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| Author | SHA1 | Date | |
|---|---|---|---|
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6639a043f1 |
@@ -1864,8 +1864,7 @@ section
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variable {α : Type u}
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variable (r : α → α → Prop)
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instance Quotient.decidableEq {α : Sort u} {s : Setoid α} [d : ∀ (a b : α), Decidable (a ≈ b)]
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: DecidableEq (Quotient s) :=
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instance {α : Sort u} {s : Setoid α} [d : ∀ (a b : α), Decidable (a ≈ b)] : DecidableEq (Quotient s) :=
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fun (q₁ q₂ : Quotient s) =>
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Quotient.recOnSubsingleton₂ q₁ q₂
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fun a₁ a₂ =>
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@@ -607,13 +607,17 @@ protected def appendList (as : Array α) (bs : List α) : Array α :=
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instance : HAppend (Array α) (List α) (Array α) := ⟨Array.appendList⟩
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@[inline]
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def concatMapM [Monad m] (f : α → m (Array β)) (as : Array α) : m (Array β) :=
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def flatMapM [Monad m] (f : α → m (Array β)) (as : Array α) : m (Array β) :=
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as.foldlM (init := empty) fun bs a => do return bs ++ (← f a)
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@[deprecated concatMapM (since := "2024-10-16")] abbrev concatMapM := @flatMapM
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@[inline]
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def concatMap (f : α → Array β) (as : Array α) : Array β :=
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def flatMap (f : α → Array β) (as : Array α) : Array β :=
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as.foldl (init := empty) fun bs a => bs ++ f a
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@[deprecated flatMap (since := "2024-10-16")] abbrev concatMap := @flatMap
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/-- Joins array of array into a single array.
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`flatten #[#[a₁, a₂, ⋯], #[b₁, b₂, ⋯], ⋯]` = `#[a₁, a₂, ⋯, b₁, b₂, ⋯]`
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@@ -242,14 +242,17 @@ abbrev map_data := @toList_map
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cases arr
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simp
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theorem foldl_toList_eq_bind (l : List α) (acc : Array β)
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theorem foldl_toList_eq_flatMap (l : List α) (acc : Array β)
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(F : Array β → α → Array β) (G : α → List β)
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(H : ∀ acc a, (F acc a).toList = acc.toList ++ G a) :
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(l.foldl F acc).toList = acc.toList ++ l.bind G := by
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induction l generalizing acc <;> simp [*, List.bind]
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(l.foldl F acc).toList = acc.toList ++ l.flatMap G := by
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induction l generalizing acc <;> simp [*, List.flatMap]
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@[deprecated foldl_toList_eq_bind (since := "2024-09-09")]
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abbrev foldl_data_eq_bind := @foldl_toList_eq_bind
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@[deprecated foldl_toList_eq_flatMap (since := "2024-10-16")]
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abbrev foldl_toList_eq_bind := @foldl_toList_eq_flatMap
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@[deprecated foldl_toList_eq_flatMap (since := "2024-10-16")]
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abbrev foldl_data_eq_bind := @foldl_toList_eq_flatMap
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theorem foldl_toList_eq_map (l : List α) (acc : Array β) (G : α → β) :
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(l.foldl (fun acc a => acc.push (G a)) acc).toList = acc.toList ++ l.map G := by
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@@ -286,19 +286,6 @@ theorem getLsbD_ofNat (n : Nat) (x : Nat) (i : Nat) :
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@[simp] theorem getMsbD_zero : (0#w).getMsbD i = false := by simp [getMsbD]
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@[simp] theorem getLsbD_one : (1#w).getLsbD i = (decide (0 < w) && decide (i = 0)) := by
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simp only [getLsbD, toNat_ofNat, Nat.testBit_mod_two_pow]
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by_cases h : i = 0
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<;> simp [h, Nat.testBit_to_div_mod, Nat.div_eq_of_lt]
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@[simp] theorem getElem_one (h : i < w) : (1#w)[i] = decide (i = 0) := by
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simp [← getLsbD_eq_getElem, getLsbD_one, h, show 0 < w by omega]
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/-- The msb at index `w-1` is the least significant bit, and is true when the width is nonzero. -/
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@[simp] theorem getMsbD_one : (1#w).getMsbD i = (decide (i = w - 1) && decide (0 < w)) := by
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simp only [getMsbD]
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by_cases h : 0 < w <;> by_cases h' : i = w - 1 <;> simp [h, h'] <;> omega
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@[simp] theorem toNat_mod_cancel (x : BitVec n) : x.toNat % (2^n) = x.toNat :=
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Nat.mod_eq_of_lt x.isLt
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@@ -360,10 +347,6 @@ theorem getElem_ofBool {b : Bool} {i : Nat} : (ofBool b)[0] = b := by
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@[simp] theorem msb_zero : (0#w).msb = false := by simp [BitVec.msb, getMsbD]
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@[simp] theorem msb_one : (1#w).msb = decide (w = 1) := by
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simp [BitVec.msb, getMsbD_one, ← Bool.decide_and]
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omega
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theorem msb_eq_getLsbD_last (x : BitVec w) :
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x.msb = x.getLsbD (w - 1) := by
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simp only [BitVec.msb, getMsbD]
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@@ -2090,11 +2073,6 @@ theorem sub_eq_xor {a b : BitVec 1} : a - b = a ^^^ b := by
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have hb : b = 0 ∨ b = 1 := eq_zero_or_eq_one _
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rcases ha with h | h <;> (rcases hb with h' | h' <;> (simp [h, h']))
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@[simp]
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theorem sub_eq_self {x : BitVec 1} : -x = x := by
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have ha : x = 0 ∨ x = 1 := eq_zero_or_eq_one _
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rcases ha with h | h <;> simp [h]
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theorem not_neg (x : BitVec w) : ~~~(-x) = x + -1#w := by
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rcases w with _ | w
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· apply Subsingleton.elim
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@@ -2363,24 +2341,6 @@ theorem toNat_sdiv {x y : BitVec w} : (x.sdiv y).toNat =
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simp only [sdiv_eq, toNat_udiv]
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by_cases h : x.msb <;> by_cases h' : y.msb <;> simp [h, h']
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@[simp]
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theorem zero_sdiv {x : BitVec w} : (0#w).sdiv x = 0#w := by
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simp only [sdiv_eq]
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rcases x.msb with msb | msb <;> simp
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@[simp]
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theorem sdiv_zero {x : BitVec n} : x.sdiv 0#n = 0#n := by
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simp only [sdiv_eq, msb_zero]
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rcases x.msb with msb | msb <;> apply eq_of_toNat_eq <;> simp
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@[simp]
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theorem sdiv_one {x : BitVec w} : x.sdiv 1#w = x := by
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simp only [sdiv_eq]
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· by_cases h : w = 1
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· subst h
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rcases x.msb with msb | msb <;> simp
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· rcases x.msb with msb | msb <;> simp [h]
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theorem sdiv_eq_and (x y : BitVec 1) : x.sdiv y = x &&& y := by
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have hx : x = 0#1 ∨ x = 1#1 := by bv_omega
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have hy : y = 0#1 ∨ y = 1#1 := by bv_omega
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@@ -2389,13 +2349,9 @@ theorem sdiv_eq_and (x y : BitVec 1) : x.sdiv y = x &&& y := by
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rfl
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@[simp]
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theorem sdiv_self {x : BitVec w} :
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x.sdiv x = if x == 0#w then 0#w else 1#w := by
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simp [sdiv_eq]
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· by_cases h : w = 1
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· subst h
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rcases x.msb with msb | msb <;> simp
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· rcases x.msb with msb | msb <;> simp [h]
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theorem sdiv_zero {x : BitVec n} : x.sdiv 0#n = 0#n := by
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simp only [sdiv_eq, msb_zero]
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rcases x.msb with msb | msb <;> apply eq_of_toNat_eq <;> simp
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/-! ### smod -/
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@@ -2697,6 +2653,14 @@ theorem twoPow_zero {w : Nat} : twoPow w 0 = 1#w := by
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apply eq_of_toNat_eq
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simp
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@[simp]
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theorem getLsbD_one {w i : Nat} : (1#w).getLsbD i = (decide (0 < w) && decide (0 = i)) := by
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rw [← twoPow_zero, getLsbD_twoPow]
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@[simp]
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theorem getElem_one {w i : Nat} (h : i < w) : (1#w)[i] = decide (i = 0) := by
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rw [← twoPow_zero, getElem_twoPow]
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theorem shiftLeft_eq_mul_twoPow (x : BitVec w) (n : Nat) :
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x <<< n = x * (BitVec.twoPow w n) := by
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ext i
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@@ -2716,6 +2680,7 @@ theorem shiftLeft_eq_mul_twoPow (x : BitVec w) (n : Nat) :
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@[simp] theorem zero_concat_true : concat 0#w true = 1#(w + 1) := by
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ext
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simp [getLsbD_concat]
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omega
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/- ### setWidth, setWidth, and bitwise operations -/
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@@ -2756,7 +2721,7 @@ theorem and_one_eq_setWidth_ofBool_getLsbD {x : BitVec w} :
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ext i
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simp only [getLsbD_and, getLsbD_one, getLsbD_setWidth, Fin.is_lt, decide_True, getLsbD_ofBool,
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Bool.true_and]
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by_cases h : ((i : Nat) = 0) <;> simp [h] <;> omega
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by_cases h : (0 = (i : Nat)) <;> simp [h] <;> omega
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@[simp]
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theorem replicate_zero_eq {x : BitVec w} : x.replicate 0 = 0#0 := by
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@@ -639,14 +639,16 @@ and simplifies these to the function directly taking the value.
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| nil => simp
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| cons a l ih => simp [ih, hf, filterMap_cons]
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@[simp] theorem bind_subtype {p : α → Prop} {l : List { x // p x }}
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@[simp] theorem flatMap_subtype {p : α → Prop} {l : List { x // p x }}
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{f : { x // p x } → List β} {g : α → List β} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
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(l.bind f) = l.unattach.bind g := by
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(l.flatMap f) = l.unattach.flatMap g := by
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unfold unattach
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induction l with
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| nil => simp
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| cons a l ih => simp [ih, hf]
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@[deprecated flatMap_subtype (since := "2024-10-16")] abbrev bind_subtype := @flatMap_subtype
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@[simp] theorem unattach_filter {p : α → Prop} {l : List { x // p x }}
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{f : { x // p x } → Bool} {g : α → Bool} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
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(l.filter f).unattach = l.unattach.filter g := by
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@@ -563,23 +563,30 @@ def flatten : List (List α) → List α
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/-- `pure x = [x]` is the `pure` operation of the list monad. -/
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@[inline] protected def pure {α : Type u} (a : α) : List α := [a]
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/-! ### bind -/
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/-! ### flatMap -/
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/--
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`bind xs f` is the bind operation of the list monad. It applies `f` to each element of `xs`
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`flatMap xs f` applies `f` to each element of `xs`
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to get a list of lists, and then concatenates them all together.
