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Author SHA1 Message Date
Kim Morrison
fd7377eb54 chore: upstream Subarray.empty 2024-09-29 15:33:54 +10:00
25 changed files with 159 additions and 427 deletions

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@@ -810,27 +810,11 @@ def split (as : Array α) (p : α → Bool) : Array α × Array α :=
as.foldl (init := (#[], #[])) fun (as, bs) a =>
if p a then (as.push a, bs) else (as, bs.push a)
/-! ## Auxiliary functions used in metaprogramming.
/-! ### Auxiliary functions used in metaprogramming.
We do not intend to provide verification theorems for these functions.
-/
/-! ### eraseReps -/
/--
`O(|l|)`. Erase repeated adjacent elements. Keeps the first occurrence of each run.
* `eraseReps #[1, 3, 2, 2, 2, 3, 5] = #[1, 3, 2, 3, 5]`
-/
def eraseReps {α} [BEq α] (as : Array α) : Array α :=
if h : 0 < as.size then
let last, r := as.foldl (init := (as[0], #[])) fun last, r a =>
if a == last then last, r else a, r.push last
r.push last
else
#[]
/-! ### allDiff -/
private def allDiffAuxAux [BEq α] (as : Array α) (a : α) : forall (i : Nat), i < as.size Bool
| 0, _ => true
| i+1, h =>
@@ -848,8 +832,6 @@ decreasing_by simp_wf; decreasing_trivial_pre_omega
def allDiff [BEq α] (as : Array α) : Bool :=
allDiffAux as 0
/-! ### getEvenElems -/
@[inline] def getEvenElems (as : Array α) : Array α :=
(·.2) <| as.foldl (init := (true, Array.empty)) fun (even, r) a =>
if even then

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@@ -424,18 +424,12 @@ theorem getElem_mem_toList (a : Array α) (h : i < a.size) : a[i] ∈ a.toList :
@[deprecated getElem_mem_toList (since := "2024-09-09")]
abbrev getElem_mem_data := @getElem_mem_toList
theorem getElem?_eq_toList_getElem? (a : Array α) (i : Nat) : a[i]? = a.toList[i]? := by
by_cases i < a.size <;> simp_all [getElem?_pos, getElem?_neg]
@[deprecated getElem?_eq_toList_getElem? (since := "2024-09-30")]
theorem getElem?_eq_toList_get? (a : Array α) (i : Nat) : a[i]? = a.toList.get? i := by
by_cases i < a.size <;> simp_all [getElem?_pos, getElem?_neg, List.get?_eq_get, eq_comm]
set_option linter.deprecated false in
@[deprecated getElem?_eq_toList_getElem? (since := "2024-09-09")]
@[deprecated getElem?_eq_toList_get? (since := "2024-09-09")]
abbrev getElem?_eq_data_get? := @getElem?_eq_toList_get?
set_option linter.deprecated false in
theorem get?_eq_toList_get? (a : Array α) (i : Nat) : a.get? i = a.toList.get? i :=
getElem?_eq_toList_get? ..
@@ -449,7 +443,7 @@ theorem get!_eq_get? [Inhabited α] (a : Array α) : a.get! n = (a.get? n).getD
simp [back, back?]
@[simp] theorem back?_push (a : Array α) : (a.push x).back? = some x := by
simp [back?, getElem?_eq_toList_getElem?]
simp [back?, getElem?_eq_toList_get?]
theorem back_push [Inhabited α] (a : Array α) : (a.push x).back = x := by simp
@@ -608,11 +602,12 @@ abbrev data_range := @toList_range
theorem getElem_range {n : Nat} {x : Nat} (h : x < (Array.range n).size) : (Array.range n)[x] = x := by
simp [getElem_eq_getElem_toList]
set_option linter.deprecated false in
@[simp] theorem reverse_toList (a : Array α) : a.reverse.toList = a.toList.reverse := by
let rec go (as : Array α) (i j hj)
(h : i + j + 1 = a.size) (h₂ : as.size = a.size)
(H : k, as.toList[k]? = if i k k j then a.toList[k]? else a.toList.reverse[k]?)
(k : Nat) : (reverse.loop as i j, hj).toList[k]? = a.toList.reverse[k]? := by
(H : k, as.toList.get? k = if i k k j then a.toList.get? k else a.toList.reverse.get? k)
(k) : (reverse.loop as i j, hj).toList.get? k = a.toList.reverse.get? k := by
rw [reverse.loop]; dsimp; split <;> rename_i h₁
· match j with | j+1 => ?_
simp only [Nat.add_sub_cancel]
@@ -620,34 +615,34 @@ theorem getElem_range {n : Nat} {x : Nat} (h : x < (Array.range n).size) : (Arra
· rwa [Nat.add_right_comm i]
· simp [size_swap, h₂]
· intro k
rw [ getElem?_eq_toList_getElem?, get?_swap]
simp only [H, getElem_eq_getElem_toList, List.getElem?_eq_getElem, Nat.le_of_lt h₁,
getElem?_eq_toList_getElem?]
rw [ getElem?_eq_toList_get?, get?_swap]
simp only [H, getElem_eq_toList_get, List.get?_eq_get, Nat.le_of_lt h₁,
getElem?_eq_toList_get?]
split <;> rename_i h₂
· simp only [ h₂, Nat.not_le.2 (Nat.lt_succ_self _), Nat.le_refl, and_false]
exact (List.getElem?_reverse' (j+1) i (Eq.trans (by simp_arith) h)).symm
exact (List.get?_reverse' (j+1) i (Eq.trans (by simp_arith) h)).symm
split <;> rename_i h₃
· simp only [ h₃, Nat.not_le.2 (Nat.lt_succ_self _), Nat.le_refl, false_and]
exact (List.getElem?_reverse' i (j+1) (Eq.trans (by simp_arith) h)).symm
exact (List.get?_reverse' i (j+1) (Eq.trans (by simp_arith) h)).symm
simp only [Nat.succ_le, Nat.lt_iff_le_and_ne.trans (and_iff_left h₃),
Nat.lt_succ.symm.trans (Nat.lt_iff_le_and_ne.trans (and_iff_left (Ne.symm h₂)))]
· rw [H]; split <;> rename_i h₂
· cases Nat.le_antisymm (Nat.not_lt.1 h₁) (Nat.le_trans h₂.1 h₂.2)
cases Nat.le_antisymm h₂.1 h₂.2
exact (List.getElem?_reverse' _ _ h).symm
exact (List.get?_reverse' _ _ h).symm
· rfl
termination_by j - i
simp only [reverse]
split
· match a with | [] | [_] => rfl
· have := Nat.sub_add_cancel (Nat.le_of_not_le _)
refine List.ext_getElem? <| go _ _ _ _ (by simp [this]) rfl fun k => ?_
refine List.ext_get? <| go _ _ _ _ (by simp [this]) rfl fun k => ?_
split
· rfl
· rename_i h
simp only [ show k < _ + 1 _ from Nat.lt_succ (n := a.size - 1), this, Nat.zero_le,
true_and, Nat.not_lt] at h
rw [List.getElem?_eq_none_iff.2 _, List.getElem?_eq_none_iff.2 (a.toList.length_reverse _)]
rw [List.get?_eq_none.2 _, List.get?_eq_none.2 (a.toList.length_reverse _)]
/-! ### foldl / foldr -/

