[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.

4 files changed, 34 insertions, 22 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
   ()
diff --git a/plugins/ltac/g_obligations.mlg b/plugins/ltac/g_obligations.mlg
index 81ee6ed5bb..fa176482bf 100644
--- a/plugins/ltac/g_obligations.mlg
+++ b/plugins/ltac/g_obligations.mlg
@@ -80,14 +80,14 @@ GRAMMAR EXTEND Gram
 
 open Declare.Obls
 
-let obligation obl tac = with_tac (fun t -> obligation obl t) tac
-let next_obligation obl tac = with_tac (fun t -> next_obligation obl t) tac
+let obligation ~pm obl tac = with_tac (fun t -> obligation ~pm obl t) tac
+let next_obligation ~pm obl tac = with_tac (fun t -> next_obligation ~pm obl t) tac
 
 let classify_obbl _ = Vernacextend.(VtStartProof (Doesn'tGuaranteeOpacity,[]))
 
 }
 
-VERNAC COMMAND EXTEND Obligations CLASSIFIED BY { classify_obbl } STATE open_proof
+VERNAC COMMAND EXTEND Obligations CLASSIFIED BY { classify_obbl } STATE declare_program
 | [ "Obligation" integer(num) "of" ident(name) ":" lglob(t) withtac(tac) ] ->
     { obligation (num, Some name, Some t) tac }
 | [ "Obligation" integer(num) "of" ident(name) withtac(tac) ] ->
@@ -101,14 +101,14 @@ VERNAC COMMAND EXTEND Obligations CLASSIFIED BY { classify_obbl } STATE open_pro
 | [ "Next" "Obligation" withtac(tac) ] -> { next_obligation None tac }
 END
 
-VERNAC COMMAND EXTEND Solve_Obligation CLASSIFIED AS SIDEFF
+VERNAC COMMAND EXTEND Solve_Obligation CLASSIFIED AS SIDEFF STATE program
 | [ "Solve" "Obligation" integer(num) "of" ident(name) "with" tactic(t) ] ->
     { try_solve_obligation num (Some name) (Some (Tacinterp.interp t)) }
 | [ "Solve" "Obligation" integer(num) "with" tactic(t) ] ->
     { try_solve_obligation num None (Some (Tacinterp.interp t)) }
 END
 
-VERNAC COMMAND EXTEND Solve_Obligations CLASSIFIED AS SIDEFF
+VERNAC COMMAND EXTEND Solve_Obligations CLASSIFIED AS SIDEFF STATE program
 | [ "Solve" "Obligations" "of" ident(name) "with" tactic(t) ] ->
     { try_solve_obligations (Some name) (Some (Tacinterp.interp t)) }
 | [ "Solve" "Obligations" "with" tactic(t) ] ->
@@ -117,14 +117,14 @@ VERNAC COMMAND EXTEND Solve_Obligations CLASSIFIED AS SIDEFF
     { try_solve_obligations None None }
 END
 
-VERNAC COMMAND EXTEND Solve_All_Obligations CLASSIFIED AS SIDEFF
+VERNAC COMMAND EXTEND Solve_All_Obligations CLASSIFIED AS SIDEFF STATE program
 | [ "Solve" "All" "Obligations" "with" tactic(t) ] ->
     { solve_all_obligations (Some (Tacinterp.interp t)) }
 | [ "Solve" "All" "Obligations" ] ->
     { solve_all_obligations None }
 END
 
-VERNAC COMMAND EXTEND Admit_Obligations CLASSIFIED AS SIDEFF
+VERNAC COMMAND EXTEND Admit_Obligations CLASSIFIED AS SIDEFF STATE program
 | [ "Admit" "Obligations" "of" ident(name) ] -> { admit_obligations (Some name) }
 | [ "Admit" "Obligations" ] -> { admit_obligations None }
 END
@@ -148,14 +148,14 @@ VERNAC COMMAND EXTEND Show_Solver CLASSIFIED AS QUERY
     Feedback.msg_notice (str"Program obligation tactic is " ++ print_default_tactic ()) }
 END
 
-VERNAC COMMAND EXTEND Show_Obligations CLASSIFIED AS QUERY
+VERNAC COMMAND EXTEND Show_Obligations CLASSIFIED AS QUERY STATE read_program
 | [ "Obligations" "of" ident(name) ] -> { show_obligations (Some name) }
 | [ "Obligations" ] -> { show_obligations None }
 END
 
-VERNAC COMMAND EXTEND Show_Preterm CLASSIFIED AS QUERY
-| [ "Preterm" "of" ident(name) ] -> { Feedback.msg_notice (show_term (Some name)) }
-| [ "Preterm" ] -> { Feedback.msg_notice (show_term None) }
+VERNAC COMMAND EXTEND Show_Preterm CLASSIFIED AS QUERY STATE read_program
+| [ "Preterm" "of" ident(name) ] -> { fun ~pm -> Feedback.msg_notice (show_term ~pm (Some name)) }
+| [ "Preterm" ] -> { fun ~pm -> Feedback.msg_notice (show_term ~pm None) }
 END
 
 {