Postpone the search for the recursive argument index from the user given

name after internalisation, to get the correct behavior with typeclass
binders. This simplifies the pretty printing and translation
of the recursive argument name in various places too. Use this
opportunity to factorize the different internalization and
interpretation functions of binders as well.
This definitely fixes part 2 of bug
#1846 and makes it possible to use fixpoint definitions with typeclass arguments in
program too, with an example given in EquivDec. 
At the same time, one fix and one enhancement in Program:
- fix a de Bruijn bug in subtac_cases
- introduce locations of obligations and use them in case the obligation tactic
raises a failure when tried on a particular obligation, as suggested by
Sean Wilson.


git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10889 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 23 insertions, 2 deletions

diff --git a/theories/Classes/EquivDec.v b/theories/Classes/EquivDec.v
index 17f8970fc..62744b1d1 100644
--- a/theories/Classes/EquivDec.v
+++ b/theories/Classes/EquivDec.v
@@ -29,12 +29,12 @@ Require Import Coq.Logic.Decidable.
 
 Open Scope equiv_scope.
 
-Class [ Equivalence A ] => DecidableEquivalence :=
+Class [ equiv : Equivalence A ] => DecidableEquivalence :=
   setoid_decidable : forall x y : A, decidable (x === y).
 
 (** The [EqDec] class gives a decision procedure for a particular setoid equality. *)
 
-Class [ Equivalence A ] => EqDec :=
+Class [ equiv : Equivalence A ] => EqDec :=
   equiv_dec : forall x y : A, { x === y } + { x =/= y }.
 
 (** We define the [==] overloaded notation for deciding equality. It does not take precedence
@@ -135,3 +135,24 @@ Program Instance [ EqDec A eq ] => bool_function_eqdec : ! EqDec (bool -> A) eq
     extensionality x.
     destruct x ; auto.
   Qed.
+
+Require Import List.
+
+Program Instance [ eqa : EqDec A eq ] => list_eqdec : ! EqDec (list A) eq :=
+  equiv_dec := 
+    fix aux (x : list A) y { struct x } :=
+    match x, y with
+      | nil, nil => in_left
+      | cons hd tl, cons hd' tl' => 
+        if hd == hd' then
+          if aux tl tl' then in_left else in_right
+          else in_right
+      | _, _ => in_right
+    end.
+
+  Solve Obligations using unfold equiv, complement in * ; program_simpl ; intuition (discriminate || eauto).
+
+  Next Obligation.
+  Proof. clear aux. red in H0. subst. 
+    destruct y; intuition (discriminate || eauto).
+  Defined.
\ No newline at end of file