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@@ -5,7 +5,6 @@ Authors: Leonardo de Moura
-/
prelude
import Init.Data.Array.Basic
import Init.Data.Ord
namespace Array
-- TODO: remove the [Inhabited α] parameters as soon as we have the tactic framework for automating proof generation and using Array.fget
@@ -45,11 +44,4 @@ def qpartition (as : Array α) (lt : αα → Bool) (lo hi : Nat) : Nat ×
else as
sort as low high
set_option linter.unusedVariables.funArgs false in
/--
Sort an array using `compare` to compare elements.
-/
def qsortOrd [ord : Ord α] (xs : Array α) : Array α :=
xs.qsort fun x y => compare x y |>.isLT
end Array

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@@ -799,6 +799,7 @@ theorem umod_eq_divRec (hd : 0#w < d) :
have := lawful_divRec this
apply DivModState.umod_eq_of_lawful this (wn_divRec ..)
@[simp]
theorem divRec_succ' (m : Nat) (args : DivModArgs w) (qr : DivModState w) :
divRec (m+1) args qr =
let wn := qr.wn - 1

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@@ -72,35 +72,21 @@ instance floatDecLt (a b : Float) : Decidable (a < b) := Float.decLt a b
instance floatDecLe (a b : Float) : Decidable (a b) := Float.decLe a b
@[extern "lean_float_to_string"] opaque Float.toString : Float String
/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
If negative or NaN, returns 0.
If larger than the maximum value for UInt8 (including Inf), returns maximum value of UInt8
(i.e. UInt8.size - 1).
-/
/-- If the given float is positive, truncates the value to the nearest positive integer.
If negative or larger than the maximum value for UInt8, returns 0. -/
@[extern "lean_float_to_uint8"] opaque Float.toUInt8 : Float UInt8
/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
If negative or NaN, returns 0.
If larger than the maximum value for UInt16 (including Inf), returns maximum value of UInt16
(i.e. UInt16.size - 1).
-/
/-- If the given float is positive, truncates the value to the nearest positive integer.
If negative or larger than the maximum value for UInt16, returns 0. -/
@[extern "lean_float_to_uint16"] opaque Float.toUInt16 : Float UInt16
/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
If negative or NaN, returns 0.
If larger than the maximum value for UInt32 (including Inf), returns maximum value of UInt32
(i.e. UInt32.size - 1).
-/
/-- If the given float is positive, truncates the value to the nearest positive integer.
If negative or larger than the maximum value for UInt32, returns 0. -/
@[extern "lean_float_to_uint32"] opaque Float.toUInt32 : Float UInt32
/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
If negative or NaN, returns 0.
If larger than the maximum value for UInt64 (including Inf), returns maximum value of UInt64
(i.e. UInt64.size - 1).
-/
/-- If the given float is positive, truncates the value to the nearest positive integer.
If negative or larger than the maximum value for UInt64, returns 0. -/
@[extern "lean_float_to_uint64"] opaque Float.toUInt64 : Float UInt64
/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
If negative or NaN, returns 0.
If larger than the maximum value for USize (including Inf), returns maximum value of USize
(i.e. USize.size - 1; Note that this value is platform dependent).
-/
/-- If the given float is positive, truncates the value to the nearest positive integer.
If negative or larger than the maximum value for USize, returns 0. -/
@[extern "lean_float_to_usize"] opaque Float.toUSize : Float USize
@[extern "lean_float_isnan"] opaque Float.isNaN : Float Bool

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@@ -43,7 +43,7 @@ The operations are organized as follow:
* Logic: `any`, `all`, `or`, and `and`.
* Zippers: `zipWith`, `zip`, `zipWithAll`, and `unzip`.
* Ranges and enumeration: `range`, `iota`, `enumFrom`, and `enum`.
* Minima and maxima: `min?` and `max?`.
* Minima and maxima: `minimum?` and `maximum?`.
* Other functions: `intersperse`, `intercalate`, `eraseDups`, `eraseReps`, `span`, `groupBy`,
`removeAll`
(currently these functions are mostly only used in meta code,
@@ -1464,34 +1464,30 @@ def enum : List α → List (Nat × α) := enumFrom 0
/-! ## Minima and maxima -/
/-! ### min? -/
/-! ### minimum? -/
/--
Returns the smallest element of the list, if it is not empty.
* `[].min? = none`
* `[4].min? = some 4`
* `[1, 4, 2, 10, 6].min? = some 1`
* `[].minimum? = none`
* `[4].minimum? = some 4`
* `[1, 4, 2, 10, 6].minimum? = some 1`
-/
def min? [Min α] : List α Option α
def minimum? [Min α] : List α Option α
| [] => none
| a::as => some <| as.foldl min a
@[inherit_doc min?, deprecated min? (since := "2024-09-29")] abbrev minimum? := @min?
/-! ### max? -/
/-! ### maximum? -/
/--
Returns the largest element of the list, if it is not empty.
* `[].max? = none`
* `[4].max? = some 4`
* `[1, 4, 2, 10, 6].max? = some 10`
* `[].maximum? = none`
* `[4].maximum? = some 4`
* `[1, 4, 2, 10, 6].maximum? = some 10`
-/
def max? [Max α] : List α Option α
def maximum? [Max α] : List α Option α
| [] => none
| a::as => some <| as.foldl max a
@[inherit_doc max?, deprecated max? (since := "2024-09-29")] abbrev maximum? := @max?
/-! ## Other list operations
The functions are currently mostly used in meta code,

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@@ -31,7 +31,7 @@ The following operations are still missing `@[csimp]` replacements:
The following operations are not recursive to begin with
(or are defined in terms of recursive primitives):
`isEmpty`, `isSuffixOf`, `isSuffixOf?`, `rotateLeft`, `rotateRight`, `insert`, `zip`, `enum`,
`min?`, `max?`, and `removeAll`.
`minimum?`, `maximum?`, and `removeAll`.
The following operations were already given `@[csimp]` replacements in `Init/Data/List/Basic.lean`:
`length`, `map`, `filter`, `replicate`, `leftPad`, `unzip`, `range'`, `iota`, `intersperse`.

