diff --git a/Batteries/Data/Array/OfFn.lean b/Batteries/Data/Array/OfFn.lean index e02be7cba1..5233fd1f96 100644 --- a/Batteries/Data/Array/OfFn.lean +++ b/Batteries/Data/Array/OfFn.lean @@ -11,8 +11,4 @@ namespace Array /-! ### ofFn -/ -@[simp] -theorem toList_ofFn (f : Fin n → α) : (ofFn f).toList = List.ofFn f := by - apply ext_getElem <;> simp - end Array diff --git a/Batteries/Data/Fin/Basic.lean b/Batteries/Data/Fin/Basic.lean index b61481e33a..346f3006e5 100644 --- a/Batteries/Data/Fin/Basic.lean +++ b/Batteries/Data/Fin/Basic.lean @@ -14,57 +14,3 @@ def enum (n) : Array (Fin n) := Array.ofFn id /-- `list n` is the list of all elements of `Fin n` in order -/ def list (n) : List (Fin n) := (enum n).toList - -/-- -Folds a monadic function over `Fin n` from left to right: -``` -Fin.foldlM n f x₀ = do - let x₁ ← f x₀ 0 - let x₂ ← f x₁ 1 - ... - let xₙ ← f xₙ₋₁ (n-1) - pure xₙ -``` --/ -@[inline] def foldlM [Monad m] (n) (f : α → Fin n → m α) (init : α) : m α := loop init 0 where - /-- - Inner loop for `Fin.foldlM`. - ``` - Fin.foldlM.loop n f xᵢ i = do - let xᵢ₊₁ ← f xᵢ i - ... - let xₙ ← f xₙ₋₁ (n-1) - pure xₙ - ``` - -/ - loop (x : α) (i : Nat) : m α := do - if h : i < n then f x ⟨i, h⟩ >>= (loop · (i+1)) else pure x - termination_by n - i - -/-- -Folds a monadic function over `Fin n` from right to left: -``` -Fin.foldrM n f xₙ = do - let xₙ₋₁ ← f (n-1) xₙ - let xₙ₋₂ ← f (n-2) xₙ₋₁ - ... - let x₀ ← f 0 x₁ - pure x₀ -``` --/ -@[inline] def foldrM [Monad m] (n) (f : Fin n → α → m α) (init : α) : m α := - loop ⟨n, Nat.le_refl n⟩ init where - /-- - Inner loop for `Fin.foldrM`. - ``` - Fin.foldrM.loop n f i xᵢ = do - let xᵢ₋₁ ← f (i-1) xᵢ - ... - let x₁ ← f 1 x₂ - let x₀ ← f 0 x₁ - pure x₀ - ``` - -/ - loop : {i // i ≤ n} → α → m α - | ⟨0, _⟩, x => pure x - | ⟨i+1, h⟩, x => f ⟨i, h⟩ x >>= loop ⟨i, Nat.le_of_lt h⟩ diff --git a/Batteries/Data/Fin/Lemmas.lean b/Batteries/Data/Fin/Lemmas.lean index 5010e1310f..d799e2e6f3 100644 --- a/Batteries/Data/Fin/Lemmas.lean +++ b/Batteries/Data/Fin/Lemmas.lean @@ -56,32 +56,6 @@ theorem list_reverse (n) : (list n).reverse = (list n).map rev := by /-! ### foldlM -/ -theorem foldlM_loop_lt [Monad m] (f : α → Fin n → m α) (x) (h : i < n) : - foldlM.loop n f x i = f x ⟨i, h⟩ >>= (foldlM.loop n f . (i+1)) := by - rw [foldlM.loop, dif_pos h] - -theorem foldlM_loop_eq [Monad m] (f : α → Fin n → m α) (x) : foldlM.loop n f x n = pure x := by - rw [foldlM.loop, dif_neg (Nat.lt_irrefl _)] - -theorem foldlM_loop [Monad m] (f : α → Fin (n+1) → m α) (x) (h : i < n+1) : - foldlM.loop (n+1) f x i = f x ⟨i, h⟩ >>= (foldlM.loop n (fun x j => f x j.succ) . i) := by - if h' : i < n then - rw [foldlM_loop_lt _ _ h] - congr; funext - rw [foldlM_loop_lt _ _ h', foldlM_loop]; rfl - else - cases Nat.le_antisymm (Nat.le_of_lt_succ h) (Nat.not_lt.1 h') - rw [foldlM_loop_lt] - congr; funext - rw [foldlM_loop_eq, foldlM_loop_eq] -termination_by n - i - -@[simp] theorem foldlM_zero [Monad m] (f : α → Fin 0 → m α) (x) : foldlM 0 f x = pure x := - foldlM_loop_eq .. - -theorem foldlM_succ [Monad m] (f : α → Fin (n+1) → m α) (x) : - foldlM (n+1) f x = f x 0 >>= foldlM n (fun x j => f x j.succ) := foldlM_loop .. - theorem foldlM_eq_foldlM_list [Monad m] (f : α → Fin n → m α) (x) : foldlM n f x = (list n).foldlM f x := by induction n generalizing x with @@ -93,32 +67,6 @@ theorem foldlM_eq_foldlM_list [Monad m] (f : α → Fin n → m