09a5b34931
This PR adjusts the experimental module system to make `private` the default visibility modifier in `module`s, introducing `public` as a new modifier instead. `public section` can be used to revert the default for an entire section, though this is more intended to ease gradual adoption of the new semantics such as in `Init` (and soon `Std`) where they should be replaced by a future decl-by-decl re-review of visibilities.
55 lines
2.2 KiB
Text
55 lines
2.2 KiB
Text
/-
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Copyright (c) 2018 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Leonardo de Moura
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-/
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module
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prelude
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public import Init.Data.Array.Basic
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public section
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set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
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set_option linter.indexVariables true -- Enforce naming conventions for index variables.
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namespace Array
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/-! ### getLit -/
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-- auxiliary declaration used in the equation compiler when pattern matching array literals.
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abbrev getLit {α : Type u} {n : Nat} (xs : Array α) (i : Nat) (h₁ : xs.size = n) (h₂ : i < n) : α :=
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have := h₁.symm ▸ h₂
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xs[i]
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theorem extLit {n : Nat}
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(xs ys : Array α)
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(hsz₁ : xs.size = n) (hsz₂ : ys.size = n)
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(h : (i : Nat) → (hi : i < n) → xs.getLit i hsz₁ hi = ys.getLit i hsz₂ hi) : xs = ys :=
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Array.ext (hsz₁.trans hsz₂.symm) fun i hi₁ _ => h i (hsz₁ ▸ hi₁)
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-- has to be expose for array literal support
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@[expose] def toListLitAux (xs : Array α) (n : Nat) (hsz : xs.size = n) : ∀ (i : Nat), i ≤ xs.size → List α → List α
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| 0, _, acc => acc
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| (i+1), hi, acc => toListLitAux xs n hsz i (Nat.le_of_succ_le hi) (xs.getLit i hsz (Nat.lt_of_lt_of_eq (Nat.lt_of_lt_of_le (Nat.lt_succ_self i) hi) hsz) :: acc)
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-- has to be expose for array literal support
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@[expose] def toArrayLit (xs : Array α) (n : Nat) (hsz : xs.size = n) : Array α :=
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List.toArray <| toListLitAux xs n hsz n (hsz ▸ Nat.le_refl _) []
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theorem toArrayLit_eq (xs : Array α) (n : Nat) (hsz : xs.size = n) : xs = toArrayLit xs n hsz := by
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apply ext'
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simp [toArrayLit, List.toList_toArray]
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have hle : n ≤ xs.size := hsz ▸ Nat.le_refl _
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have hge : xs.size ≤ n := hsz ▸ Nat.le_refl _
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have := go n hle
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rw [List.drop_eq_nil_of_le hge] at this
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rw [this]
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where
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getLit_eq (xs : Array α) (i : Nat) (h₁ : xs.size = n) (h₂ : i < n) : xs.getLit i h₁ h₂ = getElem xs.toList i ((id (α := xs.toList.length = n) h₁) ▸ h₂) :=
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rfl
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go (i : Nat) (hi : i ≤ xs.size) : toListLitAux xs n hsz i hi (xs.toList.drop i) = xs.toList := by
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induction i <;> simp only [List.drop, toListLitAux, getLit_eq, List.getElem_cons_drop_succ_eq_drop, *]
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end Array
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