fork for Matita version B

[helm.git] / matitaB / matita / contribs / ng_assembly / num / quatern.ma

diff --git a/matitaB/matita/contribs/ng_assembly/num/quatern.ma b/matitaB/matita/contribs/ng_assembly/num/quatern.ma
new file mode 100755 (executable)
index 0000000..a6bc134
--- /dev/null
+++ b/matitaB/matita/contribs/ng_assembly/num/quatern.ma
@@ -0,0 +1,66 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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))
+ ].