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@@ -55,7 +55,7 @@ See also
* `Init.Data.List.Erase` for lemmas about `List.eraseP` and `List.erase`.
* `Init.Data.List.Find` for lemmas about `List.find?`, `List.findSome?`, `List.findIdx`,
`List.findIdx?`, and `List.indexOf`
* `Init.Data.List.MinMax` for lemmas about `List.min?` and `List.max?`.
* `Init.Data.List.MinMax` for lemmas about `List.minimum?` and `List.maximum?`.
* `Init.Data.List.Pairwise` for lemmas about `List.Pairwise` and `List.Nodup`.
* `Init.Data.List.Sublist` for lemmas about `List.Subset`, `List.Sublist`, `List.IsPrefix`,
`List.IsSuffix`, and `List.IsInfix`.
@@ -203,9 +203,6 @@ theorem get?_eq_none : l.get? n = none ↔ length l ≤ n :=
@[simp] theorem get_eq_getElem (l : List α) (i : Fin l.length) : l.get i = l[i.1]'i.2 := rfl
theorem getElem?_eq_some {l : List α} : l[i]? = some a h : i < l.length, l[i]'h = a := by
simpa using get?_eq_some
/--
If one has `l.get i` in an expression (with `i : Fin l.length`) and `h : l = l'`,
`rw [h]` will give a "motive it not type correct" error, as it cannot rewrite the
@@ -492,7 +489,7 @@ 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 _
@[simp] theorem getElem_mem : {l : List α} {n} (h : n < l.length), l[n]'h l
theorem getElem_mem : {l : List α} {n} (h : n < l.length), l[n]'h l
| _ :: _, 0, _ => .head ..
| _ :: l, _+1, _ => .tail _ (getElem_mem (l := l) ..)
@@ -881,20 +878,6 @@ theorem foldr_map' {α β : Type u} (g : α → β) (f : ααα) (f' :
· simp
· simp [*, h]
theorem foldl_assoc {op : α α α} [ha : Std.Associative op] :
{l : List α} {a₁ a₂}, l.foldl op (op a₁ a₂) = op a₁ (l.foldl op a₂)
| [], a₁, a₂ => rfl
| a :: l, a₁, a₂ => by
simp only [foldl_cons, ha.assoc]
rw [foldl_assoc]
theorem foldr_assoc {op : α α α} [ha : Std.Associative op] :
{l : List α} {a₁ a₂}, l.foldr op (op a₁ a₂) = op (l.foldr op a₁) a₂
| [], a₁, a₂ => rfl
| a :: l, a₁, a₂ => by
simp only [foldr_cons, ha.assoc]
rw [foldr_assoc]
theorem foldl_hom (f : α₁ α₂) (g₁ : α₁ β α₁) (g₂ : α₂ β α₂) (l : List β) (init : α₁)
(H : x y, g₂ (f x) y = f (g₁ x y)) : l.foldl g₂ (f init) = f (l.foldl g₁ init) := by
induction l generalizing init <;> simp [*, H]
@@ -1021,7 +1004,7 @@ theorem getLast_eq_getLastD (a l h) : @getLast α (a::l) h = getLastD l a := by
theorem getLast!_cons [Inhabited α] : @getLast! α _ (a::l) = getLastD l a := by
simp [getLast!, getLast_eq_getLastD]
@[simp] theorem getLast_mem : {l : List α} (h : l []), getLast l h l
theorem getLast_mem : {l : List α} (h : l []), getLast l h l
| [], h => absurd rfl h
| [_], _ => .head ..
| _::a::l, _ => .tail _ <| getLast_mem (cons_ne_nil a l)
@@ -1119,7 +1102,7 @@ theorem head?_eq_some_iff {xs : List α} {a : α} : xs.head? = some a ↔ ∃ ys
@[simp] theorem head?_isSome : l.head?.isSome l [] := by
cases l <;> simp
@[simp] theorem head_mem : {l : List α} (h : l []), head l h l
theorem head_mem : {l : List α} (h : l []), head l h l
| [], h => absurd rfl h
| _::_, _ => .head ..
@@ -2409,10 +2392,6 @@ theorem map_eq_replicate_iff {l : List α} {f : α → β} {b : β} :
@[simp] theorem map_const (l : List α) (b : β) : map (Function.const α b) l = replicate l.length b :=
map_eq_replicate_iff.mpr fun _ _ => rfl
@[simp] theorem map_const_fun (x : β) : map (Function.const α x) = (replicate ·.length x) := by
funext l
simp
/-- Variant of `map_const` using a lambda rather than `Function.const`. -/
-- This can not be a `@[simp]` lemma because it would fire on every `List.map`.
theorem map_const' (l : List α) (b : β) : map (fun _ => b) l = replicate l.length b :=