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* `[2, 3, 2].bind range = [0, 1, 0, 1, 2, 0, 1]`
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-/
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@[inline] protected def bind {α : Type u} {β : Type v} (a : List α) (b : α → List β) : List β := flatten (map b a)
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@[inline] def flatMap {α : Type u} {β : Type v} (a : List α) (b : α → List β) : List β := flatten (map b a)
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@[simp] theorem bind_nil (f : α → List β) : List.bind [] f = [] := by simp [flatten, List.bind]
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@[simp] theorem bind_cons x xs (f : α → List β) :
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List.bind (x :: xs) f = f x ++ List.bind xs f := by simp [flatten, List.bind]
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@[simp] theorem flatMap_nil (f : α → List β) : List.flatMap [] f = [] := by simp [flatten, List.flatMap]
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@[simp] theorem flatMap_cons x xs (f : α → List β) :
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List.flatMap (x :: xs) f = f x ++ List.flatMap xs f := by simp [flatten, List.flatMap]
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set_option linter.missingDocs false in
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@[deprecated bind_nil (since := "2024-06-15")] abbrev nil_bind := @bind_nil
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@[deprecated flatMap (since := "2024-10-16")] abbrev bind := @flatMap
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set_option linter.missingDocs false in
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@[deprecated bind_cons (since := "2024-06-15")] abbrev cons_bind := @bind_cons
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@[deprecated flatMap_nil (since := "2024-10-16")] abbrev nil_flatMap := @flatMap_nil
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set_option linter.missingDocs false in
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@[deprecated flatMap_cons (since := "2024-10-16")] abbrev cons_flatMap := @flatMap_cons
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set_option linter.missingDocs false in
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@[deprecated flatMap_nil (since := "2024-06-15")] abbrev nil_bind := @flatMap_nil
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set_option linter.missingDocs false in
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@[deprecated flatMap_cons (since := "2024-06-15")] abbrev cons_bind := @flatMap_cons
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/-! ### replicate -/
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@@ -1398,17 +1405,8 @@ def unzip : List (α × β) → List α × List β
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/-! ## Ranges and enumeration -/
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/-- Sum of a list.
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`List.sum [a, b, c] = a + (b + (c + 0))` -/
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def sum {α} [Add α] [Zero α] : List α → α :=
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foldr (· + ·) 0
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@[simp] theorem sum_nil [Add α] [Zero α] : ([] : List α).sum = 0 := rfl
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@[simp] theorem sum_cons [Add α] [Zero α] {a : α} {l : List α} : (a::l).sum = a + l.sum := rfl
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/-- Sum of a list of natural numbers. -/
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-- We intend to subsequently deprecate this in favor of `List.sum`.
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-- This is not in the `List` namespace as later `List.sum` will be defined polymorphically.
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protected def _root_.Nat.sum (l : List Nat) : Nat := l.foldr (·+·) 0
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@[simp] theorem _root_.Nat.sum_nil : Nat.sum ([] : List Nat) = 0 := rfl
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@@ -156,7 +156,7 @@ theorem countP_filterMap (p : β → Bool) (f : α → Option β) (l : List α)
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simp (config := { contextual := true }) [Option.getD_eq_iff, Option.isSome_eq_isSome]
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@[simp] theorem countP_flatten (l : List (List α)) :
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countP p l.flatten = (l.map (countP p)).sum := by
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countP p l.flatten = Nat.sum (l.map (countP p)) := by
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simp only [countP_eq_length_filter, filter_flatten]
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simp [countP_eq_length_filter']
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@@ -232,7 +232,7 @@ theorem count_singleton (a b : α) : count a [b] = if b == a then 1 else 0 := by
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@[simp] theorem count_append (a : α) : ∀ l₁ l₂, count a (l₁ ++ l₂) = count a l₁ + count a l₂ :=
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countP_append _
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theorem count_flatten (a : α) (l : List (List α)) : count a l.flatten = (l.map (count a)).sum := by
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theorem count_flatten (a : α) (l : List (List α)) : count a l.flatten = Nat.sum (l.map (count a)) := by
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simp only [count_eq_countP, countP_flatten, count_eq_countP']
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@[deprecated count_flatten (since := "2024-10-14")] abbrev count_join := @count_flatten
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@@ -378,14 +378,18 @@ theorem find?_flatten_eq_some {xs : List (List α)} {p : α → Bool} {a : α} :
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· exact h₁ l ml a m
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· exact h₂ a m
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@[simp] theorem find?_bind (xs : List α) (f : α → List β) (p : β → Bool) :
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(xs.bind f).find? p = xs.findSome? (fun x => (f x).find? p) := by
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simp [bind_def, findSome?_map]; rfl
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@[simp] theorem find?_flatMap (xs : List α) (f : α → List β) (p : β → Bool) :
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(xs.flatMap f).find? p = xs.findSome? (fun x => (f x).find? p) := by
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simp [flatMap_def, findSome?_map]; rfl
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theorem find?_bind_eq_none {xs : List α} {f : α → List β} {p : β → Bool} :
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(xs.bind f).find? p = none ↔ ∀ x ∈ xs, ∀ y ∈ f x, !p y := by
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@[deprecated find?_flatMap (since := "2024-10-16")] abbrev find?_bind := @find?_flatMap
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theorem find?_flatMap_eq_none {xs : List α} {f : α → List β} {p : β → Bool} :
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(xs.flatMap f).find? p = none ↔ ∀ x ∈ xs, ∀ y ∈ f x, !p y := by
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simp
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@[deprecated find?_flatMap_eq_none (since := "2024-10-16")] abbrev find?_bind_eq_none := @find?_flatMap_eq_none
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theorem find?_replicate : find? p (replicate n a) = if n = 0 then none else if p a then some a else none := by
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cases n
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· simp
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@@ -789,7 +793,7 @@ theorem findIdx?_of_eq_none {xs : List α} {p : α → Bool} (w : xs.findIdx? p
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theorem findIdx?_flatten {l : List (List α)} {p : α → Bool} :
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l.flatten.findIdx? p =
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(l.findIdx? (·.any p)).map
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fun i => ((l.take i).map List.length).sum +
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fun i => Nat.sum ((l.take i).map List.length) +
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(l[i]?.map fun xs => xs.findIdx p).getD 0 := by
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induction l with
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| nil => simp
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@@ -93,29 +93,29 @@ The following operations are given `@[csimp]` replacements below:
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@[csimp] theorem foldr_eq_foldrTR : @foldr = @foldrTR := by
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funext α β f init l; simp [foldrTR, Array.foldr_eq_foldr_toList, -Array.size_toArray]
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/-! ### bind -/
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/-! ### flatMap -/
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/-- Tail recursive version of `List.bind`. -/
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@[inline] def bindTR (as : List α) (f : α → List β) : List β := go as #[] where
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/-- Auxiliary for `bind`: `bind.go f as = acc.toList ++ bind f as` -/
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/-- Tail recursive version of `List.flatMap`. -/
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@[inline] def flatMapTR (as : List α) (f : α → List β) : List β := go as #[] where
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/-- Auxiliary for `flatMap`: `flatMap.go f as = acc.toList ++ bind f as` -/
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@[specialize] go : List α → Array β → List β
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| [], acc => acc.toList
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| x::xs, acc => go xs (acc ++ f x)
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||||
@[csimp] theorem bind_eq_bindTR : @List.bind = @bindTR := by
|
||||
@[csimp] theorem flatMap_eq_flatMapTR : @List.flatMap = @flatMapTR := by
|
||||
funext α β as f
|
||||
let rec go : ∀ as acc, bindTR.go f as acc = acc.toList ++ as.bind f
|
||||
| [], acc => by simp [bindTR.go, bind]
|
||||
| x::xs, acc => by simp [bindTR.go, bind, go xs]
|
||||
let rec go : ∀ as acc, flatMapTR.go f as acc = acc.toList ++ as.flatMap f
|
||||
| [], acc => by simp [flatMapTR.go, flatMap]
|
||||
| x::xs, acc => by simp [flatMapTR.go, flatMap, go xs]
|
||||
exact (go as #[]).symm
|
||||
|
||||
/-! ### flatten -/
|
||||
|
||||
/-- Tail recursive version of `List.flatten`. -/
|
||||
@[inline] def flattenTR (l : List (List α)) : List α := bindTR l id
|
||||
