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 include "static_2/notation/functions/snitem2_3.ma".
  16 include "static_2/notation/functions/star_0.ma".
  17 include "static_2/notation/functions/snabstpos_2.ma".
  18 include "static_2/notation/functions/snabbr_3.ma".
  19 include "static_2/notation/functions/snabbrpos_2.ma".
  20 include "static_2/notation/functions/snabbrneg_2.ma".
  21 include "alpha_1/notation/functions/snitem1_2.ma".
  22 include "alpha_1/notation/functions/snstar_2.ma".
  23 include "alpha_1/notation/functions/snlref_2.ma".
  24 include "alpha_1/notation/functions/sngref_2.ma".
  25 include "alpha_1/notation/functions/snabstneg_1.ma".
  26 include "alpha_1/notation/functions/snproj_3.ma".
  27 include "alpha_1/notation/functions/snprojpos_2.ma".
  28 include "alpha_1/notation/functions/snprojneg_2.ma".
  29 include "alpha_1/syntax/item.ma".
  30
  31 (* TERMS ********************************************************************)
  32
  33 (* terms *)
  34 inductive term: Type[0] ≝
  35   | TAtom:         term                (* atomic item construction *)
  36   | TUnit: item1 → term → term         (* unary item construction *)
  37   | TPair: item2 → term → term → term  (* binary item construction *)
  38 .
  39
  40 interpretation "top (term)"
  41    'Star = TAtom.
  42
  43 interpretation "term construction (unary)"
  44    'SnItem1 I T = (TUnit I T).
  45
  46 interpretation "term construction (binary)"
  47    'SnItem2 I T1 T2 = (TPair I T1 T2).
  48
  49 interpretation "character (term)"
  50    'SnStar s T = (TUnit (Char s) T).
  51
  52 interpretation "local reference (term)"
  53    'SnLRef i T = (TUnit (LRef i) T).
  54
  55 interpretation "global reference (term)"
  56    'SnGRef l T = (TUnit (GRef l) T).
  57
  58 interpretation "negative abbreviation (term)"
  59    'SnAbbrNeg T = (TUnit Decl T).
  60
  61 interpretation "positive abstraction (term)"
  62    'SnAbstPos T1 T2 = (TPair Abst T1 T2).
  63
  64 interpretation "abbreviation (term)"
  65    'SnAbbr p T1 T2 = (TPair (Abbr p) T1 T2).
  66
  67 interpretation "positive abbreviation (term)"
  68    'SnAbbrPos T1 T2 = (TPair (Abbr true) T1 T2).
  69
  70 interpretation "negative abbreviation (term)"
  71    'SnAbbrNeg T1 T2 = (TPair (Abbr false) T1 T2).
  72
  73 interpretation "projection (term)"
  74    'SnProj p T1 T2 = (TPair (Proj p) T1 T2).
  75
  76 interpretation "positive projection (term)"
  77    'SnProjPos T1 T2 = (TPair (Proj true) T1 T2).
  78
  79 interpretation "negative projection (term)"
  80    'SnProjNeg T1 T2 = (TPair (Proj false) T1 T2).