₂ := h')]
conv => rhs; unfold Array.size; rw [ List.getElem_append_right (h₁ := hle) (h₂ := h')]
apply List.get_of_eq; rw [toList_append]
theorem getElem?_append_left {xs ys : Array α} {i : Nat} (hn : i < xs.size) :
@@ -2025,7 +2026,7 @@ theorem append_eq_append_iff {ws xs ys zs : Array α} :
xs ++ ys.set (i - xs.size) x (by simp at h; omega) := by
rcases xs with s
rcases ys with t
simp only [List.append_toArray, List.set_toArray, List.set_append]
simp only [List.append_toArray, List.set_toArray, List.set_append, Array.size]
split <;> simp
@[simp] theorem set_append_left {xs ys : Array α} {i : Nat} {x : α} (h : i < xs.size) :
@@ -2045,7 +2046,7 @@ theorem append_eq_append_iff {ws xs ys zs : Array α} :
xs ++ ys.setIfInBounds (i - xs.size) x := by
rcases xs with s
rcases ys with t
simp only [List.append_toArray, List.setIfInBounds_toArray, List.set_append]
simp only [List.append_toArray, List.setIfInBounds_toArray, List.set_append, Array.size]
split <;> simp
@[simp] theorem setIfInBounds_append_left {xs ys : Array α} {i : Nat} {x : α} (h : i < xs.size) :
@@ -4500,6 +4501,7 @@ abbrev contains_def [DecidableEq α] {a : α} {xs : Array α} : xs.contains a
@[simp] theorem size_zipWith {xs : Array α} {ys : Array β} {f : α β γ} :
(zipWith f xs ys).size = min xs.size ys.size := by
rw [size_eq_length_toList, toList_zipWith, List.length_zipWith]
simp only [Array.size]
@[simp] theorem size_zip {xs : Array α} {ys : Array β} :
(zip xs ys).size = min xs.size ys.size :=
@@ -4572,7 +4574,7 @@ theorem toListRev_toArray {l : List α} : l.toArray.toListRev = l.reverse := by
| nil => simp
| cons a l ih =>
simp only [foldlM_toArray] at ih
rw [size_toArray, mapM'_cons, foldlM_toArray]
rw [size_toArray, mapM'_cons]
simp [ih]
theorem uset_toArray {l : List α} {i : USize} {a : α} {h : i.toNat < l.toArray.size} :

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@@ -192,7 +192,8 @@ theorem mapFinIdx_empty {f : (i : Nat) → α → (h : i < 0) → β} : mapFinId
theorem mapFinIdx_eq_ofFn {xs : Array α} {f : (i : Nat) α (h : i < xs.size) β} :
xs.mapFinIdx f = Array.ofFn fun i : Fin xs.size => f i xs[i] i.2 := by
cases xs
simp [List.mapFinIdx_eq_ofFn]
simp only [List.mapFinIdx_toArray, List.mapFinIdx_eq_ofFn, Fin.getElem_fin, List.getElem_toArray]
simp [Array.size]
theorem mapFinIdx_append {xs ys : Array α} {f : (i : Nat) α (h : i < (xs ++ ys).size) β} :
(xs ++ ys).mapFinIdx f =
@@ -200,7 +201,7 @@ theorem mapFinIdx_append {xs ys : Array α} {f : (i : Nat) → α → (h : i < (
ys.mapFinIdx (fun i a h => f (i + xs.size) a (by simp; omega)) := by
cases xs
cases ys
simp [List.mapFinIdx_append]
simp [List.mapFinIdx_append, Array.size]
@[simp]
theorem mapFinIdx_push {xs : Array α} {a : α} {f : (i : Nat) α (h : i < (xs.push a).size) β} :
@@ -264,12 +265,12 @@ theorem mapFinIdx_eq_append_iff {xs : Array α} {f : (i : Nat) → α → (h : i
toArray_eq_append_iff]
constructor
· rintro l₁, l₂, rfl, rfl, rfl
refine l₁.toArray, l₂.toArray, by simp_all
refine l₁.toArray, l₂.toArray, by simp_all [Array.size]
· rintro l₁, l₂, rfl, h₁, h₂
simp [ toList_inj] at h₁ h₂
obtain rfl := h₁
obtain rfl := h₂
refine l₁, l₂, by simp_all
refine l₁, l₂, by simp_all [Array.size]
theorem mapFinIdx_eq_push_iff {xs : Array α} {b : β} {f : (i : Nat) α (h : i < xs.size) β} :
xs.mapFinIdx f = ys.push b
@@ -307,7 +308,7 @@ abbrev mapFinIdx_eq_mkArray_iff := @mapFinIdx_eq_replicate_iff
@[simp] theorem mapFinIdx_reverse {xs : Array α} {f : (i : Nat) α (h : i < xs.reverse.size) β} :
xs.reverse.mapFinIdx f = (xs.mapFinIdx (fun i a h => f (xs.size - 1 - i) a (by simp; omega))).reverse := by
rcases xs with l
simp [List.mapFinIdx_reverse]
simp [List.mapFinIdx_reverse, Array.size]
/-! ### mapIdx -/
@@ -486,7 +487,7 @@ namespace List
| x :: xs => simp only [mapFinIdxM.go, mapIdxM.go, go]
unfold Array.mapIdxM
rw [mapFinIdxM_toArray]
simp only [mapFinIdxM, mapIdxM]
simp only [mapFinIdxM, mapIdxM, Array.size]
rw [go]
end List

