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:                                           *)
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   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 include "basic_2/notation.ma".
  17
  18 (* ITEMS ********************************************************************)
  19
  20 (* atomic items *)
  21 inductive item0: Type[0] ≝
  22    | Sort: nat → item0 (* sort: starting at 0 *)
  23    | LRef: nat → item0 (* reference by index: starting at 0 *)
  24    | GRef: nat → item0 (* reference by position: starting at 0 *)
  25 .
  26
  27 (* binary binding items *)
  28 inductive bind2: Type[0] ≝
  29   | Abbr: bind2 (* abbreviation *)
  30   | Abst: bind2 (* abstraction *)
  31 .
  32
  33 (* binary non-binding items *)
  34 inductive flat2: Type[0] ≝
  35   | Appl: flat2 (* application *)
  36   | Cast: flat2 (* explicit type annotation *)
  37 .
  38
  39 (* binary items *)
  40 inductive item2: Type[0] ≝
  41   | Bind2: bool → bind2 → item2 (* polarized binding item *)
  42   | Flat2: flat2 → item2        (* non-binding item *)
  43 .
  44
  45 (* Basic properties *********************************************************)
  46
  47 axiom item0_eq_dec: ∀I1,I2:item0. Decidable (I1 = I2).
  48
  49 (* Basic_1: was: bind_dec *)
  50 axiom bind2_eq_dec: ∀I1,I2:bind2. Decidable (I1 = I2).
  51
  52 (* Basic_1: was: flat_dec *)
  53 axiom flat2_eq_dec: ∀I1,I2:flat2. Decidable (I1 = I2).
  54
  55 (* Basic_1: was: kind_dec *)
  56 axiom item2_eq_dec: ∀I1,I2:item2. Decidable (I1 = I2).
  57
  58 (* Basic_1: removed theorems 21:
  59             s_S s_plus s_plus_sym s_minus minus_s_s s_le s_lt s_inj s_inc
  60             s_arith0 s_arith1
  61             r_S r_plus r_plus_sym r_minus r_dis s_r r_arith0 r_arith1
  62             not_abbr_abst bind_dec_not
  63 *)