@[inline] def flattenTR (l : List (List α)) : List α := flatMapTR l id
|
||||
|
||||
@[csimp] theorem flatten_eq_flattenTR : @flatten = @flattenTR := by
|
||||
funext α l; rw [← List.bind_id, List.bind_eq_bindTR]; rfl
|
||||
funext α l; rw [← List.flatMap_id, List.flatMap_eq_flatMapTR]; rfl
|
||||
|
||||
/-! ## Sublists -/
|
||||
|
||||
|
||||
@@ -2070,7 +2070,8 @@ theorem eq_nil_or_concat : ∀ l : List α, l = [] ∨ ∃ L b, l = concat L b
|
||||
|
||||
/-! ### flatten -/
|
||||
|
||||
@[simp] theorem length_flatten (L : List (List α)) : (flatten L).length = (L.map length).sum := by
|
||||
|
||||
@[simp] theorem length_flatten (L : List (List α)) : (flatten L).length = Nat.sum (L.map length) := by
|
||||
induction L with
|
||||
| nil => rfl
|
||||
| cons =>
|
||||
@@ -2097,8 +2098,8 @@ theorem forall_mem_flatten {p : α → Prop} {L : List (List α)} :
|
||||
simp only [mem_flatten, forall_exists_index, and_imp]
|
||||
constructor <;> (intros; solve_by_elim)
|
||||
|
||||
theorem flatten_eq_bind {L : List (List α)} : flatten L = L.bind id := by
|
||||
induction L <;> simp [List.bind]
|
||||
theorem flatten_eq_flatMap {L : List (List α)} : flatten L = L.flatMap id := by
|
||||
induction L <;> simp [List.flatMap]
|
||||
|
||||
theorem head?_flatten {L : List (List α)} : (flatten L).head? = L.findSome? fun l => l.head? := by
|
||||
induction L with
|
||||
@@ -2215,86 +2216,86 @@ theorem eq_iff_flatten_eq : ∀ {L L' : List (List α)},
|
||||
obtain ⟨rfl, h⟩ := append_inj h₁ h₂
|
||||
exact ⟨rfl, h, h₃⟩
|
||||
|
||||
/-! ### bind -/
|
||||
/-! ### flatMap -/
|
||||
|
||||
theorem bind_def (l : List α) (f : α → List β) : l.bind f = flatten (map f l) := by rfl
|
||||
theorem flatMap_def (l : List α) (f : α → List β) : l.flatMap f = flatten (map f l) := by rfl
|
||||
|
||||
@[simp] theorem bind_id (l : List (List α)) : List.bind l id = l.flatten := by simp [bind_def]
|
||||
@[simp] theorem flatMap_id (l : List (List α)) : List.flatMap l id = l.flatten := by simp [flatMap_def]
|
||||
|
||||
@[simp] theorem mem_bind {f : α → List β} {b} {l : List α} : b ∈ l.bind f ↔ ∃ a, a ∈ l ∧ b ∈ f a := by
|
||||
simp [bind_def, mem_flatten]
|
||||
@[simp] theorem mem_flatMap {f : α → List β} {b} {l : List α} : b ∈ l.flatMap f ↔ ∃ a, a ∈ l ∧ b ∈ f a := by
|
||||
simp [flatMap_def, mem_flatten]
|
||||
exact ⟨fun ⟨_, ⟨a, h₁, rfl⟩, h₂⟩ => ⟨a, h₁, h₂⟩, fun ⟨a, h₁, h₂⟩ => ⟨_, ⟨a, h₁, rfl⟩, h₂⟩⟩
|
||||
|
||||
theorem exists_of_mem_bind {b : β} {l : List α} {f : α → List β} :
|
||||
b ∈ l.bind f → ∃ a, a ∈ l ∧ b ∈ f a := mem_bind.1
|
||||
theorem exists_of_mem_flatMap {b : β} {l : List α} {f : α → List β} :
|
||||
b ∈ l.flatMap f → ∃ a, a ∈ l ∧ b ∈ f a := mem_flatMap.1
|
||||
|
||||
theorem mem_bind_of_mem {b : β} {l : List α} {f : α → List β} {a} (al : a ∈ l) (h : b ∈ f a) :
|
||||
b ∈ l.bind f := mem_bind.2 ⟨a, al, h⟩
|
||||
theorem mem_flatMap_of_mem {b : β} {l : List α} {f : α → List β} {a} (al : a ∈ l) (h : b ∈ f a) :
|
||||
b ∈ l.flatMap f := mem_flatMap.2 ⟨a, al, h⟩
|
||||
|
||||
@[simp]
|
||||
theorem bind_eq_nil_iff {l : List α} {f : α → List β} : List.bind l f = [] ↔ ∀ x ∈ l, f x = [] :=
|
||||
theorem flatMap_eq_nil_iff {l : List α} {f : α → List β} : List.flatMap l f = [] ↔ ∀ x ∈ l, f x = [] :=
|
||||
flatten_eq_nil_iff.trans <| by
|
||||
simp only [mem_map, forall_exists_index, and_imp, forall_apply_eq_imp_iff₂]
|
||||
|
||||
@[deprecated bind_eq_nil_iff (since := "2024-09-05")] abbrev bind_eq_nil := @bind_eq_nil_iff
|
||||
@[deprecated flatMap_eq_nil_iff (since := "2024-09-05")] abbrev bind_eq_nil := @flatMap_eq_nil_iff
|
||||
|
||||
theorem forall_mem_bind {p : β → Prop} {l : List α} {f : α → List β} :
|
||||
(∀ (x) (_ : x ∈ l.bind f), p x) ↔ ∀ (a) (_ : a ∈ l) (b) (_ : b ∈ f a), p b := by
|
||||
simp only [mem_bind, forall_exists_index, and_imp]
|
||||
theorem forall_mem_flatMap {p : β → Prop} {l : List α} {f : α → List β} :
|
||||
(∀ (x) (_ : x ∈ l.flatMap f), p x) ↔ ∀ (a) (_ : a ∈ l) (b) (_ : b ∈ f a), p b := by
|
||||
simp only [mem_flatMap, forall_exists_index, and_imp]
|
||||
constructor <;> (intros; solve_by_elim)
|
||||
|
||||
theorem bind_singleton (f : α → List β) (x : α) : [x].bind f = f x :=
|
||||
theorem flatMap_singleton (f : α → List β) (x : α) : [x].flatMap f = f x :=
|
||||
append_nil (f x)
|
||||
|
||||
@[simp] theorem bind_singleton' (l : List α) : (l.bind fun x => [x]) = l := by
|
||||
@[simp] theorem flatMap_singleton' (l : List α) : (l.flatMap fun x => [x]) = l := by
|
||||
induction l <;> simp [*]
|
||||
|
||||
theorem head?_bind {l : List α} {f : α → List β} :
|
||||
(l.bind f).head? = l.findSome? fun a => (f a).head? := by
|
||||
theorem head?_flatMap {l : List α} {f : α → List β} :
|
||||
(l.flatMap f).head? = l.findSome? fun a => (f a).head? := by
|
||||
induction l with
|
||||
| nil => rfl
|
||||
| cons =>
|
||||
simp only [findSome?_cons]
|
||||
split <;> simp_all
|
||||
|
||||
@[simp] theorem bind_append (xs ys : List α) (f : α → List β) :
|
||||
(xs ++ ys).bind f = xs.bind f ++ ys.bind f := by
|
||||
induction xs; {rfl}; simp_all [bind_cons, append_assoc]
|
||||
@[simp] theorem flatMap_append (xs ys : List α) (f : α → List β) :
|
||||
(xs ++ ys).flatMap f = xs.flatMap f ++ ys.flatMap f := by
|
||||
induction xs; {rfl}; simp_all [flatMap_cons, append_assoc]
|
||||
|
||||
@[deprecated bind_append (since := "2024-07-24")] abbrev append_bind := @bind_append
|
||||
@[deprecated flatMap_append (since := "2024-07-24")] abbrev append_bind := @flatMap_append
|
||||
|
||||
theorem bind_assoc {α β} (l : List α) (f : α → List β) (g : β → List γ) :
|
||||
(l.bind f).bind g = l.bind fun x => (f x).bind g := by
|
||||
theorem flatMap_assoc {α β} (l : List α) (f : α → List β) (g : β → List γ) :
|
||||
(l.flatMap f).flatMap g = l.flatMap fun x => (f x).flatMap g := by
|
||||
induction l <;> simp [*]
|
||||
|
||||
theorem map_bind (f : β → γ) (g : α → List β) :
|
||||
∀ l : List α, (l.bind g).map f = l.bind fun a => (g a).map f
|
||||
theorem map_flatMap (f : β → γ) (g : α → List β) :
|
||||
∀ l : List α, (l.flatMap g).map f = l.flatMap fun a => (g a).map f
|
||||
| [] => rfl
|
||||
| a::l => by simp only [bind_cons, map_append, map_bind _ _ l]
|
||||
| a::l => by simp only [flatMap_cons, map_append, map_flatMap _ _ l]
|
||||
|
||||
theorem bind_map (f : α → β) (g : β → List γ) (l : List α) :
|
||||
(map f l).bind g = l.bind (fun a => g (f a)) := by
|
||||
induction l <;> simp [bind_cons, *]
|
||||
theorem flatMap_map (f : α → β) (g : β → List γ) (l : List α) :
|
||||
(map f l).flatMap g = l.flatMap (fun a => g (f a)) := by
|
||||
induction l <;> simp [flatMap_cons, *]
|
||||
|
||||
theorem map_eq_bind {α β} (f : α → β) (l : List α) : map f l = l.bind fun x => [f x] := by
|
||||
theorem map_eq_flatMap {α β} (f : α → β) (l : List α) : map f l = l.flatMap fun x => [f x] := by
|
||||
simp only [← map_singleton]
|
||||
rw [← bind_singleton' l, map_bind, bind_singleton']
|
||||
rw [← flatMap_singleton' l, map_flatMap, flatMap_singleton']
|
||||
|
||||
theorem filterMap_bind {β γ} (l : List α) (g : α → List β) (f : β → Option γ) :
|
||||
(l.bind g).filterMap f = l.bind fun a => (g a).filterMap f := by
|
||||
theorem filterMap_flatMap {β γ} (l : List α) (g : α → List β) (f : β → Option γ) :
|
||||
(l.flatMap g).filterMap f = l.flatMap fun a => (g a).filterMap f := by
|
||||
induction l <;> simp [*]
|
||||
|
||||
theorem filter_bind (l : List α) (g : α → List β) (f : β → Bool) :
|
||||
(l.bind g).filter f = l.bind fun a => (g a).filter f := by
|
||||
theorem filter_flatMap (l : List α) (g : α → List β) (f : β → Bool) :
|
||||
(l.flatMap g).filter f = l.flatMap fun a => (g a).filter f := by
|
||||
induction l <;> simp [*]
|
||||
|
||||
theorem bind_eq_foldl (f : α → List β) (l : List α) :
|
||||
l.bind f = l.foldl (fun acc a => acc ++ f a) [] := by
|
||||
suffices ∀ l', l' ++ l.bind f = l.foldl (fun acc a => acc ++ f a) l' by simpa using this []
|
||||
theorem flatMap_eq_foldl (f : α → List β) (l : List α) :
|
||||
l.flatMap f = l.foldl (fun acc a => acc ++ f a) [] := by
|
||||
suffices ∀ l', l' ++ l.flatMap f = l.foldl (fun acc a => acc ++ f a) l' by simpa using this []
|
||||
intro l'
|
||||
induction l generalizing l'
|
||||
· simp
|
||||
· next ih => rw [bind_cons, ← append_assoc, ih, foldl_cons]
|
||||
· next ih => rw [flatMap_cons, ← append_assoc, ih, foldl_cons]
|
||||
|
||||
/-! ### replicate -/
|
||||
|
||||
@@ -2484,10 +2485,10 @@ theorem filterMap_replicate_of_some {f : α → Option β} (h : f a = some b) :
|
||||
simp only [replicate_succ, flatten_cons, ih, append_replicate_replicate, replicate_inj, or_true,
|
||||
and_true, add_one_mul, Nat.add_comm]
|
||||
|
||||
theorem bind_replicate {β} (f : α → List β) : (replicate n a).bind f = (replicate n (f a)).flatten := by
|
||||
theorem flatMap_replicate {β} (f : α → List β) : (replicate n a).flatMap f = (replicate n (f a)).flatten := by
|
||||
induction n with
|
||||
| zero => simp
|
||||
| succ n ih => simp only [replicate_succ, bind_cons, ih, flatten_cons]
|
||||
| succ n ih => simp only [replicate_succ, flatMap_cons, ih, flatten_cons]
|
||||
|
||||
@[simp] theorem isEmpty_replicate : (replicate n a).isEmpty = decide (n = 0) := by
|
||||
cases n <;> simp [replicate_succ]
|
||||
@@ -2672,10 +2673,10 @@ theorem flatten_reverse (L : List (List α)) :
|
||||
L.reverse.flatten = (L.map reverse).flatten.reverse := by
|
||||
induction L <;> simp_all
|
||||
|
||||
theorem reverse_bind {β} (l : List α) (f : α → List β) : (l.bind f).reverse = l.reverse.bind (reverse ∘ f) := by
|
||||
theorem reverse_flatMap {β} (l : List α) (f : α → List β) : (l.flatMap f).reverse = l.reverse.flatMap (reverse ∘ f) := by
|
||||
induction l <;> simp_all
|
||||
|
||||
theorem bind_reverse {β} (l : List α) (f : α → List β) : (l.reverse.bind f) = (l.bind (reverse ∘ f)).reverse := by
|
||||
theorem flatMap_reverse {β} (l : List α) (f : α → List β) : (l.reverse.flatMap f) = (l.flatMap (reverse ∘ f)).reverse := by
|
||||
induction l <;> simp_all
|
||||
|
||||
@[simp] theorem reverseAux_eq (as bs : List α) : reverseAux as bs = reverse as ++ bs :=
|
||||
@@ -2783,15 +2784,15 @@ theorem getLast_filterMap_of_eq_some {f : α → Option β} {l : List α} {w : l
|
||||
rw [head_filterMap_of_eq_some (by simp_all)]
|
||||
simp_all
|
||||
|
||||
theorem getLast?_bind {L : List α} {f : α → List β} :
|
||||
(L.bind f).getLast? = L.reverse.findSome? fun a => (f a).getLast? := by
|
||||
simp only [← head?_reverse, reverse_bind]
|
||||
rw [head?_bind]
|
||||
theorem getLast?_flatMap {L : List α} {f : α → List β} :
|
||||
(L.flatMap f).getLast? = L.reverse.findSome? fun a => (f a).getLast? := by
|
||||
simp only [← head?_reverse, reverse_flatMap]
|
||||
rw [head?_flatMap]
|
||||
rfl
|
||||
|
||||
theorem getLast?_flatten {L : List (List α)} :
|
||||
(flatten L).getLast? = L.reverse.findSome? fun l => l.getLast? := by
|
||||
simp [← bind_id, getLast?_bind]
|
||||
simp [← flatMap_id, getLast?_flatMap]
|
||||
|
||||
theorem getLast?_replicate (a : α) (n : Nat) : (replicate n a).getLast? = if n = 0 then none else some a := by
|
||||
simp only [← head?_reverse, reverse_replicate, head?_replicate]
|
||||
@@ -3300,12 +3301,12 @@ theorem all_eq_not_any_not (l : List α) (p : α → Bool) : l.all p = !l.any (!
