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.

2 files changed, 4 insertions, 0 deletions

diff --git a/kernel/names.ml b/kernel/names.ml
index 13761ca245..be65faf234 100644
--- a/kernel/names.ml
+++ b/kernel/names.ml
@@ -1115,3 +1115,5 @@ let eq_egr e1 e2 = match e1, e2 with
 type lident = Id.t CAst.t
 type lname = Name.t CAst.t
 type lstring = string CAst.t
+
+let lident_eq = CAst.eq Id.equal
diff --git a/kernel/names.mli b/kernel/names.mli
index 74a4e6f7d0..747299bb12 100644
--- a/kernel/names.mli
+++ b/kernel/names.mli
@@ -727,3 +727,5 @@ val eq_egr : evaluable_global_reference ->  evaluable_global_reference -> bool
 type lident = Id.t CAst.t
 type lname = Name.t CAst.t
 type lstring = string CAst.t
+
+val lident_eq : lident -> lident -> bool