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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 1.9.2.1 2004/07/16 19:29:59 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 : forall (n:Z) (T:Set), T -> array n T.
+
+Parameter access : forall (n:Z) (T:Set), array n T -> Z -> T.
+
+Parameter store : forall (n:Z) (T:Set), array n T -> Z -> T -> array n T.
+
+
+(* Axioms *)
+
+Axiom
+  new_def :
+    forall (n:Z) (T:Set) (v0:T) (i:Z),
+      (0 <= i < n)%Z -> access (new n v0) i = v0.
+
+Axiom
+  store_def_1 :
+    forall (n:Z) (T:Set) (t:array n T) (v:T) (i:Z),
+      (0 <= i < n)%Z -> access (store t i v) i = v.
+
+Axiom
+  store_def_2 :
+    forall (n:Z) (T:Set) (t:array n T) (v:T) (i j:Z),
+      (0 <= i < n)%Z ->
+      (0 <= j < n)%Z -> i <> j -> access (store t i v) j = access t j.
+
+Hint Resolve new_def store_def_1 store_def_2: datatypes v62.
+
+(* A tactic to simplify access in arrays *)
+
+Ltac array_access 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 at level 0).
+\ No newline at end of file