matita/matita/contribs/lambdadelta/delayed_updating/syntax/label.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 (* A SYSTEM OF λ-CALCULUS WITH DELAYED UPDATING
  16  * Initial invocation: - Patience on me to gain peace and perfection! -
  17  *)
  18
  19 include "ground/arith/pnat.ma".
  20 include "delayed_updating/notation/functions/nodelabel_d_1.ma".
  21 include "delayed_updating/notation/functions/nodelabel_m_0.ma".
  22 include "delayed_updating/notation/functions/edgelabel_l_0.ma".
  23 include "delayed_updating/notation/functions/edgelabel_a_0.ma".
  24 include "delayed_updating/notation/functions/edgelabel_s_0.ma".
  25
  26 (* LABEL ********************************************************************)
  27
  28 inductive label: Type[0] ≝
  29 | label_d: pnat → label
  30 | label_m: label
  31 | label_L: label
  32 | label_A: label
  33 | label_S: label
  34 .
  35
  36 interpretation
  37   "variable reference by depth (label)"
  38   'NodeLabelD k = (label_d k).
  39
  40 interpretation
  41   "mark (label)"
  42   'NodeLabelM = (label_m).
  43
  44 interpretation
  45   "name-free functional abstruction (label)"
  46   'EdgeLabelL = (label_L).
  47
  48 interpretation
  49   "application (label)"
  50   'EdgeLabelA = (label_A).
  51
  52 interpretation
  53   "side branch (label)"
  54   'EdgeLabelS = (label_S).