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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 *)
-(************************************************************************)
-
-(* $Id: Quote.v 6295 2004-11-12 16:40:39Z gregoire $ *)
-
-(***********************************************************************
- The "abstract" type index is defined to represent variables.
-
- index : Set
- index_eq : index -> bool
- index_eq_prop: (n,m:index)(index_eq n m)=true -> n=m
- index_lt : index -> bool
- varmap : Type -> Type.
- varmap_find : (A:Type)A -> index -> (varmap A) -> A.
-
- The first arg. of varmap_find is the default value to take
- if the object is not found in the varmap.
-
- index_lt defines a total well-founded order, but we don't prove that.
-
-***********************************************************************)
-
-Set Implicit Arguments.
-Unset Boxed Definitions.
-
-Section variables_map.
-
-Variable A : Type.
-
-Inductive varmap : Type :=
- | Empty_vm : varmap
- | Node_vm : A -> varmap -> varmap -> varmap.
-
-Inductive index : Set :=
- | Left_idx : index -> index
- | Right_idx : index -> index
- | End_idx : index.
-
-Fixpoint varmap_find (default_value:A) (i:index) (v:varmap) {struct v} : A :=
- match i, v with
- | End_idx, Node_vm x _ _ => x
- | Right_idx i1, Node_vm x v1 v2 => varmap_find default_value i1 v2
- | Left_idx i1, Node_vm x v1 v2 => varmap_find default_value i1 v1
- | _, _ => default_value
- end.
-
-Fixpoint index_eq (n m:index) {struct m} : bool :=
- match n, m with
- | End_idx, End_idx => true
- | Left_idx n', Left_idx m' => index_eq n' m'
- | Right_idx n', Right_idx m' => index_eq n' m'
- | _, _ => false
- end.
-
-Fixpoint index_lt (n m:index) {struct m} : bool :=
- match n, m with
- | End_idx, Left_idx _ => true
- | End_idx, Right_idx _ => true
- | Left_idx n', Right_idx m' => true
- | Right_idx n', Right_idx m' => index_lt n' m'
- | Left_idx n', Left_idx m' => index_lt n' m'
- | _, _ => false
- end.
-
-Lemma index_eq_prop : forall n m:index, index_eq n m = true -> n = m.
- simple induction n; simple induction m; simpl in |- *; intros.
- rewrite (H i0 H1); reflexivity.
- discriminate.
- discriminate.
- discriminate.
- rewrite (H i0 H1); reflexivity.
- discriminate.
- discriminate.
- discriminate.
- reflexivity.
-Qed.
-
-End variables_map.
-
-Unset Implicit Arguments.