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3 (*      ||M||                                                             *)
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14
15 (* THE FORMAL SYSTEM λα: MATITA SOURCE FILES
16  * Initial invocation: - Patience on me to gain peace and perfection! -
17  * Conceived since: 2014 July 25
18  * Developed since: 2021 June 17
19  *)
20
21 include "ground/arith/nat.ma".
22 include "static_2/notation/functions/star_1.ma".
23 include "static_2/notation/functions/gref_1.ma".
24 include "static_2/notation/functions/snappl_2.ma".
25 include "static_2/notation/functions/snabbr_2.ma".
26 include "alpha_1/notation/functions/snabst_1.ma".
27
28 (* TERMS ********************************************************************)
29
30 (* terms *)
31 inductive term: Type[0] ≝
32   | TChar: nat → term          (* character: starts at 0 *)
33   | TGRef: nat → term          (* reference by level: starts at 0 *)
34   | TAbst: term → term         (* abstraction: scope *)
35   | TAbbr: term → term → term  (* abbreviation: definition, scope *)
36   | TCons: term → term → term  (* group: body, tail *) 
37 .
38
39 interpretation
40   "character (terms)"
41   'Star c = (TChar c).
42
43 interpretation
44   "reference (terms)"
45   'GRef l = (TGRef l).
46
47 interpretation
48   "group (terms)"
49   'SnAppl T1 T2 = (TCons T1 T2).
50
51 interpretation
52   "abbreviation (terms)"
53   'SnAbbr T1 T2 = (TAbbr T1 T2).
54
55 interpretation
56   "abstraction (terms)"
57   'SnAbst T = (TAbst T).