Change Hint Resolve, Immediate to take a global reference as argument

instead of a general constr: this is the most common case and does
not loose generality (one can simply define constrs before Hint Resolving
them). Benefits:
- Natural semantics for typeclasses, not class resolution needed at
Hint Resolve time, meaning less trouble for users as well.
- Ability to [Hint Remove] any hint so declared.
- Simplifies the implementation as well.


git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15930 85f007b7-540e-0410-9357-904b9bb8a0f7

5 files changed, 14 insertions, 17 deletions

diff --git a/theories/MSets/MSetAVL.v b/theories/MSets/MSetAVL.v
index 1e66e2b5b..2182504dd 100644
--- a/theories/MSets/MSetAVL.v
+++ b/theories/MSets/MSetAVL.v
@@ -306,7 +306,7 @@ Include MSetGenTree.Props X I.
 Local Hint Immediate MX.eq_sym.
 Local Hint Unfold In lt_tree gt_tree Ok.
 Local Hint Constructors InT bst.
-Local Hint Resolve MX.eq_refl MX.eq_trans MX.lt_trans @ok.
+Local Hint Resolve MX.eq_refl MX.eq_trans MX.lt_trans ok.
 Local Hint Resolve lt_leaf gt_leaf lt_tree_node gt_tree_node.
 Local Hint Resolve lt_tree_not_in lt_tree_trans gt_tree_not_in gt_tree_trans.
 Local Hint Resolve elements_spec2.
diff --git a/theories/MSets/MSetGenTree.v b/theories/MSets/MSetGenTree.v
index cacd91343..b7f3f96c9 100644
--- a/theories/MSets/MSetGenTree.v
+++ b/theories/MSets/MSetGenTree.v
@@ -341,7 +341,7 @@ Module Import MX := OrderedTypeFacts X.
 Scheme tree_ind := Induction for tree Sort Prop.
 Scheme bst_ind := Induction for bst Sort Prop.
 
-Local Hint Resolve MX.eq_refl MX.eq_trans MX.lt_trans @ok.
+Local Hint Resolve MX.eq_refl MX.eq_trans MX.lt_trans ok.
 Local Hint Immediate MX.eq_sym.
 Local Hint Unfold In lt_tree gt_tree.
 Local Hint Constructors InT bst.
diff --git a/theories/MSets/MSetList.v b/theories/MSets/MSetList.v
index d9b1fd9bb..b0e09b719 100644
--- a/theories/MSets/MSetList.v
+++ b/theories/MSets/MSetList.v
@@ -228,16 +228,14 @@ Module MakeRaw (X: OrderedType) <: RawSets X.
   Notation Inf := (lelistA X.lt).
   Notation In := (InA X.eq).
 
-  (* TODO: modify proofs in order to avoid these hints *)
-  Hint Resolve (@Equivalence_Reflexive _ _ X.eq_equiv).
-  Hint Immediate (@Equivalence_Symmetric _ _ X.eq_equiv).
-  Hint Resolve (@Equivalence_Transitive _ _ X.eq_equiv).
+  Existing Instance X.eq_equiv.
+  Hint Extern 20 => solve [order].
 
   Definition IsOk s := Sort s.
 
   Class Ok (s:t) : Prop := ok : Sort s.
 
-  Hint Resolve @ok.
+  Hint Resolve ok.
   Hint Unfold Ok.
 
   Instance Sort_Ok s `(Hs : Sort s) : Ok s := { ok := Hs }.
@@ -343,7 +341,6 @@ Module MakeRaw (X: OrderedType) <: RawSets X.
   induction s; simpl; intros.
   intuition. inv; auto.
   elim_compare x a; inv; rewrite !InA_cons, ?IHs; intuition.
-  left; order.
   Qed.
 
   Lemma remove_inf :
@@ -402,8 +399,8 @@ Module MakeRaw (X: OrderedType) <: RawSets X.
   Global Instance union_ok s s' : forall `(Ok s, Ok s'), Ok (union s s').
   Proof.
   repeat rewrite <- isok_iff; revert s s'.
-  induction2; constructors; try apply @ok; auto.
-  apply Inf_eq with x'; auto; apply union_inf; auto; apply Inf_eq with x; auto.
+  induction2; constructors; try apply @ok; auto. 
+  apply Inf_eq with x'; auto; apply union_inf; auto; apply Inf_eq with x; auto; order.
   change (Inf x' (union (x :: l) l')); auto.
   Qed.
 
@@ -412,7 +409,6 @@ Module MakeRaw (X: OrderedType) <: RawSets X.
    In x (union s s') <-> In x s \/ In x s'.
   Proof.
   induction2; try rewrite ?InA_cons, ?Hrec, ?Hrec'; intuition; inv; auto.
-  left; order.
   Qed.
 
   Lemma inter_inf :
@@ -440,7 +436,6 @@ Module MakeRaw (X: OrderedType) <: RawSets X.
   Proof.
   induction2; try rewrite ?InA_cons, ?Hrec, ?Hrec'; intuition; inv; auto;
    try sort_inf_in; try order.
-  left; order.
   Qed.
 
   Lemma diff_inf :
diff --git a/theories/MSets/MSetRBT.v b/theories/MSets/MSetRBT.v
index b838495f9..92ad2fcfb 100644
--- a/theories/MSets/MSetRBT.v
+++ b/theories/MSets/MSetRBT.v
@@ -452,7 +452,7 @@ Local Notation Bk := (Node Black).
 Local Hint Immediate MX.eq_sym.
 Local Hint Unfold In lt_tree gt_tree Ok.
 Local Hint Constructors InT bst.
-Local Hint Resolve MX.eq_refl MX.eq_trans MX.lt_trans @ok.
+Local Hint Resolve MX.eq_refl MX.eq_trans MX.lt_trans ok.
 Local Hint Resolve lt_leaf gt_leaf lt_tree_node gt_tree_node.
 Local Hint Resolve lt_tree_not_in lt_tree_trans gt_tree_not_in gt_tree_trans.
 Local Hint Resolve elements_spec2.
diff --git a/theories/MSets/MSetWeakList.v b/theories/MSets/MSetWeakList.v
index fd4114cd4..7c8c5e6de 100644
--- a/theories/MSets/MSetWeakList.v
+++ b/theories/MSets/MSetWeakList.v
@@ -118,16 +118,18 @@ Module MakeRaw (X:DecidableType) <: WRawSets X.
   Notation In := (InA X.eq).
 
   (* TODO: modify proofs in order to avoid these hints *)
-  Hint Resolve (@Equivalence_Reflexive _ _ X.eq_equiv).
-  Hint Immediate (@Equivalence_Symmetric _ _ X.eq_equiv).
-  Hint Resolve (@Equivalence_Transitive _ _ X.eq_equiv).
+  Let eqr:= (@Equivalence_Reflexive _ _ X.eq_equiv).
+  Let eqsym:= (@Equivalence_Symmetric _ _ X.eq_equiv).
+  Let eqtrans:= (@Equivalence_Transitive _ _ X.eq_equiv).
+  Hint Resolve eqr eqtrans.
+  Hint Immediate eqsym.
 
   Definition IsOk := NoDup.
 
   Class Ok (s:t) : Prop := ok : NoDup s.
 
   Hint Unfold Ok.
-  Hint Resolve @ok.
+  Hint Resolve ok.
 
   Instance NoDup_Ok s (nd : NoDup s) : Ok s := { ok := nd }.