tentative specification of Conway's construction for surreal numbers

[helm.git] / matita / matita / contribs / ONAG / game.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* ON NUMBERS AND GAMES: MATITA SOURCE FILES
+ * Invocation:
+ *   - Patience on me to gain peace and perfection! -
+ * 2012 May 25:
+ *   specification starts.
+ *)
+
+include "basics/pts.ma".
+include "notation.ma".
+
+(* GAMES ********************************************************************)
+
+inductive Game: Type[1] ≝
+| game: ∀L,R:Type[0]. (L → Game) → (R → Game) → Game
+.
+
+interpretation  "game" 'Game = Game.
+(*
+notation > 
+  "'Let' term 46 g ≡ { L , l | R , r } 'in' term 46 t"
+  non associative with precedence 46
+  for @{ 'Destructor (match $g with [ game ${ident L} ${ident R} ${ident l} ${ident r} ⇒ $t]) }.
+*)
+interpretation "game destructor" 'Destructor x = x.
+
+definition pippo ≝ λx.
+match x with [ game L R F G ⇒ x ].
+
+(*
+notation < "hvbox('if' \nbsp term 46 e \nbsp break 'then' \nbsp term 46 t \nbsp break 'else' \nbsp term 49 f \nbsp)" non associative with precedence 46
+ for @{ match $e return $T with [ true ⇒ $t | false ⇒ $f]  }.
+*)
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