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@@ -7,7 +7,7 @@ prelude
import Init.Data.List.Lemmas
/-!
# Lemmas about `List.min?` and `List.max?.
# Lemmas about `List.minimum?` and `List.maximum?.
-/
namespace List
@@ -16,24 +16,24 @@ open Nat
/-! ## Minima and maxima -/
/-! ### min? -/
/-! ### minimum? -/
@[simp] theorem min?_nil [Min α] : ([] : List α).min? = none := rfl
@[simp] theorem minimum?_nil [Min α] : ([] : List α).minimum? = none := rfl
-- We don't put `@[simp]` on `min?_cons`,
-- We don't put `@[simp]` on `minimum?_cons`,
-- because the definition in terms of `foldl` is not useful for proofs.
theorem min?_cons [Min α] {xs : List α} : (x :: xs).min? = foldl min x xs := rfl
theorem minimum?_cons [Min α] {xs : List α} : (x :: xs).minimum? = foldl min x xs := rfl
@[simp] theorem min?_eq_none_iff {xs : List α} [Min α] : xs.min? = none xs = [] := by
cases xs <;> simp [min?]
@[simp] theorem minimum?_eq_none_iff {xs : List α} [Min α] : xs.minimum? = none xs = [] := by
cases xs <;> simp [minimum?]
theorem min?_mem [Min α] (min_eq_or : a b : α, min a b = a min a b = b) :
{xs : List α} xs.min? = some a a xs := by
theorem minimum?_mem [Min α] (min_eq_or : a b : α, min a b = a min a b = b) :
{xs : List α} xs.minimum? = some a a xs := by
intro xs
match xs with
| nil => simp
| x :: xs =>
simp only [min?_cons, Option.some.injEq, List.mem_cons]
simp only [minimum?_cons, Option.some.injEq, List.mem_cons]
intro eq
induction xs generalizing x with
| nil =>
@@ -49,12 +49,12 @@ theorem min?_mem [Min α] (min_eq_or : ∀ a b : α, min a b = a min a b = b
-- See also `Init.Data.List.Nat.Basic` for specialisations of the next two results to `Nat`.
theorem le_min?_iff [Min α] [LE α]
theorem le_minimum?_iff [Min α] [LE α]
(le_min_iff : a b c : α, a min b c a b a c) :
{xs : List α} xs.min? = some a {x}, x a b, b xs x b
{xs : List α} xs.minimum? = some a {x}, x a b, b xs x b
| nil => by simp
| cons x xs => by
rw [min?]
rw [minimum?]
intro eq y
simp only [Option.some.injEq] at eq
induction xs generalizing x with
@@ -67,46 +67,46 @@ theorem le_min?_iff [Min α] [LE α]
-- This could be refactored by designing appropriate typeclasses to replace `le_refl`, `min_eq_or`,
-- and `le_min_iff`.
theorem min?_eq_some_iff [Min α] [LE α] [anti : Antisymm ((· : α) ·)]
theorem minimum?_eq_some_iff [Min α] [LE α] [anti : Antisymm ((· : α) ·)]
(le_refl : a : α, a a)
(min_eq_or : a b : α, min a b = a min a b = b)
(le_min_iff : a b c : α, a min b c a b a c) {xs : List α} :
xs.min? = some a a xs b, b xs a b := by
refine fun h => min?_mem min_eq_or h, (le_min?_iff le_min_iff h).1 (le_refl _), ?_
xs.minimum? = some a a xs b, b xs a b := by
refine fun h => minimum?_mem min_eq_or h, (le_minimum?_iff le_min_iff h).1 (le_refl _), ?_
intro h₁, h₂
cases xs with
| nil => simp at h₁
| cons x xs =>
exact congrArg some <| anti.1
((le_min?_iff le_min_iff (xs := x::xs) rfl).1 (le_refl _) _ h₁)
(h₂ _ (min?_mem min_eq_or (xs := x::xs) rfl))
((le_minimum?_iff le_min_iff (xs := x::xs) rfl).1 (le_refl _) _ h₁)
(h₂ _ (minimum?_mem min_eq_or (xs := x::xs) rfl))
theorem min?_replicate [Min α] {n : Nat} {a : α} (w : min a a = a) :
(replicate n a).min? = if n = 0 then none else some a := by
theorem minimum?_replicate [Min α] {n : Nat} {a : α} (w : min a a = a) :
(replicate n a).minimum? = if n = 0 then none else some a := by
induction n with
| zero => rfl
| succ n ih => cases n <;> simp_all [replicate_succ, min?_cons]
| succ n ih => cases n <;> simp_all [replicate_succ, minimum?_cons]
@[simp] theorem min?_replicate_of_pos [Min α] {n : Nat} {a : α} (w : min a a = a) (h : 0 < n) :
(replicate n a).min? = some a := by
simp [min?_replicate, Nat.ne_of_gt h, w]
@[simp] theorem minimum?_replicate_of_pos [Min α] {n : Nat} {a : α} (w : min a a = a) (h : 0 < n) :
(replicate n a).minimum? = some a := by
simp [minimum?_replicate, Nat.ne_of_gt h, w]
/-! ### max? -/
/-! ### maximum? -/
@[simp] theorem max?_nil [Max α] : ([] : List α).max? = none := rfl
@[simp] theorem maximum?_nil [Max α] : ([] : List α).maximum? = none := rfl
-- We don't put `@[simp]` on `max?_cons`,
-- We don't put `@[simp]` on `maximum?_cons`,
-- because the definition in terms of `foldl` is not useful for proofs.
theorem max?_cons [Max α] {xs : List α} : (x :: xs).max? = foldl max x xs := rfl
theorem maximum?_cons [Max α] {xs : List α} : (x :: xs).maximum? = foldl max x xs := rfl
@[simp] theorem max?_eq_none_iff {xs : List α} [Max α] : xs.max? = none xs = [] := by
cases xs <;> simp [max?]
@[simp] theorem maximum?_eq_none_iff {xs : List α} [Max α] : xs.maximum? = none xs = [] := by
cases xs <;> simp [maximum?]
theorem max?_mem [Max α] (min_eq_or : a b : α, max a b = a max a b = b) :
{xs : List α} xs.max? = some a a xs
theorem maximum?_mem [Max α] (min_eq_or : a b : α, max a b = a max a b = b) :
{xs : List α} xs.maximum? = some a a xs
| nil => by simp
| cons x xs => by
rw [max?]; rintro
rw [maximum?]; rintro
induction xs generalizing x with simp at *
| cons y xs ih =>
rcases ih (max x y) with h | h <;> simp [h]
@@ -114,57 +114,40 @@ theorem max?_mem [Max α] (min_eq_or : ∀ a b : α, max a b = a max a b = b
-- See also `Init.Data.List.Nat.Basic` for specialisations of the next two results to `Nat`.
theorem max?_le_iff [Max α] [LE α]
theorem maximum?_le_iff [Max α] [LE α]
(max_le_iff : a b c : α, max b c a b a c a) :
{xs : List α} xs.max? = some a {x}, a x b xs, b x
{xs : List α} xs.maximum? = some a {x}, a x b xs, b x
| nil => by simp
| cons x xs => by
rw [max?]; rintro y
rw [maximum?]; rintro y
induction xs generalizing x with
| nil => simp
| cons y xs ih => simp [ih, max_le_iff, and_assoc]
-- This could be refactored by designing appropriate typeclasses to replace `le_refl`, `max_eq_or`,
-- and `le_min_iff`.
theorem max?_eq_some_iff [Max α] [LE α] [anti : Antisymm ((· : α) ·)]
theorem maximum?_eq_some_iff [Max α] [LE α] [anti : Antisymm ((· : α) ·)]
(le_refl : a : α, a a)
(max_eq_or : a b : α, max a b = a max a b = b)
(max_le_iff : a b c : α, max b c a b a c a) {xs : List α} :
xs.max? = some a a xs b xs, b a := by
refine fun h => max?_mem max_eq_or h, (max?_le_iff max_le_iff h).1 (le_refl _), ?_
xs.maximum? = some a a xs b xs, b a := by
refine fun h => maximum?_mem max_eq_or h, (maximum?_le_iff max_le_iff h).1 (le_refl _), ?_
intro h₁, h₂
cases xs with
| nil => simp at h₁
| cons x xs =>
exact congrArg some <| anti.1
(h₂ _ (max?_mem max_eq_or (xs := x::xs) rfl))
((max?_le_iff max_le_iff (xs := x::xs) rfl).1 (le_refl _) _ h₁)
(h₂ _ (maximum?_mem max_eq_or (xs := x::xs) rfl))
((maximum?_le_iff max_le_iff (xs := x::xs) rfl).1 (le_refl _) _ h₁)
theorem max?_replicate [Max α] {n : Nat} {a : α} (w : max a a = a) :
(replicate n a).max? = if n = 0 then none else some a := by
theorem maximum?_replicate [Max α] {n : Nat} {a : α} (w : max a a = a) :
(replicate n a).maximum? = if n = 0 then none else some a := by
induction n with
| zero => rfl
| succ n ih => cases n <;> simp_all [replicate_succ, max?_cons]
| succ n ih => cases n <;> simp_all [replicate_succ, maximum?_cons]
@[simp] theorem max?_replicate_of_pos [Max α] {n : Nat} {a : α} (w : max a a = a) (h : 0 < n) :
(replicate n a).max? = some a := by
simp [max?_replicate, Nat.ne_of_gt h, w]
@[deprecated min?_nil (since := "2024-09-29")] abbrev minimum?_nil := @min?_nil
@[deprecated min?_cons (since := "2024-09-29")] abbrev minimum?_cons := @min?_cons
@[deprecated min?_eq_none_iff (since := "2024-09-29")] abbrev mininmum?_eq_none_iff := @min?_eq_none_iff
@[deprecated min?_mem (since := "2024-09-29")] abbrev minimum?_mem := @min?_mem
@[deprecated le_min?_iff (since := "2024-09-29")] abbrev le_minimum?_iff := @le_min?_iff
@[deprecated min?_eq_some_iff (since := "2024-09-29")] abbrev minimum?_eq_some_iff := @min?_eq_some_iff
@[deprecated min?_replicate (since := "2024-09-29")] abbrev minimum?_replicate := @min?_replicate
@[deprecated min?_replicate_of_pos (since := "2024-09-29")] abbrev minimum?_replicate_of_pos := @min?_replicate_of_pos
@[deprecated max?_nil (since := "2024-09-29")] abbrev maximum?_nil := @max?_nil
@[deprecated max?_cons (since := "2024-09-29")] abbrev maximum?_cons := @max?_cons
@[deprecated max?_eq_none_iff (since := "2024-09-29")] abbrev maximum?_eq_none_iff := @max?_eq_none_iff
@[deprecated max?_mem (since := "2024-09-29")] abbrev maximum?_mem := @max?_mem
@[deprecated max?_le_iff (since := "2024-09-29")] abbrev maximum?_le_iff := @max?_le_iff
@[deprecated max?_eq_some_iff (since := "2024-09-29")] abbrev maximum?_eq_some_iff := @max?_eq_some_iff
@[deprecated max?_replicate (since := "2024-09-29")] abbrev maximum?_replicate := @max?_replicate
@[deprecated max?_replicate_of_pos (since := "2024-09-29")] abbrev maximum?_replicate_of_pos := @max?_replicate_of_pos
@[simp] theorem maximum?_replicate_of_pos [Max α] {n : Nat} {a : α} (w : max a a = a) (h : 0 < n) :
(replicate n a).maximum? = some a := by
simp [maximum?_replicate, Nat.ne_of_gt h, w]
end List

