Stuff moved from old Matita.

[helm.git] / matita / matita / tests / Ztest.ma

diff --git a/matita/matita/tests/Ztest.ma b/matita/matita/tests/Ztest.ma
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+(**************************************************************************)
+(*       ___                                                               *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||       A.Asperti, C.Sacerdoti Coen,                          *)
+(*      ||A||       E.Tassi, S.Zacchiroli                                 *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU Lesser General Public License Version 2.1         *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "arithmetics/nat.ma".
+
+ninductive Z : Type ≝
+  OZ : Z
+| pos : nat → Z
+| neg : nat → Z.
+
+interpretation "Integers" 'Z = Z.
+
+(* TODO: move the following two to datatypes/compare.ma *)
+ninductive compare : Type[0] ≝
+| LT : compare
+| EQ : compare
+| GT : compare.
+
+nlet rec nat_compare n m: compare ≝
+match n with
+[ O ⇒ match m with 
+      [ O ⇒ EQ
+      | (S q) ⇒ LT ]
+| S p ⇒ match m with 
+      [ O ⇒ GT
+      | S q ⇒ nat_compare p q]].
+
+ndefinition Zplus : Z → Z → Z ≝
+  λx,y. match x with
+    [ OZ ⇒ y
+    | pos m ⇒
+        match y with
+         [ OZ ⇒ x
+         | pos n ⇒ (pos (pred ((S m)+(S n))))
+         | neg n ⇒ 
+              match nat_compare m n with
+                [ LT ⇒ (neg (pred (n-m)))
+                | EQ ⇒ OZ
+                | GT ⇒ (pos (pred (m-n)))] ]
+    | neg m ⇒
+        match y with
+         [ OZ ⇒ x
+         | pos n ⇒
+              match nat_compare m n with
+                [ LT ⇒ (pos (pred (n-m)))
+                | EQ ⇒ OZ
+                | GT ⇒ (neg (pred (m-n)))]     
+         | neg n ⇒ (neg (pred ((S m)+(S n))))] ].
+
+interpretation "integer plus" 'plus x y = (Zplus x y).
+
+ndefinition Z_of_nat ≝
+λn. match n with
+[ O ⇒ OZ 
+| S n ⇒ pos n].
+
+nlemma fails : ∀p. p + Z_of_nat 1 = Z_of_nat 1 + p.
+#p;nnormalize;