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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
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(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
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(** Contributed by Laurent Théry (INRIA); Adapted to Coq V8 by the Coq Development Team *)
(** * Definition of ascii characters *)
(** Definition of ascii character as a 8 bits constructor *)
Inductive ascii : Set := Ascii (_ _ _ _ _ _ _ _ : bool).
Declare Scope char_scope.
Delimit Scope char_scope with char.
Bind Scope char_scope with ascii.
Definition zero := Ascii false false false false false false false false.
Definition one := Ascii true false false false false false false false.
Definition shift (c : bool) (a : ascii) :=
match a with
| Ascii a1 a2 a3 a4 a5 a6 a7 a8 => Ascii c a1 a2 a3 a4 a5 a6 a7
end.
(** Definition of a decidable function that is effective *)
Definition ascii_dec : forall a b : ascii, {a = b} + {a <> b}.
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 ].
(** * Concrete syntax *)
(** Ascii characters can be represented in scope char_scope as follows: - ["c"]   represents itself if c is a character of code < 128, - [""""]  is an exception: it represents the ascii character 34 (double quote), - ["nnn"] represents the ascii character of decimal code nnn.  For instance, both ["065"] and ["A"] denote the character `uppercase A', and both ["034"] and [""""] denote the character `double quote'.  Notice that the ascii characters of code >= 128 do not denote stand-alone utf8 characters so that only the notation "nnn" is available for them (unless your terminal is able to represent them, which is typically not the case in coqide). *)
Definition ascii_of_byte (b : byte) : ascii
:= let '(b0, (b1, (b2, (b3, (b4, (b5, (b6, b7))))))) := Byte.to_bits b in
Ascii b0 b1 b2 b3 b4 b5 b6 b7.
Definition byte_of_ascii (a : ascii) : byte
:= let (b0, b1, b2, b3, b4, b5, b6, b7) := a in
Byte.of_bits (b0, (b1, (b2, (b3, (b4, (b5, (b6, b7))))))).

Lemma ascii_of_byte_via_N x : ascii_of_byte x = ascii_of_N (Byte.to_N x).