helm/software/matita/library/Q/q/q.ma

   1 (**************************************************************************)
   2 (*       ___                                                                *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||       A.Asperti, C.Sacerdoti Coen,                          *)
   8 (*      ||A||       E.Tassi, S.Zacchiroli                                 *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU Lesser General Public License Version 2.1         *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "Q/ratio/ratio.ma".
  16
  17 (* a rational number is either O or a ratio with a sign *)
  18 inductive Q : Set \def
  19     OQ : Q
  20   | Qpos : ratio  \to Q
  21   | Qneg : ratio  \to Q.
  22
  23 definition Q_of_nat ≝
  24  λn.
  25   match factorize n with
  26    [ nfa_zero ⇒ OQ
  27    | nfa_one ⇒ Qpos one
  28    | nfa_proper l ⇒ Qpos (frac (nat_fact_to_fraction l))
  29    ].