matita/matita/contribs/lambdadelta/basic_2/grammar/item.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 "ground_2/arith.ma".
  16
  17 (* ITEMS ********************************************************************)
  18
  19 (* atomic items *)
  20 inductive item0: Type[0] ≝
  21    | Sort: nat → item0 (* sort: starting at 0 *)
  22    | LRef: nat → item0 (* reference by index: starting at 0 *)
  23    | GRef: nat → item0 (* reference by position: starting at 0 *)
  24 .
  25
  26 (* binary binding items *)
  27 inductive bind2: Type[0] ≝
  28   | Abbr: bind2 (* abbreviation *)
  29   | Abst: bind2 (* abstraction *)
  30 .
  31
  32 (* binary non-binding items *)
  33 inductive flat2: Type[0] ≝
  34   | Appl: flat2 (* application *)
  35   | Cast: flat2 (* explicit type annotation *)
  36 .
  37
  38 (* binary items *)
  39 inductive item2: Type[0] ≝
  40   | Bind2: bool → bind2 → item2 (* polarized binding item *)
  41   | Flat2: flat2 → item2        (* non-binding item *)
  42 .
  43
  44 (* Basic properties *********************************************************)
  45
  46 axiom eq_item0_dec: ∀I1,I2:item0. Decidable (I1 = I2).
  47
  48 (* Basic_1: was: bind_dec *)
  49 axiom eq_bind2_dec: ∀I1,I2:bind2. Decidable (I1 = I2).
  50
  51 (* Basic_1: was: flat_dec *)
  52 axiom eq_flat2_dec: ∀I1,I2:flat2. Decidable (I1 = I2).
  53
  54 (* Basic_1: was: kind_dec *)
  55 axiom eq_item2_dec: ∀I1,I2:item2. Decidable (I1 = I2).
  56
  57 (* Basic_1: removed theorems 21:
  58             s_S s_plus s_plus_sym s_minus minus_s_s s_le s_lt s_inj s_inc
  59             s_arith0 s_arith1
  60             r_S r_plus r_plus_sym r_minus r_dis s_r r_arith0 r_arith1
  61             not_abbr_abst bind_dec_not
  62 *)