[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, 4 insertions, 2 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