71dd8653bc
We need this to take advantage of the new indexing structure we are going to add to improve performance.
111 lines
3.9 KiB
Text
111 lines
3.9 KiB
Text
/-
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Copyright (c) 2016 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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Author: Leonardo de Moura
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-/
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prelude
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import init.data.nat.basic
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open nat
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@[reducible] def is_valid_char (n : nat) : Prop :=
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n < 0xd800 ∨ (0xdfff < n ∧ n < 0x110000)
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lemma is_valid_char_range_1 (n : nat) (h : n < 0xd800) : is_valid_char n :=
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or.inl h
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lemma is_valid_char_range_2 (n : nat) (h₁ : 0xdfff < n) (h₂ : n < 0x110000) : is_valid_char n :=
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or.inr ⟨h₁, h₂⟩
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/-- The `char` type represents an unicode scalar value.
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See http://www.unicode.org/glossary/#unicode_scalar_value). -/
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structure char :=
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(val : nat) (valid : is_valid_char val)
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instance : has_sizeof char :=
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⟨λ c, c.val⟩
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namespace char
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protected def lt (a b : char) : Prop := a.val < b.val
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protected def le (a b : char) : Prop := a.val ≤ b.val
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instance : has_lt char := ⟨char.lt⟩
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instance : has_le char := ⟨char.le⟩
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instance decidable_lt (a b : char) : decidable (a < b) :=
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nat.decidable_lt _ _
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instance decidable_le (a b : char) : decidable (a ≤ b) :=
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nat.decidable_le _ _
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/-
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We cannot use tactics dec_trivial or comp_val here because the tactic framework has not been defined yet.
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We also do not use `zero_lt_succ _` as a proof term because this proof may not be trivial to check by
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external type checkers. See discussion at: https://github.com/leanprover/tc/issues/8
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-/
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lemma zero_lt_d800 : 0 < 0xd800 :=
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nat.zero_lt_bit0 $ nat.bit0_ne_zero $ nat.bit0_ne_zero $ nat.bit0_ne_zero $
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nat.bit0_ne_zero $ nat.bit0_ne_zero $ nat.bit0_ne_zero $ nat.bit0_ne_zero $
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nat.bit0_ne_zero $ nat.bit0_ne_zero $ nat.bit0_ne_zero $ nat.bit1_ne_zero 13
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@[pattern] def of_nat (n : nat) : char :=
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if h : is_valid_char n then {val := n, valid := h} else {val := 0, valid := or.inl zero_lt_d800}
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def to_nat (c : char) : nat :=
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c.val
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lemma eq_of_veq : ∀ {c d : char}, c.val = d.val → c = d
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| ⟨v, h⟩ ⟨_, _⟩ rfl := rfl
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lemma veq_of_eq : ∀ {c d : char}, c = d → c.val = d.val
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| _ _ rfl := rfl
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lemma ne_of_vne {c d : char} (h : c.val ≠ d.val) : c ≠ d :=
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λ h', absurd (veq_of_eq h') h
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lemma vne_of_ne {c d : char} (h : c ≠ d) : c.val ≠ d.val :=
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λ h', absurd (eq_of_veq h') h
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instance : decidable_eq char :=
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{dec_eq := λ i j, decidable_of_decidable_of_iff
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(dec_eq i.val j.val) ⟨char.eq_of_veq, char.veq_of_eq⟩}
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instance : inhabited char :=
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⟨'A'⟩
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def is_whitespace (c : char) : bool :=
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c = ' ' || c = '\t' || c = '\n'
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def is_upper (c : char) : bool :=
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c.val ≥ 65 && c.val ≤ 90
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def is_lower (c : char) : bool :=
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c.val ≥ 97 && c.val ≤ 122
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def is_alpha (c : char) : bool :=
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c.is_upper || c.is_lower
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def is_digit (c : char) : bool :=
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c.val ≥ 48 && c.val ≤ 57
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def is_alphanum (c : char) : bool :=
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c.is_alpha || c.is_digit
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def to_lower (c : char) : char :=
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let n := to_nat c in
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if n >= 65 ∧ n <= 90 then of_nat (n + 32) else c
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theorem val_of_nat_eq_of_is_valid {n : nat} : is_valid_char n → (of_nat n).val = n :=
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λ h, show (if h' : is_valid_char n then {char . val := n, valid := h'} else {val := 0, valid := or.inl zero_lt_d800}).val = n, from
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(@dif_pos _ _ h _ (λ h', {char . val := n, valid := h'}) (λ _, {val := 0, valid := or.inl zero_lt_d800})).symm ▸ rfl
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theorem val_of_nat_eq_of_not_is_valid {n : nat} : ¬ is_valid_char n → (of_nat n).val = 0 :=
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λ h, show (if h' : is_valid_char n then {char . val := n, valid := h'} else {val := 0, valid := or.inl zero_lt_d800}).val = 0, from
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(@dif_neg _ _ h _ (λ h', {char . val := n, valid := h'}) (λ _, {val := 0, valid := or.inl zero_lt_d800})).symm ▸ rfl
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theorem of_nat_eq_of_not_is_valid {n : nat} : ¬ is_valid_char n → of_nat n = of_nat 0 :=
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λ h, eq_of_veq ((val_of_nat_eq_of_not_is_valid h).symm ▸ rfl)
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theorem of_nat_ne_of_ne {n₁ n₂ : nat} (h₁ : n₁ ≠ n₂) (h₂ : is_valid_char n₁) (h₃ : is_valid_char n₂) : of_nat n₁ ≠ of_nat n₂ :=
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ne_of_vne ((val_of_nat_eq_of_is_valid h₂).symm ▸ (val_of_nat_eq_of_is_valid h₃).symm ▸ h₁)
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end char
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