matita/matita/contribs/lambdadelta/alpha_1/syntax/term.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 (* THE FORMAL SYSTEM λα: MATITA SOURCE FILES
  16  * Initial invocation: - Patience on me to gain peace and perfection! -
  17  * Conceived since: 2014 July 25
  18  * Developed since: 2021 June 17
  19  *)
  20
  21 include "ground/arith/nat.ma".
  22 include "static_2/notation/functions/star_1.ma".
  23 include "static_2/notation/functions/gref_1.ma".
  24 include "static_2/notation/functions/snappl_2.ma".
  25 include "static_2/notation/functions/snabbr_2.ma".
  26 include "alpha_1/notation/functions/snabst_1.ma".
  27
  28 (* TERMS ********************************************************************)
  29
  30 (* terms *)
  31 inductive term: Type[0] ≝
  32   | TChar: nat → term          (* character: starts at 0 *)
  33   | TGRef: nat → term          (* reference by level: starts at 0 *)
  34   | TAbst: term → term         (* abstraction: scope *)
  35   | TAbbr: term → term → term  (* abbreviation: definition, scope *)
  36   | TCons: term → term → term  (* group: body, tail *)
  37 .
  38
  39 interpretation
  40   "character (terms)"
  41   'Star c = (TChar c).
  42
  43 interpretation
  44   "reference (terms)"
  45   'GRef l = (TGRef l).
  46
  47 interpretation
  48   "group (terms)"
  49   'SnAppl T1 T2 = (TCons T1 T2).
  50
  51 interpretation
  52   "abbreviation (terms)"
  53   'SnAbbr T1 T2 = (TAbbr T1 T2).
  54
  55 interpretation
  56   "abstraction (terms)"
  57   'SnAbst T = (TAbst T).