--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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 "num/bool.ma".
+
+(* ********** *)
+(* QUATERNARI *)
+(* ********** *)
+
+ninductive quatern : Type ≝
+ q0 : quatern
+| q1 : quatern
+| q2 : quatern
+| q3 : quatern.
+
+(* operatore = *)
+ndefinition eq_qu ≝
+λn1,n2:quatern.
+ match n1 with
+ [ q0 ⇒ match n2 with [ q0 ⇒ true | _ ⇒ false ]
+ | q1 ⇒ match n2 with [ q1 ⇒ true | _ ⇒ false ]
+ | q2 ⇒ match n2 with [ q2 ⇒ true | _ ⇒ false ]
+ | q3 ⇒ match n2 with [ q3 ⇒ true | _ ⇒ false ]
+ ].
+
+(* iteratore sui quaternari *)
+ndefinition forall_qu ≝ λP.
+ P q0 ⊗ P q1 ⊗ P q2 ⊗ P q3.
+
+(* operatore successorre *)
+ndefinition succ_qu ≝
+λn.match n with
+ [ q0 ⇒ q1 | q1 ⇒ q2 | q2 ⇒ q3 | q3 ⇒ q0 ].
+
+(* quaternari ricorsivi *)
+ninductive rec_quatern : quatern → Type ≝
+ qu_O : rec_quatern q0
+| qu_S : ∀n.rec_quatern n → rec_quatern (succ_qu n).
+
+(* quaternari → quaternari ricorsivi *)
+ndefinition qu_to_recqu ≝
+λn.match n return λx.rec_quatern x with
+ [ q0 ⇒ qu_O
+ | q1 ⇒ qu_S ? qu_O
+ | q2 ⇒ qu_S ? (qu_S ? qu_O)
+ | q3 ⇒ qu_S ? (qu_S ? (qu_S ? qu_O))
+ ].