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[helm.git] / matitaB / matita / contribs / ng_assembly2 / num / bool.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(*                          Progetto FreeScale                            *)
+(*                                                                        *)
+(*   Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it              *)
+(*   Sviluppo: 2008-2010                                                  *)
+(*                                                                        *)
+(* ********************************************************************** *)
+
+include "common/theory.ma".
+
+(* ******** *)
+(* BOOLEANI *)
+(* ******** *)
+
+ninductive bool : Type ≝ 
+  true : bool
+| false : bool.
+
+(* operatori booleani *)
+ndefinition eq_bool ≝
+λb1,b2:bool.match b1 with
+ [ true ⇒ match b2 with [ true ⇒ true | false ⇒ false ]
+ | false ⇒ match b2 with [ true ⇒ false | false ⇒ true ]
+ ].
+
+ndefinition not_bool ≝
+λb:bool.match b with [ true ⇒ false | false ⇒ true ].
+
+ndefinition and_bool ≝
+λb1,b2:bool.match b1 with
+ [ true ⇒ b2 | false ⇒ false ].
+
+ndefinition or_bool ≝
+λb1,b2:bool.match b1 with
+ [ true ⇒ true | false ⇒ b2 ].
+
+ndefinition xor_bool ≝
+λb1,b2:bool.match b1 with
+ [ true ⇒ not_bool b2
+ | false ⇒ b2 ].
+
+(* \ominus *)
+notation "hvbox(⊖ a)" non associative with precedence 36
+ for @{ 'not_bool $a }.
+interpretation "not_bool" 'not_bool x = (not_bool x).
+
+(* \otimes *)
+notation "hvbox(a break ⊗ b)" left associative with precedence 35
+ for @{ 'and_bool $a $b }.
+interpretation "and_bool" 'and_bool x y = (and_bool x y).
+
+(* \oplus *)
+notation "hvbox(a break ⊕ b)" left associative with precedence 34
+ for @{ 'or_bool $a $b }.
+interpretation "or_bool" 'or_bool x y = (or_bool x y).
+
+(* \odot *)
+notation "hvbox(a break ⊙ b)" left associative with precedence 33
+ for @{ 'xor_bool $a $b }.
+interpretation "xor_bool" 'xor_bool x y = (xor_bool x y).
+
+(* iteratore sugli esadecimali *)
+ndefinition forall_bool ≝ λP.P true ⊗ P false.
+
+ndefinition boolRelation : Type → Type ≝
+λA:Type.A → A → bool.