View File

@@ -86,26 +86,26 @@ theorem mem_eraseIdx_iff_getElem? {x : α} {l} {k} : x ∈ eraseIdx l k ↔ ∃
obtain h', - := getElem?_eq_some_iff.1 h
exact h', h
/-! ### min? -/
/-! ### minimum? -/
-- A specialization of `min?_eq_some_iff` to Nat.
theorem min?_eq_some_iff' {xs : List Nat} :
xs.min? = some a (a xs b xs, a b) :=
min?_eq_some_iff
-- A specialization of `minimum?_eq_some_iff` to Nat.
theorem minimum?_eq_some_iff' {xs : List Nat} :
xs.minimum? = some a (a xs b xs, a b) :=
minimum?_eq_some_iff
(le_refl := Nat.le_refl)
(min_eq_or := fun _ _ => Nat.min_def .. by split <;> simp)
(le_min_iff := fun _ _ _ => Nat.le_min)
(min_eq_or := fun _ _ => by omega)
(le_min_iff := fun _ _ _ => by omega)
-- This could be generalized,
-- but will first require further work on order typeclasses in the core repository.
theorem min?_cons' {a : Nat} {l : List Nat} :
(a :: l).min? = some (match l.min? with
theorem minimum?_cons' {a : Nat} {l : List Nat} :
(a :: l).minimum? = some (match l.minimum? with
| none => a
| some m => min a m) := by
rw [min?_eq_some_iff']
rw [minimum?_eq_some_iff']
split <;> rename_i h m
· simp_all
· rw [min?_eq_some_iff'] at m
· rw [minimum?_eq_some_iff'] at m
obtain m, le := m
rw [Nat.min_def]
constructor
@@ -122,11 +122,11 @@ theorem min?_cons' {a : Nat} {l : List Nat} :
theorem foldl_min
{α : Type _} [Min α] [Std.IdempotentOp (min : α α α)] [Std.Associative (min : α α α)]
{l : List α} {a : α} :
l.foldl (init := a) min = min a (l.min?.getD a) := by
l.foldl (init := a) min = min a (l.minimum?.getD a) := by
cases l with
| nil => simp [Std.IdempotentOp.idempotent]
| cons b l =>
simp only [min?]
simp only [minimum?]
induction l generalizing a b with
| nil => simp
| cons c l ih => simp [ih, Std.Associative.assoc]
@@ -134,7 +134,7 @@ theorem foldl_min
theorem foldl_min_right {α β : Type _}
[Min β] [Std.IdempotentOp (min : β β β)] [Std.Associative (min : β β β)]
{l : List α} {b : β} {f : α β} :
(l.foldl (init := b) fun acc a => min acc (f a)) = min b ((l.map f).min?.getD b) := by
(l.foldl (init := b) fun acc a => min acc (f a)) = min b ((l.map f).minimum?.getD b) := by
rw [ foldl_map, foldl_min]
theorem foldl_min_le {l : List Nat} {a : Nat} : l.foldl (init := a) min a := by
@@ -148,12 +148,12 @@ theorem foldl_min_min_of_le {l : List Nat} {a b : Nat} (h : a ≤ b) :
l.foldl (init := a) min b :=
Nat.le_trans (foldl_min_le) h
theorem min?_getD_le_of_mem {l : List Nat} {a k : Nat} (h : a l) :
l.min?.getD k a := by
theorem minimum?_getD_le_of_mem {l : List Nat} {a k : Nat} (h : a l) :
l.minimum?.getD k a := by
cases l with
| nil => simp at h
| cons b l =>
simp [min?_cons]
simp [minimum?_cons]
simp at h
rcases h with (rfl | h)
· exact foldl_min_le
@@ -166,26 +166,26 @@ theorem min?_getD_le_of_mem {l : List Nat} {a k : Nat} (h : a ∈ l) :
· exact foldl_min_min_of_le (Nat.min_le_right _ _)
· exact ih _ h
/-! ### max? -/
/-! ### maximum? -/
-- A specialization of `max?_eq_some_iff` to Nat.
theorem max?_eq_some_iff' {xs : List Nat} :
xs.max? = some a (a xs b xs, b a) :=
max?_eq_some_iff
-- A specialization of `maximum?_eq_some_iff` to Nat.
theorem maximum?_eq_some_iff' {xs : List Nat} :
xs.maximum? = some a (a xs b xs, b a) :=
maximum?_eq_some_iff
(le_refl := Nat.le_refl)
(max_eq_or := fun _ _ => Nat.max_def .. by split <;> simp)
(max_le_iff := fun _ _ _ => Nat.max_le)
(max_eq_or := fun _ _ => by omega)
(max_le_iff := fun _ _ _ => by omega)
-- This could be generalized,
-- but will first require further work on order typeclasses in the core repository.
theorem max?_cons' {a : Nat} {l : List Nat} :
(a :: l).max? = some (match l.max? with
theorem maximum?_cons' {a : Nat} {l : List Nat} :
(a :: l).maximum? = some (match l.maximum? with
| none => a
| some m => max a m) := by
rw [max?_eq_some_iff']
rw [maximum?_eq_some_iff']
split <;> rename_i h m
· simp_all
· rw [max?_eq_some_iff'] at m
· rw [maximum?_eq_some_iff'] at m
obtain m, le := m
rw [Nat.max_def]
constructor
@@ -202,11 +202,11 @@ theorem max?_cons' {a : Nat} {l : List Nat} :
theorem foldl_max
{α : Type _} [Max α] [Std.IdempotentOp (max : α α α)] [Std.Associative (max : α α α)]
{l : List α} {a : α} :
l.foldl (init := a) max = max a (l.max?.getD a) := by
l.foldl (init := a) max = max a (l.maximum?.getD a) := by
cases l with
| nil => simp [Std.IdempotentOp.idempotent]
| cons b l =>
simp only [max?]
simp only [maximum?]
induction l generalizing a b with
| nil => simp
| cons c l ih => simp [ih, Std.Associative.assoc]
@@ -214,7 +214,7 @@ theorem foldl_max
theorem foldl_max_right {α β : Type _}
[Max β] [Std.IdempotentOp (max : β β β)] [Std.Associative (max : β β β)]
{l : List α} {b : β} {f : α β} :
(l.foldl (init := b) fun acc a => max acc (f a)) = max b ((l.map f).max?.getD b) := by
(l.foldl (init := b) fun acc a => max acc (f a)) = max b ((l.map f).maximum?.getD b) := by
rw [ foldl_map, foldl_max]
theorem le_foldl_max {l : List Nat} {a : Nat} : a l.foldl (init := a) max := by
@@ -228,12 +228,12 @@ theorem le_foldl_max_of_le {l : List Nat} {a b : Nat} (h : a ≤ b) :
a l.foldl (init := b) max :=
Nat.le_trans h (le_foldl_max)
theorem le_max?_getD_of_mem {l : List Nat} {a k : Nat} (h : a l) :
a l.max?.getD k := by
theorem le_maximum?_getD_of_mem {l : List Nat} {a k : Nat} (h : a l) :
a l.maximum?.getD k := by
cases l with
| nil => simp at h
| cons b l =>
simp [max?_cons]
simp [maximum?_cons]
simp at h
rcases h with (rfl | h)
· exact le_foldl_max
@@ -246,11 +246,4 @@ theorem le_max?_getD_of_mem {l : List Nat} {a k : Nat} (h : a ∈ l) :
· exact le_foldl_max_of_le (Nat.le_max_right b a)
· exact ih _ h
@[deprecated min?_eq_some_iff' (since := "2024-09-29")] abbrev minimum?_eq_some_iff' := @min?_eq_some_iff'
@[deprecated min?_cons' (since := "2024-09-29")] abbrev minimum?_cons' := @min?_cons'
@[deprecated min?_getD_le_of_mem (since := "2024-09-29")] abbrev minimum?_getD_le_of_mem := @min?_getD_le_of_mem
@[deprecated max?_eq_some_iff' (since := "2024-09-29")] abbrev maximum?_eq_some_iff' := @max?_eq_some_iff'
@[deprecated max?_cons' (since := "2024-09-29")] abbrev maximum?_cons' := @max?_cons'
@[deprecated le_max?_getD_of_mem (since := "2024-09-29")] abbrev le_maximum?_getD_of_mem := @le_max?_getD_of_mem
end List

