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+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+(* Certification of Imperative Programs / Jean-Christophe Filliātre *)
+
+(* $Id: Arrays.v,v 1.1.2.1 2004/07/16 19:30:16 herbelin Exp $ *)
+
+(**********************************************)
+(* Functional arrays, for use in Correctness. *)
+(**********************************************)
+
+(* This is an axiomatization of arrays.
+ *
+ * The type (array N T) is the type of arrays ranging from 0 to N-1 
+ * which elements are of type T.
+ *
+ * Arrays are created with new, accessed with access and modified with store. 
+ *
+ * Operations of accessing and storing are not guarded, but axioms are.
+ * So these arrays can be viewed as arrays where accessing and storing
+ * out of the bounds has no effect.
+ *)
+
+
+Require Export ProgInt.
+
+Set Implicit Arguments.
+
+
+(* The type of arrays *)
+
+Parameter array : Z -> Set -> Set.
+
+
+(* Functions to create, access and modify arrays *)
+
+Parameter new : (n:Z)(T:Set) T -> (array n T).
+
+Parameter access : (n:Z)(T:Set) (array n T) -> Z -> T.
+
+Parameter store : (n:Z)(T:Set) (array n T) -> Z -> T -> (array n T).
+
+
+(* Axioms *)
+
+Axiom new_def : (n:Z)(T:Set)(v0:T)
+                (i:Z) `0<=i<n` -> (access (new n v0) i) = v0.
+
+Axiom store_def_1 : (n:Z)(T:Set)(t:(array n T))(v:T)
+                    (i:Z) `0<=i<n` ->
+                    (access (store t i v) i) = v.
+
+Axiom store_def_2 : (n:Z)(T:Set)(t:(array n T))(v:T)
+                    (i:Z)(j:Z) `0<=i<n` -> `0<=j<n` ->
+		    `i <> j` ->
+                    (access (store t i v) j) = (access t j).
+
+Hints Resolve new_def store_def_1 store_def_2 : datatypes v62.
+
+(* A tactic to simplify access in arrays *)
+
+Tactic Definition ArrayAccess i j H :=
+    Elim (Z_eq_dec i j); [ 
+      Intro H; Rewrite H; Rewrite store_def_1
+    | Intro H; Rewrite store_def_2; [ Idtac | Idtac | Idtac | Exact H ] ].
+
+(* Symbolic notation for access *)
+
+Notation "# t [ c ]" := (access t c) (at level 0, t ident)
+  V8only (at level 0, t at level 0).