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[helm.git] / helm / software / matita / contribs / ng_assembly / common / nat_to_num.ma

diff --git a/helm/software/matita/contribs/ng_assembly/common/nat_to_num.ma b/helm/software/matita/contribs/ng_assembly/common/nat_to_num.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/nat.ma".
+include "num/word32.ma".
+
+(* ************************ *)
+(* NUMERI FINITI → NATURALI *)
+(* ************************ *)
+
+nlet rec nat_of_qu_aux n (r:rec_quatern n) on r ≝
+ match r with
+  [ qu_O ⇒ O
+  | qu_S t n' ⇒ S (nat_of_qu_aux t n')
+  ].
+
+ndefinition nat_of_qu : quatern → nat ≝ λn.nat_of_qu_aux n (qu_to_recqu n).
+
+nlet rec nat_of_oct_aux n (r:rec_oct n) on r ≝
+ match r with
+  [ oc_O ⇒ O
+  | oc_S t n' ⇒ S (nat_of_oct_aux t n')
+  ].
+
+ndefinition nat_of_oct : oct → nat ≝ λn.nat_of_oct_aux n (oct_to_recoct n).
+
+nlet rec nat_of_ex_aux n (r:rec_exadecim n) on r ≝
+ match r with
+  [ ex_O ⇒ O
+  | ex_S t n' ⇒ S (nat_of_ex_aux t n')
+  ].
+
+ndefinition nat_of_ex : exadecim → nat ≝ λn.nat_of_ex_aux n (ex_to_recex n).
+
+nlet rec nat_of_bit_aux n (r:rec_bitrigesim n) on r ≝
+ match r with
+  [ bi_O ⇒ O
+  | bi_S t n' ⇒ S (nat_of_bit_aux t n')
+  ].
+
+ndefinition nat_of_bit : bitrigesim → nat ≝ λn.nat_of_bit_aux n (bit_to_recbit n).
+
+nlet rec nat_of_b8_aux n (r:rec_byte8 n) on r ≝
+ match r with
+  [ b8_O ⇒ O
+  | b8_S t n' ⇒ S (nat_of_b8_aux t n')
+  ].
+
+ndefinition nat_of_b8 : byte8 → nat ≝ λn:byte8.nat_of_b8_aux n (b8_to_recb8 n).
+
+nlet rec nat_of_w16_aux n (r:rec_word16 n) on r : nat ≝
+ match r with
+  [ w16_O ⇒ O
+  | w16_S t n' ⇒ S (nat_of_w16_aux t n')
+  ].
+
+ndefinition nat_of_w16 : word16 → nat ≝ λn:word16.nat_of_w16_aux n (w16_to_recw16 n).
+
+ndefinition nat_of_w32 : word32 → nat ≝ λn:word32.(nat65536 * (nat_of_w16 (w32h n))) + (nat_of_w16 (w32l n)).