α) (x) : /-! ### foldrM -/ -theorem foldrM_loop_zero [Monad m] (f : Fin n → α → m α) (x) : - foldrM.loop n f ⟨0, Nat.zero_le _⟩ x = pure x := by - rw [foldrM.loop] - -theorem foldrM_loop_succ [Monad m] (f : Fin n → α → m α) (x) (h : i < n) : - foldrM.loop n f ⟨i+1, h⟩ x = f ⟨i, h⟩ x >>= foldrM.loop n f ⟨i, Nat.le_of_lt h⟩ := by - rw [foldrM.loop] - -theorem foldrM_loop [Monad m] [LawfulMonad m] (f : Fin (n+1) → α → m α) (x) (h : i+1 ≤ n+1) : - foldrM.loop (n+1) f ⟨i+1, h⟩ x = - foldrM.loop n (fun j => f j.succ) ⟨i, Nat.le_of_succ_le_succ h⟩ x >>= f 0 := by - induction i generalizing x with - | zero => - rw [foldrM_loop_zero, foldrM_loop_succ, pure_bind] - conv => rhs; rw [←bind_pure (f 0 x)] - congr; funext; exact foldrM_loop_zero .. - | succ i ih => - rw [foldrM_loop_succ, foldrM_loop_succ, bind_assoc] - congr; funext; exact ih .. - -@[simp] theorem foldrM_zero [Monad m] (f : Fin 0 → α → m α) (x) : foldrM 0 f x = pure x := - foldrM_loop_zero .. - -theorem foldrM_succ [Monad m] [LawfulMonad m] (f : Fin (n+1) → α → m α) (x) : - foldrM (n+1) f x = foldrM n (fun i => f i.succ) x >>= f 0 := foldrM_loop .. - theorem foldrM_eq_foldrM_list [Monad m] [LawfulMonad m] (f : Fin n → α → m α) (x) : foldrM n f x = (list n).foldrM f x := by induction n with @@ -127,41 +75,6 @@ theorem foldrM_eq_foldrM_list [Monad m] [LawfulMonad m] (f : Fin n → α → m /-! ### foldl -/ -theorem foldl_loop_lt (f : α → Fin n → α) (x) (h : i < n) : - foldl.loop n f x i = foldl.loop n f (f x ⟨i, h⟩) (i+1) := by - rw [foldl.loop, dif_pos h] - -theorem foldl_loop_eq (f : α → Fin n → α) (x) : foldl.loop n f x n = x := by - rw [foldl.loop, dif_neg (Nat.lt_irrefl _)] - -theorem foldl_loop (f : α → Fin (n+1) → α) (x) (h : i < n+1) : - foldl.loop (n+1) f x i = foldl.loop n (fun x j => f x j.succ) (f x ⟨i, h⟩) i := by - if h' : i < n then - rw [foldl_loop_lt _ _ h] - rw [foldl_loop_lt _ _ h', foldl_loop]; rfl - else - cases Nat.le_antisymm (Nat.le_of_lt_succ h) (Nat.not_lt.1 h') - rw [foldl_loop_lt] - rw [foldl_loop_eq, foldl_loop_eq] - -@[simp] theorem foldl_zero (f : α → Fin 0 → α) (x) : foldl 0 f x = x := - foldl_loop_eq .. - -theorem foldl_succ (f : α → Fin (n+1) → α) (x) : - foldl (n+1) f x = foldl n (fun x i => f x i.succ) (f x 0) := - foldl_loop .. - -theorem foldl_succ_last (f : α → Fin (n+1) → α) (x) : - foldl (n+1) f x = f (foldl n (f · ·.castSucc) x) (last n) := by - rw [foldl_succ] - induction n generalizing x with - | zero => simp [foldl_succ, Fin.last] - | succ n ih => rw [foldl_succ, ih (f · ·.succ), foldl_succ]; simp [succ_castSucc] - -theorem foldl_eq_foldlM (f : α → Fin n → α) (x) : - foldl n f x = foldlM (m:=Id) n f x := by - induction n generalizing x <;> simp [foldl_succ, foldlM_succ, *] - theorem foldl_eq_foldl_list (f : α → Fin n → α) (x) : foldl n f x = (list n).foldl f x := by induction n generalizing x with | zero => rw [foldl_zero, list_zero, List.foldl_nil] @@ -169,48 +82,7 @@ theorem foldl_eq_foldl_list (f : α → Fin n → α) (x) : foldl n f x = (list /-! ### foldr -/ -theorem foldr_loop_zero (f : Fin n → α → α) (x) : - foldr.loop n f ⟨0, Nat.zero_le _⟩ x = x := by - rw [foldr.loop] - -theorem foldr_loop_succ (f : Fin n → α → α) (x) (h : i < n) : - foldr.loop n f ⟨i+1, h⟩ x = foldr.loop n f ⟨i, Nat.le_of_lt h⟩ (f ⟨i, h⟩ x) := by - rw [foldr.loop] - -theorem foldr_loop (f : Fin (n+1) → α → α) (x) (h : i+1 ≤ n+1) : - foldr.loop (n+1) f ⟨i+1, h⟩ x = - f 0 (foldr.loop n (fun j => f j.succ) ⟨i, Nat.le_of_succ_le_succ h⟩ x) := by - induction i generalizing x <;> simp [foldr_loop_zero, foldr_loop_succ, *] - -@[simp] theorem foldr_zero (f : Fin 0 → α → α) (x) : foldr 0 f x = x := - foldr_loop_zero .. - -theorem foldr_succ (f : Fin (n+1) → α → α) (x) : - foldr (n+1) f x = f 0 (foldr n (fun i => f i.succ) x) := foldr_loop .. - -theorem foldr_succ_last (f : Fin (n+1) → α → α) (x) : - foldr (n+1) f x = foldr n (f ·.castSucc) (f (last n) x) := by - induction n generalizing x with - | zero => simp [foldr_succ, Fin.last] - | succ n ih => rw [foldr_succ, ih (f ·.succ), foldr_succ]; simp [succ_castSucc] - -theorem foldr_eq_foldrM (f : Fin n → α → α) (x) : - foldr n f x = foldrM (m:=Id) n f x := by - induction n <;> simp [foldr_succ, foldrM_succ, *] - theorem foldr_eq_foldr_list (f : Fin n → α → α) (x) : foldr n f x = (list n).foldr f x := by induction n with | zero => rw [foldr_zero, list_zero, List.foldr_nil] | succ n ih => rw [foldr_succ, ih, list_succ, List.foldr_cons, List.foldr_map] - -theorem foldl_rev (f : Fin n → α → α) (x) : - foldl n (fun x i => f i.rev x) x = foldr n f x := by - induction n generalizing x with - | zero => simp - | succ n ih => rw [foldl_succ, foldr_succ_last, ← ih]; simp [rev_succ] - -theorem foldr_rev (f : α → Fin n → α) (x) : - foldr n (fun i x => f x i.rev) x = foldl n f x := by - induction n generalizing x with - | zero => simp - | succ n ih => rw [foldl_succ_last, foldr_succ, ← ih]; simp [rev_succ] diff --git a/Batteries/Data/List/Basic.lean b/Batteries/Data/List/Basic.lean index 3e2460f18c..da8e21f3b8 100644 --- a/Batteries/Data/List/Basic.lean +++ b/Batteries/Data/List/Basic.lean @@ -548,14 +548,6 @@ def sigmaTR {σ : α → Type _} (l₁ : List α) (l₂ : ∀ a, List (σ a)) : rw [Array.foldl_toList_eq_flatMap]; rfl intros; apply Array.foldl_toList_eq_map -/-- -`ofFn f` with `f : fin n → α` returns the list whose ith element is `f i` -``` -ofFn f = [f 0, f 1, ... , f (n - 1)] -``` --/ -def ofFn {n} (f : Fin n → α) : List α := Fin.foldr n (f · :: ·) [] - /-- `ofFnNthVal f i` returns `some (f i)` if `i < n` and `none` otherwise. -/ def ofFnNthVal {n} (f : Fin n → α) (i : Nat) : Option α := if h : i < n then some (f ⟨i, h⟩) else none diff --git a/Batteries/Data/List/OfFn.lean b/Batteries/Data/List/OfFn.lean index 93214cc99b..c66846e61a 100644 --- a/Batteries/Data/List/OfFn.lean +++ b/Batteries/Data/List/OfFn.lean @@ -12,38 +12,4 @@ import Batteries.Data.Fin.Lemmas namespace List -@[simp] -theorem length_ofFn (f : Fin n → α) : (ofFn f).length = n := by - simp only [ofFn] - induction n with - | zero => simp - | succ n ih => simp [Fin.foldr_succ, ih] - -@[simp] -protected theorem getElem_ofFn (f : Fin n → α) (i : Nat) (h : i < (ofFn f).length) : - (ofFn f)[i] = f ⟨i, by simp_all⟩ := by - simp only [ofFn] - induction n generalizing i with - | zero => simp at h - | succ n ih => - match i with - | 0 => simp [Fin.foldr_succ] - | i+1 => - simp only [Fin.foldr_succ] - apply ih - simp_all - -@[simp] -protected theorem getElem?_ofFn (f : Fin n → α) (i) : (ofFn f)[i]? = ofFnNthVal f i := - if h : i < (ofFn f).length - then by - rw [getElem?_eq_getElem h, List.getElem_ofFn] - · simp only [length_ofFn] at h; simp [ofFnNthVal, h] - else by - rw [ofFnNthVal, dif_neg] <;> - simpa using h - -@[simp] theorem toArray_ofFn (f : Fin n → α) : (ofFn f).toArray = Array.ofFn f := by - ext <;> simp - end List