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@@ -42,7 +42,7 @@ theorem getElem_take' (L : List α) {i j : Nat} (hi : i < L.length) (hj : i < j)
/-- The `i`-th element of a list coincides with the `i`-th element of any of its prefixes of
length `> i`. Version designed to rewrite from the small list to the big list. -/
@[simp] theorem getElem_take (L : List α) {j i : Nat} {h : i < (L.take j).length} :
theorem getElem_take (L : List α) {j i : Nat} {h : i < (L.take j).length} :
(L.take j)[i] =
L[i]'(Nat.lt_of_lt_of_le h (length_take_le' _ _)) := by
rw [length_take, Nat.lt_min] at h; rw [getElem_take' L _ h.1]
@@ -52,7 +52,7 @@ length `> i`. Version designed to rewrite from the big list to the small list. -
@[deprecated getElem_take' (since := "2024-06-12")]
theorem get_take (L : List α) {i j : Nat} (hi : i < L.length) (hj : i < j) :
get L i, hi = get (L.take j) i, length_take .. Nat.lt_min.mpr hj, hi := by
simp
simp [getElem_take' _ hi hj]
/-- The `i`-th element of a list coincides with the `i`-th element of any of its prefixes of
length `> i`. Version designed to rewrite from the small list to the big list. -/

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@@ -248,10 +248,6 @@ theorem countP_eq_countP_filter_add (l : List α) (p q : α → Bool) :
theorem Perm.count_eq [DecidableEq α] {l₁ l₂ : List α} (p : l₁ ~ l₂) (a) :
count a l₁ = count a l₂ := p.countP_eq _
/-
This theorem is a variant of `Perm.foldl_eq` defined in Mathlib which uses typeclasses rather
than the explicit `comm` argument.
-/
theorem Perm.foldl_eq' {f : β α β} {l₁ l₂ : List α} (p : l₁ ~ l₂)
(comm : x l₁, y l₁, (z), f (f z x) y = f (f z y) x)
(init) : foldl f init l₁ = foldl f init l₂ := by
@@ -268,28 +264,6 @@ theorem Perm.foldl_eq' {f : β → α → β} {l₁ l₂ : List α} (p : l₁ ~
refine (IH₁ comm init).trans (IH₂ ?_ _)
intros; apply comm <;> apply p₁.symm.subset <;> assumption
/-
This theorem is a variant of `Perm.foldr_eq` defined in Mathlib which uses typeclasses rather
than the explicit `comm` argument.
-/
theorem Perm.foldr_eq' {f : α β β} {l₁ l₂ : List α} (p : l₁ ~ l₂)
(comm : x l₁, y l₁, (z), f y (f x z) = f x (f y z))
(init) : foldr f init l₁ = foldr f init l₂ := by
induction p using recOnSwap' generalizing init with
| nil => simp
| cons x _p IH =>
simp only [foldr]
congr 1
apply IH; intros; apply comm <;> exact .tail _ _
| swap' x y _p IH =>
simp only [foldr]
rw [comm x (.tail _ <| .head _) y (.head _)]
congr 2
apply IH; intros; apply comm <;> exact .tail _ (.tail _ _)
| trans p₁ _p₂ IH₁ IH₂ =>
refine (IH₁ comm init).trans (IH₂ ?_ _)
intros; apply comm <;> apply p₁.symm.subset <;> assumption
theorem Perm.rec_heq {β : List α Sort _} {f : a l, β l β (a :: l)} {b : β []} {l l' : List α}
(hl : l ~ l') (f_congr : {a l l' b b'}, l ~ l' HEq b b' HEq (f a l b) (f a l' b'))
(f_swap : {a a' l b}, HEq (f a (a' :: l) (f a' l b)) (f a' (a :: l) (f a l b))) :

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@@ -277,7 +277,6 @@ where
| _ => mkAtomLinearCombo e
| (``Min.min, #[_, _, a, b]) => rewrite e (mkApp2 (.const ``Int.ofNat_min []) a b)
| (``Max.max, #[_, _, a, b]) => rewrite e (mkApp2 (.const ``Int.ofNat_max []) a b)
| (``Int.toNat, #[n]) => rewrite e (mkApp (.const ``Int.toNat_eq_max []) n)
| (``HShiftLeft.hShiftLeft, #[_, _, _, _, a, b]) =>
rewrite e (mkApp2 (.const ``Int.ofNat_shiftLeft_eq []) a b)
| (``HShiftRight.hShiftRight, #[_, _, _, _, a, b]) =>

View File

@@ -29,14 +29,12 @@ The minimum non-zero entry in a list of natural numbers, or zero if all entries
We completely characterize the function via
`nonzeroMinimum_eq_zero_iff` and `nonzeroMinimum_eq_nonzero_iff` below.
-/
def nonzeroMinimum (xs : List Nat) : Nat := xs.filter (· 0) |>.min? |>.getD 0
def nonzeroMinimum (xs : List Nat) : Nat := xs.filter (· 0) |>.minimum? |>.getD 0
-- A specialization of `minimum?_eq_some_iff` to Nat.
-- This is a duplicate `min?_eq_some_iff'` proved in `Init.Data.List.Nat.Basic`,
-- and could be deduplicated but the import hierarchy is awkward.
theorem min?_eq_some_iff'' {xs : List Nat} :
xs.min? = some a (a xs b xs, a b) :=
min?_eq_some_iff
theorem minimum?_eq_some_iff' {xs : List Nat} :
xs.minimum? = some a (a xs b xs, a b) :=
minimum?_eq_some_iff
(le_refl := Nat.le_refl)
(min_eq_or := fun _ _ => Nat.min_def .. by split <;> simp)
(le_min_iff := fun _ _ _ => Nat.le_min)
@@ -44,27 +42,27 @@ theorem min?_eq_some_iff'' {xs : List Nat} :
open Classical in
@[simp] theorem nonzeroMinimum_eq_zero_iff {xs : List Nat} :
xs.nonzeroMinimum = 0 x xs, x = 0 := by
simp [nonzeroMinimum, Option.getD_eq_iff, min?_eq_none_iff, min?_eq_some_iff'',
simp [nonzeroMinimum, Option.getD_eq_iff, minimum?_eq_none_iff, minimum?_eq_some_iff',
filter_eq_nil_iff, mem_filter]
theorem nonzeroMinimum_mem {xs : List Nat} (w : xs.nonzeroMinimum 0) :
xs.nonzeroMinimum xs := by
dsimp [nonzeroMinimum] at *
generalize h : (xs.filter (· 0) |>.min?) = m at *
generalize h : (xs.filter (· 0) |>.minimum?) = m at *
match m, w with
| some (m+1), _ => simp_all [min?_eq_some_iff'', mem_filter]
| some (m+1), _ => simp_all [minimum?_eq_some_iff', mem_filter]
theorem nonzeroMinimum_pos {xs : List Nat} (m : a xs) (h : a 0) : 0 < xs.nonzeroMinimum :=
Nat.pos_iff_ne_zero.mpr fun w => h (nonzeroMinimum_eq_zero_iff.mp w _ m)
theorem nonzeroMinimum_le {xs : List Nat} (m : a xs) (h : a 0) : xs.nonzeroMinimum a := by
have : (xs.filter (· 0) |>.min?) = some xs.nonzeroMinimum := by
have : (xs.filter (· 0) |>.minimum?) = some xs.nonzeroMinimum := by
have w := nonzeroMinimum_pos m h
dsimp [nonzeroMinimum] at *
generalize h : (xs.filter (· 0) |>.min?) = m? at *
generalize h : (xs.filter (· 0) |>.minimum?) = m? at *
match m?, w with
| some m?, _ => rfl
rw [min?_eq_some_iff''] at this
rw [minimum?_eq_some_iff'] at this
apply this.2
simp [List.mem_filter]
exact m, h
@@ -144,4 +142,4 @@ theorem minNatAbs_eq_nonzero_iff (xs : List Int) (w : z ≠ 0) :
@[simp] theorem minNatAbs_nil : ([] : List Int).minNatAbs = 0 := rfl
/-- The maximum absolute value in a list of integers. -/
def maxNatAbs (xs : List Int) : Nat := xs.map Int.natAbs |>.max? |>.getD 0
def maxNatAbs (xs : List Int) : Nat := xs.map Int.natAbs |>.maximum? |>.getD 0

