matita/matita/contribs/lambda-delta/Basic-2/grammar/item.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  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 λδ - MATITA SOURCE SCRIPTS
  16  * Specification started: 2011 April 17
  17  * - Patience on me so that I gain peace and perfection! -
  18  * [ suggested invocation to start formal specifications with ]
  19  *)
  20
  21 include "Ground-2/list.ma".
  22 include "Basic-2/notation.ma".
  23
  24 (* ITEMS ********************************************************************)
  25
  26 (* atomic items *)
  27 inductive item0: Type[0] ≝
  28    | Sort: nat → item0 (* sort: starting at 0 *)
  29    | LRef: nat → item0 (* reference by index: starting at 0 *)
  30 .
  31
  32 (* binary binding items *)
  33 inductive bind2: Type[0] ≝
  34   | Abbr: bind2 (* abbreviation *)
  35   | Abst: bind2 (* abstraction *)
  36 .
  37
  38 (* binary non-binding items *)
  39 inductive flat2: Type[0] ≝
  40   | Appl: flat2 (* application *)
  41   | Cast: flat2 (* explicit type annotation *)
  42 .
  43
  44 (* binary items *)
  45 inductive item2: Type[0] ≝
  46   | Bind: bind2 → item2 (* binding item *)
  47   | Flat: flat2 → item2 (* non-binding item *)
  48 .
  49
  50 coercion item2_of_bind2: ∀I:bind2.item2 ≝ Bind on _I:bind2 to item2.
  51
  52 coercion item2_of_flat2: ∀I:flat2.item2 ≝ Flat on _I:flat2 to item2.
  53
  54 (* Basic-1: removed theorems 19:
  55             s_S s_plus s_plus_sym s_minus minus_s_s s_le s_lt s_inj s_inc
  56             s_arith0 s_arith1
  57             r_S r_plus r_plus_sym r_minus r_dis s_r r_arith0 r_arith1
  58 *)