[obligations] Functionalize Program state

In our quest to unify all the declaration paths, an important step
is to account for the state pertaining to `Program` declarations.

Whereas regular proofs keep are kept in a stack-like structure;
obligations for constants defined by `Program` are stored in a global
map which is manipulated by almost regular open/close proof primitives.

We make this manipulation explicit by handling the program state
functionally, in a similar way than we already do for lemmas.

This requires to extend the proof DSL a bit; but IMO changes are
acceptable given the gain.

Most of the PR is routine; only remarkable change is that the hook is
called explicitly in `finish_admitted` as it had to learn about the
different types of proof_endings.

Note that we could have gone deeper and use the type system to refine
the core proof type; IMO it is still too preliminary so it is better
to do this step as an intermediate one towards a deeper unification.

1 files changed, 13 insertions, 5 deletions

diff --git a/plugins/funind/recdef.ml b/plugins/funind/recdef.ml
index 64f62ba1fb..7b00191026 100644
--- a/plugins/funind/recdef.ml
+++ b/plugins/funind/recdef.ml
@@ -58,8 +58,10 @@ let declare_fun name kind ?univs value =
     (Declare.declare_constant ~name ~kind (Declare.DefinitionEntry ce))
 
 let defined lemma =
-  let (_ : _ list) =
-    Declare.Proof.save ~proof:lemma ~opaque:Vernacexpr.Transparent ~idopt:None
+  let pm = Declare.OblState.empty in
+  let _pm, _ =
+    Declare.Proof.save ~pm ~proof:lemma ~opaque:Vernacexpr.Transparent
+      ~idopt:None
   in
   ()
 
@@ -1502,8 +1504,9 @@ let open_new_goal ~lemma build_proof sigma using_lemmas ref_ goal_name
                      [Hints.Hint_db.empty TransparentState.empty false] ]))
     in
     let lemma = build_proof env (Evd.from_env env) start_tac end_tac in
-    let (_ : _ list) =
-      Declare.Proof.save ~proof:lemma ~opaque:opacity ~idopt:None
+    let pm = Declare.OblState.empty in
+    let _pm, _ =
+      Declare.Proof.save ~pm ~proof:lemma ~opaque:opacity ~idopt:None
     in
     ()
   in
@@ -1662,7 +1665,12 @@ let com_eqn uctx nb_arg eq_name functional_ref f_ref terminate_ref
   in
   let _ =
     Flags.silently
-      (fun () -> Declare.Proof.save ~proof:lemma ~opaque:opacity ~idopt:None)
+      (fun () ->
+        let pm = Declare.OblState.empty in
+        let _pm =
+          Declare.Proof.save ~pm ~proof:lemma ~opaque:opacity ~idopt:None
+        in
+        ())
       ()
   in
   ()