View File

@@ -573,33 +573,15 @@ where
catch _ =>
return some mvarId
/--
Discharges assumptions of the form `∀ …, a = b` using `rfl`. This is particularly useful for higher
order assumptions of the form `∀ …, e = ?g x y` to instaniate a paramter `g` even if that does not
appear on the lhs of the rule.
-/
def dischargeRfl (e : Expr) : SimpM (Option Expr) := do
forallTelescope e fun xs e => do
let some (t, a, b) := e.eq? | return .none
unless a.getAppFn.isMVar || b.getAppFn.isMVar do return .none
if ( withReducible <| isDefEq a b) then
trace[Meta.Tactic.simp.discharge] "Discharging with rfl: {e}"
let u getLevel t
let proof := mkApp2 (.const ``rfl [u]) t a
let proof mkLambdaFVars xs proof
return .some proof
return .none
def dischargeDefault? (e : Expr) : SimpM (Option Expr) := do
let e := e.cleanupAnnotations
if isEqnThmHypothesis e then
if let some r dischargeUsingAssumption? e then return some r
if let some r dischargeEqnThmHypothesis? e then return some r
if let some r dischargeUsingAssumption? e then
return some r
if let some r dischargeEqnThmHypothesis? e then
return some r
let r simp e
if let some p dischargeRfl r.expr then
return some ( mkEqMPR ( r.getProof) p)
else if r.expr.isTrue then
if r.expr.isTrue then
return some ( mkOfEqTrue ( r.getProof))
else
return none

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@@ -360,8 +360,7 @@ def pushToken (info : SourceInfo) (tk : String) : FormatterM Unit := do
modify fun st => { st with leadWord := if tk.trimLeft == tk then tk ++ st.leadWord else "" }
else
-- stopped after `tk` => add space
pushLine
push tk
push $ tk ++ " "
modify fun st => { st with leadWord := if tk.trimLeft == tk then tk else "" }
else
-- already separated => use `tk` as is

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@@ -237,7 +237,7 @@ partial def InfoTree.hoverableInfoAt? (t : InfoTree) (hoverPos : String.Pos) (in
let _ := @lexOrd
let _ := @leOfOrd.{0}
let _ := @maxOfLe
results.map (·.1) |>.max?
results.map (·.1) |>.maximum?
let res? := results.find? (·.1 == maxPrio?) |>.map (·.2)
if let some i := res? then
if let .ofTermInfo ti := i.info then
@@ -380,7 +380,7 @@ partial def InfoTree.goalsAt? (text : FileMap) (t : InfoTree) (hoverPos : String
priority := if hoverPos.byteIdx == tailPos.byteIdx + trailSize then 0 else 1
}]
return gs
let maxPrio? := gs.map (·.priority) |>.max?
let maxPrio? := gs.map (·.priority) |>.maximum?
gs.filter (some ·.priority == maxPrio?)
where
hasNestedTactic (pos tailPos) : InfoTree Bool

View File

@@ -15,12 +15,12 @@ namespace CNF
/--
Obtain the literal with the largest identifier in `c`.
-/
def Clause.maxLiteral (c : Clause Nat) : Option Nat := (c.map (·.1)) |>.max?
def Clause.maxLiteral (c : Clause Nat) : Option Nat := (c.map (·.1)) |>.maximum?
theorem Clause.of_maxLiteral_eq_some (c : Clause Nat) (h : c.maxLiteral = some maxLit) :
lit, Mem lit c lit maxLit := by
intro lit hlit
simp only [maxLiteral, List.max?_eq_some_iff', List.mem_map, forall_exists_index, and_imp,
simp only [maxLiteral, List.maximum?_eq_some_iff', List.mem_map, forall_exists_index, and_imp,
forall_apply_eq_imp_iff₂] at h
simp only [Mem] at hlit
rcases h with _, hbar
@@ -35,25 +35,25 @@ theorem Clause.maxLiteral_eq_some_of_mem (c : Clause Nat) (h : Mem l c) :
cases h <;> rename_i h
all_goals
have h1 := List.ne_nil_of_mem h
have h2 := not_congr <| @List.max?_eq_none_iff _ (c.map (·.1)) _
have h2 := not_congr <| @List.maximum?_eq_none_iff _ (c.map (·.1)) _
simp [ Option.ne_none_iff_exists', h1, h2, maxLiteral]
theorem Clause.of_maxLiteral_eq_none (c : Clause Nat) (h : c.maxLiteral = none) :
lit, ¬Mem lit c := by
intro lit hlit
simp only [maxLiteral, List.max?_eq_none_iff, List.map_eq_nil_iff] at h
simp only [maxLiteral, List.maximum?_eq_none_iff, List.map_eq_nil_iff] at h
simp only [h, not_mem_nil] at hlit
/--
Obtain the literal with the largest identifier in `f`.
-/
def maxLiteral (f : CNF Nat) : Option Nat :=
List.filterMap Clause.maxLiteral f |>.max?
List.filterMap Clause.maxLiteral f |>.maximum?
theorem of_maxLiteral_eq_some' (f : CNF Nat) (h : f.maxLiteral = some maxLit) :
clause, clause f clause.maxLiteral = some localMax localMax maxLit := by
intro clause hclause1 hclause2
simp [maxLiteral, List.max?_eq_some_iff'] at h
simp [maxLiteral, List.maximum?_eq_some_iff'] at h
rcases h with _, hclause3
apply hclause3 localMax clause hclause1 hclause2
@@ -70,7 +70,7 @@ theorem of_maxLiteral_eq_some (f : CNF Nat) (h : f.maxLiteral = some maxLit) :
theorem of_maxLiteral_eq_none (f : CNF Nat) (h : f.maxLiteral = none) :
lit, ¬Mem lit f := by
intro lit hlit
simp only [maxLiteral, List.max?_eq_none_iff] at h
simp only [maxLiteral, List.maximum?_eq_none_iff] at h
dsimp [Mem] at hlit
rcases hlit with clause, hclause1, hclause2
have := Clause.of_maxLiteral_eq_none clause (List.forall_none_of_filterMap_eq_nil h clause hclause1) lit

