diff options
Diffstat (limited to 'theories/Strings/Ascii.v')
| -rw-r--r-- | theories/Strings/Ascii.v | 34 |
1 files changed, 34 insertions, 0 deletions
diff --git a/theories/Strings/Ascii.v b/theories/Strings/Ascii.v index 5154b75b..31a7fb8a 100644 --- a/theories/Strings/Ascii.v +++ b/theories/Strings/Ascii.v @@ -40,6 +40,40 @@ Proof. decide equality; apply bool_dec. Defined. +Local Open Scope lazy_bool_scope. + +Definition eqb (a b : ascii) : bool := + match a, b with + | Ascii a0 a1 a2 a3 a4 a5 a6 a7, + Ascii b0 b1 b2 b3 b4 b5 b6 b7 => + Bool.eqb a0 b0 &&& Bool.eqb a1 b1 &&& Bool.eqb a2 b2 &&& Bool.eqb a3 b3 + &&& Bool.eqb a4 b4 &&& Bool.eqb a5 b5 &&& Bool.eqb a6 b6 &&& Bool.eqb a7 b7 + end. + +Infix "=?" := eqb : char_scope. + +Lemma eqb_spec (a b : ascii) : reflect (a = b) (a =? b)%char. +Proof. + destruct a, b; simpl. + do 8 (case Bool.eqb_spec; [ intros -> | constructor; now intros [= ] ]). + now constructor. +Qed. + +Local Ltac t_eqb := + repeat first [ congruence + | progress subst + | apply conj + | match goal with + | [ |- context[eqb ?x ?y] ] => destruct (eqb_spec x y) + end + | intro ]. +Lemma eqb_refl x : (x =? x)%char = true. Proof. t_eqb. Qed. +Lemma eqb_sym x y : (x =? y)%char = (y =? x)%char. Proof. t_eqb. Qed. +Lemma eqb_eq n m : (n =? m)%char = true <-> n = m. Proof. t_eqb. Qed. +Lemma eqb_neq x y : (x =? y)%char = false <-> x <> y. Proof. t_eqb. Qed. +Lemma eqb_compat: Morphisms.Proper (Morphisms.respectful eq (Morphisms.respectful eq eq)) eqb. +Proof. t_eqb. Qed. + (** * Conversion between natural numbers modulo 256 and ascii characters *) (** Auxiliary function that turns a positive into an ascii by |