|
||||
|
||||
@[deprecated all_flatten (since := "2024-10-14")] abbrev all_join := @all_flatten
|
||||
|
||||
@[simp] theorem any_bind {l : List α} {f : α → List β} :
|
||||
(l.bind f).any p = l.any fun a => (f a).any p := by
|
||||
@[simp] theorem any_flatMap {l : List α} {f : α → List β} :
|
||||
(l.flatMap f).any p = l.any fun a => (f a).any p := by
|
||||
induction l <;> simp_all
|
||||
|
||||
@[simp] theorem all_bind {l : List α} {f : α → List β} :
|
||||
(l.bind f).all p = l.all fun a => (f a).all p := by
|
||||
@[simp] theorem all_flatMap {l : List α} {f : α → List β} :
|
||||
(l.flatMap f).all p = l.all fun a => (f a).all p := by
|
||||
induction l <;> simp_all
|
||||
|
||||
@[simp] theorem any_reverse {l : List α} : l.reverse.any f = l.any f := by
|
||||
@@ -3345,7 +3346,7 @@ theorem all_eq_not_any_not (l : List α) (p : α → Bool) : l.all p = !l.any (!
|
||||
@[deprecated exists_of_mem_flatten (since := "2024-10-14")] abbrev exists_of_mem_join := @exists_of_mem_flatten
|
||||
@[deprecated mem_flatten_of_mem (since := "2024-10-14")] abbrev mem_join_of_mem := @mem_flatten_of_mem
|
||||
@[deprecated forall_mem_flatten (since := "2024-10-14")] abbrev forall_mem_join := @forall_mem_flatten
|
||||
@[deprecated flatten_eq_bind (since := "2024-10-14")] abbrev join_eq_bind := @flatten_eq_bind
|
||||
@[deprecated flatten_eq_flatMap (since := "2024-10-14")] abbrev join_eq_bind := @flatten_eq_flatMap
|
||||
@[deprecated head?_flatten (since := "2024-10-14")] abbrev head?_join := @head?_flatten
|
||||
@[deprecated foldl_flatten (since := "2024-10-14")] abbrev foldl_join := @foldl_flatten
|
||||
@[deprecated foldr_flatten (since := "2024-10-14")] abbrev foldr_join := @foldr_flatten
|
||||
@@ -3372,5 +3373,30 @@ theorem join_map_filter (p : α → Bool) (l : List (List α)) :
|
||||
@[deprecated reverse_flatten (since := "2024-10-14")] abbrev reverse_join := @reverse_flatten
|
||||
@[deprecated flatten_reverse (since := "2024-10-14")] abbrev join_reverse := @flatten_reverse
|
||||
@[deprecated getLast?_flatten (since := "2024-10-14")] abbrev getLast?_join := @getLast?_flatten
|
||||
@[deprecated flatten_eq_flatMap (since := "2024-10-16")] abbrev flatten_eq_bind := @flatten_eq_flatMap
|
||||
@[deprecated flatMap_def (since := "2024-10-16")] abbrev bind_def := @flatMap_def
|
||||
@[deprecated flatMap_id (since := "2024-10-16")] abbrev bind_id := @flatMap_id
|
||||
@[deprecated mem_flatMap (since := "2024-10-16")] abbrev mem_bind := @mem_flatMap
|
||||
@[deprecated exists_of_mem_flatMap (since := "2024-10-16")] abbrev exists_of_mem_bind := @exists_of_mem_flatMap
|
||||
@[deprecated mem_flatMap_of_mem (since := "2024-10-16")] abbrev mem_bind_of_mem := @mem_flatMap_of_mem
|
||||
@[deprecated flatMap_eq_nil_iff (since := "2024-10-16")] abbrev bind_eq_nil_iff := @flatMap_eq_nil_iff
|
||||
@[deprecated forall_mem_flatMap (since := "2024-10-16")] abbrev forall_mem_bind := @forall_mem_flatMap
|
||||
@[deprecated flatMap_singleton (since := "2024-10-16")] abbrev bind_singleton := @flatMap_singleton
|
||||
@[deprecated flatMap_singleton' (since := "2024-10-16")] abbrev bind_singleton' := @flatMap_singleton'
|
||||
@[deprecated head?_flatMap (since := "2024-10-16")] abbrev head_bind := @head?_flatMap
|
||||
@[deprecated flatMap_append (since := "2024-10-16")] abbrev bind_append := @flatMap_append
|
||||
@[deprecated flatMap_assoc (since := "2024-10-16")] abbrev bind_assoc := @flatMap_assoc
|
||||
@[deprecated map_flatMap (since := "2024-10-16")] abbrev map_bind := @map_flatMap
|
||||
@[deprecated flatMap_map (since := "2024-10-16")] abbrev bind_map := @flatMap_map
|
||||
@[deprecated map_eq_flatMap (since := "2024-10-16")] abbrev map_eq_bind := @map_eq_flatMap
|
||||
@[deprecated filterMap_flatMap (since := "2024-10-16")] abbrev filterMap_bind := @filterMap_flatMap
|
||||
@[deprecated filter_flatMap (since := "2024-10-16")] abbrev filter_bind := @filter_flatMap
|
||||
@[deprecated flatMap_eq_foldl (since := "2024-10-16")] abbrev bind_eq_foldl := @flatMap_eq_foldl
|
||||
@[deprecated flatMap_replicate (since := "2024-10-16")] abbrev bind_replicate := @flatMap_replicate
|
||||
@[deprecated reverse_flatMap (since := "2024-10-16")] abbrev reverse_bind := @reverse_flatMap
|
||||
@[deprecated flatMap_reverse (since := "2024-10-16")] abbrev bind_reverse := @flatMap_reverse
|
||||
@[deprecated getLast?_flatMap (since := "2024-10-16")] abbrev getLast?_bind := @getLast?_flatMap
|
||||
@[deprecated any_flatMap (since := "2024-10-16")] abbrev any_bind := @any_flatMap
|
||||
@[deprecated all_flatMap (since := "2024-10-16")] abbrev all_bind := @all_flatMap
|
||||
|
||||
end List
|
||||
|
||||
@@ -173,10 +173,12 @@ theorem pairwise_flatten {L : List (List α)} :
|
||||
|
||||
@[deprecated pairwise_flatten (since := "2024-10-14")] abbrev pairwise_join := @pairwise_flatten
|
||||
|
||||
theorem pairwise_bind {R : β → β → Prop} {l : List α} {f : α → List β} :
|
||||
List.Pairwise R (l.bind f) ↔
|
||||
theorem pairwise_flatMap {R : β → β → Prop} {l : List α} {f : α → List β} :
|
||||
List.Pairwise R (l.flatMap f) ↔
|
||||
(∀ a ∈ l, Pairwise R (f a)) ∧ Pairwise (fun a₁ a₂ => ∀ x ∈ f a₁, ∀ y ∈ f a₂, R x y) l := by
|
||||
simp [List.bind, pairwise_flatten, pairwise_map]
|
||||
simp [List.flatMap, pairwise_flatten, pairwise_map]
|
||||
|
||||
@[deprecated pairwise_flatMap (since := "2024-10-14")] abbrev pairwise_bind := @pairwise_flatMap
|
||||
|
||||
theorem pairwise_reverse {l : List α} :
|
||||
l.reverse.Pairwise R ↔ l.Pairwise (fun a b => R b a) := by
|
||||
|
||||
@@ -470,9 +470,11 @@ theorem Perm.flatten {l₁ l₂ : List (List α)} (h : l₁ ~ l₂) : l₁.flatt
|
||||
|
||||
@[deprecated Perm.flatten (since := "2024-10-14")] abbrev Perm.join := @Perm.flatten
|
||||
|
||||
theorem Perm.bind_right {l₁ l₂ : List α} (f : α → List β) (p : l₁ ~ l₂) : l₁.bind f ~ l₂.bind f :=
|
||||
theorem Perm.flatMap_right {l₁ l₂ : List α} (f : α → List β) (p : l₁ ~ l₂) : l₁.flatMap f ~ l₂.flatMap f :=
|
||||
(p.map _).flatten
|
||||
|
||||
@[deprecated Perm.flatMap_right (since := "2024-10-16")] abbrev Perm.bind_right := @Perm.flatMap_right
|
||||
|
||||
theorem Perm.eraseP (f : α → Bool) {l₁ l₂ : List α}
|
||||
(H : Pairwise (fun a b => f a → f b → False) l₁) (p : l₁ ~ l₂) : eraseP f l₁ ~ eraseP f l₂ := by
|
||||
induction p with
|
||||
|
||||
@@ -20,6 +20,7 @@ open Nat
|
||||
|
||||
/-! ## Ranges and enumeration -/
|
||||
|
||||
|
||||
/-! ### range' -/
|
||||
|
||||
theorem range'_succ (s n step) : range' s (n + 1) step = s :: range' (s + step) n step := by
|
||||
|
||||
@@ -976,7 +976,7 @@ theorem mem_of_mem_drop {n} {l : List α} (h : a ∈ l.drop n) : a ∈ l :=
|
||||
drop_subset _ _ h
|
||||
|
||||
theorem drop_suffix_drop_left (l : List α) {m n : Nat} (h : m ≤ n) : drop n l <:+ drop m l := by
|
||||
rw [← Nat.sub_add_cancel h, Nat.add_comm, ← drop_drop]
|
||||
rw [← Nat.sub_add_cancel h, ← drop_drop]
|
||||
apply drop_suffix
|
||||
|
||||
-- See `Init.Data.List.Nat.TakeDrop` for `take_prefix_take_left`.
