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/nat.ma".
  20 include "delayed_updating/notation/functions/nodelabel_d_1.ma".
  21 include "delayed_updating/notation/functions/nodelabel_d_2.ma".
  22 include "delayed_updating/notation/functions/nodelabel_m_0.ma".
  23 include "delayed_updating/notation/functions/edgelabel_l_0.ma".
  24 include "delayed_updating/notation/functions/edgelabel_a_0.ma".
  25 include "delayed_updating/notation/functions/edgelabel_s_0.ma".
  26
  27 (* LABEL ********************************************************************)
  28
  29 inductive label: Type[0] ≝
  30 | label_d : pnat → label
  31 | label_d2: pnat → nat → label
  32 | label_m : label
  33 | label_L : label
  34 | label_A : label
  35 | label_S : label
  36 .
  37
  38 interpretation
  39   "variable reference by depth (label)"
  40   'NodeLabelD k = (label_d k).
  41
  42 interpretation
  43   "variable reference by depth with offset (label)"
  44   'NodeLabelD k d = (label_d2 k d).
  45
  46 interpretation
  47   "mark (label)"
  48   'NodeLabelM = (label_m).
  49
  50 interpretation
  51   "name-free functional abstruction (label)"
  52   'EdgeLabelL = (label_L).
  53
  54 interpretation
  55   "application (label)"
  56   'EdgeLabelA = (label_A).
  57
  58 interpretation
  59   "side branch (label)"
  60   'EdgeLabelS = (label_S).