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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,v 1.1.2.1 2004/07/16 19:30:18 herbelin Exp $ *)
-
-(***********************************************************************
- 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.
-
-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] : A :=
- Cases i v of
- 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] : bool :=
- Cases n m of
- | 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] : bool :=
- Cases n m of
- | 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 : (n,m:index)(index_eq n m)=true -> n=m.
- Induction n; Induction m; Simpl; Intros.
- Rewrite (H i0 H1); Reflexivity.
- Discriminate.
- Discriminate.
- Discriminate.
- Rewrite (H i0 H1); Reflexivity.
- Discriminate.
- Discriminate.
- Discriminate.
- Reflexivity.
-Save.
-
-End variables_map.
-
-Unset Implicit Arguments.