|
||||
|
||||
@@ -97,14 +97,14 @@ theorem get?_take {l : List α} {n m : Nat} (h : m < n) : (l.take n).get? m = l.
|
||||
|
||||
theorem getElem?_take_of_succ {l : List α} {n : Nat} : (l.take (n + 1))[n]? = l[n]? := by simp
|
||||
|
||||
@[simp] theorem drop_drop (n : Nat) : ∀ (m) (l : List α), drop n (drop m l) = drop (m + n) l
|
||||
@[simp] theorem drop_drop (n : Nat) : ∀ (m) (l : List α), drop n (drop m l) = drop (n + m) l
|
||||
| m, [] => by simp
|
||||
| 0, l => by simp
|
||||
| m + 1, a :: l =>
|
||||
calc
|
||||
drop n (drop (m + 1) (a :: l)) = drop n (drop m l) := rfl
|
||||
_ = drop (m + n) l := drop_drop n m l
|
||||
_ = drop ((m + 1) + n) (a :: l) := by rw [Nat.add_right_comm]; rfl
|
||||
_ = drop (n + m) l := drop_drop n m l
|
||||
_ = drop (n + (m + 1)) (a :: l) := rfl
|
||||
|
||||
theorem take_drop : ∀ (m n : Nat) (l : List α), take n (drop m l) = drop m (take (m + n) l)
|
||||
| 0, _, _ => by simp
|
||||
@@ -112,7 +112,7 @@ theorem take_drop : ∀ (m n : Nat) (l : List α), take n (drop m l) = drop m (t
|
||||
| _+1, _, _ :: _ => by simpa [Nat.succ_add, take_succ_cons, drop_succ_cons] using take_drop ..
|
||||
|
||||
@[deprecated drop_drop (since := "2024-06-15")]
|
||||
theorem drop_add (m n) (l : List α) : drop (m + n) l = drop n (drop m l) := by
|
||||
theorem drop_add (m n) (l : List α) : drop (m + n) l = drop m (drop n l) := by
|
||||
simp [drop_drop]
|
||||
|
||||
@[simp]
|
||||
@@ -126,7 +126,7 @@ theorem tail_drop (l : List α) (n : Nat) : (l.drop n).tail = l.drop (n + 1) :=
|
||||
|
||||
@[simp]
|
||||
theorem drop_tail (l : List α) (n : Nat) : l.tail.drop n = l.drop (n + 1) := by
|
||||
rw [Nat.add_comm, ← drop_drop, drop_one]
|
||||
rw [← drop_drop, drop_one]
|
||||
|
||||
@[simp]
|
||||
theorem drop_eq_nil_iff {l : List α} {k : Nat} : l.drop k = [] ↔ l.length ≤ k := by
|
||||
|
||||
@@ -317,9 +317,6 @@ theorem _root_.Char.utf8Size_le_four (c : Char) : c.utf8Size ≤ 4 := by
|
||||
|
||||
@[simp] theorem pos_add_char (p : Pos) (c : Char) : (p + c).byteIdx = p.byteIdx + c.utf8Size := rfl
|
||||
|
||||
protected theorem Pos.ne_zero_of_lt : {a b : Pos} → a < b → b ≠ 0
|
||||
| _, _, hlt, rfl => Nat.not_lt_zero _ hlt
|
||||
|
||||
theorem lt_next (s : String) (i : Pos) : i.1 < (s.next i).1 :=
|
||||
Nat.add_lt_add_left (Char.utf8Size_pos _) _
|
||||
|
||||
@@ -1024,66 +1021,6 @@ instance hasBeq : BEq Substring := ⟨beq⟩
|
||||
def sameAs (ss1 ss2 : Substring) : Bool :=
|
||||
ss1.startPos == ss2.startPos && ss1 == ss2
|
||||
|
||||
/--
|
||||
Returns the longest common prefix of two substrings.
|
||||
The returned substring will use the same underlying string as `s`.
|
||||
-/
|
||||
def commonPrefix (s t : Substring) : Substring :=
|
||||
{ s with stopPos := loop s.startPos t.startPos }
|
||||
where
|
||||
/-- Returns the ending position of the common prefix, working up from `spos, tpos`. -/
|
||||
loop spos tpos :=
|
||||
if h : spos < s.stopPos ∧ tpos < t.stopPos then
|
||||
if s.str.get spos == t.str.get tpos then
|
||||
have := Nat.sub_lt_sub_left h.1 (s.str.lt_next spos)
|
||||
loop (s.str.next spos) (t.str.next tpos)
|
||||
else
|
||||
spos
|
||||
else
|
||||
spos
|
||||
termination_by s.stopPos.byteIdx - spos.byteIdx
|
||||
|
||||
/--
|
||||
Returns the longest common suffix of two substrings.
|
||||
The returned substring will use the same underlying string as `s`.
|
||||
-/
|
||||
def commonSuffix (s t : Substring) : Substring :=
|
||||
{ s with startPos := loop s.stopPos t.stopPos }
|
||||
where
|
||||
/-- Returns the starting position of the common prefix, working down from `spos, tpos`. -/
|
||||
loop spos tpos :=
|
||||
if h : s.startPos < spos ∧ t.startPos < tpos then
|
||||
let spos' := s.str.prev spos
|
||||
let tpos' := t.str.prev tpos
|
||||
if s.str.get spos' == t.str.get tpos' then
|
||||
have : spos' < spos := s.str.prev_lt_of_pos spos (String.Pos.ne_zero_of_lt h.1)
|
||||
loop spos' tpos'
|
||||
else
|
||||
spos
|
||||
else
|
||||
spos
|
||||
termination_by spos.byteIdx
|
||||
|
||||
/--
|
||||
If `pre` is a prefix of `s`, i.e. `s = pre ++ t`, returns the remainder `t`.
|
||||
-/
|
||||
def dropPrefix? (s : Substring) (pre : Substring) : Option Substring :=
|
||||
let t := s.commonPrefix pre
|
||||
if t.bsize = pre.bsize then
|
||||
some { s with startPos := t.stopPos }
|
||||
else
|
||||
none
|
||||
|
||||
/--
|
||||
If `suff` is a suffix of `s`, i.e. `s = t ++ suff`, returns the remainder `t`.
|
||||
-/
|
||||
def dropSuffix? (s : Substring) (suff : Substring) : Option Substring :=
|
||||
let t := s.commonSuffix suff
|
||||
if t.bsize = suff.bsize then
|
||||
some { s with stopPos := t.startPos }
|
||||
else
|
||||
none
|
||||
|
||||
end Substring
|
||||
|
||||
namespace String
|
||||
@@ -1145,28 +1082,6 @@ namespace String
|
||||
@[inline] def decapitalize (s : String) :=
|
||||
s.set 0 <| s.get 0 |>.toLower
|
||||
|
||||
/--
|
||||
If `pre` is a prefix of `s`, i.e. `s = pre ++ t`, returns the remainder `t`.
|
||||
-/
|
||||
def dropPrefix? (s : String) (pre : Substring) : Option Substring :=
|
||||
s.toSubstring.dropPrefix? pre
|
||||
|
||||
/--
|
||||
If `suff` is a suffix of `s`, i.e. `s = t ++ suff`, returns the remainder `t`.
|
||||
-/
|
||||
def dropSuffix? (s : String) (suff : Substring) : Option Substring :=
|
||||
s.toSubstring.dropSuffix? suff
|
||||
|
||||
/-- `s.stripPrefix pre` will remove `pre` from the beginning of `s` if it occurs there,
|
||||
or otherwise return `s`. -/
|
||||
def stripPrefix (s : String) (pre : Substring) : String :=
|
||||
s.dropPrefix? pre |>.map Substring.toString |>.getD s
|
||||
|
||||
/-- `s.stripSuffix suff` will remove `suff` from the end of `s` if it occurs there,
|
||||
or otherwise return `s`. -/
|
||||
def stripSuffix (s : String) (suff : Substring) : String :=
|
||||
s.dropSuffix? suff |>.map Substring.toString |>.getD s
|
||||
|
||||
end String
|
||||
|
||||
namespace Char
|
||||
|
||||
@@ -117,10 +117,10 @@ def utf8EncodeChar (c : Char) : List UInt8 :=
|
||||
/-- Converts the given `String` to a [UTF-8](https://en.wikipedia.org/wiki/UTF-8) encoded byte array. -/
|
||||
@[extern "lean_string_to_utf8"]
|
||||
def toUTF8 (a : @& String) : ByteArray :=
|
||||
⟨⟨a.data.bind utf8EncodeChar⟩⟩
|
||||
⟨⟨a.data.flatMap utf8EncodeChar⟩⟩
|
||||
|
||||
@[simp] theorem size_toUTF8 (s : String) : s.toUTF8.size = s.utf8ByteSize := by
|
||||
simp [toUTF8, ByteArray.size, Array.size, utf8ByteSize, List.bind]
|
||||
simp [toUTF8, ByteArray.size, Array.size, utf8ByteSize, List.flatMap]
|
||||
induction s.data <;> simp [List.map, List.flatten, utf8ByteSize.go, Nat.add_comm, *]
|
||||
|
||||
/-- Accesses a byte in the UTF-8 encoding of the `String`. O(1) -/
|
||||
|
||||
@@ -910,15 +910,6 @@ macro_rules | `(tactic| trivial) => `(tactic| simp)
|
||||
-/
|
||||
syntax "trivial" : tactic
|
||||
|
||||
/--
|
||||
`classical tacs` runs `tacs` in a scope where `Classical.propDecidable` is a low priority
|
||||
local instance.
|
||||
|
||||
Note that `classical` is a scoping tactic: it adds the instance only within the
|
||||
scope of the tactic.
|
||||
-/
|
||||
syntax (name := classical) "classical" ppDedent(tacticSeq) : tactic
|
||||
|
||||
/--
|
||||
The `split` tactic is useful for breaking nested if-then-else and `match` expressions into separate cases.
|
||||
For a `match` expression with `n` cases, the `split` tactic generates at most `n` subgoals.
