(* *)
(**************************************************************************)
-include "static_2/notation/functions/snitem2_3.ma".
-include "static_2/notation/functions/star_0.ma".
-include "static_2/notation/functions/snabstpos_2.ma".
-include "static_2/notation/functions/snabbr_3.ma".
-include "static_2/notation/functions/snabbrpos_2.ma".
-include "static_2/notation/functions/snabbrneg_2.ma".
-include "alpha_1/notation/functions/snitem1_2.ma".
-include "alpha_1/notation/functions/snstar_2.ma".
-include "alpha_1/notation/functions/snlref_2.ma".
-include "alpha_1/notation/functions/sngref_2.ma".
-include "alpha_1/notation/functions/snabstneg_1.ma".
-include "alpha_1/notation/functions/snproj_3.ma".
-include "alpha_1/notation/functions/snprojpos_2.ma".
-include "alpha_1/notation/functions/snprojneg_2.ma".
-include "alpha_1/syntax/item.ma".
+(* THE FORMAL SYSTEM λα: MATITA SOURCE FILES
+ * Initial invocation: - Patience on me to gain peace and perfection! -
+ * Conceived since: 2014 July 25
+ * Developed since: 2021 June 17
+ *)
+
+include "ground/arith/nat.ma".
+include "static_2/notation/functions/star_1.ma".
+include "static_2/notation/functions/gref_1.ma".
+include "static_2/notation/functions/snappl_2.ma".
+include "static_2/notation/functions/snabbr_2.ma".
+include "alpha_1/notation/functions/snabst_1.ma".
(* TERMS ********************************************************************)
(* terms *)
inductive term: Type[0] ≝
- | TAtom: term (* atomic item construction *)
- | TUnit: item1 → term → term (* unary item construction *)
- | TPair: item2 → term → term → term (* binary item construction *)
+ | TChar: nat → term (* character: starts at 0 *)
+ | TGRef: nat → term (* reference by level: starts at 0 *)
+ | TAbst: term → term (* abstraction: scope *)
+ | TAbbr: term → term → term (* abbreviation: definition, scope *)
+ | TCons: term → term → term (* group: body, tail *)
.
-interpretation "top (term)"
- 'Star = TAtom.
+interpretation
+ "character (terms)"
+ 'Star c = (TChar c).
-interpretation "term construction (unary)"
- 'SnItem1 I T = (TUnit I T).
+interpretation
+ "reference (terms)"
+ 'GRef l = (TGRef l).
-interpretation "term construction (binary)"
- 'SnItem2 I T1 T2 = (TPair I T1 T2).
+interpretation
+ "group (terms)"
+ 'SnAppl T1 T2 = (TCons T1 T2).
-interpretation "character (term)"
- 'SnStar k T = (TUnit (Char k) T).
+interpretation
+ "abbreviation (terms)"
+ 'SnAbbr T1 T2 = (TAbbr T1 T2).
-interpretation "local reference (term)"
- 'SnLRef i T = (TUnit (LRef i) T).
-
-interpretation "global reference (term)"
- 'SnGRef p T = (TUnit (GRef p) T).
-
-interpretation "negative abbreviation (term)"
- 'SnAbbrNeg T = (TUnit Decl T).
-
-interpretation "positive abstraction (term)"
- 'SnAbstPos T1 T2 = (TPair Abst T1 T2).
-
-interpretation "abbreviation (term)"
- 'SnAbbr a T1 T2 = (TPair (Abbr a) T1 T2).
-
-interpretation "positive abbreviation (term)"
- 'SnAbbrPos T1 T2 = (TPair (Abbr true) T1 T2).
-
-interpretation "negative abbreviation (term)"
- 'SnAbbrNeg T1 T2 = (TPair (Abbr false) T1 T2).
-
-interpretation "projection (term)"
- 'SnProj a T1 T2 = (TPair (Proj a) T1 T2).
-
-interpretation "positive projection (term)"
- 'SnProjPos T1 T2 = (TPair (Proj true) T1 T2).
-
-interpretation "negative projection (term)"
- 'SnProjNeg T1 T2 = (TPair (Proj false) T1 T2).
+interpretation
+ "abstraction (terms)"
+ 'SnAbst T = (TAbst T).