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@@ -19,29 +19,12 @@ def tst1 : IO Unit := do
IO.println (0 / 0 : Float).toUInt16
IO.println (0 / 0 : Float).toUInt32
IO.println (0 / 0 : Float).toUInt64
IO.println (0 / 0 : Float).toUSize
IO.println (-1 : Float).toUInt8
IO.println (256 : Float).toUInt8
IO.println (1 / 0 : Float).toUInt8
IO.println (-1 : Float).toUInt16
IO.println (2^16 : Float).toUInt16
IO.println (1 / 0 : Float).toUInt16
IO.println (-1 : Float).toUInt32
IO.println (2^32 : Float).toUInt32
IO.println (1 / 0 : Float).toUInt32
IO.println (-1 : Float).toUInt64
IO.println (2^64 : Float).toUInt64
IO.println (1 / 0 : Float).toUInt64
let platBits := USize.size.log2.toFloat
IO.println (-1 : Float).toUSize
IO.println ((2^platBits).toUSize.toNat == (USize.size - 1))
IO.println ((1 / 0 : Float).toUSize.toNat == (USize.size - 1))
IO.println (let x : Float := 1.4; (x, x.isNaN, x.isInf, x.isFinite, x.frExp))
IO.println (let x : Float := 0 / 0; (x, x.isNaN, x.isInf, x.isFinite, x.frExp))
IO.println (let x : Float := -0 / 0; (x, x.isNaN, x.isInf, x.isFinite, x.frExp))

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@@ -18,21 +18,11 @@ true
0
0
0
0
255
255
0
65535
65535
0
4294967295
4294967295
0
18446744073709551615
18446744073709551615
0
true
true
(1.400000, (false, (false, (true, (0.700000, 1)))))
(NaN, (true, (false, (false, (NaN, 0)))))
(NaN, (true, (false, (false, (NaN, 0)))))

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@@ -1,21 +0,0 @@
/-!
# Long runs of identifiers should include line breaks
-/
set_option linter.unusedVariables false
def foo (a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15 a16 a17 a18 a19 a20
a21 a22 a23 a24 a25 a26 a27 a28 a29 a30 a31 a32 a33 a34 a35 a36 a37 a38 a39 a40
a41 a42 a43 a44 a45 a46 a47 a48 a49 a50 a51 a52 a53 a54 a55 a56 a57 a58 a59 a60
a61 a62 a63 a64 a65 a66 a67 a68 a69 a70 a71 a72 a73 a74 a75 a76 a77 a78 a79 a80
a81 a82 a83 a84 a85 a86 a87 a88 a89 a90 a91 a92 a93 a94 a95 a96 a97 a98 a99 : Nat) : Nat := 0
/--
info: foo
(a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15 a16 a17 a18 a19 a20 a21 a22 a23 a24 a25 a26 a27 a28 a29 a30 a31
a32 a33 a34 a35 a36 a37 a38 a39 a40 a41 a42 a43 a44 a45 a46 a47 a48 a49 a50 a51 a52 a53 a54 a55 a56 a57 a58 a59 a60
a61 a62 a63 a64 a65 a66 a67 a68 a69 a70 a71 a72 a73 a74 a75 a76 a77 a78 a79 a80 a81 a82 a83 a84 a85 a86 a87 a88 a89
a90 a91 a92 a93 a94 a95 a96 a97 a98 a99 : Nat) :
Nat
-/
#guard_msgs(whitespace := exact) in #check foo

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@@ -1,2 +0,0 @@
example : Array.eraseReps #[1, 3, 2, 2, 2, 3, 5] = #[1, 3, 2, 3, 5] := rfl
example : List.eraseReps [1, 3, 2, 2, 2, 3, 5] = [1, 3, 2, 3, 5] := rfl

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@@ -336,21 +336,21 @@ variable (h : n ≤ m) in
-- unzip
#check_simp unzip (replicate n (x, y)) ~> (replicate n x, replicate n y)
-- min?
-- minimum?
-- Note this relies on the fact that we do not have `replicate_succ` as a `@[simp]` lemma
#check_simp (replicate (n+1) 7).min? ~> some 7
#check_simp (replicate (n+1) 7).minimum? ~> some 7
variable (h : 0 < n) in
#check_tactic (replicate n 7).min? ~> some 7 by simp [h]
#check_tactic (replicate n 7).minimum? ~> some 7 by simp [h]
-- max?
-- maximum?
-- Note this relies on the fact that we do not have `replicate_succ` as a `@[simp]` lemma
#check_simp (replicate (n+1) 7).max? ~> some 7
#check_simp (replicate (n+1) 7).maximum? ~> some 7
variable (h : 0 < n) in
#check_tactic (replicate n 7).max? ~> some 7 by simp [h]
#check_tactic (replicate n 7).maximum? ~> some 7 by simp [h]
end
@@ -456,9 +456,9 @@ end Pairwise
/-! ### enumFrom -/
/-! ### min? -/
/-! ### minimum? -/
/-! ### max? -/
/-! ### maximum? -/
/-! ## Monadic operations -/

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@@ -458,14 +458,6 @@ example (a : Nat) :
(((a + (2 ^ 64 - 1)) % 2 ^ 64 + 1) * 8 - 1 - (a + (2 ^ 64 - 1)) % 2 ^ 64 * 8 + 1) = 8 := by
omega
/-! ### Int.toNat -/
example (z : Int) : z.toNat = 0 z 0 := by
omega
example (z : Int) (a : Fin z.toNat) (h : 0 z) : a z := by
omega
/-! ### BitVec -/
open BitVec

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@@ -1,69 +0,0 @@
/-!
This test checks that simp is able to instantiate the parameter `g` below. It does not
appear on the lhs of the rule, but solving `hf` fully determines it.
-/
theorem List.foldl_subtype (p : α Prop) (l : List (Subtype p)) (f : β Subtype p β)
(g : β α β) (b : β)
(hf : b x h, f b x, h = g b x) :
l.foldl f b = (l.map (·.val)).foldl g b := by
induction l generalizing b with
| nil => simp
| cons a l ih => simp [hf, ih]
example (l : List Nat) :
l.attach.foldl (fun acc t => max acc (t.val)) 0 = l.foldl (fun acc t => max acc t) 0 := by
simp [List.foldl_subtype]
example (l : List Nat) :
l.attach.foldl (fun acc t, _ => max acc t) 0 = l.foldl (fun acc t => max acc t) 0 := by
simp [List.foldl_subtype]
theorem foldr_to_sum (l : List Nat) (f : Nat Nat Nat) (g : Nat Nat)
(h : acc x, f x acc = g x + acc) :
l.foldr f 0 = Nat.sum (l.map g) := by
rw [Nat.sum, List.foldr_map]
congr
funext x acc
apply h
-- this works:
example (l : List Nat) :
l.foldr (fun x a => x*x + a) 0 = Nat.sum (l.map (fun x => x * x)) := by
simp [foldr_to_sum]
-- this does not, so such a pattern is still quite fragile
/-- error: simp made no progress -/
#guard_msgs in
example (l : List Nat) :
l.foldr (fun x a => a + x*x) 0 = Nat.sum (l.map (fun x => x * x)) := by
simp [foldr_to_sum]
-- but with stronger simp normal forms, it would work:
@[simp]
theorem add_eq_add_cancel (a x y : Nat) : (a + x = y + a) (x = y) := by omega
example (l : List Nat) :
l.foldr (fun x a => a + x*x) 0 = Nat.sum (l.map (fun x => x * x)) := by
simp [foldr_to_sum]
-- An example with zipWith
theorem zipWith_ignores_right
(l₁ : List α) (l₂ : List β) (f : α β γ) (g : α γ)
(h : a b, f a b = g a) :
List.zipWith f l₁ l₂ = List.map g (l₁.take l₂.length) := by
induction l₁ generalizing l₂ with
| nil => simp
| cons x xs ih =>
cases l₂
· simp
· simp [List.zipWith, h, ih]
example (l₁ l₂ : List Nat) (hlen: l₁.length = l₂.length):
List.zipWith (fun x y => x*x) l₁ l₂ = l₁.map (fun x => x * x) := by
simp only [zipWith_ignores_right, hlen.symm, List.take_length]