|
||||
|
||||
@@ -459,7 +459,7 @@ mutual
|
||||
|
||||
let z ← optional (Content.Character <$> CharData)
|
||||
pure #[y, z]
|
||||
let xs := #[x] ++ xs.concatMap id |>.filterMap id
|
||||
let xs := #[x] ++ xs.flatMap id |>.filterMap id
|
||||
let mut res := #[]
|
||||
for x in xs do
|
||||
if res.size > 0 then
|
||||
|
||||
@@ -229,7 +229,7 @@ private def replaceBinderAnnotation (binder : TSyntax ``Parser.Term.bracketedBin
|
||||
|
||||
@[builtin_command_elab «variable»] def elabVariable : CommandElab
|
||||
| `(variable $binders*) => do
|
||||
let binders ← binders.concatMapM replaceBinderAnnotation
|
||||
let binders ← binders.flatMapM replaceBinderAnnotation
|
||||
-- Try to elaborate `binders` for sanity checking
|
||||
runTermElabM fun _ => Term.withSynthesize <| Term.withAutoBoundImplicit <|
|
||||
Term.elabBinders binders fun _ => pure ()
|
||||
@@ -348,7 +348,7 @@ def failIfSucceeds (x : CommandElabM Unit) : CommandElabM Unit := do
|
||||
@[builtin_command_elab Lean.Parser.Command.include] def elabInclude : CommandElab
|
||||
| `(Lean.Parser.Command.include| include $ids*) => do
|
||||
let sc ← getScope
|
||||
let vars ← sc.varDecls.concatMapM getBracketedBinderIds
|
||||
let vars ← sc.varDecls.flatMapM getBracketedBinderIds
|
||||
let mut uids := #[]
|
||||
for id in ids do
|
||||
if let some idx := vars.findIdx? (· == id.getId) then
|
||||
|
||||
@@ -571,7 +571,7 @@ def getBracketedBinderIds : Syntax → CommandElabM (Array Name)
|
||||
private def mkTermContext (ctx : Context) (s : State) : CommandElabM Term.Context := do
|
||||
let scope := s.scopes.head!
|
||||
let mut sectionVars := {}
|
||||
for id in (← scope.varDecls.concatMapM getBracketedBinderIds), uid in scope.varUIds do
|
||||
for id in (← scope.varDecls.flatMapM getBracketedBinderIds), uid in scope.varUIds do
|
||||
sectionVars := sectionVars.insert id uid
|
||||
return {
|
||||
macroStack := ctx.macroStack
|
||||
@@ -714,7 +714,7 @@ def expandDeclId (declId : Syntax) (modifiers : Modifiers) : CommandElabM Expand
|
||||
let currNamespace ← getCurrNamespace
|
||||
let currLevelNames ← getLevelNames
|
||||
let r ← Elab.expandDeclId currNamespace currLevelNames declId modifiers
|
||||
for id in (← (← getScope).varDecls.concatMapM getBracketedBinderIds) do
|
||||
for id in (← (← getScope).varDecls.flatMapM getBracketedBinderIds) do
|
||||
if id == r.shortName then
|
||||
throwError "invalid declaration name '{r.shortName}', there is a section variable with the same name"
|
||||
return r
|
||||
|
||||
@@ -151,7 +151,7 @@ def runFrontend
|
||||
snaps.runAndReport opts jsonOutput
|
||||
|
||||
if let some ileanFileName := ileanFileName? then
|
||||
let trees := snaps.getAll.concatMap (match ·.infoTree? with | some t => #[t] | _ => #[])
|
||||
let trees := snaps.getAll.flatMap (match ·.infoTree? with | some t => #[t] | _ => #[])
|
||||
let references := Lean.Server.findModuleRefs inputCtx.fileMap trees (localVars := false)
|
||||
let ilean := { module := mainModuleName, references := ← references.toLspModuleRefs : Lean.Server.Ilean }
|
||||
IO.FS.writeFile ileanFileName $ Json.compress $ toJson ilean
|
||||
|
||||
@@ -226,7 +226,7 @@ def allCombinations (xss : Array (Array α)) : Option (Array (Array α)) :=
|
||||
else
|
||||
let rec go i acc : Array (Array α):=
|
||||
if h : i < xss.size then
|
||||
xss[i].concatMap fun x => go (i + 1) (acc.push x)
|
||||
xss[i].flatMap fun x => go (i + 1) (acc.push x)
|
||||
else
|
||||
#[acc]
|
||||
some (go 0 #[])
|
||||
|
||||
@@ -43,4 +43,3 @@ import Lean.Elab.Tactic.Rewrites
|
||||
import Lean.Elab.Tactic.DiscrTreeKey
|
||||
import Lean.Elab.Tactic.BVDecide
|
||||
import Lean.Elab.Tactic.BoolToPropSimps
|
||||
import Lean.Elab.Tactic.Classical
|
||||
|
||||
@@ -1,34 +0,0 @@
|
||||
/-
|
||||
Copyright (c) 2021 Mario Carneiro. All rights reserved.
|
||||
Released under Apache 2.0 license as described in the file LICENSE.
|
||||
Authors: Mario Carneiro, Kim Morrison
|
||||
-/
|
||||
prelude
|
||||
import Lean.Elab.Tactic.Basic
|
||||
|
||||
/-! # `classical` tactic -/
|
||||
|
||||
namespace Lean.Elab.Tactic
|
||||
open Lean Meta Elab.Tactic
|
||||
|
||||
/--
|
||||
`classical t` runs `t` in a scope where `Classical.propDecidable` is a low priority
|
||||
local instance.
|
||||
-/
|
||||
def classical [Monad m] [MonadEnv m] [MonadFinally m] [MonadLiftT MetaM m] (t : m α) :
|
||||
m α := do
|
||||
modifyEnv Meta.instanceExtension.pushScope
|
||||
Meta.addInstance ``Classical.propDecidable .local 10
|
||||
try
|
||||
t
|
||||
finally
|
||||
modifyEnv Meta.instanceExtension.popScope
|
||||
|
||||
@[builtin_tactic Lean.Parser.Tactic.classical]
|
||||
def evalClassical : Tactic := fun stx => do
|
||||
match stx with
|
||||
| `(tactic| classical $tacs:tacticSeq) =>
|
||||
classical <| Elab.Tactic.evalTactic tacs
|
||||
| _ => throwUnsupportedSyntax
|
||||
|
||||
end Lean.Elab.Tactic
|
||||
@@ -67,6 +67,29 @@ instance : ToString RecursorInfo := ⟨fun info =>
|
||||
|
||||
end RecursorInfo
|
||||
|
||||
private def mkRecursorInfoForKernelRec (declName : Name) (val : RecursorVal) : MetaM RecursorInfo := do
|
||||
let ival ← getConstInfoInduct val.getInduct
|
||||
let numLParams := ival.levelParams.length
|
||||
let univLevelPos := (List.range numLParams).map RecursorUnivLevelPos.majorType
|
||||
let univLevelPos := if val.levelParams.length == numLParams then univLevelPos else RecursorUnivLevelPos.motive :: univLevelPos
|
||||
let produceMotive := List.replicate val.numMinors true
|
||||
let paramsPos := (List.range val.numParams).map some
|
||||
let indicesPos := (List.range val.numIndices).map fun pos => val.numParams + pos
|
||||
let numArgs := val.numIndices + val.numParams + val.numMinors + val.numMotives + 1
|
||||
pure {
|
||||
recursorName := declName,
|
||||
typeName := val.getInduct,
|
||||
univLevelPos := univLevelPos,
|
||||
majorPos := val.getMajorIdx,
|
||||
depElim := true,
|
||||
recursive := ival.isRec,
|
||||
produceMotive := produceMotive,
|
||||
paramsPos := paramsPos,
|
||||
indicesPos := indicesPos,
|
||||
numArgs := numArgs
|
||||
}
|
||||
|
||||
|
||||
private def getMajorPosIfAuxRecursor? (declName : Name) (majorPos? : Option Nat) : MetaM (Option Nat) :=
|
||||
if majorPos?.isSome then pure majorPos?
|
||||
else do
|
||||
@@ -179,8 +202,8 @@ private def checkMotiveResultType (declName : Name) (motiveArgs : Array Expr) (m
|
||||
if !motiveResultType.isSort || motiveArgs.size != motiveTypeParams.size then
|
||||
throwError "invalid user defined recursor '{declName}', motive must have a type of the form (C : Pi (i : B A), I A i -> Type), where A is (possibly empty) sequence of variables (aka parameters), (i : B A) is a (possibly empty) telescope (aka indices), and I is a constant"
|
||||
|
||||
private def mkRecursorInfoCore (declName : Name) (majorPos? : Option Nat) : MetaM RecursorInfo := do
|
||||
let cinfo ← getConstInfo declName
|
||||
private def mkRecursorInfoAux (cinfo : ConstantInfo) (majorPos? : Option Nat) : MetaM RecursorInfo := do
|
||||
let declName := cinfo.name
|
||||
let majorPos? ← getMajorPosIfAuxRecursor? declName majorPos?
|
||||
forallTelescopeReducing cinfo.type fun xs type => type.withApp fun motive motiveArgs => do
|
||||
checkMotive declName motive motiveArgs
|
||||
@@ -227,6 +250,12 @@ def Attribute.Recursor.getMajorPos (stx : Syntax) : AttrM Nat := do
|
||||
else
|
||||
throwErrorAt stx "unexpected attribute argument, numeral expected"
|
||||
|
||||
private def mkRecursorInfoCore (declName : Name) (majorPos? : Option Nat := none) : MetaM RecursorInfo := do
|
||||
let cinfo ← getConstInfo declName
|
||||
match cinfo with
|
||||
| ConstantInfo.recInfo val => mkRecursorInfoForKernelRec declName val
|
||||
| _ => mkRecursorInfoAux cinfo majorPos?
|
||||
|
||||
builtin_initialize recursorAttribute : ParametricAttribute Nat ←
|
||||
registerParametricAttribute {
|
||||
name := `recursor,
|
||||
@@ -240,7 +269,11 @@ def getMajorPos? (env : Environment) (declName : Name) : Option Nat :=
|
||||
recursorAttribute.getParam? env declName
|
||||
|
||||
def mkRecursorInfo (declName : Name) (majorPos? : Option Nat := none) : MetaM RecursorInfo := do
|
||||
let majorPos? := majorPos? <|> getMajorPos? (← getEnv) declName
|
||||
mkRecursorInfoCore declName majorPos?
|
||||
let cinfo ← getConstInfo declName
|
||||
match cinfo with
|
||||
| ConstantInfo.recInfo val => mkRecursorInfoForKernelRec declName val
|
||||
| _ => match majorPos? with
|
||||
| none => do mkRecursorInfoAux cinfo (getMajorPos? (← getEnv) declName)
|
||||
| _ => mkRecursorInfoAux cinfo majorPos?
|
||||
|
||||
end Lean.Meta
|
||||
|
||||
@@ -164,11 +164,7 @@ does not start with a forall, lambda or let. -/
|
||||
abbrev _root_.Lean.MVarId.intro1P (mvarId : MVarId) : MetaM (FVarId × MVarId) :=
|
||||
intro1Core mvarId true
|
||||
|
||||
/--
|
||||
Calculate the number of new hypotheses that would be created by `intros`,
|
||||
i.e. the number of binders which can be introduced without unfolding definitions.
|
||||
-/
|
||||
partial def getIntrosSize : Expr → Nat
|
||||
private partial def getIntrosSize : Expr → Nat
|
||||
| .forallE _ _ b _ => getIntrosSize b + 1
|
||||
| .letE _ _ _ b _ => getIntrosSize b + 1
|
||||
| .mdata _ b => getIntrosSize b
|
||||
|
||||
@@ -62,12 +62,12 @@ builtin_simproc [simp, seval] reduceNe (( _ : Fin _) ≠ _) := reduceBinPred `
|
||||
builtin_dsimproc [simp, seval] reduceBEq (( _ : Fin _) == _) := reduceBoolPred ``BEq.beq 4 (. == .)