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@@ -310,7 +310,7 @@ namespace List
@[simp] theorem filterM_toArray' [Monad m] [LawfulMonad m] {l : List α} {p : α m Bool} (w : stop = l.length) :
l.toArray.filterM p 0 stop = toArray <$> l.filterM p := by
subst w
rw [filterM_toArray]
simp [ filterM_toArray]
@[grind =] theorem filterRevM_toArray [Monad m] [LawfulMonad m] {l : List α} {p : α m Bool} :
l.toArray.filterRevM p = toArray <$> l.filterRevM p := by
@@ -322,7 +322,7 @@ namespace List
@[simp] theorem filterRevM_toArray' [Monad m] [LawfulMonad m] {l : List α} {p : α m Bool} (w : start = l.length) :
l.toArray.filterRevM p start 0 = toArray <$> l.filterRevM p := by
subst w
rw [filterRevM_toArray]
simp [ filterRevM_toArray]
@[grind =] theorem filterMapM_toArray [Monad m] [LawfulMonad m] {l : List α} {f : α m (Option β)} :
l.toArray.filterMapM f = toArray <$> l.filterMapM f := by
@@ -340,7 +340,7 @@ namespace List
@[simp] theorem filterMapM_toArray' [Monad m] [LawfulMonad m] {l : List α} {f : α m (Option β)} (w : stop = l.length) :
l.toArray.filterMapM f 0 stop = toArray <$> l.filterMapM f := by
subst w
rw [filterMapM_toArray]
simp [ filterMapM_toArray]
@[simp, grind =] theorem flatMapM_toArray [Monad m] [LawfulMonad m] {l : List α} {f : α m (Array β)} :
l.toArray.flatMapM f = toArray <$> l.flatMapM (fun a => Array.toList <$> f a) := by

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@@ -550,7 +550,7 @@ def zipIdxTR (l : List α) (n : Nat := 0) : List (α × Nat) :=
(as.foldr (fun a (n, acc) => (n-1, (a, n-1) :: acc)) (n + as.size, [])).2
@[csimp] theorem zipIdx_eq_zipIdxTR : @zipIdx = @zipIdxTR := by
funext α l n; simp only [zipIdxTR, size_toArray]
funext α l n; simp only [zipIdxTR]
let f := fun (a : α) (n, acc) => (n-1, (a, n-1) :: acc)
let rec go : l i, l.foldr f (i + l.length, []) = (i, zipIdx l i)
| [], n => rfl
@@ -571,7 +571,7 @@ def enumFromTR (n : Nat) (l : List α) : List (Nat × α) :=
set_option linter.deprecated false in
@[deprecated zipIdx_eq_zipIdxTR (since := "2025-01-21"), csimp]
theorem enumFrom_eq_enumFromTR : @enumFrom = @enumFromTR := by
funext α n l; simp only [enumFromTR, size_toArray]
funext α n l; simp only [enumFromTR]
let f := fun (a : α) (n, acc) => (n-1, (n-1, a) :: acc)
let rec go : l n, l.foldr f (n + l.length, []) = (n, enumFrom n l)
| [], n => rfl

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@@ -320,7 +320,7 @@ theorem mapIdx_nil {f : Nat → α → β} : mapIdx f [] = [] :=
theorem mapIdx_go_length {acc : Array β} :
length (mapIdx.go f l acc) = length l + acc.size := by
induction l generalizing acc with
| nil => simp only [mapIdx.go, length_nil, Nat.zero_add]
| nil => simp [mapIdx.go]
| cons _ _ ih =>
simp only [mapIdx.go, ih, Array.size_push, Nat.add_succ, length_cons, Nat.add_comm]

