matita/matita/contribs/lambda_delta/Basic_2/grammar/item.ma

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   2 (*       ___                                                              *)
   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                  *)
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  14
  15 (* THE FORMAL SYSTEM λδ - MATITA SOURCE FILES
  16  * Specification started: 2011 April 17
  17  * Confluence of context-sensitive parallel reduction closed: 2011 September 21
  18  * Confluence of context-free parallel reduction closed: 2011 September 6
  19  * - Patience on me so that I gain peace and perfection! -
  20  * [ suggested invocation to start formal specifications with ]
  21  *)
  22
  23 include "Ground_2/list.ma".
  24 include "Ground_2/star.ma".
  25 include "Basic_2/notation.ma".
  26
  27 (* ITEMS ********************************************************************)
  28
  29 (* atomic items *)
  30 inductive item0: Type[0] ≝
  31    | Sort: nat → item0 (* sort: starting at 0 *)
  32    | LRef: nat → item0 (* reference by index: starting at 0 *)
  33 .
  34
  35 (* binary binding items *)
  36 inductive bind2: Type[0] ≝
  37   | Abbr: bind2 (* abbreviation *)
  38   | Abst: bind2 (* abstraction *)
  39 .
  40
  41 (* binary non-binding items *)
  42 inductive flat2: Type[0] ≝
  43   | Appl: flat2 (* application *)
  44   | Cast: flat2 (* explicit type annotation *)
  45 .
  46
  47 (* binary items *)
  48 inductive item2: Type[0] ≝
  49   | Bind: bind2 → item2 (* binding item *)
  50   | Flat: flat2 → item2 (* non-binding item *)
  51 .
  52
  53 coercion item2_of_bind2: ∀I:bind2.item2 ≝ Bind on _I:bind2 to item2.
  54
  55 coercion item2_of_flat2: ∀I:flat2.item2 ≝ Flat on _I:flat2 to item2.
  56
  57 (* Basic_1: removed theorems 19:
  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 *)