|
||||
builtin_dsimproc [simp, seval] reduceBNe (( _ : Fin _) != _) := reduceBoolPred ``bne 4 (. != .)
|
||||
|
||||
/-- Simplification procedure for ensuring `Fin n` literals are normalized. -/
|
||||
/-- Simplification procedure for ensuring `Fin` literals are normalized. -/
|
||||
builtin_dsimproc [simp, seval] isValue ((OfNat.ofNat _ : Fin _)) := fun e => do
|
||||
let_expr OfNat.ofNat _ m _ ← e | return .continue
|
||||
let some ⟨n, v⟩ ← getFinValue? e | return .continue
|
||||
let some m ← getNatValue? m | return .continue
|
||||
if m < n then
|
||||
if n == m then
|
||||
-- Design decision: should we return `.continue` instead of `.done` when simplifying.
|
||||
-- In the symbolic evaluator, we must return `.done`, otherwise it will unfold the `OfNat.ofNat`
|
||||
return .done e
|
||||
|
||||
@@ -124,7 +124,7 @@ def handleCodeAction (params : CodeActionParams) : RequestM (RequestTask (Array
|
||||
let names := codeActionProviderExt.getState env |>.toArray
|
||||
let caps ← names.mapM evalCodeActionProvider
|
||||
return (← builtinCodeActionProviders.get).toList.toArray ++ Array.zip names caps
|
||||
caps.concatMapM fun (providerName, cap) => do
|
||||
caps.flatMapM fun (providerName, cap) => do
|
||||
let cas ← cap params snap
|
||||
cas.mapIdxM fun i lca => do
|
||||
if lca.lazy?.isNone then return lca.eager
|
||||
|
||||
@@ -38,7 +38,7 @@ A code action which calls all `@[hole_code_action]` code actions on each hole
|
||||
unless head ≤ endPos && startPos ≤ tail do return result
|
||||
result.push (ctx, info)
|
||||
let #[(ctx, info)] := holes | return #[]
|
||||
(holeCodeActionExt.getState snap.env).2.concatMapM (· params snap ctx info)
|
||||
(holeCodeActionExt.getState snap.env).2.flatMapM (· params snap ctx info)
|
||||
|
||||
/--
|
||||
The return value of `findTactic?`.
|
||||
|
||||
@@ -197,7 +197,7 @@ def InfoTree.smallestInfo? (p : Info → Bool) (t : InfoTree) : Option (ContextI
|
||||
/-- Find an info node, if any, which should be shown on hover/cursor at position `hoverPos`. -/
|
||||
partial def InfoTree.hoverableInfoAt? (t : InfoTree) (hoverPos : String.Pos) (includeStop := false) (omitAppFns := false) (omitIdentApps := false) : Option InfoWithCtx := Id.run do
|
||||
let results := t.visitM (m := Id) (postNode := fun ctx info children results => do
|
||||
let mut results := results.bind (·.getD [])
|
||||
let mut results := results.flatMap (·.getD [])
|
||||
if omitAppFns && info.stx.isOfKind ``Parser.Term.app && info.stx[0].isIdent then
|
||||
results := results.filter (·.2.info.stx != info.stx[0])
|
||||
if omitIdentApps && info.stx.isIdent then
|
||||
|
||||
@@ -669,7 +669,7 @@ where
|
||||
let grouped := incomingCalls.groupByKey (·.«from»)
|
||||
let collapsed := grouped.toArray.map fun ⟨_, group⟩ => {
|
||||
«from» := group[0]!.«from»
|
||||
fromRanges := group.concatMap (·.fromRanges)
|
||||
fromRanges := group.flatMap (·.fromRanges)
|
||||
}
|
||||
collapsed
|
||||
|
||||
@@ -716,7 +716,7 @@ where
|
||||
let grouped := outgoingCalls.groupByKey (·.to)
|
||||
let collapsed := grouped.toArray.map fun ⟨_, group⟩ => {
|
||||
to := group[0]!.to
|
||||
fromRanges := group.concatMap (·.fromRanges)
|
||||
fromRanges := group.flatMap (·.fromRanges)
|
||||
}
|
||||
collapsed
|
||||
|
||||
|
||||
@@ -156,7 +156,7 @@ namespace DHashMap.Internal
|
||||
|
||||
/-- Internal implementation detail of the hash map -/
|
||||
def toListModel (buckets : Array (AssocList α β)) : List ((a : α) × β a) :=
|
||||
buckets.toList.bind AssocList.toList
|
||||
buckets.toList.flatMap AssocList.toList
|
||||
|
||||
/-- Internal implementation detail of the hash map -/
|
||||
@[inline] def computeSize (buckets : Array (AssocList α β)) : Nat :=
|
||||
|
||||
@@ -1720,13 +1720,13 @@ theorem containsKey_append [BEq α] {l l' : List ((a : α) × β a)} {a : α} :
|
||||
containsKey a (l ++ l') = (containsKey a l || containsKey a l') := by
|
||||
simp [containsKey_eq_isSome_getEntry?]
|
||||
|
||||
theorem containsKey_bind_eq_false [BEq α] {γ : Type w} {l : List γ} {f : γ → List ((a : α) × β a)}
|
||||
theorem containsKey_flatMap_eq_false [BEq α] {γ : Type w} {l : List γ} {f : γ → List ((a : α) × β a)}
|
||||
{a : α} (h : ∀ (i : Nat) (h : i < l.length), containsKey a (f l[i]) = false) :
|
||||
containsKey a (l.bind f) = false := by
|
||||
containsKey a (l.flatMap f) = false := by
|
||||
induction l
|
||||
· simp
|
||||
· next g t ih =>
|
||||
simp only [List.bind_cons, containsKey_append, Bool.or_eq_false_iff]
|
||||
simp only [List.flatMap_cons, containsKey_append, Bool.or_eq_false_iff]
|
||||
refine ⟨?_, ?_⟩
|
||||
· simpa using h 0 (by simp)
|
||||
· refine ih ?_
|
||||
|
||||
@@ -88,7 +88,7 @@ theorem exists_bucket_of_uset [BEq α] [Hashable α]
|
||||
containsKey k l = false) := by
|
||||
have h₀ : 0 < self.size := by omega
|
||||
obtain ⟨l₁, l₂, h₁, h₂, h₃⟩ := Array.exists_of_uset self i d hi
|
||||
refine ⟨l₁.bind AssocList.toList ++ l₂.bind AssocList.toList, ?_, ?_, ?_⟩
|
||||
refine ⟨l₁.flatMap AssocList.toList ++ l₂.flatMap AssocList.toList, ?_, ?_, ?_⟩
|
||||
· rw [toListModel, h₁]
|
||||
simpa using perm_append_comm_assoc _ _ _
|
||||
· rw [toListModel, h₃]
|
||||
@@ -96,12 +96,12 @@ theorem exists_bucket_of_uset [BEq α] [Hashable α]
|
||||
· intro _ h k hki
|
||||
simp only [containsKey_append, Bool.or_eq_false_iff]
|
||||
refine ⟨?_, ?_⟩
|
||||
· apply List.containsKey_bind_eq_false
|
||||
· apply List.containsKey_flatMap_eq_false
|
||||
intro j hj
|
||||
rw [List.getElem_append_left' (l₂ := self[i] :: l₂), getElem_congr_coll h₁.symm]
|
||||
apply (h.hashes_to j _).containsKey_eq_false h₀ k
|
||||
omega
|
||||
· apply List.containsKey_bind_eq_false
|
||||
· apply List.containsKey_flatMap_eq_false
|
||||
intro j hj
|
||||
rw [← List.getElem_cons_succ self[i] _ _
|
||||
(by simp only [Array.ugetElem_eq_getElem, List.length_cons]; omega)]
|
||||
@@ -121,7 +121,7 @@ theorem exists_bucket_of_update [BEq α] [Hashable α] (m : Array (AssocList α
|
||||
|
||||
theorem exists_bucket' [BEq α] [Hashable α]
|
||||
(self : Array (AssocList α β)) (i : USize) (hi : i.toNat < self.size) :
|
||||
∃ l, Perm (self.toList.bind AssocList.toList) (self[i.toNat].toList ++ l) ∧
|
||||
∃ l, Perm (self.toList.flatMap AssocList.toList) (self[i.toNat].toList ++ l) ∧
|
||||
(∀ [LawfulHashable α], IsHashSelf self → ∀ k,
|
||||
(mkIdx self.size (by omega) (hash k)).1.toNat = i.toNat → containsKey k l = false) := by
|
||||
obtain ⟨l, h₁, -, h₂⟩ := exists_bucket_of_uset self i hi .nil
|
||||
@@ -186,8 +186,8 @@ theorem toListModel_updateAllBuckets {m : Raw₀ α β} {f : AssocList α β →
|
||||
have := (hg (l := []) (l' := [])).length_eq
|
||||
rw [List.length_append, List.append_nil] at this
|
||||
omega
|
||||
rw [updateAllBuckets, toListModel, Array.toList_map, List.bind_eq_foldl, List.foldl_map,
|
||||
toListModel, List.bind_eq_foldl]
|
||||
rw [updateAllBuckets, toListModel, Array.toList_map, List.flatMap_eq_foldl, List.foldl_map,
|
||||
toListModel, List.flatMap_eq_foldl]
|
||||
suffices ∀ (l : List (AssocList α β)) (l' : List ((a: α) × δ a)) (l'' : List ((a : α) × β a)),
|
||||
Perm (g l'') l' →
|
||||
Perm (l.foldl (fun acc a => acc ++ (f a).toList) l')
|
||||
|
||||
@@ -31,14 +31,14 @@ namespace Std.DHashMap.Internal
|
||||
@[simp]
|
||||
theorem toListModel_mkArray_nil {c} :
|
||||
toListModel (mkArray c (AssocList.nil : AssocList α β)) = [] := by
|
||||
suffices ∀ d, (List.replicate d AssocList.nil).bind AssocList.toList = [] from this _
|
||||
suffices ∀ d, (List.replicate d AssocList.nil).flatMap AssocList.toList = [] from this _
|
||||
intro d
|
||||
induction d <;> simp_all [List.replicate]
|
||||
|
||||
@[simp]
|
||||
theorem computeSize_eq {buckets : Array (AssocList α β)} :
|
||||
computeSize buckets = (toListModel buckets).length := by
|
||||
rw [computeSize, toListModel, List.bind_eq_foldl, Array.foldl_eq_foldl_toList]
|
||||
rw [computeSize, toListModel, List.flatMap_eq_foldl, Array.foldl_eq_foldl_toList]
|
||||
suffices ∀ (l : List (AssocList α β)) (l' : List ((a : α) × β a)),
|
||||
