[proof] Move proofs that have an associated constant to `Lemmas`

The main idea of this PR is to distinguish the types of "proof object"
`Proof_global.t` and the type of "proof object associated to a
constant, the new `Lemmas.t`.

This way, we can move the terminator setup to the higher layer in
`vernac`, which is the one that really knows about constants, paving
the way for further simplification and in particular for a unified
handling of constant saving by removal of the control inversion here.

Terminators are now internal to `Lemmas`, as it is the only part of
the code applying them.

As a consequence, proof nesting is now handled by `Lemmas`, and
`Proof_global.t` is just a single `Proof.t` plus some environmental
meta-data.

We are also enable considerable simplification in a future PR, as this
patch makes `Proof.t` and `Proof_global.t` essentially the same, so we
should expect to handle them under a unified interface.

1 files changed, 4 insertions, 4 deletions

diff --git a/vernac/comFixpoint.ml b/vernac/comFixpoint.ml
index fd88c6c4ad..3a25cb496c 100644
--- a/vernac/comFixpoint.ml
+++ b/vernac/comFixpoint.ml
@@ -267,10 +267,10 @@ let declare_fixpoint_interactive local poly ((fixnames,fixrs,fixdefs,fixtypes),p
     Some (List.map (Option.cata (EConstr.of_constr %> Tactics.exact_no_check) Tacticals.New.tclIDTAC)
       fixdefs) in
   let evd = Evd.from_ctx ctx in
-  let pstate = Lemmas.start_proof_with_initialization (local,poly,DefinitionBody Fixpoint)
+  let lemma = Lemmas.start_lemma_with_initialization (local,poly,DefinitionBody Fixpoint)
     evd pl (Some(false,indexes,init_tac)) thms None in
   declare_fixpoint_notations ntns;
-  pstate
+  lemma
 
 let declare_fixpoint local poly ((fixnames,fixrs,fixdefs,fixtypes),pl,ctx,fiximps) indexes ntns =
   (* We shortcut the proof process *)
@@ -304,11 +304,11 @@ let declare_cofixpoint_interactive local poly ((fixnames,fixrs,fixdefs,fixtypes)
     Some (List.map (Option.cata (EConstr.of_constr %> Tactics.exact_no_check) Tacticals.New.tclIDTAC)
       fixdefs) in
   let evd = Evd.from_ctx ctx in
-  let pstate = Lemmas.start_proof_with_initialization
+  let lemma = Lemmas.start_lemma_with_initialization
     (Global ImportDefaultBehavior,poly, DefinitionBody CoFixpoint)
     evd pl (Some(true,[],init_tac)) thms None in
   declare_cofixpoint_notations ntns;
-  pstate
+  lemma
 
 let declare_cofixpoint local poly ((fixnames,fixrs,fixdefs,fixtypes),pl,ctx,fiximps) ntns =
   (* We shortcut the proof process *)