[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.

3 files changed, 23 insertions, 11 deletions

diff --git a/plugins/funind/functional_principles_proofs.ml b/plugins/funind/functional_principles_proofs.ml
index 14d0c04212..b743329e7d 100644
--- a/plugins/funind/functional_principles_proofs.ml
+++ b/plugins/funind/functional_principles_proofs.ml
@@ -863,8 +863,10 @@ let generate_equation_lemma evd fnames f fun_num nb_params nb_args rec_args_num
   let lemma, _ =
     Declare.Proof.by (Proofview.V82.tactic prove_replacement) lemma
   in
-  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
   evd
 
diff --git a/plugins/funind/gen_principle.ml b/plugins/funind/gen_principle.ml
index ffce2f8c85..730cf42fe8 100644
--- a/plugins/funind/gen_principle.ml
+++ b/plugins/funind/gen_principle.ml
@@ -1526,8 +1526,9 @@ let derive_correctness (funs : Constr.pconstant list) (graphs : inductive list)
           let lemma =
             fst @@ Declare.Proof.by (Proofview.V82.tactic (proving_tac i)) lemma
           in
-          let (_ : GlobRef.t list) =
-            Declare.Proof.save ~proof:lemma ~opaque:Vernacexpr.Transparent
+          let pm = Declare.OblState.empty in
+          let _pm, _ =
+            Declare.Proof.save ~pm ~proof:lemma ~opaque:Vernacexpr.Transparent
               ~idopt:None
           in
           let finfo =
@@ -1598,8 +1599,9 @@ let derive_correctness (funs : Constr.pconstant list) (graphs : inductive list)
                        (proving_tac i)))
                  lemma)
           in
-          let (_ : _ list) =
-            Declare.Proof.save ~proof:lemma ~opaque:Vernacexpr.Transparent
+          let pm = Declare.OblState.empty in
+          let _pm, _ =
+            Declare.Proof.save ~pm ~proof:lemma ~opaque:Vernacexpr.Transparent
               ~idopt:None
           in
           let finfo =
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
   ()