l.foldl (fun d b => d + b.toList.length) l'.length =
|
||||
(l.foldl (fun acc a => acc ++ a.toList) l').length
|
||||
@@ -129,7 +129,7 @@ theorem expand.go_eq [BEq α] [Hashable α] [PartialEquivBEq α] (source : Array
|
||||
(target : {d : Array (AssocList α β) // 0 < d.size}) : expand.go 0 source target =
|
||||
(toListModel source).foldl (fun acc p => reinsertAux hash acc p.1 p.2) target := by
|
||||
suffices ∀ i, expand.go i source target =
|
||||
((source.toList.drop i).bind AssocList.toList).foldl
|
||||
((source.toList.drop i).flatMap AssocList.toList).foldl
|
||||
(fun acc p => reinsertAux hash acc p.1 p.2) target by
|
||||
simpa using this 0
|
||||
intro i
|
||||
@@ -139,10 +139,10 @@ theorem expand.go_eq [BEq α] [Hashable α] [PartialEquivBEq α] (source : Array
|
||||
rw [expand.go_pos hi]
|
||||
refine ih.trans ?_
|
||||
simp only [Array.get_eq_getElem, AssocList.foldl_eq, Array.toList_set]
|
||||
rw [List.drop_eq_getElem_cons hi, List.bind_cons, List.foldl_append,
|
||||
rw [List.drop_eq_getElem_cons hi, List.flatMap_cons, List.foldl_append,
|
||||
List.drop_set_of_lt _ _ (by omega), Array.getElem_eq_getElem_toList]
|
||||
· next i source target hi =>
|
||||
rw [expand.go_neg hi, List.drop_eq_nil_of_le, bind_nil, foldl_nil]
|
||||
rw [expand.go_neg hi, List.drop_eq_nil_of_le, flatMap_nil, foldl_nil]
|
||||
rwa [Array.size_eq_length_toList, Nat.not_lt] at hi
|
||||
|
||||
theorem isHashSelf_expand [BEq α] [Hashable α] [LawfulHashable α] [EquivBEq α]
|
||||
|
||||
@@ -29,7 +29,7 @@ def buildImportsAndDeps (leanFile : FilePath) (imports : Array Module) : FetchM
|
||||
let precompileImports ← computePrecompileImportsAux leanFile imports
|
||||
let pkgs := precompileImports.foldl (·.insert ·.pkg) OrdPackageSet.empty |>.toArray
|
||||
let externLibJob ← BuildJob.collectArray <| ←
|
||||
pkgs.concatMapM (·.externLibs.mapM (·.dynlib.fetch))
|
||||
pkgs.flatMapM (·.externLibs.mapM (·.dynlib.fetch))
|
||||
let precompileJob ← BuildJob.collectArray <| ←
|
||||
precompileImports.mapM (·.dynlib.fetch)
|
||||
let job ←
|
||||
|
||||
@@ -60,7 +60,7 @@ def LeanLib.leanArtsFacetConfig : LibraryFacetConfig leanArtsFacet :=
|
||||
""
|
||||
withRegisterJob s!"{self.name}:static{suffix}" do
|
||||
let mods ← self.modules.fetch
|
||||
let oJobs ← mods.concatMapM fun mod =>
|
||||
let oJobs ← mods.flatMapM fun mod =>
|
||||
mod.nativeFacets shouldExport |>.mapM fun facet => fetch <| mod.facet facet.name
|
||||
let libFile := if shouldExport then self.staticExportLibFile else self.staticLibFile
|
||||
buildStaticLib libFile oJobs
|
||||
@@ -80,10 +80,10 @@ protected def LeanLib.recBuildShared
|
||||
(self : LeanLib) : FetchM (BuildJob FilePath) := do
|
||||
withRegisterJob s!"{self.name}:shared" do
|
||||
let mods ← self.modules.fetch
|
||||
let oJobs ← mods.concatMapM fun mod =>
|
||||
let oJobs ← mods.flatMapM fun mod =>
|
||||
mod.nativeFacets true |>.mapM fun facet => fetch <| mod.facet facet.name
|
||||
let pkgs := mods.foldl (·.insert ·.pkg) OrdPackageSet.empty |>.toArray
|
||||
let externJobs ← pkgs.concatMapM (·.externLibs.mapM (·.shared.fetch))
|
||||
let externJobs ← pkgs.flatMapM (·.externLibs.mapM (·.shared.fetch))
|
||||
buildLeanSharedLib self.sharedLibFile (oJobs ++ externJobs) self.weakLinkArgs self.linkArgs
|
||||
|
||||
/-- The `LibraryFacetConfig` for the builtin `sharedFacet`. -/
|
||||
|
||||
@@ -113,7 +113,7 @@ def resolveTargetInPackage (ws : Workspace)
|
||||
throw <| CliError.missingTarget pkg.name (target.toString false)
|
||||
|
||||
def resolveDefaultPackageTarget (ws : Workspace) (pkg : Package) : Except CliError (Array BuildSpec) :=
|
||||
pkg.defaultTargets.concatMapM (resolveTargetInPackage ws pkg · .anonymous)
|
||||
pkg.defaultTargets.flatMapM (resolveTargetInPackage ws pkg · .anonymous)
|
||||
|
||||
def resolvePackageTarget (ws : Workspace) (pkg : Package) (facet : Name) : Except CliError (Array BuildSpec) :=
|
||||
if facet.isAnonymous then
|
||||
|
||||
@@ -47,4 +47,4 @@ def OrderedTagAttribute.hasTag (attr : OrderedTagAttribute) (env : Environment)
|
||||
/-- Get all tagged declaration names, both those imported and those in the current module. -/
|
||||
def OrderedTagAttribute.getAllEntries (attr : OrderedTagAttribute) (env : Environment) : Array Name :=
|
||||
let s := attr.ext.toEnvExtension.getState env
|
||||
s.importedEntries.concatMap id ++ s.state
|
||||
s.importedEntries.flatMap id ++ s.state
|
||||
|
||||
@@ -1,53 +0,0 @@
|
||||
import Std.Tactic.BVDecide
|
||||
|
||||
/-! Smaller real-world problems taken from https://github.com/leanprover/LNSym,
|
||||
which previously had a bad interaction with the normalization pass -/
|
||||
|
||||
variable (a1 a2 b1 b2 a b c d k n : BitVec 64)
|
||||
|
||||
example :
|
||||
(!decide (b1 - a1 ≤ a2 - a1) && !decide (b2 - a1 ≤ a2 - a1) && !decide (a1 - b1 ≤ b2 - b1) &&
|
||||
!decide (a2 - b1 ≤ b2 - b1)) =
|
||||
(!decide (a1 - b1 ≤ b2 - b1) && !decide (a2 - b1 ≤ b2 - b1) && !decide (b1 - a1 ≤ a2 - a1) &&
|
||||
!decide (b2 - a1 ≤ a2 - a1)) := by
|
||||
bv_decide
|
||||
|
||||
example :
|
||||
a2 - a1 < b1 - a1
|
||||
→ a2 - a1 < b2 - a1
|
||||
→ b2 - b1 < a1 - b1
|
||||
→ b2 - b1 < a2 - b1
|
||||
→ ¬a1 = b1 := by
|
||||
bv_decide
|
||||
|
||||
example : ¬a = b ↔ 0#64 < b - a ∧ 0#64 < a - b := by
|
||||
bv_decide
|
||||
|
||||
example :
|
||||
b - a < c - a → b - a < d - a → d - c < a - c → d - c < b - c
|
||||
→ (0#64 < c - a ∧ 0#64 < d - a) ∧ d - c < a - c := by
|
||||
bv_decide
|
||||
|
||||
set_option sat.timeout 120 in
|
||||
example :
|
||||
n < 18446744073709551615#64 - k →
|
||||
((a + k - a < a + k + 1#64 - a ∧ a + k - a < a + k + 1#64 + n - a) ∧
|
||||
a + k + 1#64 + n - (a + k + 1#64) < a - (a + k + 1#64)) ∧
|
||||
a + k + 1#64 + n - (a + k + 1#64) < a + k - (a + k + 1#64) := by
|
||||
bv_decide
|
||||
|
||||
example :
|
||||
n < 18446744073709551615 →
|
||||
(0#64 < addr + 1#64 - addr ∧ 0#64 < addr + 1#64 + n - addr)
|
||||
∧ addr + 1#64 + n - (addr + 1#64) < addr - (addr + 1#64) := by
|
||||
bv_decide
|
||||
|
||||
set_option sat.timeout 120 in
|
||||
example :
|
||||
a2 - a1 < b1 - a1 → a2 - a1 < b2 - a1 →
|
||||
b2 - b1 < a1 - b1 → b2 - b1 < a2 - b1 →
|
||||
b2 - b1 = 18446744073709551615#64 ∨ c2 - b1 ≤ b2 - b1 ∧ c1 - b1 ≤ c2 - b1 →
|
||||
((a2 - a1 < c1 - a1 ∧ a2 - a1 < c2 - a1)
|
||||
∧ c2 - c1 < a1 - c1)
|
||||
∧ c2 - c1 < a2 - c1 := by
|
||||
bv_decide
|
||||
@@ -356,9 +356,3 @@
|
||||
run_config:
|
||||
<<: *time
|
||||
cmd: lean bv_decide_mod.lean
|
||||
- attributes:
|
||||
description: bv_decide_inequality.lean
|
||||
tags: [fast]
|
||||
run_config:
|
||||
<<: *time
|
||||
cmd: lean bv_decide_inequality.lean
|
||||
|
||||
@@ -1,21 +0,0 @@
|
||||
example : Bool := by
|
||||
fail_if_success have := ∀ p, decide p -- no classical in scope
|
||||
classical
|
||||
have := ∀ p, decide p -- uses the classical instance
|
||||
guard_expr decide (0 < 1) = @decide (0 < 1) (Nat.decLt 0 1)
|
||||
exact decide (0 < 1) -- will use the decidable instance
|
||||
|
||||
-- double check no leakage
|
||||
example : Bool := by
|
||||
fail_if_success have := ∀ p, decide p -- no classical in scope
|
||||
exact decide (0 < 1) -- uses the decidable instance
|
||||
|
||||
-- check that classical respects tactic blocks
|
||||
example : Bool := by
|
||||
fail_if_success have := ∀ p, decide p -- no classical in scope
|
||||
( -- start a scope
|
||||
classical
|
||||
have := ∀ p, decide p -- uses the classical instance
|
||||
)
|
||||
fail_if_success have := ∀ p, decide p -- no classical in scope again
|
||||
exact decide (0 < 1) -- will use the decidable instance
|
||||
@@ -1,15 +0,0 @@
|
||||
|
||||
example (n : Fin 25) (P : Fin 25 → Prop) : P 26 := by
|
||||
simp only [Fin.isValue]
|
||||
guard_target = P 1
|
||||
sorry
|
||||
|
||||
example (n : Fin 25) (P : Fin 25 → Prop) : P 25 := by
|
||||
simp only [Fin.isValue]
|
||||
guard_target = P 0
|
||||
sorry
|
||||
|
||||
example (n : Fin 25) (P : Fin 25 → Prop) : P 24 := by
|
||||
fail_if_success simp only [Fin.isValue]
|
||||
guard_target = P 24
|
||||
sorry
|
||||
Reference in New Issue
Block a user