diff options
author | 2004-07-28 21:54:47 +0000 | |
---|---|---|
committer | 2004-07-28 21:54:47 +0000 | |
commit | 6b649aba925b6f7462da07599fe67ebb12a3460e (patch) | |
tree | 43656bcaa51164548f3fa14e5b10de5ef1088574 /contrib7/ring/Quote.v |
Imported Upstream version 8.0pl1upstream/8.0pl1
Diffstat (limited to 'contrib7/ring/Quote.v')
-rw-r--r-- | contrib7/ring/Quote.v | 85 |
1 files changed, 85 insertions, 0 deletions
diff --git a/contrib7/ring/Quote.v b/contrib7/ring/Quote.v new file mode 100644 index 00000000..12a51c9f --- /dev/null +++ b/contrib7/ring/Quote.v @@ -0,0 +1,85 @@ +(************************************************************************) +(* 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. |