changes location of coq.ma (now "legacy/coq.ma")

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

diff --git a/helm/matita/tests/coercions.ma b/helm/matita/tests/coercions.ma
index 1e92364fe61387e0918c1657f39be361050368e8..20b15cd2650d8a7f7840d68696da39423af2248c 100644 (file)
--- a/helm/matita/tests/coercions.ma
+++ b/helm/matita/tests/coercions.ma
@@ -1,50 +1,64 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
 
-Inductive nat : Set \def
-| O : nat
-| S : nat \to nat.
-
-Inductive list (A:Set) : Set \def
-| nil : list A
-| cons : A \to list A \to list A.
+set "baseuri" "cic:/matita/tests/coercions/".
+include "legacy/coq.ma".
 
-Inductive bool: Set \def
-| true : bool
-| false : bool.
+inductive pos: Set \def
+| one : pos
+| next : pos \to pos.
 
+inductive nat:Set \def
+| O : nat
+| S : nat \to nat.
 
+inductive int: Set \def
+| positive: nat \to int
+| negative : nat \to int.
 
+inductive empty : Set \def .
 
-let rec len (A:Set)(l:list A) on l : nat \def
- match l:list with [
-   nil \Rightarrow O
- | (cons e tl) \Rightarrow (S (len A tl))].
+let rec pos2nat x \def 
+  match x with  
+  [ one \Rightarrow (S O)
+  | (next z) \Rightarrow S (pos2nat z)].
 
-let rec plus (n,m:nat) : nat \def
- match n:nat with [
-   O \Rightarrow m
- | (S x) \Rightarrow (S (plus x m)) ].  
+definition nat2int \def \lambda x. positive x.
 
-let rec is_zero (n:nat) : bool \def
-  match n:nat with [
-    O \Rightarrow true
-  | (S x) \Rightarrow false].  
+coercion cic:/matita/tests/coercions/pos2nat.con.
 
-let rec nat_eq_dec (n,m:nat) : bool \def
-  match n:nat with [
-    O \Rightarrow 
-         match m:nat with [
-           O \Rightarrow true
-        | (S x) \Rightarrow false]
-  | (S x) \Rightarrow
-             match m:nat with [
-               O \Rightarrow false
-            | (S y) \Rightarrow (nat_eq_dec x y)]
-  ].
+coercion cic:/matita/tests/coercions/nat2int.con.
 
+definition fst \def \lambda x,y:int.x.
 
-Coercion is_zero.
-Coercion len.
+theorem a: fst O one = fst (positive O) (next one).
+reflexivity.
+qed.
 
-Print Coer.
-Print Env.
+definition double: 
+  \forall f:int \to int. pos \to int 
+\def 
+  \lambda f:int \to int. \lambda x : pos .f (nat2int x).
+  
+definition double1: 
+  \forall f:int \to int. pos \to int 
+\def 
+  \lambda f:int \to int. \lambda x : pos .f (pos2nat x).
 
+definition double2: 
+  \forall f:int \to int. pos \to int 
+\def 
+  \lambda f:int \to int. \lambda x : pos .f (nat2int (pos2nat x)).
+  
+