Separate interning and pretyping of universes

This allows proper treatment in notations, ie fixes #13303

The "glob" representation of universes (what pretyping sees) contains
only fully interpreted (kernel) universes and unbound universe
ids (for non Strict Universe Declaration).

This means universes need to be understood at intern time, so intern
now has a new "universe binders" argument. We cannot avoid this due to
the following example:

~~~coq
Module Import M. Universe i. End M.
Definition foo@{i} := Type@{i}.
~~~

When interning `Type@{i}` we need to know that `i` is locally bound to
avoid interning it as `M.i`.

Extern has a symmetrical problem:

~~~coq
Module Import M. Universe i. End M.
Polymorphic Definition foo@{i} := Type@{M.i} -> Type@{i}.
Print foo. (* must not print Type@{i} -> Type@{i} *)
~~~
(Polymorphic as otherwise the local `i` will be called `foo.i`)

Therefore extern also takes a universe binders argument.

Note that the current implementation actually replaces local universes
with names at detype type. (Asymmetrical to pretyping which only gets
names in glob terms for dynamically declared univs, although it's
capable of understanding bound univs too)

As such extern only really needs the domain of the universe
binders (ie the set of bound universe ids), we just arbitrarily pass
the whole universe binders to avoid putting `Id.Map.domain` at every
entry point.

Note that if we want to change so that detyping does not name locally
bound univs we would need to pass the reverse universe binders (map
from levels to ids, contained in the ustate ie in the evar map) to
extern.

1 files changed, 9 insertions, 20 deletions

diff --git a/pretyping/detyping.ml b/pretyping/detyping.ml
index a12a832f76..402a6f6ed3 100644
--- a/pretyping/detyping.ml
+++ b/pretyping/detyping.ml
@@ -648,26 +648,16 @@ let detype_cofix detype flags avoid env sigma n (names,tys,bodies) =
        Array.map (fun (_,_,ty) -> ty) v,
        Array.map (fun (_,bd,_) -> bd) v)
 
-(* TODO use some algebraic type with a case for unnamed univs so we
-   can cleanly detype them. NB: this corresponds to a hack in
-   Pretyping.interp_universe_level_name to convert Foo.xx strings into
-   universes. *)
-let hack_qualid_of_univ_level sigma l =
-  match Termops.reference_of_level sigma l with
-  | Some qid -> qid
-  | None ->
-    let path = String.split_on_char '.' (Univ.Level.to_string l) in
-    let path = List.rev_map Id.of_string_soft path in
-    Libnames.qualid_of_dirpath (DirPath.make path)
+let detype_level_name sigma l =
+  if Univ.Level.is_sprop l then GSProp else
+  if Univ.Level.is_prop l then GProp else
+  if Univ.Level.is_set l then GSet else
+    match UState.id_of_level (Evd.evar_universe_context sigma) l with
+    | Some id -> GLocalUniv (CAst.make id)
+    | None -> GUniv l
 
 let detype_universe sigma u =
-  let fn (l, n) =
-    let s =
-      if Univ.Level.is_prop l then GProp else
-      if Univ.Level.is_set l then GSet else
-      GType (hack_qualid_of_univ_level sigma l) in
-    (s, n) in
-  List.map fn (Univ.Universe.repr u)
+  List.map (on_fst (detype_level_name sigma)) (Univ.Universe.repr u)
 
 let detype_sort sigma = function
   | SProp -> UNamed [GSProp,0]
@@ -684,8 +674,7 @@ type binder_kind = BProd | BLambda | BLetIn
 (* Main detyping function                                             *)
 
 let detype_level sigma l =
-  let l = hack_qualid_of_univ_level sigma l in
-  UNamed (GType l)
+  UNamed (detype_level_name sigma l)
 
 let detype_instance sigma l =
   let l = EInstance.kind sigma l in