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

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   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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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    | GRef: nat → item0 (* reference by position: starting at 0 *)
  34 .
  35
  36 (* binary binding items *)
  37 inductive bind2: Type[0] ≝
  38   | Abbr: bind2 (* abbreviation *)
  39   | Abst: bind2 (* abstraction *)
  40 .
  41
  42 (* binary non-binding items *)
  43 inductive flat2: Type[0] ≝
  44   | Appl: flat2 (* application *)
  45   | Cast: flat2 (* explicit type annotation *)
  46 .
  47
  48 (* binary items *)
  49 inductive item2: Type[0] ≝
  50   | Bind: bind2 → item2 (* binding item *)
  51   | Flat: flat2 → item2 (* non-binding item *)
  52 .
  53
  54 coercion item2_of_bind2: ∀I:bind2.item2 ≝ Bind on _I:bind2 to item2.
  55
  56 coercion item2_of_flat2: ∀I:flat2.item2 ≝ Flat on _I:flat2 to item2.
  57
  58 (* Basic_1: removed theorems 19:
  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 *)