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Diffstat (limited to 'theories/Strings/Ascii.v')
| -rw-r--r-- | theories/Strings/Ascii.v | 78 |
1 files changed, 39 insertions, 39 deletions
diff --git a/theories/Strings/Ascii.v b/theories/Strings/Ascii.v index 919989fd..1c02be7f 100644 --- a/theories/Strings/Ascii.v +++ b/theories/Strings/Ascii.v @@ -6,17 +6,17 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(* $Id: Ascii.v 8026 2006-02-11 19:40:49Z herbelin $ *) +(* $Id: Ascii.v 9245 2006-10-17 12:53:34Z notin $ *) -(* Contributed by Laurent Théry (INRIA); - Adapted to Coq V8 by the Coq Development Team *) +(** Contributed by Laurent Théry (INRIA); + Adapted to Coq V8 by the Coq Development Team *) Require Import Bool. Require Import BinPos. -(** *** Definition of ascii characters *) +(** * Definition of ascii characters *) -(* Definition of ascii character as a 8 bits constructor *) +(** Definition of ascii character as a 8 bits constructor *) Inductive ascii : Set := Ascii (_ _ _ _ _ _ _ _ : bool). @@ -29,86 +29,86 @@ Definition one := Ascii true false false false false false false false. Definition app1 (f : bool -> bool) (a : ascii) := match a with - | Ascii a1 a2 a3 a4 a5 a6 a7 a8 => + | Ascii a1 a2 a3 a4 a5 a6 a7 a8 => Ascii (f a1) (f a2) (f a3) (f a4) (f a5) (f a6) (f a7) (f a8) end. Definition app2 (f : bool -> bool -> bool) (a b : ascii) := match a, b with - | Ascii a1 a2 a3 a4 a5 a6 a7 a8, Ascii b1 b2 b3 b4 b5 b6 b7 b8 => + | Ascii a1 a2 a3 a4 a5 a6 a7 a8, Ascii b1 b2 b3 b4 b5 b6 b7 b8 => Ascii (f a1 b1) (f a2 b2) (f a3 b3) (f a4 b4) - (f a5 b5) (f a6 b6) (f a7 b7) (f a8 b8) + (f a5 b5) (f a6 b6) (f a7 b7) (f a8 b8) end. 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 + | 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 of a decidable function that is effective *) Definition ascii_dec : forall a b : ascii, {a = b} + {a <> b}. - decide equality; apply bool_dec. + decide equality; apply bool_dec. Defined. -(** *** Conversion between natural numbers modulo 256 and ascii characters *) +(** * Conversion between natural numbers modulo 256 and ascii characters *) -(* Auxillary function that turns a positive into an ascii by +(** Auxillary function that turns a positive into an ascii by looking at the last n bits, ie z mod 2^n *) Fixpoint ascii_of_pos_aux (res acc : ascii) (z : positive) - (n : nat) {struct n} : ascii := + (n : nat) {struct n} : ascii := match n with - | O => res - | S n1 => + | O => res + | S n1 => match z with - | xH => app2 orb res acc - | xI z' => ascii_of_pos_aux (app2 orb res acc) (shift false acc) z' n1 - | xO z' => ascii_of_pos_aux res (shift false acc) z' n1 + | xH => app2 orb res acc + | xI z' => ascii_of_pos_aux (app2 orb res acc) (shift false acc) z' n1 + | xO z' => ascii_of_pos_aux res (shift false acc) z' n1 end end. -(* Function that turns a positive into an ascii by - looking at the last 8 bits, ie a mod 8 *) +(** Function that turns a positive into an ascii by + looking at the last 8 bits, ie a mod 8 *) Definition ascii_of_pos (a : positive) := ascii_of_pos_aux zero one a 8. - -(* Function that turns a Peano number into an ascii by converting it - to positive *) + +(** Function that turns a Peano number into an ascii by converting it + to positive *) Definition ascii_of_nat (a : nat) := match a with - | O => zero - | S a' => ascii_of_pos (P_of_succ_nat a') + | O => zero + | S a' => ascii_of_pos (P_of_succ_nat a') end. -(* The opposite function *) +(** The opposite function *) Definition nat_of_ascii (a : ascii) : nat := let (a1, a2, a3, a4, a5, a6, a7, a8) := a in - 2 * + 2 * + (2 * (2 * - (2 * (2 * - (2 * (2 * - (2 * (if a8 then 1 else 0) - + (if a7 then 1 else 0)) - + (if a6 then 1 else 0)) - + (if a5 then 1 else 0)) - + (if a4 then 1 else 0)) + (2 * + (2 * (if a8 then 1 else 0) + + (if a7 then 1 else 0)) + + (if a6 then 1 else 0)) + + (if a5 then 1 else 0)) + + (if a4 then 1 else 0)) + (if a3 then 1 else 0)) - + (if a2 then 1 else 0)) - + (if a1 then 1 else 0). + + (if a2 then 1 else 0)) + + (if a1 then 1 else 0). Theorem ascii_nat_embedding : forall a : ascii, ascii_of_nat (nat_of_ascii a) = a. Proof. destruct a as [[|][|][|][|][|][|][|][|]]; compute; reflexivity. -Abort. +Qed. -(** *** Concrete syntax *) +(** * Concrete syntax *) (** Ascii characters can be represented in scope char_scope as follows: |