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@@ -302,7 +302,7 @@ termination_by l.length - j
@[simp, grind =] theorem findIdx?_toArray (p : α Bool) (l : List α) :
l.toArray.findIdx? p = l.findIdx? p := by
rw [Array.findIdx?_eq_map_findFinIdx?_val, findIdx?_eq_map_findFinIdx?_val]
simp
simp [Array.size]
private theorem idxAuxOf_toArray [BEq α] (a : α) (l : List α) (j : Nat) (w : l' = l.drop j) (h) :
l.toArray.idxOfAux a j = findFinIdx?.go (fun x => x == a) l l' j h := by
@@ -339,11 +339,11 @@ termination_by l.length - j
@[simp, grind =] theorem idxOf?_toArray [BEq α] (a : α) (l : List α) :
l.toArray.idxOf? a = l.idxOf? a := by
rw [Array.idxOf?, idxOf?]
simp [finIdxOf?, findIdx?_eq_map_findFinIdx?_val]
simp [finIdxOf?, findIdx?_eq_map_findFinIdx?_val, Array.size]
@[simp, grind =] theorem findIdx_toArray {as : List α} {p : α Bool} :
as.toArray.findIdx p = as.findIdx p := by
rw [Array.findIdx, findIdx?_toArray, findIdx_eq_getD_findIdx?]
rw [Array.findIdx, findIdx?_toArray, findIdx_eq_getD_findIdx?, Array.size]
@[simp, grind =] theorem idxOf_toArray [BEq α] {as : List α} {a : α} :
as.toArray.idxOf a = as.idxOf a := by
@@ -670,9 +670,9 @@ theorem replace_toArray [BEq α] [LawfulBEq α] (l : List α) (a b : α) :
split <;> rename_i i h
· simp only [finIdxOf?_toArray, finIdxOf?_eq_none_iff] at h
rw [replace_of_not_mem]
simpa
exact finIdxOf?_eq_none_iff.mp h
· simp_all only [finIdxOf?_toArray, finIdxOf?_eq_some_iff, Fin.getElem_fin, set_toArray,
mk.injEq]
mk.injEq, Array.size]
apply List.ext_getElem
· simp
· intro j h₁ h₂

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@@ -84,7 +84,7 @@ theorem toArray_eq_singleton_iff {o : Option α} : o.toArray = #[a] ↔ o = some
theorem size_toArray_eq_zero_iff {o : Option α} :
o.toArray.size = 0 o = none := by
simp
simp [Array.size]
@[simp]
theorem size_toArray_eq_one_iff {o : Option α} :

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@@ -45,7 +45,7 @@ theorem countP_singleton {a : α} : countP p #v[a] = if p a then 1 else 0 := by
theorem size_eq_countP_add_countP {xs : Vector α n} : n = countP p xs + countP (fun a => ¬p a) xs := by
rcases xs with xs, rfl
simp [List.length_eq_countP_add_countP (p := p)]
simp [Array.size_eq_countP_add_countP (p := p)]
theorem countP_le_size {xs : Vector α n} : countP p xs n := by
rcases xs with xs, rfl

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@@ -698,7 +698,7 @@ protected theorem eq_empty {xs : Vector α 0} : xs = #v[] := by
theorem eq_empty_of_size_eq_zero {xs : Vector α n} (h : n = 0) : xs = #v[].cast h.symm := by
rcases xs with xs, rfl
apply toArray_inj.1
simp only [List.length_eq_zero_iff, Array.toList_eq_nil_iff] at h
simp only [Array.size_eq_zero_iff] at h
simp [h]
theorem size_eq_one {xs : Vector α 1} : a, xs = #v[a] := by

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@@ -3000,7 +3000,7 @@ This is a cached value, so it is `O(1)` to access. The space allocated for an ar
its _capacity_, is at least as large as its size, but may be larger. The capacity of an array is an
internal detail that's not observable by Lean code.
-/
@[reducible, extern "lean_array_get_size"]
@[extern "lean_array_get_size"]
def Array.size {α : Type u} (a : @& Array α) : Nat :=
a.toList.length

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@@ -22,7 +22,7 @@ detect equalities between array access terms.
-/
/--
trace: [Meta.debug] [i < a.toList.length, j < a.toList.length, j < b.toList.length]
trace: [Meta.debug] [i < a.size, j < a.size, j < b.size]
[Meta.debug] [a[i], b[j], a[j]]
-/
#guard_msgs (trace) in
@@ -30,7 +30,7 @@ example (i j : Nat) (a b : Array Nat) (h1 : j < a.size) (h : j < b.size) (h2 : i
grind -mbtc on_failure fallback
/--
trace: [Meta.debug] [i < a.toList.length, j < a.toList.length, j < b.toList.length]
trace: [Meta.debug] [i < a.size, j < a.size, j < b.size]
[Meta.debug] [a[i], a[j]]
-/
#guard_msgs (trace) in